LMFDB - Embedded newform 18.7.d.a.11.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [18,7,Mod(5,18)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(18, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("18.5");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 18 = 2 \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	18.d (of order $6$, degree $2$, 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:	$4.14097350516$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 370x^{10} + 51793x^{8} + 3491832x^{6} + 117603792x^{4} + 1832032512x^{2} + 10453017600 $ x^12 + 370x^10 + 51793x^8 + 3491832x^6 + 117603792x^4 + 1832032512*x^2 + 10453017600
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{10}\cdot 3^{10} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.4
Root			$8.15670i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.7.d.a.5.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.89898 + 2.82843i) q^{2} +(-23.6571 + 13.0130i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-95.8504 + 55.3393i) q^{5} +(-152.702 - 3.16189i) q^{6} +(-163.169 + 282.617i) q^{7} +181.019i q^{8} +(390.321 - 615.703i) q^{9} +O(q^{10})$	\(q+(4.89898 + 2.82843i) q^{2} +(-23.6571 + 13.0130i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-95.8504 + 55.3393i) q^{5} +(-152.702 - 3.16189i) q^{6} +(-163.169 + 282.617i) q^{7} +181.019i q^{8} +(390.321 - 615.703i) q^{9} -626.092 q^{10} +(541.817 + 312.818i) q^{11} +(-739.142 - 447.397i) q^{12} +(1014.01 + 1756.31i) q^{13} +(-1598.72 + 923.023i) q^{14} +(1547.42 - 2556.48i) q^{15} +(-512.000 + 886.810i) q^{16} -4126.55i q^{17} +(3653.65 - 1912.32i) q^{18} +12194.5 q^{19} +(-3067.21 - 1770.86i) q^{20} +(182.406 - 8809.24i) q^{21} +(1769.57 + 3064.98i) q^{22} +(-18576.6 + 10725.2i) q^{23} +(-2355.61 - 4282.40i) q^{24} +(-1687.63 + 2923.06i) q^{25} +11472.2i q^{26} +(-1221.72 + 19645.0i) q^{27} -10442.8 q^{28} +(-21435.3 - 12375.7i) q^{29} +(14811.6 - 8147.37i) q^{30} +(20265.9 + 35101.6i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(-16888.6 - 349.699i) q^{33} +(11671.6 - 20215.9i) q^{34} -36118.6i q^{35} +(23308.0 + 965.656i) q^{36} -30093.7 q^{37} +(59740.6 + 34491.3i) q^{38} +(-46843.4 - 28354.0i) q^{39} +(-10017.5 - 17350.8i) q^{40} +(51294.6 - 29614.9i) q^{41} +(25809.9 - 42640.4i) q^{42} +(43967.8 - 76154.5i) q^{43} +20020.4i q^{44} +(-3339.92 + 80615.5i) q^{45} -121342. q^{46} +(112384. + 64885.1i) q^{47} +(572.363 - 27642.1i) q^{48} +(5576.24 + 9658.34i) q^{49} +(-16535.3 + 9546.68i) q^{50} +(53698.9 + 97622.3i) q^{51} +(-32448.2 + 56201.9i) q^{52} -165599. i q^{53} +(-61549.8 + 92785.1i) q^{54} -69244.6 q^{55} +(-51159.1 - 29536.7i) q^{56} +(-288487. + 158688. i) q^{57} +(-70007.5 - 121257. i) q^{58} +(46116.0 - 26625.1i) q^{59} +(95605.8 + 1979.64i) q^{60} +(133491. - 231213. i) q^{61} +229282. i q^{62} +(110320. + 210775. i) q^{63} -32768.0 q^{64} +(-194386. - 112229. i) q^{65} +(-81747.7 - 49481.3i) q^{66} +(203640. + 352715. i) q^{67} +(114358. - 66024.7i) q^{68} +(299902. - 495467. i) q^{69} +(102159. - 176944. i) q^{70} +186563. i q^{71} +(111454. + 70655.7i) q^{72} -242102. q^{73} +(-147429. - 85117.9i) q^{74} +(1886.60 - 91112.5i) q^{75} +(195112. + 337944. i) q^{76} +(-176816. + 102085. i) q^{77} +(-149288. - 271399. i) q^{78} +(63186.3 - 109442. i) q^{79} -113335. i q^{80} +(-226739. - 480644. i) q^{81} +335055. q^{82} +(-59731.2 - 34485.8i) q^{83} +(247047. - 135893. i) q^{84} +(228360. + 395531. i) q^{85} +(430795. - 248720. i) q^{86} +(668144. + 13834.7i) q^{87} +(-56626.2 + 98079.4i) q^{88} +413126. i q^{89} +(-244377. + 385487. i) q^{90} -661817. q^{91} +(-594452. - 343207. i) q^{92} +(-936211. - 566682. i) q^{93} +(367045. + 635741. i) q^{94} +(-1.16885e6 + 674835. i) q^{95} +(80987.6 - 133799. i) q^{96} +(-489221. + 847356. i) q^{97} +63088.0i q^{98} +(404086. - 211499. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9}+O(q^{10}) $ 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9	\( 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9} + 378 q^{11} + 384 q^{12} + 1680 q^{13} - 4752 q^{14} - 10872 q^{15} - 6144 q^{16} - 2976 q^{18} - 2820 q^{19} + 13824 q^{20} + 24876 q^{21} - 3600 q^{22} - 76248 q^{23} - 6144 q^{24} + 8094 q^{25} + 127008 q^{27} + 15360 q^{28} + 97092 q^{29} + 34272 q^{30} + 21480 q^{31} - 246258 q^{33} - 27360 q^{34} + 38208 q^{36} - 25536 q^{37} + 97632 q^{38} + 42204 q^{39} - 410562 q^{41} - 222144 q^{42} + 71430 q^{43} + 13716 q^{45} - 135072 q^{46} + 347652 q^{47} + 55296 q^{48} - 135954 q^{49} + 311040 q^{50} + 336402 q^{51} - 53760 q^{52} - 173520 q^{54} + 580392 q^{55} - 152064 q^{56} - 522282 q^{57} + 159264 q^{58} + 369738 q^{59} - 170496 q^{60} + 135744 q^{61} - 103800 q^{63} - 393216 q^{64} - 753840 q^{65} + 909216 q^{66} - 289938 q^{67} + 744768 q^{68} + 2059272 q^{69} + 155952 q^{70} - 374784 q^{72} - 977700 q^{73} - 2197152 q^{74} - 2115342 q^{75} - 45120 q^{76} - 159192 q^{77} - 631488 q^{78} - 764796 q^{79} - 1428282 q^{81} + 1073088 q^{82} + 396900 q^{83} + 1441536 q^{84} + 1619568 q^{85} + 3264624 q^{86} + 3072636 q^{87} + 115200 q^{88} - 1987200 q^{90} + 355584 q^{91} - 2439936 q^{92} - 2526576 q^{93} - 736848 q^{94} - 2089260 q^{95} - 49152 q^{96} - 38874 q^{97} + 4398804 q^{99}+O(q^{100}) \) 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9 + 378 * q^11 + 384 * q^12 + 1680 * q^13 - 4752 * q^14 - 10872 * q^15 - 6144 * q^16 - 2976 * q^18 - 2820 * q^19 + 13824 * q^20 + 24876 * q^21 - 3600 * q^22 - 76248 * q^23 - 6144 * q^24 + 8094 * q^25 + 127008 * q^27 + 15360 * q^28 + 97092 * q^29 + 34272 * q^30 + 21480 * q^31 - 246258 * q^33 - 27360 * q^34 + 38208 * q^36 - 25536 * q^37 + 97632 * q^38 + 42204 * q^39 - 410562 * q^41 - 222144 * q^42 + 71430 * q^43 + 13716 * q^45 - 135072 * q^46 + 347652 * q^47 + 55296 * q^48 - 135954 * q^49 + 311040 * q^50 + 336402 * q^51 - 53760 * q^52 - 173520 * q^54 + 580392 * q^55 - 152064 * q^56 - 522282 * q^57 + 159264 * q^58 + 369738 * q^59 - 170496 * q^60 + 135744 * q^61 - 103800 * q^63 - 393216 * q^64 - 753840 * q^65 + 909216 * q^66 - 289938 * q^67 + 744768 * q^68 + 2059272 * q^69 + 155952 * q^70 - 374784 * q^72 - 977700 * q^73 - 2197152 * q^74 - 2115342 * q^75 - 45120 * q^76 - 159192 * q^77 - 631488 * q^78 - 764796 * q^79 - 1428282 * q^81 + 1073088 * q^82 + 396900 * q^83 + 1441536 * q^84 + 1619568 * q^85 + 3264624 * q^86 + 3072636 * q^87 + 115200 * q^88 - 1987200 * q^90 + 355584 * q^91 - 2439936 * q^92 - 2526576 * q^93 - 736848 * q^94 - 2089260 * q^95 - 49152 * q^96 - 38874 * q^97 + 4398804 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	4.89898	+	2.82843i	0.612372	+	0.353553i
$2$	4.89898	+	2.82843i	0.612372	+	0.353553i
$3$	−23.6571	+	13.0130i	−0.876191	+	0.481965i
$3$	−23.6571	+	13.0130i	−0.876191	+	0.481965i
$4$	16.0000	+	27.7128i	0.250000	+	0.433013i
$5$	−95.8504	+	55.3393i	−0.766803	+	0.442714i	−0.831733	−	0.555176i	$-0.812651\pi$
$5$	−95.8504	+	55.3393i	−0.766803	+	0.442714i	0.0649297	+	0.997890i	$0.479318\pi$
$6$	−152.702	−	3.16189i	−0.706955	−	0.0146384i
$7$	−163.169	+	282.617i	−0.475711	+	0.823956i	−0.999613	−	0.0278225i	$-0.991143\pi$
$7$	−163.169	+	282.617i	−0.475711	+	0.823956i	0.523901	+	0.851779i	$0.324476\pi$
$8$			181.019i			0.353553i
$9$	390.321	−	615.703i	0.535420	−	0.844586i
$10$	−626.092			−0.626092
$11$	541.817	+	312.818i	0.407075	+	0.235025i	0.689532	−	0.724255i	$-0.257816\pi$
$11$	541.817	+	312.818i	0.407075	+	0.235025i	−0.282457	+	0.959280i	$0.591149\pi$
$12$	−739.142	−	447.397i	−0.427744	−	0.258911i
$13$	1014.01	+	1756.31i	0.461541	+	0.799412i	0.999038	−	0.0438534i	$-0.0139635\pi$
$13$	1014.01	+	1756.31i	0.461541	+	0.799412i	−0.537497	+	0.843266i	$0.680630\pi$
$14$	−1598.72	+	923.023i	−0.582625	+	0.336379i
$15$	1547.42	−	2556.48i	0.458493	−	0.757474i
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$		−	4126.55i		−	0.839924i	−0.907542	−	0.419962i	$-0.862043\pi$
