LMFDB - Embedded newform 18.7.d.a.5.4

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			5.4
Root			$-8.15670i$ of defining polynomial
Character	$\chi$	$=$	18.5
Dual form			18.7.d.a.11.4

$q$-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 $\left(\mathbb{Z}/18\mathbb{Z}\right)^\times$.

$n$	$11$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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	0.0649297	−	0.997890i	$-0.479318\pi$
$5$	−95.8504	−	55.3393i	−0.766803	−	0.442714i	−0.831733	+	0.555176i	$0.812651\pi$
$6$	−152.702	+	3.16189i	−0.706955	+	0.0146384i
$7$	−163.169	−	282.617i	−0.475711	−	0.823956i	0.523901	−	0.851779i	$-0.324476\pi$
$7$	−163.169	−	282.617i	−0.475711	−	0.823956i	−0.999613	+	0.0278225i	$0.991143\pi$
$8$		−	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	−0.282457	−	0.959280i	$-0.591149\pi$
$11$	541.817	−	312.818i	0.407075	−	0.235025i	0.689532	+	0.724255i	$0.257816\pi$
$12$	−739.142	+	447.397i	−0.427744	+	0.258911i
$13$	1014.01	−	1756.31i	0.461541	−	0.799412i	−0.537497	−	0.843266i	$-0.680630\pi$
$13$	1014.01	−	1756.31i	0.461541	−	0.799412i	0.999038	+	0.0438534i	$0.0139635\pi$
$14$	−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	$0.137957\pi$
$17$			4126.55i			0.839924i	−0.907542	+	0.419962i	$0.862043\pi$
$18$	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	−0.999493	−	0.0318293i	$-0.989867\pi$
$23$	−18576.6	−	10725.2i	−1.52680	−	0.881501i	−0.527312	−	0.849672i	$-0.676800\pi$
$24$	−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	−0.870293	−	0.492534i	$-0.836071\pi$
$29$	−21435.3	+	12375.7i	−0.878893	+	0.507429i	−0.00859997	+	0.999963i	$0.502737\pi$
$30$	14811.6	+	8147.37i	0.548576	+	0.301754i
$31$	20265.9	−	35101.6i	0.680269	−	1.17826i	−0.294630	−	0.955612i	$-0.595196\pi$
$31$	20265.9	−	35101.6i	0.680269	−	1.17826i	0.974899	−	0.222649i	$-0.0714704\pi$
$32$	−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	0.823613	−	0.567152i	$-0.191955\pi$
$41$	51294.6	+	29614.9i	0.744252	+	0.429694i	−0.0793613	+	0.996846i	$0.525288\pi$
$42$	25809.9	+	42640.4i	0.348368	+	0.575537i
$43$	43967.8	+	76154.5i	0.553006	+	0.957834i	0.998056	+	0.0623286i	$0.0198527\pi$
$43$	43967.8	+	76154.5i	0.553006	+	0.957834i	−0.445050	+	0.895506i	$0.646814\pi$
$44$		−	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	0.150901	−	0.988549i	$-0.451783\pi$
$47$	112384.	−	64885.1i	1.08246	−	0.624958i	0.931559	+	0.363590i	$0.118449\pi$
$48$	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	$0.187726\pi$
$53$			165599.i			1.11232i	−0.831074	+	0.556161i	$0.812274\pi$
$54$	−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	0.608051	−	0.793898i	$-0.291952\pi$
$59$	46116.0	+	26625.1i	0.224541	+	0.129639i	−0.383510	+	0.923537i	$0.625285\pi$
$60$	95605.8	−	1979.64i	0.442619	−	0.00916498i
$61$	133491.	+	231213.i	0.588115	+	1.01864i	0.994479	+	0.104933i	$0.0334629\pi$
$61$	133491.	+	231213.i	0.588115	+	1.01864i	−0.406365	+	0.913711i	$0.633204\pi$
$62$		−	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	−0.298778	−	0.954323i	$-0.596579\pi$
$67$	203640.	−	352715.i	0.677079	−	1.17273i	0.975857	−	0.218412i	$-0.0700876\pi$
$68$	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	$-0.916071\pi$