$17$		−	4126.55i		−	0.839924i	0.907542	−	0.419962i	$-0.137957\pi$
$18$	3653.65	−	1912.32i	0.626483	−	0.327901i
$19$	12194.5			1.77788			0.888942	−	0.458020i	$-0.151441\pi$
$19$	12194.5			1.77788			0.888942	+	0.458020i	$0.151441\pi$
$20$	−3067.21	−	1770.86i	−0.383402	−	0.221357i
$21$	182.406	−	8809.24i	0.0196962	−	0.951219i
$22$	1769.57	+	3064.98i	0.166188	+	0.287846i
$23$	−18576.6	+	10725.2i	−1.52680	+	0.881501i	−0.527312	+	0.849672i	$0.676800\pi$
$23$	−18576.6	+	10725.2i	−1.52680	+	0.881501i	−0.999493	+	0.0318293i	$0.989867\pi$
$24$	−2355.61	−	4282.40i	−0.170400	−	0.309780i
$25$	−1687.63	+	2923.06i	−0.108008	+	0.187076i
$26$			11472.2i			0.652717i
$27$	−1221.72	+	19645.0i	−0.0620699	+	0.998072i
$28$	−10442.8			−0.475711
$29$	−21435.3	−	12375.7i	−0.878893	−	0.507429i	−0.00859997	−	0.999963i	$-0.502737\pi$
$29$	−21435.3	−	12375.7i	−0.878893	−	0.507429i	−0.870293	+	0.492534i	$0.836071\pi$
$30$	14811.6	−	8147.37i	0.548576	−	0.301754i
$31$	20265.9	+	35101.6i	0.680269	+	1.17826i	0.974899	+	0.222649i	$0.0714704\pi$
$31$	20265.9	+	35101.6i	0.680269	+	1.17826i	−0.294630	+	0.955612i	$0.595196\pi$
$32$	−5016.55	+	2896.31i	−0.153093	+	0.0883883i
$33$	−16888.6	−	349.699i	−0.469950	−	0.00973088i
$34$	11671.6	−	20215.9i	0.296958	−	0.514346i
$35$		−	36118.6i		−	0.842417i
$36$	23308.0	+	965.656i	0.499571	+	0.0206974i
$37$	−30093.7			−0.594115			−0.297058	−	0.954860i	$-0.596005\pi$
$37$	−30093.7			−0.594115			−0.297058	+	0.954860i	$0.596005\pi$
$38$	59740.6	+	34491.3i	1.08873	+	0.628577i
$39$	−46843.4	−	28354.0i	−0.789686	−	0.477991i
$40$	−10017.5	−	17350.8i	−0.156523	−	0.271106i
$41$	51294.6	−	29614.9i	0.744252	−	0.429694i	−0.0793613	−	0.996846i	$-0.525288\pi$
$41$	51294.6	−	29614.9i	0.744252	−	0.429694i	0.823613	+	0.567152i	$0.191955\pi$
$42$	25809.9	−	42640.4i	0.348368	−	0.575537i
$43$	43967.8	−	76154.5i	0.553006	−	0.957834i	−0.445050	−	0.895506i	$-0.646814\pi$
$43$	43967.8	−	76154.5i	0.553006	−	0.957834i	0.998056	−	0.0623286i	$-0.0198527\pi$
$44$			20020.4i			0.235025i
$45$	−3339.92	+	80615.5i	−0.0366521	+	0.884669i
$46$	−121342.			−1.24663
$47$	112384.	+	64885.1i	1.08246	+	0.624958i	0.931559	−	0.363590i	$-0.118449\pi$
$47$	112384.	+	64885.1i	1.08246	+	0.624958i	0.150901	+	0.988549i	$0.451783\pi$
$48$	572.363	−	27642.1i	0.00517545	−	0.249946i
$49$	5576.24	+	9658.34i	0.0473973	+	0.0820945i
$50$	−16535.3	+	9546.68i	−0.132283	+	0.0763734i
$51$	53698.9	+	97622.3i	0.404814	+	0.735934i
$52$	−32448.2	+	56201.9i	−0.230770	+	0.399706i
$53$		−	165599.i		−	1.11232i	−0.831074	−	0.556161i	$-0.812274\pi$
$53$		−	165599.i		−	1.11232i	0.831074	−	0.556161i	$-0.187726\pi$
$54$	−61549.8	+	92785.1i	−0.390882	+	0.589247i
$55$	−69244.6			−0.416196
$56$	−51159.1	−	29536.7i	−0.291313	−	0.168189i
$57$	−288487.	+	158688.i	−1.55777	+	0.856877i
$58$	−70007.5	−	121257.i	−0.358807	−	0.621471i
$59$	46116.0	−	26625.1i	0.224541	−	0.129639i	−0.383510	−	0.923537i	$-0.625285\pi$
$59$	46116.0	−	26625.1i	0.224541	−	0.129639i	0.608051	+	0.793898i	$0.291952\pi$
$60$	95605.8	+	1979.64i	0.442619	+	0.00916498i
$61$	133491.	−	231213.i	0.588115	−	1.01864i	−0.406365	−	0.913711i	$-0.633204\pi$
$61$	133491.	−	231213.i	0.588115	−	1.01864i	0.994479	−	0.104933i	$-0.0334629\pi$
$62$			229282.i			0.962046i
$63$	110320.	+	210775.i	0.441196	+	0.842942i
$64$	−32768.0			−0.125000
$65$	−194386.	−	112229.i	−0.707822	−	0.408661i
$66$	−81747.7	−	49481.3i	−0.284344	−	0.172111i
$67$	203640.	+	352715.i	0.677079	+	1.17273i	0.975857	+	0.218412i	$0.0700876\pi$
$67$	203640.	+	352715.i	0.677079	+	1.17273i	−0.298778	+	0.954323i	$0.596579\pi$
$68$	114358.	−	66024.7i	0.363698	−	0.209981i
$69$	299902.	−	495467.i	0.912920	−	1.50823i
$70$	102159.	−	176944.i	0.297839	−	0.515873i
$71$			186563.i			0.521254i	0.965440	+	0.260627i	$0.0839293\pi$
$71$			186563.i			0.521254i	−0.965440	+	0.260627i	$0.916071\pi$
$72$	111454.	+	70655.7i	0.298606	+	0.189300i
$73$	−242102.			−0.622344			−0.311172	−	0.950354i	$-0.600721\pi$
$73$	−242102.			−0.622344			−0.311172	+	0.950354i	$0.600721\pi$
$74$	−147429.	−	85117.9i	−0.363820	−	0.210051i
$75$	1886.60	−	91112.5i	0.00447193	−	0.215970i
$76$	195112.	+	337944.i	0.444471	+	0.769846i
$77$	−176816.	+	102085.i	−0.387301	+	0.223608i
$78$	−149288.	−	271399.i	−0.314587	−	0.571905i
$79$	63186.3	−	109442.i	0.128157	−	0.221974i	−0.794806	−	0.606864i	$-0.792427\pi$
$79$	63186.3	−	109442.i	0.128157	−	0.221974i	0.922963	+	0.384890i	$0.125761\pi$
$80$		−	113335.i		−	0.221357i
$81$	−226739.	−	480644.i	−0.426650	−	0.904417i
$82$	335055.			0.607679
$83$	−59731.2	−	34485.8i	−0.104464	−	0.0603124i	0.446858	−	0.894605i	$-0.352543\pi$
$83$	−59731.2	−	34485.8i	−0.104464	−	0.0603124i	−0.551322	+	0.834293i	$0.685876\pi$
$84$	247047.	−	135893.i	0.416814	−	0.229276i
$85$	228360.	+	395531.i	0.371846	+	0.644057i
$86$	430795.	−	248720.i	0.677291	−	0.391034i
$87$	668144.	+	13834.7i	1.01464	+	0.0210094i
$88$	−56626.2	+	98079.4i	−0.0830939	+	0.143923i
$89$			413126.i			0.586020i	0.956109	+	0.293010i	$0.0946569\pi$
$89$			413126.i			0.586020i	−0.956109	+	0.293010i	$0.905343\pi$
$90$	−244377.	+	385487.i	−0.335223	+	0.528789i
$91$	−661817.			−0.878241
$92$	−594452.	−	343207.i	−0.763402	−	0.440751i
$93$	−936211.	−	566682.i	−1.16393	−	0.704515i
$94$	367045.	+	635741.i	0.441912	+	0.765415i
$95$	−1.16885e6	+	674835.i	−1.36329	+	0.787094i
$96$	80987.6	−	133799.i	0.0915387	−	0.151231i
$97$	−489221.	+	847356.i	−0.536031	+	0.928434i	0.463081	+	0.886316i	$0.346744\pi$
$97$	−489221.	+	847356.i	−0.536031	+	0.928434i	−0.999113	+	0.0421177i	$0.986590\pi$
$98$			63088.0i			0.0670299i
$99$	404086.	−	211499.i	0.416455	−	0.217973i
$100$	−108008.			−0.108008
$101$	975354.	+	563121.i	0.946669	+	0.546560i	0.892045	−	0.451947i	$-0.149271\pi$
$101$	975354.	+	563121.i	0.946669	+	0.546560i	0.0546243	+	0.998507i	$0.482604\pi$
$102$	−13047.7	+	630133.i	−0.0122951	+	0.593789i
$103$	−528792.	−	915894.i	−0.483919	−	0.838173i	0.515910	−	0.856643i	$-0.327454\pi$
$103$	−528792.	−	915894.i	−0.483919	−	0.838173i	−0.999829	+	0.0184698i	$0.994121\pi$
$104$	−317926.	+	183555.i	−0.282635	+	0.163179i
$105$	470013.	+	854464.i	0.406015	+	0.738118i
$106$	468385.	−	811267.i	0.393265	−	0.681156i
$107$		−	607244.i		−	0.495692i	−0.968799	−	0.247846i	$-0.920277\pi$
$107$		−	607244.i		−	0.495692i	0.968799	−	0.247846i	$-0.0797227\pi$
$108$	−563967.	+	280463.i	−0.447695	+	0.222641i
$109$	961305.			0.742303			0.371152	−	0.928572i	$-0.378963\pi$
$109$	961305.			0.742303			0.371152	+	0.928572i	$0.378963\pi$
$110$	−339228.	−	195853.i	−0.254867	−	0.147147i
$111$	711932.	−	391611.i	0.520558	−	0.286343i
$112$	−167085.	−	289400.i	−0.118928	−	0.205989i
$113$	1.15941e6	−	669388.i	0.803532	−	0.463919i	−0.0411727	−	0.999152i	$-0.513109\pi$
$113$	1.15941e6	−	669388.i	0.803532	−	0.463919i	0.844705	+	0.535233i	$0.179776\pi$
$114$	−1.86213e6	−	38557.7i	−1.25688	−	0.0260253i
$115$	1.18705e6	−	2.05603e6i	0.780506	−	1.35188i
$116$		−	792044.i		−	0.507429i
$117$	1.47715e6	+	61198.8i	0.922290	+	0.0382107i
$118$	301228.			0.183337
$119$	1.16623e6	+	673325.i	0.692061	+	0.399561i
$120$	462771.	+	280112.i	0.267808	+	0.162102i
$121$	−690070.	−	1.19524e6i	−0.389526	−	0.674679i
$122$	1.30794e6	−	755138.i	0.720290	−	0.415860i
$123$	−828103.	+	1.36810e6i	−0.445009	+	0.735197i
$124$	−648509.	+	1.12325e6i	−0.340135	+	0.589130i
$125$		−	2.10292e6i		−	1.07670i
$126$	−55707.7	+	1.34461e6i	−0.0278486	+	0.672181i
$127$	−1.62823e6			−0.794885			−0.397443	−	0.917627i	$-0.630102\pi$
$127$	−1.62823e6			−0.794885			−0.397443	+	0.917627i	$0.630102\pi$
$128$	−160530.	−	92681.9i	−0.0765466	−	0.0441942i
$129$	−49151.5	+	2.37375e6i	−0.0228964	+	1.10577i
$130$	−634861.	−	1.09961e6i	−0.288967	−	0.500506i
$131$	−1.19601e6	+	690515.i	−0.532010	+	0.307156i	−0.741835	−	0.670583i	$-0.766044\pi$
$131$	−1.19601e6	+	690515.i	−0.532010	+	0.307156i	0.209824	+	0.977739i	$0.432711\pi$
$132$	−260526.	−	473625.i	−0.113274	−	0.205927i
$133$	−1.98977e6	+	3.44637e6i	−0.845760	+	1.46490i
$134$			2.30393e6i			0.957534i
$135$	−970040.	−	1.95060e6i	−0.394265	−	0.792804i
$136$	746985.			0.296958
$137$	3.07236e6	+	1.77383e6i	1.19484	+	0.689842i	0.959401	−	0.282046i	$-0.0910132\pi$
$137$	3.07236e6	+	1.77383e6i	1.19484	+	0.689842i	0.235441	+	0.971889i	$0.424347\pi$
$138$	2.87061e6	−	1.57903e6i	1.09229	−	0.600832i
$139$	−1.61016e6	−	2.78888e6i	−0.599548	−	1.03845i	−0.992888	−	0.119055i	$-0.962014\pi$
$139$	−1.61016e6	−	2.78888e6i	−0.599548	−	1.03845i	0.393339	−	0.919393i	$-0.371320\pi$
$140$	1.00095e6	−	577898.i	0.364777	−	0.210604i
$141$	−3.50304e6	−	72534.8i	−1.24965	−	0.0258755i
$142$	−527678.	+	913966.i	−0.184291	+	0.319202i
$143$			1.26880e6i			0.433895i
$144$	346167.	+	661381.i	0.115931	+	0.221495i
$145$	2.73945e6			0.898585
$146$	−1.18605e6	−	684769.i	−0.381106	−	0.220032i
$147$	−257602.	−	155925.i	−0.0810957	−	0.0490866i
$148$	−481500.	−	833982.i	−0.148529	−	0.257259i
$149$	−791423.	+	456928.i	−0.239249	+	0.138130i	−0.614832	−	0.788658i	$-0.710776\pi$
$149$	−791423.	+	456928.i	−0.239249	+	0.138130i	0.375583	+	0.926789i	$0.377443\pi$
$150$	266947.	−	441022.i	0.0790955	−	0.130673i
$151$	−799451.	+	1.38469e6i	−0.232199	+	0.402181i	−0.958455	−	0.285244i	$-0.907925\pi$
$151$	−799451.	+	1.38469e6i	−0.232199	+	0.402181i	0.726256	+	0.687425i	$0.241259\pi$
$152$			2.20744e6i			0.628577i
$153$	−2.54073e6	−	1.61068e6i	−0.709388	−	0.449712i
$154$	−1.15495e6			−0.316230
$155$	−3.88499e6	−	2.24300e6i	−1.04327	−	0.602329i
$156$	36273.7	−	1.75183e6i	0.00955472	−	0.461442i
$157$	2.83537e6	+	4.91100e6i	0.732673	+	1.26903i	0.955737	+	0.294224i	$0.0950611\pi$
$157$	2.83537e6	+	4.91100e6i	0.732673	+	1.26903i	−0.223063	+	0.974804i	$0.571606\pi$
$158$	619097.	−	357436.i	0.156959	−	0.0906206i
$159$	2.15495e6	+	3.91761e6i	0.536100	+	0.974607i
$160$	320559.	−	555225.i	0.0782615	−	0.135553i
$161$		−	7.00010e6i		−	1.67736i
$162$	248675.	−	2.99598e6i	0.0584908	−	0.704683i
$163$	5.58510e6			1.28964			0.644820	−	0.764335i	$-0.276932\pi$
$163$	5.58510e6			1.28964			0.644820	+	0.764335i	$0.276932\pi$
$164$	1.64143e6	+	947678.i	0.372126	+	0.214847i
$165$	1.63813e6	−	901083.i	0.364667	−	0.200592i
$166$	−195081.	−	337891.i	−0.0426473	−	0.0738673i
$167$	−5.13451e6	+	2.96441e6i	−1.10243	+	0.636486i	−0.936857	−	0.349712i	$-0.886279\pi$
$167$	−5.13451e6	+	2.96441e6i	−1.10243	+	0.636486i	−0.165569	+	0.986198i	$0.552946\pi$
$168$	1.59464e6	+	33019.0i	0.336307	+	0.00696364i
$169$	356991.	−	618327.i	0.0739601	−	0.128103i
$170$			2.58360e6i			0.525870i
$171$	4.75978e6	−	7.50819e6i	0.951915	−	1.50158i
$172$	2.81394e6			0.553006
$173$	−1.94362e6	−	1.12215e6i	−0.375382	−	0.216727i	0.300425	−	0.953805i	$-0.402871\pi$
$173$	−1.94362e6	−	1.12215e6i	−0.375382	−	0.216727i	−0.675807	+	0.737079i	$0.736205\pi$
$174$	3.23409e6	+	1.95757e6i	0.613910	+	0.371595i
$175$	−550738.	−	953906.i	−0.102762	−	0.177988i
$176$	−554821.	+	320326.i	−0.101769	+	0.0587563i
$177$	−744499.	+	1.22998e6i	−0.134259	+	0.221809i
$178$	−1.16850e6	+	2.02389e6i	−0.207189	+	0.358862i
$179$			777450.i			0.135554i	0.997700	+	0.0677772i	$0.0215907\pi$
$179$			777450.i			0.135554i	−0.997700	+	0.0677772i	$0.978409\pi$
$180$	−2.28752e6	+	1.19729e6i	−0.392236	+	0.205297i
$181$	4.10696e6			0.692604			0.346302	−	0.938123i	$-0.387437\pi$
$181$	4.10696e6			0.692604			0.346302	+	0.938123i	$0.387437\pi$
$182$	−3.24223e6	−	1.87190e6i	−0.537811	−	0.310505i
$183$	−149229.	+	7.20696e6i	−0.0243501	+	1.17598i
$184$	−1.94147e6	−	3.36273e6i	−0.311658	−	0.539807i
$185$	2.88450e6	−	1.66536e6i	0.455570	−	0.263023i
$186$	−2.98366e6	−	5.42417e6i	−0.463672	−	0.842935i
$187$	1.29086e6	−	2.23584e6i	0.197403	−	0.341912i
$188$			4.15264e6i			0.624958i
$189$	−5.35268e6	−	3.55074e6i	−0.792840	−	0.525937i
$190$	−7.63489e6			−1.11312
$191$	−3.69615e6	−	2.13397e6i	−0.530456	−	0.306259i	0.210746	−	0.977541i	$-0.432411\pi$
$191$	−3.69615e6	−	2.13397e6i	−0.530456	−	0.306259i	−0.741202	+	0.671282i	$0.765744\pi$
$192$	775197.	−	426411.i	0.109524	−	0.0602456i
$193$	4.05006e6	+	7.01491e6i	0.563365	+	0.975777i	0.997200	+	0.0747842i	$0.0238268\pi$
$193$	4.05006e6	+	7.01491e6i	0.563365	+	0.975777i	−0.433835	+	0.900992i	$0.642840\pi$
$194$	−4.79337e6	+	2.76745e6i	−0.656502	+	0.379031i
$195$	6.05905e6	+	125460.i	0.817147	+	0.0169200i
$196$	−178440.	+	309067.i	−0.0236986	+	0.0410473i
$197$			4.08228e6i			0.533955i	0.963703	+	0.266977i	$0.0860249\pi$
$197$			4.08228e6i			0.533955i	−0.963703	+	0.266977i	$0.913975\pi$
$198$	2.57782e6	+	106800.i	0.332091	+	0.0137586i
$199$	1.02814e6			0.130464			0.0652322	−	0.997870i	$-0.479221\pi$
$199$	1.02814e6			0.130464			0.0652322	+	0.997870i	$0.479221\pi$
$200$	−529131.	−	305494.i	−0.0661413	−	0.0381867i
$201$	−9.40744e6	−	5.69426e6i	−1.15847	−	0.701211i
$202$	3.18549e6	+	5.51743e6i	0.386476	+	0.669396i
$203$	6.99516e6	−	4.03866e6i	0.836199	−	0.482780i
$204$	−1.84621e6	+	3.05011e6i	−0.217465	+	0.359273i
$205$	−3.27774e6	+	5.67721e6i	−0.380463	+	0.658982i
$206$		−	5.98260e6i		−	0.684365i
$207$	−647305.	+	1.56240e7i	−0.0729790	+	1.76149i
$208$	−2.07668e6			−0.230770
$209$	6.60720e6	+	3.81467e6i	0.723733	+	0.417847i
$210$	−114203.	+	5.51540e6i	−0.0123316	+	0.595551i
$211$	−7.72519e6	−	1.33804e7i	−0.822359	−	1.42437i	−0.903921	−	0.427700i	$-0.859324\pi$
$211$	−7.72519e6	−	1.33804e7i	−0.822359	−	1.42437i	0.0815616	−	0.996668i	$-0.474009\pi$
$212$	4.58922e6	−	2.64959e6i	0.481650	−	0.278081i
$213$	−2.42775e6	−	4.41354e6i	−0.251226	−	0.456718i
$214$	1.71755e6	−	2.97488e6i	0.175254	−	0.303548i
$215$			9.73259e6i			0.979294i
$216$	−3.55613e6	−	221155.i	−0.352872	−	0.0219450i
$217$	−1.32271e7			−1.29445
$218$	4.70941e6	+	2.71898e6i	0.454566	+	0.262444i
$219$	5.72745e6	−	3.15049e6i	0.545292	−	0.299948i
$220$	−1.10791e6	−	1.91896e6i	−0.104049	−	0.180218i
$221$	7.24749e6	−	4.18434e6i	0.671445	−	0.387659i
$222$	4.59538e6	+	95153.0i	0.420013	+	0.00869688i
$223$	1.40565e6	−	2.43465e6i	0.126754	−	0.219544i	−0.795663	−	0.605739i	$-0.792877\pi$
$223$	1.40565e6	−	2.43465e6i	0.126754	−	0.219544i	0.922417	+	0.386195i	$0.126211\pi$
$224$		−	1.89035e6i		−	0.168189i
$225$	1.14102e6	+	2.18001e6i	0.100172	+	0.191387i
$226$	7.57326e6			0.656081
$227$	6.45811e6	+	3.72859e6i	0.552113	+	0.318762i	0.749974	−	0.661468i	$-0.230066\pi$
$227$	6.45811e6	+	3.72859e6i	0.552113	+	0.318762i	−0.197861	+	0.980230i	$0.563399\pi$
$228$	−9.01348e6	−	5.45579e6i	−0.760480	−	0.460313i
$229$	−6.31232e6	−	1.09333e7i	−0.525633	−	0.910422i	−0.999554	−	0.0298554i	$-0.990495\pi$
$229$	−6.31232e6	−	1.09333e7i	−0.525633	−	0.910422i	0.473922	−	0.880567i	$-0.342838\pi$
$230$	1.16307e7	−	6.71498e6i	0.955921	−	0.551901i
$231$	2.85452e6	−	4.71594e6i	0.231578	−	0.382589i
$232$	2.24024e6	−	3.88021e6i	0.179403	−	0.310736i
$233$		−	1.64283e7i		−	1.29875i	−0.760469	−	0.649374i	$-0.775031\pi$
$233$		−	1.64283e7i		−	1.29875i	0.760469	−	0.649374i	$-0.224969\pi$
$234$	7.06344e6	+	4.47783e6i	0.551276	+	0.349478i
$235$	−1.43628e7			−1.10671
$236$	1.47571e6	+	852002.i	0.112270	+	0.0648194i
$237$	−70635.8	+	3.41133e6i	−0.00530615	+	0.256259i
$238$	3.80890e6	+	6.59721e6i	0.282533	+	0.489361i
$239$	−8.45060e6	+	4.87895e6i	−0.619004	+	0.357382i	−0.776481	−	0.630140i	$-0.782997\pi$
$239$	−8.45060e6	+	4.87895e6i	−0.619004	+	0.357382i	0.157477	+	0.987523i	$0.449664\pi$
$240$	1.47483e6	+	2.68118e6i	0.106686	+	0.193951i
$241$	7.37017e6	−	1.27655e7i	0.526534	−	0.911984i	−0.472988	−	0.881069i	$-0.656825\pi$
$241$	7.37017e6	−	1.27655e7i	0.526534	−	0.911984i	0.999522	−	0.0309150i	$-0.00984213\pi$
$242$		−	7.80725e6i		−	0.550873i
$243$	1.16187e7	+	8.42010e6i	0.809724	+	0.586811i
$244$	8.54341e6			0.588115
$245$	−1.06897e6	−	617171.i	−0.0726888	−	0.0419669i
$246$	−7.92644e6	+	4.36008e6i	−0.532443	+	0.292880i
$247$	1.23653e7	+	2.14173e7i	0.820566	+	1.42126i