$71$		−	186563.i		−	0.521254i	0.965440	−	0.260627i	$-0.0839293\pi$
$72$	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	0.922963	−	0.384890i	$-0.125761\pi$
$79$	63186.3	+	109442.i	0.128157	+	0.221974i	−0.794806	+	0.606864i	$0.792427\pi$
$80$			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	−0.551322	−	0.834293i	$-0.685876\pi$
$83$	−59731.2	+	34485.8i	−0.104464	+	0.0603124i	0.446858	+	0.894605i	$0.352543\pi$
$84$	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	$-0.905343\pi$
$89$		−	413126.i		−	0.586020i	0.956109	−	0.293010i	$-0.0946569\pi$
$90$	−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	−0.999113	−	0.0421177i	$-0.986590\pi$
$97$	−489221.	−	847356.i	−0.536031	−	0.928434i	0.463081	−	0.886316i	$-0.346744\pi$
$98$		−	63088.0i		−	0.0670299i
$99$	404086.	+	211499.i	0.416455	+	0.217973i
$100$	−108008.			−0.108008
$101$	975354.	−	563121.i	0.946669	−	0.546560i	0.0546243	−	0.998507i	$-0.482604\pi$
$101$	975354.	−	563121.i	0.946669	−	0.546560i	0.892045	+	0.451947i	$0.149271\pi$
$102$	−13047.7	−	630133.i	−0.0122951	−	0.593789i
$103$	−528792.	+	915894.i	−0.483919	+	0.838173i	−0.999829	−	0.0184698i	$-0.994121\pi$
$103$	−528792.	+	915894.i	−0.483919	+	0.838173i	0.515910	+	0.856643i	$0.327454\pi$
$104$	−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	$0.0797227\pi$
$107$			607244.i			0.495692i	−0.968799	+	0.247846i	$0.920277\pi$
$108$	−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	0.844705	−	0.535233i	$-0.179776\pi$
$113$	1.15941e6	+	669388.i	0.803532	+	0.463919i	−0.0411727	+	0.999152i	$0.513109\pi$
$114$	−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	0.209824	−	0.977739i	$-0.432711\pi$
$131$	−1.19601e6	−	690515.i	−0.532010	−	0.307156i	−0.741835	+	0.670583i	$0.766044\pi$
$132$	−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	0.235441	−	0.971889i	$-0.424347\pi$
$137$	3.07236e6	−	1.77383e6i	1.19484	−	0.689842i	0.959401	+	0.282046i	$0.0910132\pi$
$138$	2.87061e6	+	1.57903e6i	1.09229	+	0.600832i
$139$	−1.61016e6	+	2.78888e6i	−0.599548	+	1.03845i	0.393339	+	0.919393i	$0.371320\pi$
$139$	−1.61016e6	+	2.78888e6i	−0.599548	+	1.03845i	−0.992888	+	0.119055i	$0.962014\pi$
$140$	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	0.375583	−	0.926789i	$-0.377443\pi$
$149$	−791423.	−	456928.i	−0.239249	−	0.138130i	−0.614832	+	0.788658i	$0.710776\pi$
$150$	266947.	+	441022.i	0.0790955	+	0.130673i
$151$	−799451.	−	1.38469e6i	−0.232199	−	0.402181i	0.726256	−	0.687425i	$-0.241259\pi$
$151$	−799451.	−	1.38469e6i	−0.232199	−	0.402181i	−0.958455	+	0.285244i	$0.907925\pi$
$152$		−	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	−0.223063	−	0.974804i	$-0.571606\pi$
$157$	2.83537e6	−	4.91100e6i	0.732673	−	1.26903i	0.955737	−	0.294224i	$-0.0950611\pi$
$158$	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	−0.165569	−	0.986198i	$-0.552946\pi$
$167$	−5.13451e6	−	2.96441e6i	−1.10243	−	0.636486i	−0.936857	+	0.349712i	$0.886279\pi$
$168$	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	−0.675807	−	0.737079i	$-0.736205\pi$
$173$	−1.94362e6	+	1.12215e6i	−0.375382	+	0.216727i	0.300425	+	0.953805i	$0.402871\pi$
$174$	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	$-0.978409\pi$