$248$	−6.35406e6	+	3.66852e6i	−0.416578	+	0.240511i
$249$	1.86184e6	+	38551.6i	0.120599	+	0.00249715i
$250$	5.94796e6	−	1.03022e7i	0.380669	−	0.659339i
$251$			1.31485e7i			0.831486i	0.909482	+	0.415743i	$0.136478\pi$
$251$			1.31485e7i			0.831486i	−0.909482	+	0.415743i	$0.863522\pi$
$252$	−4.07606e6	+	6.42967e6i	−0.254706	+	0.401779i
$253$	−1.34202e7			−0.828700
$254$	−7.97666e6	−	4.60533e6i	−0.486766	−	0.281034i
$255$	−1.05494e7	−	6.38548e6i	−0.636221	−	0.385100i
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	−1.86427e7	+	1.07634e7i	−1.09827	+	0.634087i	−0.935766	−	0.352621i	$-0.885291\pi$
$257$	−1.86427e7	+	1.07634e7i	−1.09827	+	0.634087i	−0.162505	+	0.986708i	$0.551957\pi$
$258$	−6.95479e6	+	1.14900e7i	−0.404972	+	0.669051i
$259$	4.91036e6	−	8.50500e6i	0.282627	−	0.489525i
$260$		−	7.18263e6i		−	0.408661i
$261$	−1.59864e7	+	8.36730e6i	−0.899145	+	0.470613i
$262$	−7.81229e6			−0.434385
$263$	7.35362e6	+	4.24561e6i	0.404235	+	0.233385i	0.688310	−	0.725417i	$-0.258353\pi$
$263$	7.35362e6	+	4.24561e6i	0.404235	+	0.233385i	−0.284075	+	0.958802i	$0.591686\pi$
$264$	63302.2	−	3.05716e6i	0.00344039	−	0.166152i
$265$	9.16414e6	+	1.58728e7i	0.492441	+	0.852933i
$266$	−1.94956e7	+	1.12558e7i	−1.03584	+	0.598042i
$267$	−5.37602e6	−	9.77338e6i	−0.282441	−	0.513465i
$268$	−6.51649e6	+	1.12869e7i	−0.338539	+	0.586367i
$269$			883900.i			0.0454094i	0.999742	+	0.0227047i	$0.00722776\pi$
$269$			883900.i			0.0454094i	−0.999742	+	0.0227047i	$0.992772\pi$
$270$	764911.	−	1.22996e7i	0.0388615	−	0.624885i
$271$	−6.17663e6			−0.310345			−0.155172	−	0.987887i	$-0.549593\pi$
$271$	−6.17663e6			−0.310345			−0.155172	+	0.987887i	$0.549593\pi$
$272$	3.65946e6	+	2.11279e6i	0.181849	+	0.104991i
$273$	1.56567e7	−	8.61225e6i	0.769507	−	0.423281i
$274$	1.00343e7	+	1.73799e7i	0.487792	+	0.844881i
$275$	−1.82878e6	+	1.05584e6i	−0.0879351	+	0.0507693i
$276$	1.85292e7	+	383670.i	0.881312	+	0.0182487i
$277$	2.90287e6	−	5.02791e6i	0.136580	−	0.236564i	−0.789620	−	0.613596i	$-0.789722\pi$
$277$	2.90287e6	−	5.02791e6i	0.136580	−	0.236564i	0.926200	+	0.377033i	$0.123056\pi$
$278$		−	1.82169e7i		−	0.847889i
$279$	2.95223e7	+	1.22312e6i	1.35937	+	0.0563191i
$280$	6.53817e6			0.297839
$281$	−1.17606e7	−	6.78998e6i	−0.530042	−	0.306020i	0.210992	−	0.977488i	$-0.432331\pi$
$281$	−1.17606e7	−	6.78998e6i	−0.530042	−	0.306020i	−0.741033	+	0.671468i	$0.765664\pi$
$282$	−1.69562e7	−	1.02634e7i	−0.756102	−	0.457663i
$283$	−2.53102e6	−	4.38385e6i	−0.111670	−	0.193418i	0.804774	−	0.593582i	$-0.202287\pi$
$283$	−2.53102e6	−	4.38385e6i	−0.111670	−	0.193418i	−0.916444	+	0.400164i	$0.868953\pi$
$284$	−5.17017e6	+	2.98500e6i	−0.225710	+	0.130313i
$285$	1.88700e7	−	3.11749e7i	0.815148	−	1.34670i
$286$	−3.58870e6	+	6.21582e6i	−0.153405	+	0.265705i
$287$			1.93290e7i			0.817642i
$288$	−174802.	+	4.21920e6i	−0.00731762	+	0.176625i
$289$	7.10918e6			0.294528
$290$	1.34205e7	+	7.74833e6i	0.550268	+	0.317698i
$291$	546899.	−	2.64123e7i	0.0221936	−	1.07183i
$292$	−3.87364e6	−	6.70933e6i	−0.155586	−	0.269483i
$293$	3.26203e7	−	1.88334e7i	1.29684	−	0.748730i	0.316981	−	0.948432i	$-0.397331\pi$
$293$	3.26203e7	−	1.88334e7i	1.29684	−	0.748730i	0.979857	+	0.199702i	$0.0639974\pi$
$294$	−820967.	−	1.49248e6i	−0.0323060	−	0.0587310i
$295$	−2.94682e6	+	5.10405e6i	−0.114786	+	0.198815i
$296$		−	5.44755e6i		−	0.210051i
$297$	−6.80728e6	+	1.02619e7i	−0.259839	+	0.391703i
$298$	−5.16956e6			−0.195346
$299$	−3.76736e7	−	2.17509e7i	−1.40937	−	0.813698i
$300$	2.55517e6	−	1.40552e6i	0.0946359	−	0.0520562i
$301$	1.43484e7	+	2.48521e7i	0.526143	+	0.911306i
$302$	−7.83298e6	+	4.52238e6i	−0.284385	+	0.164190i
$303$	−3.04020e7	−	629511.i	−1.09288	−	0.0226295i
$304$	−6.24359e6	+	1.08142e7i	−0.222235	+	0.384923i
$305$			2.95491e7i			1.04147i
$306$	−7.89128e6	−	1.50769e7i	−0.275412	−	0.526198i
$307$	4.60441e7			1.59132			0.795662	−	0.605740i	$-0.207123\pi$
$307$	4.60441e7			1.59132			0.795662	+	0.605740i	$0.207123\pi$
$308$	−5.65810e6	−	3.26671e6i	−0.193650	−	0.111804i
$309$	2.44283e7	+	1.47863e7i	0.827975	+	0.501167i
$310$	−1.26883e7	−	2.19768e7i	−0.425911	−	0.737700i
$311$	2.47086e7	−	1.42655e7i	0.821423	−	0.474249i	−0.0294839	−	0.999565i	$-0.509386\pi$
$311$	2.47086e7	−	1.42655e7i	0.821423	−	0.474249i	0.850907	+	0.525316i	$0.176053\pi$
$312$	5.13261e6	−	8.47956e6i	0.168995	−	0.279196i
$313$	−1.10257e7	+	1.90970e7i	−0.359560	+	0.622776i	−0.987887	−	0.155173i	$-0.950407\pi$
$313$	−1.10257e7	+	1.90970e7i	−0.359560	+	0.622776i	0.628327	+	0.777949i	$0.283740\pi$
$314$			3.20785e7i			1.03616i
$315$	−2.22383e7	−	1.40979e7i	−0.711493	−	0.451047i
$316$	4.04392e6			0.128157
$317$	1.49989e7	+	8.65961e6i	0.470848	+	0.271844i	0.716595	−	0.697490i	$-0.245700\pi$
$317$	1.49989e7	+	8.65961e6i	0.470848	+	0.271844i	−0.245746	+	0.969334i	$0.579033\pi$
$318$	−523607.	+	2.52874e7i	−0.0162826	+	0.786362i
$319$	−7.74269e6	−	1.34107e7i	−0.238517	−	0.413124i
$320$	3.14083e6	−	1.81336e6i	0.0958504	−	0.0553393i
$321$	7.90209e6	+	1.43657e7i	0.238906	+	0.434321i
$322$	1.97993e7	−	3.42933e7i	0.593037	−	1.02717i
$323$		−	5.03212e7i		−	1.49329i
$324$	9.69217e6	−	1.39739e7i	0.284961	−	0.410849i
$325$	−6.84506e6			−0.199401
$326$	2.73613e7	+	1.57971e7i	0.789740	+	0.455956i
$327$	−2.27417e7	+	1.25095e7i	−0.650399	+	0.357764i
$328$	5.36088e6	+	9.28531e6i	0.151920	+	0.263133i
$329$	−3.66752e7	+	2.11745e7i	−1.02988	+	0.594600i
$330$	1.05738e7	+	218944.i	0.294232	+	0.00609243i
$331$	−7.07998e6	+	1.22629e7i	−0.195231	+	0.338149i	−0.946976	−	0.321304i	$-0.895879\pi$
$331$	−7.07998e6	+	1.22629e7i	−0.195231	+	0.338149i	0.751745	+	0.659453i	$0.229212\pi$
$332$		−	2.20709e6i		−	0.0603124i
$333$	−1.17462e7	+	1.85288e7i	−0.318101	+	0.501781i
$334$	−3.35385e7			−0.900127
$335$	−3.90380e7	−	2.25386e7i	−1.03837	−	0.599505i
$336$	7.71873e6	+	4.67209e6i	0.203483	+	0.123167i
$337$	−2.40697e7	−	4.16899e7i	−0.628898	−	1.08928i	−0.987773	−	0.155898i	$-0.950173\pi$
$337$	−2.40697e7	−	4.16899e7i	−0.628898	−	1.08928i	0.358875	−	0.933386i	$-0.383160\pi$
$338$	3.49779e6	−	2.01945e6i	0.0905823	−	0.0522977i
$339$	−1.87177e7	+	3.09233e7i	−0.480455	+	0.793756i
$340$	−7.30752e6	+	1.26570e7i	−0.185923	+	0.322028i
$341$			2.53582e7i			0.639521i
$342$	4.45544e7	−	2.33198e7i	1.11381	−	0.582971i
$343$	−4.20328e7			−1.04161
$344$	1.37854e7	+	7.95903e6i	0.338646	+	0.195517i
$345$	−1.32700e6	+	6.40871e7i	−0.0323158	+	1.56068i
$346$	−6.34784e6	−	1.09948e7i	−0.153249	−	0.265435i
$347$	4.75029e7	−	2.74258e7i	1.13692	−	0.656404i	0.191258	−	0.981540i	$-0.438743\pi$
$347$	4.75029e7	−	2.74258e7i	1.13692	−	0.656404i	0.945667	+	0.325136i	$0.105410\pi$
$348$	1.03069e7	+	1.87375e7i	0.244563	+	0.444605i
$349$	8.59925e6	−	1.48943e7i	0.202295	−	0.350385i	−0.746973	−	0.664855i	$-0.768493\pi$
$349$	8.59925e6	−	1.48943e7i	0.202295	−	0.350385i	0.949267	+	0.314470i	$0.101827\pi$
$350$		−	6.23089e6i		−	0.145327i
$351$	−3.57416e7	+	1.77745e7i	−0.826519	+	0.411031i
$352$	−3.62408e6			−0.0830939
$353$	−6.25279e6	−	3.61005e6i	−0.142151	−	0.0820709i	0.427238	−	0.904139i	$-0.359487\pi$
$353$	−6.25279e6	−	3.61005e6i	−0.142151	−	0.0820709i	−0.569389	+	0.822068i	$0.692820\pi$
$354$	−7.12620e6	+	3.91990e6i	−0.160638	+	0.0883619i
$355$	−1.03242e7	−	1.78821e7i	−0.230767	−	0.399699i
$356$	−1.14489e7	+	6.61001e6i	−0.253754	+	0.146505i
$357$	−3.63517e7	−	752707.i	−0.798952	−	0.0165433i
$358$	−2.19896e6	+	3.80871e6i	−0.0479257	+	0.0830097i
$359$			1.62223e6i			0.0350614i	0.999846	+	0.0175307i	$0.00558048\pi$
$359$			1.62223e6i			0.0350614i	−0.999846	+	0.0175307i	$0.994420\pi$
$360$	−1.45930e7	−	604590.i	−0.312778	−	0.0129585i
$361$	1.01660e8			2.16087
$362$	2.01199e7	+	1.16162e7i	0.424131	+	0.244872i
$363$	3.18787e7	+	1.92960e7i	0.666471	+	0.403410i
$364$	−1.05891e7	−	1.83408e7i	−0.219560	−	0.380289i
$365$	2.32056e7	−	1.33978e7i	0.477215	−	0.275520i
$366$	−2.11154e7	+	3.48847e7i	−0.430682	+	0.711527i
$367$	−1.08645e7	+	1.88180e7i	−0.219793	+	0.380692i	−0.954745	−	0.297427i	$-0.903871\pi$
$367$	−1.08645e7	+	1.88180e7i	−0.219793	+	0.380692i	0.734952	+	0.678119i	$0.237205\pi$
$368$		−	2.19653e7i		−	0.440751i
$369$	1.78737e6	−	4.31416e7i	0.0355741	−	0.858652i
$370$	1.88415e7			0.371971
$371$	4.68012e7	+	2.70207e7i	0.916505	+	0.529145i
$372$	724966.	−	3.50120e7i	0.0140828	−	0.680123i
$373$	−3.03671e7	−	5.25974e7i	−0.585163	−	1.01353i	−0.994855	−	0.101309i	$-0.967697\pi$
$373$	−3.03671e7	−	5.25974e7i	−0.585163	−	1.01353i	0.409692	−	0.912224i	$-0.365636\pi$
$374$	1.26478e7	−	7.30221e6i	0.241769	−	0.139585i
$375$	2.73654e7	+	4.97491e7i	0.518929	+	0.943391i
$376$	−1.17455e7	+	2.03437e7i	−0.220956	+	0.382707i
$377$		−	5.01961e7i		−	0.936797i
$378$	−1.61796e7	−	3.25347e7i	−0.299567	−	0.602381i
$379$	2.01121e7			0.369437			0.184719	−	0.982791i	$-0.440863\pi$
$379$	2.01121e7			0.369437			0.184719	+	0.982791i	$0.440863\pi$
$380$	−3.74032e7	−	2.15947e7i	−0.681644	−	0.393547i
$381$	3.85193e7	−	2.11882e7i	0.696471	−	0.383106i
$382$	−1.20716e7	−	2.09086e7i	−0.216558	−	0.375089i
$383$	4.09187e7	−	2.36244e7i	0.728326	−	0.420499i	−0.0894836	−	0.995988i	$-0.528522\pi$
$383$	4.09187e7	−	2.36244e7i	0.728326	−	0.420499i	0.817809	+	0.575489i	$0.195188\pi$
$384$	5.00375e6	+	103609.i	0.0883694	+	0.00182980i
$385$	1.12986e7	−	1.95697e7i	0.197989	−	0.342927i
$386$			4.58212e7i			0.796718i
$387$	−2.97270e7	−	5.67959e7i	−0.512883	−	0.979905i
$388$	−3.13102e7			−0.536031
$389$	1.67687e7	+	9.68140e6i	0.284872	+	0.164471i	0.635627	−	0.771996i	$-0.280742\pi$
$389$	1.67687e7	+	9.68140e6i	0.284872	+	0.164471i	−0.350755	+	0.936467i	$0.614075\pi$
$390$	2.93283e7	+	1.77522e7i	0.494416	+	0.299267i
$391$	4.42581e7	+	7.66574e7i	0.740394	+	1.28240i
$392$	−1.74835e6	+	1.00941e6i	−0.0290248	+	0.0167575i
$393$	1.93084e7	−	3.18993e7i	0.318104	−	0.525538i
$394$	−1.15464e7	+	1.99990e7i	−0.188782	+	0.326979i
$395$			1.39867e7i			0.226947i
$396$	1.23266e7	+	7.81438e6i	0.198499	+	0.125837i
$397$	−3.66656e7			−0.585986			−0.292993	−	0.956115i	$-0.594651\pi$
$397$	−3.66656e7			−0.585986			−0.292993	+	0.956115i	$0.594651\pi$
$398$	5.03682e6	+	2.90801e6i	0.0798928	+	0.0461261i
$399$	2.22435e6	−	1.07424e8i	0.0350175	−	1.69116i
$400$	−1.72813e6	−	2.99321e6i	−0.0270021	−	0.0467690i
$401$	−1.04853e8	+	6.05366e7i	−1.62609	+	0.938826i	−0.640852	+	0.767665i	$0.721419\pi$
$401$	−1.04853e8	+	6.05366e7i	−1.62609	+	0.938826i	−0.985243	+	0.171162i	$0.945248\pi$
$402$	−2.99811e7	−	5.45043e7i	−0.461497	−	0.838982i
$403$	−4.10994e7	+	7.11863e7i	−0.627944	+	1.08763i
$404$			3.60397e7i			0.546560i
$405$	4.83316e7	+	3.35224e7i	0.727555	+	0.504626i
$406$	4.56922e7			0.682754
$407$	−1.63053e7	−	9.41387e6i	−0.241850	−	0.139632i
$408$	−1.76715e7	+	9.72055e6i	−0.260192	+	0.143123i
$409$	−1.99142e7	−	3.44925e7i	−0.291067	−	0.504144i	0.682995	−	0.730423i	$-0.260677\pi$
$409$	−1.99142e7	−	3.44925e7i	−0.291067	−	0.504144i	−0.974062	+	0.226279i	$0.927344\pi$
$410$	−3.21152e7	+	1.85417e7i	−0.465970	+	0.269028i
$411$	−9.57662e7	−	1.98296e6i	−1.37939	−	0.0285619i
$412$	1.69213e7	−	2.93086e7i	0.241960	−	0.419086i
$413$			1.73775e7i			0.246683i
$414$	−4.73624e7	+	7.47107e7i	−0.667472	+	1.05289i
$415$	7.63369e6			0.106805
$416$	−1.01736e7	−	5.87375e6i	−0.141317	−	0.0815897i
$417$	7.43835e7	+	4.50238e7i	1.02581	+	0.620918i
$418$	2.15790e7	+	3.73759e7i	0.295463	+	0.511756i
$419$	4.69066e7	−	2.70815e7i	0.637664	−	0.368155i	−0.146050	−	0.989277i	$-0.546656\pi$
$419$	4.69066e7	−	2.70815e7i	0.637664	−	0.368155i	0.783714	+	0.621122i	$0.213323\pi$
$420$	−1.61594e7	+	2.66968e7i	−0.218111	+	0.360339i
$421$	−2.70636e7	+	4.68755e7i	−0.362693	+	0.628203i	−0.988403	−	0.151853i	$-0.951476\pi$
$421$	−2.70636e7	+	4.68755e7i	−0.362693	+	0.628203i	0.625710	+	0.780056i	$0.284809\pi$
$422$		−	8.74005e7i		−	1.16299i
$423$	8.38159e7	−	4.38693e7i	1.10740	−	0.579615i
$424$	2.99767e7			0.393265
$425$	1.20621e7	+	6.96408e6i	0.157130	+	0.0907188i
$426$	589890.	−	2.84885e7i	0.00763031	−	0.368503i
$427$	4.35631e7	+	7.54536e7i	0.559546	+	0.969161i
$428$	1.68284e7	−	9.71590e6i	0.214641	−	0.123923i
$429$	−1.65109e7	−	3.00161e7i	−0.209122	−	0.380175i
$430$	−2.75279e7	+	4.76798e7i	−0.346233	+	0.599693i
$431$			8.08186e7i			1.00944i	0.863284	+	0.504719i	$0.168404\pi$
$431$			8.08186e7i			1.00944i	−0.863284	+	0.504719i	$0.831596\pi$
$432$	−1.67959e7	−	1.11417e7i	−0.208330	−	0.138198i
$433$	−1.33718e7			−0.164713			−0.0823563	−	0.996603i	$-0.526245\pi$
$433$	−1.33718e7			−0.164713			−0.0823563	+	0.996603i	$0.526245\pi$
$434$	−6.47991e7	−	3.74118e7i	−0.792684	−	0.457656i
$435$	−6.48075e7	+	3.56485e7i	−0.787331	+	0.433086i
$436$	1.53809e7	+	2.66405e7i	0.185576	+	0.321427i
$437$	−2.26533e8	+	1.30789e8i	−2.71448	+	1.56721i
$438$	3.69696e7	+	765501.i	0.439969	+	0.00911010i
$439$	3.81803e7	−	6.61302e7i	0.451280	−	0.781640i	−0.547186	−	0.837011i	$-0.684301\pi$
$439$	3.81803e7	−	6.61302e7i	0.451280	−	0.781640i	0.998466	+	0.0553714i	$0.0176343\pi$
$440$		−	1.25346e7i		−	0.147147i
$441$	8.12320e6	+	336546.i	0.0947133	+	0.00392399i
$442$	4.73404e7			0.548233
$443$	−9.63056e7	−	5.56020e7i	−1.10775	−	0.639557i	−0.169501	−	0.985530i	$-0.554216\pi$
$443$	−9.63056e7	−	5.56020e7i	−1.10775	−	0.639557i	−0.938245	+	0.345973i	$0.887549\pi$
$444$	2.22435e7	+	1.34639e7i	0.254130	+	0.153823i
$445$	−2.28621e7	−	3.95983e7i	−0.259439	−	0.449362i
$446$	1.37725e7	−	7.95154e6i	0.155241	−	0.0896286i
$447$	1.27768e7	−	2.11085e7i	0.143054	−	0.236338i
$448$	5.34672e6	−	9.26079e6i	0.0594639	−	0.102995i
$449$		−	1.36515e8i		−	1.50814i	−0.656793	−	0.754071i	$-0.728087\pi$
$449$		−	1.36515e8i		−	1.50814i	0.656793	−	0.754071i	$-0.271913\pi$
$450$	−576175.	+	1.39071e7i	−0.00632291	+	0.152616i
$451$	3.70564e7			0.403956
$452$	3.71012e7	+	2.14204e7i	0.401766	+	0.231960i
$453$	893703.	−	4.31611e7i	0.00961388	−	0.464299i
$454$	2.10921e7	+	3.65326e7i	0.225399	+	0.390403i
$455$	6.34354e7	−	3.66245e7i	0.673438	−	0.388810i
$456$	−2.87255e7	−	5.22218e7i	−0.302952	−	0.550753i
$457$	5.42046e7	−	9.38851e7i	0.567920	−	0.983667i	−0.428851	−	0.903375i	$-0.641081\pi$
$457$	5.42046e7	−	9.38851e7i	0.567920	−	0.983667i	0.996771	−	0.0802917i	$-0.0255852\pi$
$458$		−	7.14157e7i		−	0.743357i
$459$	8.10662e7	+	5.04149e6i	0.838305	+	0.0521340i
$460$	7.59713e7			0.780506
$461$	1.42152e8	+	8.20712e7i	1.45094	+	0.837699i	0.998535	−	0.0541143i	$-0.0172335\pi$
$461$	1.42152e8	+	8.20712e7i	1.45094	+	0.837699i	0.452403	+	0.891814i	$0.350567\pi$
$462$	2.73229e7	−	1.50295e7i	0.277078	−	0.152412i
$463$	−1.86985e7	−	3.23867e7i	−0.188392	−	0.326305i	0.756322	−	0.654199i	$-0.226994\pi$
$463$	−1.86985e7	−	3.23867e7i	−0.188392	−	0.326305i	−0.944714	+	0.327895i	$0.893661\pi$
$464$	2.19498e7	−	1.26727e7i	0.219723	−	0.126857i
$465$	1.21096e8	+	2.50744e6i	1.20440	+	0.0249386i
$466$	4.64663e7	−	8.04820e7i	0.459177	−	0.795318i
$467$			1.45951e8i			1.43304i	0.697569	+	0.716518i	$0.254265\pi$
$467$			1.45951e8i			1.43304i	−0.697569	+	0.716518i	$0.745735\pi$
$468$	2.19384e7	+	4.19152e7i	0.214027	+	0.408916i
$469$	−1.32911e8			−1.28838
$470$	−7.03629e7	−	4.06240e7i	−0.677720	−	0.391282i
$471$	−1.30984e8	−	7.92835e7i	−1.25359	−	0.758788i
$472$	4.81965e6	+	8.34788e6i	0.0458342	+	0.0793872i
$473$	4.76451e7	−	2.75079e7i	0.450230	−	0.259941i
$474$	−9.99474e6	+	1.65122e7i	−0.0938505	+	0.155050i
$475$	−2.05798e7	+	3.56453e7i	−0.192026	+	0.332599i
$476$			4.30928e7i			0.399561i
$477$	−1.01960e8	−	6.46369e7i	−0.939452	−	0.595560i
$478$	−5.51991e7			−0.505415
$479$	1.15157e8	+	6.64861e7i	1.04782	+	0.604957i	0.922037	−	0.387102i	$-0.126524\pi$
$479$	1.15157e8	+	6.64861e7i	1.04782	+	0.604957i	0.125779	+	0.992058i	$0.459857\pi$
$480$	−358352.	+	1.73065e7i	−0.00324031	+	0.156490i
$481$	−3.05152e7	−	5.28539e7i	−0.274208	−	0.474943i
$482$	7.22127e7	−	4.16920e7i	0.644870	−	0.372316i
$483$	9.10926e7	+	1.65602e8i	0.808428	+	1.46969i
$484$	2.20822e7	−	3.82475e7i	0.194763	−	0.337340i