$179$		−	777450.i		−	0.135554i	0.997700	−	0.0677772i	$-0.0215907\pi$
$180$	−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	−0.741202	−	0.671282i	$-0.765744\pi$
$191$	−3.69615e6	+	2.13397e6i	−0.530456	+	0.306259i	0.210746	+	0.977541i	$0.432411\pi$
$192$	775197.	+	426411.i	0.109524	+	0.0602456i
$193$	4.05006e6	−	7.01491e6i	0.563365	−	0.975777i	−0.433835	−	0.900992i	$-0.642840\pi$
$193$	4.05006e6	−	7.01491e6i	0.563365	−	0.975777i	0.997200	−	0.0747842i	$-0.0238268\pi$
$194$	−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	$-0.913975\pi$
$197$		−	4.08228e6i		−	0.533955i	0.963703	−	0.266977i	$-0.0860249\pi$
$198$	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	0.0815616	+	0.996668i	$0.474009\pi$
$211$	−7.72519e6	+	1.33804e7i	−0.822359	+	1.42437i	−0.903921	+	0.427700i	$0.859324\pi$
$212$	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	0.922417	−	0.386195i	$-0.126211\pi$
$223$	1.40565e6	+	2.43465e6i	0.126754	+	0.219544i	−0.795663	+	0.605739i	$0.792877\pi$
$224$			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	−0.197861	−	0.980230i	$-0.563399\pi$
$227$	6.45811e6	−	3.72859e6i	0.552113	−	0.318762i	0.749974	+	0.661468i	$0.230066\pi$
$228$	−9.01348e6	+	5.45579e6i	−0.760480	+	0.460313i
$229$	−6.31232e6	+	1.09333e7i	−0.525633	+	0.910422i	0.473922	+	0.880567i	$0.342838\pi$
$229$	−6.31232e6	+	1.09333e7i	−0.525633	+	0.910422i	−0.999554	+	0.0298554i	$0.990495\pi$
$230$	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	$0.224969\pi$
$233$			1.64283e7i			1.29875i	−0.760469	+	0.649374i	$0.775031\pi$
$234$	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	0.157477	−	0.987523i	$-0.449664\pi$
$239$	−8.45060e6	−	4.87895e6i	−0.619004	−	0.357382i	−0.776481	+	0.630140i	$0.782997\pi$
$240$	1.47483e6	−	2.68118e6i	0.106686	−	0.193951i
$241$	7.37017e6	+	1.27655e7i	0.526534	+	0.911984i	0.999522	+	0.0309150i	$0.00984213\pi$
$241$	7.37017e6	+	1.27655e7i	0.526534	+	0.911984i	−0.472988	+	0.881069i	$0.656825\pi$
$242$			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	$-0.863522\pi$
$251$		−	1.31485e7i		−	0.831486i	0.909482	−	0.415743i	$-0.136478\pi$
$252$	−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	−0.162505	−	0.986708i	$-0.551957\pi$
$257$	−1.86427e7	−	1.07634e7i	−1.09827	−	0.634087i	−0.935766	+	0.352621i	$0.885291\pi$
$258$	−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	−0.284075	−	0.958802i	$-0.591686\pi$
$263$	7.35362e6	−	4.24561e6i	0.404235	−	0.233385i	0.688310	+	0.725417i	$0.258353\pi$
$264$	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	$-0.992772\pi$
$269$		−	883900.i		−	0.0454094i	0.999742	−	0.0227047i	$-0.00722776\pi$
$270$	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	0.926200	−	0.377033i	$-0.123056\pi$
$277$	2.90287e6	+	5.02791e6i	0.136580	+	0.236564i	−0.789620	+	0.613596i	$0.789722\pi$
$278$			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	−0.741033	−	0.671468i	$-0.765664\pi$
$281$	−1.17606e7	+	6.78998e6i	−0.530042	+	0.306020i	0.210992	+	0.977488i	$0.432331\pi$
$282$	−1.69562e7	+	1.02634e7i	−0.756102	+	0.457663i
$283$	−2.53102e6	+	4.38385e6i	−0.111670	+	0.193418i	−0.916444	−	0.400164i	$-0.868953\pi$
$283$	−2.53102e6	+	4.38385e6i	−0.111670	+	0.193418i	0.804774	+	0.593582i	$0.202287\pi$