$485$		−	1.08293e8i		−	0.949235i
$486$	3.31039e7	+	7.41124e7i	0.288383	+	0.645628i
$487$	−4.62190e7			−0.400160			−0.200080	−	0.979780i	$-0.564120\pi$
$487$	−4.62190e7			−0.400160			−0.200080	+	0.979780i	$0.564120\pi$
$488$	4.18540e7	+	2.41644e7i	0.360145	+	0.207930i
$489$	−1.32128e8	+	7.26792e7i	−1.12997	+	0.621561i
$490$	−3.49124e6	−	6.04701e6i	−0.0296751	−	0.0513988i
$491$	−7.93099e7	+	4.57896e7i	−0.670012	+	0.386832i	−0.796081	−	0.605190i	$-0.793097\pi$
$491$	−7.93099e7	+	4.57896e7i	−0.670012	+	0.386832i	0.126069	+	0.992021i	$0.459764\pi$
$492$	−5.11637e7	−	1.05941e6i	−0.429602	−	0.00889544i
$493$	−5.10689e7	+	8.84539e7i	−0.426202	+	0.738204i
$494$			1.39897e8i			1.16046i
$495$	−2.70276e7	+	4.26341e7i	−0.222840	+	0.351513i
$496$	−4.15046e7			−0.340135
$497$	−5.27257e7	−	3.04412e7i	−0.429490	−	0.247966i
$498$	9.01206e6	+	5.45493e6i	0.0729686	+	0.0441674i
$499$	2.85950e7	+	4.95279e7i	0.230138	+	0.398610i	0.957848	−	0.287274i	$-0.0927490\pi$
$499$	2.85950e7	+	4.95279e7i	0.230138	+	0.398610i	−0.727711	+	0.685884i	$0.759416\pi$
$500$	5.82779e7	−	3.36467e7i	0.466223	−	0.269174i
$501$	8.28919e7	−	1.36945e8i	0.659172	−	1.08901i
$502$	−3.71896e7	+	6.44142e7i	−0.293975	+	0.509179i
$503$		−	1.85206e8i		−	1.45530i	−0.685950	−	0.727649i	$-0.740613\pi$
$503$		−	1.85206e8i		−	1.45530i	0.685950	−	0.727649i	$-0.259387\pi$
$504$	−3.81544e7	+	1.99700e7i	−0.298025	+	0.155986i
$505$	−1.24651e8			−0.967879
$506$	−6.57453e7	−	3.79580e7i	−0.507473	−	0.292990i
$507$	−399080.	+	1.92734e7i	−0.00306221	+	0.147889i
$508$	−2.60517e7	−	4.51228e7i	−0.198721	−	0.344195i
$509$	1.08544e8	−	6.26677e7i	0.823097	−	0.475215i	−0.0283864	−	0.999597i	$-0.509037\pi$
$509$	1.08544e8	−	6.26677e7i	0.823097	−	0.475215i	0.851483	+	0.524382i	$0.175704\pi$
$510$	−3.36205e7	−	6.11206e7i	−0.253451	−	0.460762i
$511$	3.95036e7	−	6.84222e7i	0.296056	−	0.512784i
$512$		−	5.93164e6i		−	0.0441942i
$513$	−1.48983e7	+	2.39562e8i	−0.110353	+	1.77446i
$514$	−1.21774e8			−0.896734
$515$	1.01370e8	+	5.85259e7i	0.742142	+	0.428476i
$516$	−6.65699e7	+	3.66180e7i	−0.484539	+	0.266529i
$517$	4.05945e7	+	7.03117e7i	0.293762	+	0.508811i
$518$	4.81115e7	−	2.77772e7i	0.346146	−	0.199848i
$519$	6.05831e7	+	1.25445e6i	0.433361	+	0.00897326i
$520$	2.03155e7	−	3.51876e7i	0.144484	−	0.250253i
$521$			1.64203e8i			1.16109i	0.814227	+	0.580546i	$0.197161\pi$
$521$			1.64203e8i			1.16109i	−0.814227	+	0.580546i	$0.802839\pi$
$522$	−1.01983e8	−	4.22520e6i	−0.716998	−	0.0297054i
$523$	−1.39702e8			−0.976559			−0.488280	−	0.872687i	$-0.662375\pi$
$523$	−1.39702e8			−0.976559			−0.488280	+	0.872687i	$0.662375\pi$
$524$	−3.82722e7	−	2.20965e7i	−0.266005	−	0.153578i
$525$	2.54421e7	+	1.53999e7i	0.175823	+	0.106424i
$526$	2.40168e7	+	4.15983e7i	0.165028	+	0.285837i
$527$	1.44848e8	−	8.36282e7i	0.989649	−	0.571374i
$528$	8.95707e6	−	1.47979e7i	0.0608505	−	0.100531i
$529$	1.56043e8	−	2.70274e8i	1.05409	−	1.82574i
$530$			1.03680e8i			0.696417i
$531$	1.60692e6	−	3.87861e7i	0.0107327	−	0.259055i
$532$	−1.27345e8			−0.845760
$533$	1.04026e8	+	6.00594e7i	0.687005	+	0.396643i
$534$	1.30626e6	−	6.30853e7i	0.00857838	−	0.414290i
$535$	3.36044e7	+	5.82046e7i	0.219450	+	0.380098i
$536$	−6.38483e7	+	3.68628e7i	−0.414624	+	0.239383i
$537$	−1.01170e7	−	1.83923e7i	−0.0653324	−	0.118771i
$538$	−2.50005e6	+	4.33021e6i	−0.0160547	+	0.0278075i
$539$			6.97741e6i			0.0445582i
$540$	3.85358e7	−	5.80921e7i	0.244728	−	0.368923i
$541$	1.45535e8			0.919130			0.459565	−	0.888144i	$-0.348005\pi$
$541$	1.45535e8			0.919130			0.459565	+	0.888144i	$0.348005\pi$
$542$	−3.02592e7	−	1.74702e7i	−0.190046	−	0.109723i
$543$	−9.71590e7	+	5.34441e7i	−0.606853	+	0.333810i
$544$	1.19518e7	+	2.07010e7i	0.0742395	+	0.128587i
$545$	−9.21415e7	+	5.31979e7i	−0.569201	+	0.328628i
$546$	1.01061e8	+	2.09259e6i	0.620877	+	0.0128560i
$547$	4.28578e6	−	7.42318e6i	0.0261859	−	0.0453553i	−0.852635	−	0.522506i	$-0.824997\pi$
$547$	4.28578e6	−	7.42318e6i	0.0261859	−	0.0453553i	0.878821	+	0.477151i	$0.158330\pi$
$548$			1.13525e8i			0.689842i
$549$	−9.02541e7	−	1.72438e8i	−0.545444	−	1.04212i
$550$	−1.19455e7			−0.0717987
$551$	−2.61393e8	−	1.50915e8i	−1.56257	−	0.902150i
$552$	8.96891e7	+	5.42881e7i	0.533240	+	0.322766i
$553$	2.06201e7	+	3.57151e7i	0.121931	+	0.211191i
$554$	2.84422e7	−	1.64211e7i	0.167276	−	0.0965767i
$555$	−4.65675e7	+	7.69339e7i	−0.272398	+	0.450027i
$556$	5.15251e7	−	8.92440e7i	0.299774	−	0.519224i
$557$		−	8.68427e7i		−	0.502536i	−0.967918	−	0.251268i	$-0.919152\pi$
$557$		−	8.68427e7i		−	0.502536i	0.967918	−	0.251268i	$-0.0808476\pi$
$558$	1.41170e8	+	8.94938e7i	0.812530	+	0.515099i
$559$	1.78335e8			1.02094
$560$	3.20304e7	+	1.84927e7i	0.182389	+	0.105302i
$561$	−1.44305e6	+	6.96915e7i	−0.00817320	+	0.394722i
$562$	−3.84099e7	−	6.65279e7i	−0.216389	−	0.374796i
$563$	−5.26034e6	+	3.03706e6i	−0.0294774	+	0.0170188i	−0.514666	−	0.857391i	$-0.672084\pi$
$563$	−5.26034e6	+	3.03706e6i	−0.0294774	+	0.0170188i	0.485189	+	0.874409i	$0.338751\pi$
$564$	−5.40385e7	−	9.82397e7i	−0.301208	−	0.547583i
$565$	−7.40869e7	+	1.28322e8i	−0.410767	+	0.711470i
$566$		−	2.86352e7i		−	0.157925i
$567$	1.72835e8	+	1.43458e7i	0.948162	+	0.0787002i
$568$	−3.37714e7			−0.184291
$569$	−1.35148e8	−	7.80279e7i	−0.733624	−	0.423558i	0.0861225	−	0.996285i	$-0.472552\pi$
$569$	−1.35148e8	−	7.80279e7i	−0.733624	−	0.423558i	−0.819746	+	0.572727i	$0.805886\pi$
$570$	1.80620e8	−	9.93531e7i	0.975305	−	0.536484i
$571$	−5.10042e7	−	8.83419e7i	−0.273967	−	0.474524i	0.695907	−	0.718132i	$-0.255002\pi$
$571$	−5.10042e7	−	8.83419e7i	−0.273967	−	0.474524i	−0.969874	+	0.243608i	$0.921669\pi$
$572$	−3.51620e7	+	2.03008e7i	−0.187882	+	0.108474i
$573$	1.15210e8	+	2.38556e6i	0.612387	+	0.0126802i
$574$	−5.46706e7	+	9.46922e7i	−0.289080	+	0.500701i
$575$		−	7.24009e7i		−	0.380838i
$576$	−1.27901e7	+	2.01754e7i	−0.0669275	+	0.105573i
$577$	2.90791e8			1.51375			0.756874	−	0.653561i	$-0.226726\pi$
$577$	2.90791e8			1.51375			0.756874	+	0.653561i	$0.226726\pi$
$578$	3.48277e7	+	2.01078e7i	0.180361	+	0.104131i
$579$	−1.87098e8	−	1.13249e8i	−0.963905	−	0.583444i
$580$	4.38312e7	+	7.59178e7i	0.224646	+	0.389099i
$581$	1.94926e7	−	1.12540e7i	0.0993896	−	0.0573826i
$582$	7.73845e7	−	1.27846e8i	0.392541	−	0.648514i
$583$	5.18025e7	−	8.97246e7i	0.261424	−	0.452799i
$584$		−	4.38252e7i		−	0.220032i
$585$	−1.44972e8	+	7.58786e7i	−0.724132	+	0.379011i
$586$	2.13075e8			1.05886
$587$	−9.36918e7	−	5.40930e7i	−0.463220	−	0.267440i	0.250177	−	0.968200i	$-0.419511\pi$
$587$	−9.36918e7	−	5.40930e7i	−0.463220	−	0.267440i	−0.713397	+	0.700760i	$0.752844\pi$
$588$	199477.	−	9.63368e6i	0.000981209	−	0.0473871i
$589$	2.47133e8	+	4.28046e8i	1.20944	+	2.09481i
$590$	−2.88729e7	+	1.66698e7i	−0.140583	+	0.0811658i
$591$	−5.31229e7	−	9.65752e7i	−0.257347	−	0.467846i
$592$	1.54080e7	−	2.66874e7i	0.0742644	−	0.128630i
$593$		−	2.75079e8i		−	1.31915i	−0.751641	−	0.659573i	$-0.770737\pi$
$593$		−	2.75079e8i		−	1.31915i	0.751641	−	0.659573i	$-0.229263\pi$
$594$	−6.23736e7	+	3.10187e7i	−0.297606	+	0.148001i
$595$	−1.49045e8			−0.707566
$596$	−2.53255e7	−	1.46217e7i	−0.119624	−	0.0690652i
$597$	−2.43228e7	+	1.33792e7i	−0.114312	+	0.0628792i
$598$	−1.23041e8	−	2.13114e8i	−0.575371	−	0.996572i
$599$	−2.94213e8	+	1.69864e8i	−1.36893	+	0.790351i	−0.990791	−	0.135398i	$-0.956769\pi$
$599$	−2.94213e8	+	1.69864e8i	−1.36893	+	0.790351i	−0.378138	+	0.925749i	$0.623435\pi$
$600$	1.64931e7	+	341510.i	0.0763571	+	0.00158107i
$601$	−8.08282e7	+	1.39999e8i	−0.372340	+	0.644911i	−0.989925	−	0.141593i	$-0.954778\pi$
$601$	−8.08282e7	+	1.39999e8i	−0.372340	+	0.644911i	0.617585	+	0.786504i	$0.288111\pi$
$602$			1.62333e8i			0.744078i
$603$	2.96653e8	+	1.22904e7i	1.35300	+	0.0560549i
$604$	−5.11648e7			−0.232199
$605$	1.32287e8	+	7.63759e7i	0.597380	+	0.344898i
$606$	−1.47158e8	−	8.90738e7i	−0.661252	−	0.400251i
$607$	−1.13595e8	−	1.96752e8i	−0.507916	−	0.879737i	−0.999958	−	0.00916513i	$-0.997083\pi$
$607$	−1.13595e8	−	1.96752e8i	−0.507916	−	0.879737i	0.492042	−	0.870572i	$-0.336251\pi$
$608$	−6.11744e7	+	3.53191e7i	−0.272182	+	0.157144i
$609$	−1.12930e8	+	1.86572e8i	−0.499987	+	0.826026i
$610$	−8.35776e7	+	1.44761e8i	−0.368214	+	0.637765i
$611$			2.63175e8i			1.15378i
$612$	3.98482e6	−	9.61816e7i	0.0173842	−	0.419602i
$613$	−1.32276e8			−0.574247			−0.287124	−	0.957894i	$-0.592699\pi$
$613$	−1.32276e8			−0.574247			−0.287124	+	0.957894i	$0.592699\pi$
$614$	2.25569e8	+	1.30232e8i	0.974483	+	0.562618i
$615$	3.66417e6	−	1.76960e8i	0.0157525	−	0.760764i
$616$	−1.84793e7	−	3.20071e7i	−0.0790575	−	0.136932i
$617$	−3.09010e8	+	1.78407e8i	−1.31558	+	0.759551i	−0.983014	−	0.183528i	$-0.941248\pi$
$617$	−3.09010e8	+	1.78407e8i	−1.31558	+	0.759551i	−0.332567	+	0.943080i	$0.607915\pi$
$618$	7.78518e7	+	1.41531e8i	0.329840	+	0.599635i
$619$	−1.56034e8	+	2.70258e8i	−0.657880	+	1.13948i	0.323284	+	0.946302i	$0.395213\pi$
$619$	−1.56034e8	+	2.70258e8i	−0.657880	+	1.13948i	−0.981163	+	0.193179i	$0.938120\pi$
$620$		−	1.43552e8i		−	0.602329i
$621$	−1.88002e8	−	3.78042e8i	−0.785033	−	1.57858i
$622$	1.61396e8			0.670689
$623$	−1.16756e8	−	6.74093e7i	−0.482855	−	0.278776i
$624$	4.91284e7	−	2.70240e7i	0.202199	−	0.111223i
$625$	9.00049e7	+	1.55893e8i	0.368660	+	0.638538i
$626$	−1.08029e8	+	6.23705e7i	−0.440369	+	0.254247i
$627$	−2.05948e8	−	4.26440e6i	−0.835516	−	0.0173004i
$628$	−9.07318e7	+	1.57152e8i	−0.366337	+	0.634514i
$629$			1.24183e8i			0.499012i
$630$	−6.90704e7	−	1.31965e8i	−0.276230	−	0.527760i
$631$	1.95005e7			0.0776172			0.0388086	−	0.999247i	$-0.487644\pi$
$631$	1.95005e7			0.0776172			0.0388086	+	0.999247i	$0.487644\pi$
$632$	1.98111e7	+	1.14379e7i	0.0784797	+	0.0453103i
$633$	3.56876e8	+	2.16014e8i	1.40704	+	0.851670i
$634$	4.89862e7	+	8.48465e7i	0.192223	+	0.332940i
$635$	1.56066e8	−	9.01050e7i	0.609521	−	0.351907i
$636$	−7.40887e7	+	1.22401e8i	−0.287992	+	0.475790i
$637$	−1.13087e7	+	1.95872e7i	−0.0437516	+	0.0757799i
$638$		−	8.75985e7i		−	0.337314i
$639$	1.14867e8	+	7.28193e7i	0.440244	+	0.279090i
$640$	2.05158e7			0.0782615
$641$	3.70891e8	+	2.14134e8i	1.40823	+	0.813040i	0.995217	−	0.0976870i	$-0.0311444\pi$
$641$	3.70891e8	+	2.14134e8i	1.40823	+	0.813040i	0.413009	+	0.910727i	$0.364478\pi$
$642$	−1.92004e6	+	9.27276e7i	−0.00725613	+	0.350432i
$643$	−1.61002e8	−	2.78864e8i	−0.605619	−	1.04896i	−0.991953	−	0.126604i	$-0.959592\pi$
$643$	−1.61002e8	−	2.78864e8i	−0.605619	−	1.04896i	0.386334	−	0.922359i	$-0.373741\pi$
$644$	1.93992e8	−	1.12002e8i	0.726319	−	0.419340i
$645$	−1.26651e8	−	2.30245e8i	−0.471985	−	0.858049i
$646$	1.42330e8	−	2.46522e8i	0.527957	−	0.914448i
$647$		−	8.47366e7i		−	0.312866i	−0.987689	−	0.156433i	$-0.950001\pi$
$647$		−	8.47366e7i		−	0.312866i	0.987689	−	0.156433i	$-0.0499995\pi$
$648$	8.70059e7	−	4.10442e7i	0.319760	−	0.150844i
$649$	3.33153e7			0.121873
$650$	−3.35338e7	−	1.93608e7i	−0.122108	−	0.0704989i
$651$	3.12915e8	−	1.72124e8i	1.13418	−	0.623878i
$652$	8.93617e7	+	1.54779e8i	0.322410	+	0.558430i
$653$	3.79152e8	−	2.18903e8i	1.36167	−	0.786163i	0.371828	−	0.928302i	$-0.378731\pi$
$653$	3.79152e8	−	2.18903e8i	1.36167	−	0.786163i	0.989847	+	0.142139i	$0.0453978\pi$
$654$	−1.46793e8	−	3.03954e6i	−0.524775	−	0.0108661i
$655$	7.64252e7	−	1.32372e8i	0.271965	−	0.471057i
$656$			6.06514e7i			0.214847i
$657$	−9.44977e7	+	1.49063e8i	−0.333215	+	0.525623i
$658$	−2.39562e8			−0.840891
$659$	−2.36172e8	−	1.36354e8i	−0.825225	−	0.476444i	0.0269900	−	0.999636i	$-0.491408\pi$
$659$	−2.36172e8	−	1.36354e8i	−0.825225	−	0.476444i	−0.852215	+	0.523192i	$0.824741\pi$
$660$	5.11816e7	+	3.09799e7i	0.178025	+	0.107757i
$661$	−1.47145e8	−	2.54862e8i	−0.509495	−	0.882471i	−0.999940	−	0.0109985i	$-0.996499\pi$
$661$	−1.47145e8	−	2.54862e8i	−0.509495	−	0.882471i	0.490445	−	0.871472i	$-0.336834\pi$
$662$	−6.93694e7	+	4.00504e7i	−0.239108	+	0.138049i
$663$	−1.17004e8	+	1.93301e8i	−0.401476	+	0.663276i
$664$	6.24261e6	−	1.08125e7i	0.0213237	−	0.0369337i
$665$		−	4.40449e8i		−	1.49772i
$666$	−1.09952e8	+	5.75489e7i	−0.372203	+	0.194811i
$667$	5.30928e8			1.78920
$668$	−1.64304e8	−	9.48611e7i	−0.551213	−	0.318243i
$669$	−1.57137e6	+	7.58887e7i	−0.00524807	+	0.253454i
$670$	−1.27498e8	−	2.20832e8i	−0.423914	−	0.734240i
$671$	1.44655e8	−	8.35168e7i	0.478814	−	0.276443i
$672$	2.45992e7	+	4.47203e7i	0.0810613	+	0.147366i
$673$	−1.48525e7	+	2.57254e7i	−0.0487254	+	0.0843949i	−0.889359	−	0.457209i	$-0.848849\pi$
$673$	−1.48525e7	+	2.57254e7i	−0.0487254	+	0.0843949i	0.840634	+	0.541604i	$0.182183\pi$
$674$		−	2.72317e8i		−	0.889396i
$675$	−5.53619e7	−	3.67247e7i	−0.180011	−	0.119412i
$676$	2.28475e7			0.0739601
$677$	4.67116e8	+	2.69690e8i	1.50542	+	0.869157i	0.999980	+	0.00629800i	$0.00200473\pi$
$677$	4.67116e8	+	2.69690e8i	1.50542	+	0.869157i	0.505444	+	0.862859i	$0.331329\pi$
$678$	−1.79162e8	+	9.85512e7i	−0.574852	+	0.316208i
$679$	−1.59652e8	−	2.76525e8i	−0.509992	−	0.883333i
$680$	−7.15988e7	+	4.13376e7i	−0.227708	+	0.131468i
$681$	−2.01301e8	−	4.16818e6i	−0.637388	−	0.0131979i
$682$	−7.17238e7	+	1.24229e8i	−0.226105	+	0.391625i
$683$			5.86183e8i			1.83980i	0.392152	+	0.919901i	$0.371731\pi$
$683$			5.86183e8i			1.83980i	−0.392152	+	0.919901i	$0.628269\pi$
$684$	2.84230e8	+	1.17757e7i	0.888180	+	0.0367975i
$685$	−3.92649e8			−1.22161
$686$	−2.05918e8	−	1.18887e8i	−0.637855	−	0.368266i
$687$	2.91606e8	+	1.76507e8i	0.899346	+	0.544367i
$688$	4.50231e7	+	7.79823e7i	0.138251	+	0.239459i
$689$	2.90843e8	−	1.67919e8i	0.889204	−	0.513382i
$690$	−1.87767e8	+	3.10208e8i	−0.571572	+	0.944291i
$691$	2.34528e8	−	4.06214e8i	0.710822	−	1.23118i	−0.253728	−	0.967276i	$-0.581657\pi$
$691$	2.34528e8	−	4.06214e8i	0.710822	−	1.23118i	0.964549	−	0.263903i	$-0.0850100\pi$
$692$		−	7.18176e7i		−	0.216727i
$693$	−6.16116e6	+	1.48712e8i	−0.0185124	+	0.446833i
$694$	3.10288e8			0.928295
$695$	3.08669e8	+	1.78210e8i	0.919471	+	0.530857i
$696$	−2.50436e6	+	1.20947e8i	−0.00742794	+	0.358730i
$697$	−1.22207e8	−	2.11670e8i	−0.360910	−	0.625115i
$698$	8.42551e7	−	4.86447e7i	0.247759	−	0.143044i
$699$	2.13782e8	+	3.88647e8i	0.625951	+	1.13795i
$700$	1.76236e7	−	3.05250e7i	0.0513808	−	0.0889942i
$701$		−	5.94604e7i		−	0.172613i	−0.996269	−	0.0863065i	$-0.972494\pi$
$701$		−	5.94604e7i		−	0.172613i	0.996269	−	0.0863065i	$-0.0275064\pi$
$702$	−2.25371e8	−	1.40158e7i	−0.651459	−	0.0405141i
$703$	−3.66978e8			−1.05627
$704$	−1.77543e7	−	1.02504e7i	−0.0508844	−	0.0293781i
$705$	3.39782e8	−	1.86903e8i	0.969691	−	0.533396i
$706$	−2.04215e7	−	3.53711e7i	−0.0580329	−	0.100516i
$707$	−3.18295e8	+	1.83768e8i	−0.900682	+	0.520009i
$708$	−4.59983e7	−	952451.i	−0.129611	−	0.00268375i
$709$	−3.34021e8	+	5.78541e8i	−0.937206	+	1.62329i	−0.166553	+	0.986032i	$0.553264\pi$
$709$	−3.34021e8	+	5.78541e8i	−0.937206	+	1.62329i	−0.770652	+	0.637256i	$0.780070\pi$
$710$		−	1.16805e8i		−	0.326353i
$711$	−4.27207e7	−	8.16215e7i	−0.118858	−	0.227089i
$712$	−7.47838e7			−0.207189
$713$	−7.52944e8	−	4.34713e8i	−2.07728	−	1.19932i
$714$	−1.75957e8	−	1.06506e8i	−0.483407	−	0.292603i
$715$	−7.02144e7	−	1.21615e8i	−0.192091	−	0.332712i
$716$	−2.15453e7	+	1.24392e7i	−0.0586968	+	0.0338886i
$717$	1.36427e8	−	2.25390e8i	0.370120	−	0.611473i
$718$	−4.58836e6	+	7.94728e6i	−0.0123961	+	0.0214706i
$719$			6.40752e8i			1.72387i	0.507022	+	0.861933i	$0.330746\pi$
$719$			6.40752e8i			1.72387i	−0.507022	+	0.861933i	$0.669254\pi$
$720$	−6.97806e7	−	4.42370e7i	−0.186955	−	0.118519i
$721$	3.45130e8			0.920824
$722$	4.98031e8	+	2.87538e8i	1.32326	+	0.763983i
$723$	−8.23909e6	+	3.97904e8i	−0.0218004	+	1.05284i
$724$	6.57114e7	+	1.13815e8i	0.173151	+	0.299906i
$725$	7.23498e7	−	4.17712e7i	0.189856	−	0.109613i
$726$	1.01596e8	+	1.84697e8i	0.265501	+	0.482670i
$727$	−1.64639e8	+	2.85164e8i	−0.428480	+	0.742149i	−0.996738	−	0.0807013i	$-0.974284\pi$