$284$	−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	0.979857	−	0.199702i	$-0.0639974\pi$
$293$	3.26203e7	+	1.88334e7i	1.29684	+	0.748730i	0.316981	+	0.948432i	$0.397331\pi$
$294$	−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	0.850907	−	0.525316i	$-0.176053\pi$
$311$	2.47086e7	+	1.42655e7i	0.821423	+	0.474249i	−0.0294839	+	0.999565i	$0.509386\pi$
$312$	5.13261e6	+	8.47956e6i	0.168995	+	0.279196i
$313$	−1.10257e7	−	1.90970e7i	−0.359560	−	0.622776i	0.628327	−	0.777949i	$-0.283740\pi$
$313$	−1.10257e7	−	1.90970e7i	−0.359560	−	0.622776i	−0.987887	+	0.155173i	$0.950407\pi$
$314$		−	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	−0.245746	−	0.969334i	$-0.579033\pi$
$317$	1.49989e7	−	8.65961e6i	0.470848	−	0.271844i	0.716595	+	0.697490i	$0.245700\pi$
$318$	−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	0.751745	−	0.659453i	$-0.229212\pi$
$331$	−7.07998e6	−	1.22629e7i	−0.195231	−	0.338149i	−0.946976	+	0.321304i	$0.895879\pi$
$332$			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	0.358875	+	0.933386i	$0.383160\pi$
$337$	−2.40697e7	+	4.16899e7i	−0.628898	+	1.08928i	−0.987773	+	0.155898i	$0.950173\pi$
$338$	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	0.945667	−	0.325136i	$-0.105410\pi$
$347$	4.75029e7	+	2.74258e7i	1.13692	+	0.656404i	0.191258	+	0.981540i	$0.438743\pi$
$348$	1.03069e7	−	1.87375e7i	0.244563	−	0.444605i
$349$	8.59925e6	+	1.48943e7i	0.202295	+	0.350385i	0.949267	−	0.314470i	$-0.101827\pi$
$349$	8.59925e6	+	1.48943e7i	0.202295	+	0.350385i	−0.746973	+	0.664855i	$0.768493\pi$
$350$			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	−0.569389	−	0.822068i	$-0.692820\pi$
$353$	−6.25279e6	+	3.61005e6i	−0.142151	+	0.0820709i	0.427238	+	0.904139i	$0.359487\pi$
$354$	−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	$-0.994420\pi$
$359$		−	1.62223e6i		−	0.0350614i	0.999846	−	0.0175307i	$-0.00558048\pi$
$360$	−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	0.734952	−	0.678119i	$-0.237205\pi$
$367$	−1.08645e7	−	1.88180e7i	−0.219793	−	0.380692i	−0.954745	+	0.297427i	$0.903871\pi$
$368$			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	0.409692	+	0.912224i	$0.365636\pi$
$373$	−3.03671e7	+	5.25974e7i	−0.585163	+	1.01353i	−0.994855	+	0.101309i	$0.967697\pi$
$374$	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	0.817809	−	0.575489i	$-0.195188\pi$
$383$	4.09187e7	+	2.36244e7i	0.728326	+	0.420499i	−0.0894836	+	0.995988i	$0.528522\pi$
$384$	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	−0.350755	−	0.936467i	$-0.614075\pi$
$389$	1.67687e7	−	9.68140e6i	0.284872	−	0.164471i	0.635627	+	0.771996i	$0.280742\pi$
$390$	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	−0.985243	−	0.171162i	$-0.945248\pi$
$401$	−1.04853e8	−	6.05366e7i	−1.62609	−	0.938826i	−0.640852	−	0.767665i	$-0.721419\pi$
$402$	−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	−0.974062	−	0.226279i	$-0.927344\pi$
$409$	−1.99142e7	+	3.44925e7i	−0.291067	+	0.504144i	0.682995	+	0.730423i	$0.260677\pi$
$410$	−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	0.783714	−	0.621122i	$-0.213323\pi$
$419$	4.69066e7	+	2.70815e7i	0.637664	+	0.368155i	−0.146050	+	0.989277i	$0.546656\pi$
$420$	−1.61594e7	−	2.66968e7i	−0.218111	−	0.360339i
$421$	−2.70636e7	−	4.68755e7i	−0.362693	−	0.628203i	0.625710	−	0.780056i	$-0.284809\pi$
$421$	−2.70636e7	−	4.68755e7i	−0.362693	−	0.628203i	−0.988403	+	0.151853i	$0.951476\pi$
$422$			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	$-0.831596\pi$
$431$		−	8.08186e7i		−	1.00944i	0.863284	−	0.504719i	$-0.168404\pi$
$432$	−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	0.998466	−	0.0553714i	$-0.0176343\pi$
$439$	3.81803e7	+	6.61302e7i	0.451280	+	0.781640i	−0.547186	+	0.837011i	$0.684301\pi$
$440$			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	−0.938245	−	0.345973i	$-0.887549\pi$
$443$	−9.63056e7	+	5.56020e7i	−1.10775	+	0.639557i	−0.169501	+	0.985530i	$0.554216\pi$
$444$	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	$0.271913\pi$
$449$			1.36515e8i			1.50814i	−0.656793	+	0.754071i	$0.728087\pi$
$450$	−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	0.996771	+	0.0802917i	$0.0255852\pi$
$457$	5.42046e7	+	9.38851e7i	0.567920	+	0.983667i	−0.428851	+	0.903375i	$0.641081\pi$
$458$			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	0.452403	−	0.891814i	$-0.350567\pi$
$461$	1.42152e8	−	8.20712e7i	1.45094	−	0.837699i	0.998535	+	0.0541143i	$0.0172335\pi$
$462$	2.73229e7	+	1.50295e7i	0.277078	+	0.152412i
$463$	−1.86985e7	+	3.23867e7i	−0.188392	+	0.326305i	−0.944714	−	0.327895i	$-0.893661\pi$
$463$	−1.86985e7	+	3.23867e7i	−0.188392	+	0.326305i	0.756322	+	0.654199i	$0.226994\pi$
$464$	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	$-0.745735\pi$
$467$		−	1.45951e8i		−	1.43304i	0.697569	−	0.716518i	$-0.254265\pi$
$468$	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	0.125779	−	0.992058i	$-0.459857\pi$
$479$	1.15157e8	−	6.64861e7i	1.04782	−	0.604957i	0.922037	+	0.387102i	$0.126524\pi$
$480$	−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	0.126069	−	0.992021i	$-0.459764\pi$
$491$	−7.93099e7	−	4.57896e7i	−0.670012	−	0.386832i	−0.796081	+	0.605190i	$0.793097\pi$
$492$	−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	−0.727711	−	0.685884i	$-0.759416\pi$
$499$	2.85950e7	−	4.95279e7i	0.230138	−	0.398610i	0.957848	+	0.287274i	$0.0927490\pi$
$500$	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	$0.259387\pi$
$503$			1.85206e8i			1.45530i	−0.685950	+	0.727649i	$0.740613\pi$
$504$	−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	0.851483	−	0.524382i	$-0.175704\pi$
$509$	1.08544e8	+	6.26677e7i	0.823097	+	0.475215i	−0.0283864	+	0.999597i	$0.509037\pi$
$510$	−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	$-0.802839\pi$
$521$		−	1.64203e8i		−	1.16109i	0.814227	−	0.580546i	$-0.197161\pi$
$522$	−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	0.878821	−	0.477151i	$-0.158330\pi$
$547$	4.28578e6	+	7.42318e6i	0.0261859	+	0.0453553i	−0.852635	+	0.522506i	$0.824997\pi$
$548$		−	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	$0.0808476\pi$
$557$			8.68427e7i			0.502536i	−0.967918	+	0.251268i	$0.919152\pi$
$558$	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	0.485189	−	0.874409i	$-0.338751\pi$
$563$	−5.26034e6	−	3.03706e6i	−0.0294774	−	0.0170188i	−0.514666	+	0.857391i	$0.672084\pi$