$727$	−1.64639e8	+	2.85164e8i	−0.428480	+	0.742149i	0.568259	+	0.822850i	$0.307617\pi$
$728$		−	1.19802e8i		−	0.310505i
$729$	−3.84435e8	−	4.80016e7i	−0.992295	−	0.123900i
$730$	1.51578e8			0.389645
$731$	−3.14255e8	−	1.81435e8i	−0.804508	−	0.464483i
$732$	−2.02113e8	+	1.11176e8i	−0.515300	+	0.283450i
$733$	−1.81298e8	−	3.14017e8i	−0.460342	−	0.797335i	0.538636	−	0.842538i	$-0.318940\pi$
$733$	−1.81298e8	−	3.14017e8i	−0.460342	−	0.797335i	−0.998978	+	0.0452035i	$0.985606\pi$
$734$	−1.06450e8	+	6.14592e7i	−0.269190	+	0.155417i
$735$	3.33201e7	+	689933.i	0.0839158	+	0.00173758i
$736$	6.21271e7	−	1.07607e8i	0.155829	−	0.269904i
$737$			2.54810e8i			0.636522i
$738$	1.30779e8	−	2.06294e8i	0.325364	−	0.513237i
$739$	1.76953e7			0.0438454			0.0219227	−	0.999760i	$-0.493021\pi$
$739$	1.76953e7			0.0438454			0.0219227	+	0.999760i	$0.493021\pi$
$740$	9.23039e7	+	5.32917e7i	0.227785	+	0.131512i
$741$	−5.71232e8	−	3.45762e8i	−1.40397	−	0.849813i
$742$	1.52852e8	+	2.64747e8i	0.374162	+	0.648067i
$743$	1.11712e8	−	6.44967e7i	0.272353	−	0.157243i	−0.357604	−	0.933873i	$-0.616406\pi$
$743$	1.11712e8	−	6.44967e7i	0.272353	−	0.157243i	0.629956	+	0.776631i	$0.283073\pi$
$744$	1.02580e8	−	1.69472e8i	0.249084	−	0.411510i
$745$	5.05722e7	−	8.75936e7i	0.122305	−	0.211838i
$746$		−	3.43565e8i		−	0.827546i
$747$	−4.45474e7	+	2.33161e7i	−0.106871	+	0.0559364i
$748$	8.26150e7			0.197403
$749$	1.71617e8	+	9.90834e7i	0.408429	+	0.235806i
$750$	−6.64920e6	+	3.21121e8i	−0.0157611	+	0.761176i
$751$	1.68815e8	+	2.92395e8i	0.398557	+	0.690321i	0.993548	−	0.113411i	$-0.0361778\pi$
$751$	1.68815e8	+	2.92395e8i	0.398557	+	0.690321i	−0.594991	+	0.803732i	$0.702845\pi$
$752$	−1.15081e8	+	6.64423e7i	−0.270615	+	0.156240i
$753$	−1.71102e8	−	3.11056e8i	−0.400747	−	0.728540i
$754$	1.41976e8	−	2.45910e8i	0.331208	−	0.573669i
$755$		−	1.76964e8i		−	0.411192i
$756$	1.27582e7	−	2.05150e8i	0.0295274	−	0.474794i

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:	\( N \)	\(=\)	\( 18 = 2 \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	18.d (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.89898 + 2.82843i) q^{2} +(-23.6571 + 13.0130i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-95.8504 + 55.3393i) q^{5} +(-152.702 - 3.16189i) q^{6} +(-163.169 + 282.617i) q^{7} +181.019i q^{8} +(390.321 - 615.703i) q^{9} +O(q^{10})\)	\(q+(4.89898 + 2.82843i) q^{2} +(-23.6571 + 13.0130i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-95.8504 + 55.3393i) q^{5} +(-152.702 - 3.16189i) q^{6} +(-163.169 + 282.617i) q^{7} +181.019i q^{8} +(390.321 - 615.703i) q^{9} -626.092 q^{10} +(541.817 + 312.818i) q^{11} +(-739.142 - 447.397i) q^{12} +(1014.01 + 1756.31i) q^{13} +(-1598.72 + 923.023i) q^{14} +(1547.42 - 2556.48i) q^{15} +(-512.000 + 886.810i) q^{16} -4126.55i q^{17} +(3653.65 - 1912.32i) q^{18} +12194.5 q^{19} +(-3067.21 - 1770.86i) q^{20} +(182.406 - 8809.24i) q^{21} +(1769.57 + 3064.98i) q^{22} +(-18576.6 + 10725.2i) q^{23} +(-2355.61 - 4282.40i) q^{24} +(-1687.63 + 2923.06i) q^{25} +11472.2i q^{26} +(-1221.72 + 19645.0i) q^{27} -10442.8 q^{28} +(-21435.3 - 12375.7i) q^{29} +(14811.6 - 8147.37i) q^{30} +(20265.9 + 35101.6i) q^{31} +(-5016.55 + 2896.31i) q^{32} +(-16888.6 - 349.699i) q^{33} +(11671.6 - 20215.9i) q^{34} -36118.6i q^{35} +(23308.0 + 965.656i) q^{36} -30093.7 q^{37} +(59740.6 + 34491.3i) q^{38} +(-46843.4 - 28354.0i) q^{39} +(-10017.5 - 17350.8i) q^{40} +(51294.6 - 29614.9i) q^{41} +(25809.9 - 42640.4i) q^{42} +(43967.8 - 76154.5i) q^{43} +20020.4i q^{44} +(-3339.92 + 80615.5i) q^{45} -121342. q^{46} +(112384. + 64885.1i) q^{47} +(572.363 - 27642.1i) q^{48} +(5576.24 + 9658.34i) q^{49} +(-16535.3 + 9546.68i) q^{50} +(53698.9 + 97622.3i) q^{51} +(-32448.2 + 56201.9i) q^{52} -165599. i q^{53} +(-61549.8 + 92785.1i) q^{54} -69244.6 q^{55} +(-51159.1 - 29536.7i) q^{56} +(-288487. + 158688. i) q^{57} +(-70007.5 - 121257. i) q^{58} +(46116.0 - 26625.1i) q^{59} +(95605.8 + 1979.64i) q^{60} +(133491. - 231213. i) q^{61} +229282. i q^{62} +(110320. + 210775. i) q^{63} -32768.0 q^{64} +(-194386. - 112229. i) q^{65} +(-81747.7 - 49481.3i) q^{66} +(203640. + 352715. i) q^{67} +(114358. - 66024.7i) q^{68} +(299902. - 495467. i) q^{69} +(102159. - 176944. i) q^{70} +186563. i q^{71} +(111454. + 70655.7i) q^{72} -242102. q^{73} +(-147429. - 85117.9i) q^{74} +(1886.60 - 91112.5i) q^{75} +(195112. + 337944. i) q^{76} +(-176816. + 102085. i) q^{77} +(-149288. - 271399. i) q^{78} +(63186.3 - 109442. i) q^{79} -113335. i q^{80} +(-226739. - 480644. i) q^{81} +335055. q^{82} +(-59731.2 - 34485.8i) q^{83} +(247047. - 135893. i) q^{84} +(228360. + 395531. i) q^{85} +(430795. - 248720. i) q^{86} +(668144. + 13834.7i) q^{87} +(-56626.2 + 98079.4i) q^{88} +413126. i q^{89} +(-244377. + 385487. i) q^{90} -661817. q^{91} +(-594452. - 343207. i) q^{92} +(-936211. - 566682. i) q^{93} +(367045. + 635741. i) q^{94} +(-1.16885e6 + 674835. i) q^{95} +(80987.6 - 133799. i) q^{96} +(-489221. + 847356. i) q^{97} +63088.0i q^{98} +(404086. - 211499. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9}+O(q^{10}) \) 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9	\( 12 q - 42 q^{3} + 192 q^{4} + 432 q^{5} - 144 q^{6} + 240 q^{7} + 2190 q^{9} + 378 q^{11} + 384 q^{12} + 1680 q^{13} - 4752 q^{14} - 10872 q^{15} - 6144 q^{16} - 2976 q^{18} - 2820 q^{19} + 13824 q^{20} + 24876 q^{21} - 3600 q^{22} - 76248 q^{23} - 6144 q^{24} + 8094 q^{25} + 127008 q^{27} + 15360 q^{28} + 97092 q^{29} + 34272 q^{30} + 21480 q^{31} - 246258 q^{33} - 27360 q^{34} + 38208 q^{36} - 25536 q^{37} + 97632 q^{38} + 42204 q^{39} - 410562 q^{41} - 222144 q^{42} + 71430 q^{43} + 13716 q^{45} - 135072 q^{46} + 347652 q^{47} + 55296 q^{48} - 135954 q^{49} + 311040 q^{50} + 336402 q^{51} - 53760 q^{52} - 173520 q^{54} + 580392 q^{55} - 152064 q^{56} - 522282 q^{57} + 159264 q^{58} + 369738 q^{59} - 170496 q^{60} + 135744 q^{61} - 103800 q^{63} - 393216 q^{64} - 753840 q^{65} + 909216 q^{66} - 289938 q^{67} + 744768 q^{68} + 2059272 q^{69} + 155952 q^{70} - 374784 q^{72} - 977700 q^{73} - 2197152 q^{74} - 2115342 q^{75} - 45120 q^{76} - 159192 q^{77} - 631488 q^{78} - 764796 q^{79} - 1428282 q^{81} + 1073088 q^{82} + 396900 q^{83} + 1441536 q^{84} + 1619568 q^{85} + 3264624 q^{86} + 3072636 q^{87} + 115200 q^{88} - 1987200 q^{90} + 355584 q^{91} - 2439936 q^{92} - 2526576 q^{93} - 736848 q^{94} - 2089260 q^{95} - 49152 q^{96} - 38874 q^{97} + 4398804 q^{99}+O(q^{100}) \) 12 * q - 42 * q^3 + 192 * q^4 + 432 * q^5 - 144 * q^6 + 240 * q^7 + 2190 * q^9 + 378 * q^11 + 384 * q^12 + 1680 * q^13 - 4752 * q^14 - 10872 * q^15 - 6144 * q^16 - 2976 * q^18 - 2820 * q^19 + 13824 * q^20 + 24876 * q^21 - 3600 * q^22 - 76248 * q^23 - 6144 * q^24 + 8094 * q^25 + 127008 * q^27 + 15360 * q^28 + 97092 * q^29 + 34272 * q^30 + 21480 * q^31 - 246258 * q^33 - 27360 * q^34 + 38208 * q^36 - 25536 * q^37 + 97632 * q^38 + 42204 * q^39 - 410562 * q^41 - 222144 * q^42 + 71430 * q^43 + 13716 * q^45 - 135072 * q^46 + 347652 * q^47 + 55296 * q^48 - 135954 * q^49 + 311040 * q^50 + 336402 * q^51 - 53760 * q^52 - 173520 * q^54 + 580392 * q^55 - 152064 * q^56 - 522282 * q^57 + 159264 * q^58 + 369738 * q^59 - 170496 * q^60 + 135744 * q^61 - 103800 * q^63 - 393216 * q^64 - 753840 * q^65 + 909216 * q^66 - 289938 * q^67 + 744768 * q^68 + 2059272 * q^69 + 155952 * q^70 - 374784 * q^72 - 977700 * q^73 - 2197152 * q^74 - 2115342 * q^75 - 45120 * q^76 - 159192 * q^77 - 631488 * q^78 - 764796 * q^79 - 1428282 * q^81 + 1073088 * q^82 + 396900 * q^83 + 1441536 * q^84 + 1619568 * q^85 + 3264624 * q^86 + 3072636 * q^87 + 115200 * q^88 - 1987200 * q^90 + 355584 * q^91 - 2439936 * q^92 - 2526576 * q^93 - 736848 * q^94 - 2089260 * q^95 - 49152 * q^96 - 38874 * q^97 + 4398804 * q^99

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