$564$	−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	−0.819746	−	0.572727i	$-0.805886\pi$
$569$	−1.35148e8	+	7.80279e7i	−0.733624	+	0.423558i	0.0861225	+	0.996285i	$0.472552\pi$
$570$	1.80620e8	+	9.93531e7i	0.975305	+	0.536484i
$571$	−5.10042e7	+	8.83419e7i	−0.273967	+	0.474524i	−0.969874	−	0.243608i	$-0.921669\pi$
$571$	−5.10042e7	+	8.83419e7i	−0.273967	+	0.474524i	0.695907	+	0.718132i	$0.255002\pi$
$572$	−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	−0.713397	−	0.700760i	$-0.752844\pi$
$587$	−9.36918e7	+	5.40930e7i	−0.463220	+	0.267440i	0.250177	+	0.968200i	$0.419511\pi$
$588$	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	$0.229263\pi$
$593$			2.75079e8i			1.31915i	−0.751641	+	0.659573i	$0.770737\pi$
$594$	−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	−0.378138	−	0.925749i	$-0.623435\pi$
$599$	−2.94213e8	−	1.69864e8i	−1.36893	−	0.790351i	−0.990791	+	0.135398i	$0.956769\pi$
$600$	1.64931e7	−	341510.i	0.0763571	−	0.00158107i
$601$	−8.08282e7	−	1.39999e8i	−0.372340	−	0.644911i	0.617585	−	0.786504i	$-0.288111\pi$
$601$	−8.08282e7	−	1.39999e8i	−0.372340	−	0.644911i	−0.989925	+	0.141593i	$0.954778\pi$
$602$		−	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	0.492042	+	0.870572i	$0.336251\pi$
$607$	−1.13595e8	+	1.96752e8i	−0.507916	+	0.879737i	−0.999958	+	0.00916513i	$0.997083\pi$
$608$	−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	−0.332567	−	0.943080i	$-0.607915\pi$
$617$	−3.09010e8	−	1.78407e8i	−1.31558	−	0.759551i	−0.983014	+	0.183528i	$0.941248\pi$
$618$	7.78518e7	−	1.41531e8i	0.329840	−	0.599635i
$619$	−1.56034e8	−	2.70258e8i	−0.657880	−	1.13948i	−0.981163	−	0.193179i	$-0.938120\pi$
$619$	−1.56034e8	−	2.70258e8i	−0.657880	−	1.13948i	0.323284	−	0.946302i	$-0.395213\pi$
$620$			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	0.413009	−	0.910727i	$-0.364478\pi$
$641$	3.70891e8	−	2.14134e8i	1.40823	−	0.813040i	0.995217	+	0.0976870i	$0.0311444\pi$
$642$	−1.92004e6	−	9.27276e7i	−0.00725613	−	0.350432i
$643$	−1.61002e8	+	2.78864e8i	−0.605619	+	1.04896i	0.386334	+	0.922359i	$0.373741\pi$
$643$	−1.61002e8	+	2.78864e8i	−0.605619	+	1.04896i	−0.991953	+	0.126604i	$0.959592\pi$
$644$	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	$0.0499995\pi$
$647$			8.47366e7i			0.312866i	−0.987689	+	0.156433i	$0.950001\pi$
$648$	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	0.989847	−	0.142139i	$-0.0453978\pi$
$653$	3.79152e8	+	2.18903e8i	1.36167	+	0.786163i	0.371828	+	0.928302i	$0.378731\pi$
$654$	−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	−0.852215	−	0.523192i	$-0.824741\pi$
$659$	−2.36172e8	+	1.36354e8i	−0.825225	+	0.476444i	0.0269900	+	0.999636i	$0.491408\pi$
$660$	5.11816e7	−	3.09799e7i	0.178025	−	0.107757i
$661$	−1.47145e8	+	2.54862e8i	−0.509495	+	0.882471i	0.490445	+	0.871472i	$0.336834\pi$
$661$	−1.47145e8	+	2.54862e8i	−0.509495	+	0.882471i	−0.999940	+	0.0109985i	$0.996499\pi$
$662$	−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	0.840634	−	0.541604i	$-0.182183\pi$
$673$	−1.48525e7	−	2.57254e7i	−0.0487254	−	0.0843949i	−0.889359	+	0.457209i	$0.848849\pi$
$674$			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	0.505444	−	0.862859i	$-0.331329\pi$
$677$	4.67116e8	−	2.69690e8i	1.50542	−	0.869157i	0.999980	−	0.00629800i	$-0.00200473\pi$
$678$	−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	$-0.628269\pi$
$683$		−	5.86183e8i		−	1.83980i	0.392152	−	0.919901i	$-0.371731\pi$
$684$	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	0.964549	+	0.263903i	$0.0850100\pi$
$691$	2.34528e8	+	4.06214e8i	0.710822	+	1.23118i	−0.253728	+	0.967276i	$0.581657\pi$
$692$			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	$0.0275064\pi$
$701$			5.94604e7i			0.172613i	−0.996269	+	0.0863065i	$0.972494\pi$
$702$	−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	−0.770652	−	0.637256i	$-0.780070\pi$
$709$	−3.34021e8	−	5.78541e8i	−0.937206	−	1.62329i	−0.166553	−	0.986032i	$-0.553264\pi$
$710$			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	$-0.669254\pi$
$719$		−	6.40752e8i		−	1.72387i	0.507022	−	0.861933i	$-0.330746\pi$
$720$	−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	0.568259	−	0.822850i	$-0.307617\pi$
$727$	−1.64639e8	−	2.85164e8i	−0.428480	−	0.742149i	−0.996738	+	0.0807013i	$0.974284\pi$
$728$			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	−0.998978	−	0.0452035i	$-0.985606\pi$
$733$	−1.81298e8	+	3.14017e8i	−0.460342	+	0.797335i	0.538636	+	0.842538i	$0.318940\pi$
$734$	−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	0.629956	−	0.776631i	$-0.283073\pi$
$743$	1.11712e8	+	6.44967e7i	0.272353	+	0.157243i	−0.357604	+	0.933873i	$0.616406\pi$
$744$	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	−0.594991	−	0.803732i	$-0.702845\pi$
$751$	1.68815e8	−	2.92395e8i	0.398557	−	0.690321i	0.993548	+	0.113411i	$0.0361778\pi$
$752$	−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
$757$	−9.58119e7			−0.220868			−0.110434	−	0.993883i	$-0.535224\pi$
$757$	−9.58119e7			−0.220868			−0.110434	+	0.993883i	$0.535224\pi$
$758$	9.85290e7	−	5.68857e7i	0.226233	−	0.130616i
$759$	3.17484e8	+	1.74638e8i	0.726099	+	0.399404i
$760$	−1.22158e8	+	2.11584e8i	−0.278280	+	0.481995i
$761$	−2.89801e8	−	1.67317e8i	−0.657575	−	0.379651i	0.133777	−	0.991011i	$-0.457289\pi$
$761$	−2.89801e8	−	1.67317e8i	−0.657575	−	0.379651i	−0.791353	+	0.611360i	$0.790623\pi$
$762$	2.48634e8	−	5.14828e6i	0.561948	−	0.0116358i
$763$	−1.56855e8	−	2.71681e8i	−0.353122	−	0.611626i
$764$			1.36574e8i			0.306259i
$765$	3.32664e8	−	1.37823e7i	0.743055	−	0.0307849i
$766$	2.67280e8			0.594676
$767$	9.35237e7	−	5.39959e7i	0.207270	−	0.119667i
$768$	2.42202e7	−	1.46603e7i	0.0534681	−	0.0323638i
$769$	1.21287e8	−	2.10075e8i	0.266708	−	0.461951i	−0.701302	−	0.712864i	$-0.747398\pi$
$769$	1.21287e8	−	2.10075e8i	0.266708	−	0.461951i	0.968010	+	0.250913i	$0.0807309\pi$
$770$	1.10703e8	+	6.39144e7i	0.242486	+	0.139999i
$771$	3.00969e8	+	4.97229e8i	0.656687	+	1.08491i
$772$	−1.29602e8	−	2.24477e8i	−0.281682	−	0.487888i
$773$			2.36476e8i			0.511974i	0.966680	+	0.255987i	$0.0824005\pi$
$773$			2.36476e8i			0.511974i	−0.966680	+	0.255987i	$0.917599\pi$
$774$	1.50111e7	+	3.62323e8i	0.0323735	+	0.781398i
$775$	−1.36805e8			−0.293899
$776$	−1.53388e8	+	8.85585e7i	−0.328251	+	0.189516i
$777$	−5.48928e6	−	2.65103e8i	−0.0117018	−	0.565134i
$778$	5.47663e7	−	9.48580e7i	0.116299	−	0.201435i
$779$	6.25512e8	+	3.61140e8i	1.32319	+	0.763946i
$780$	9.34679e7	−	1.69921e8i	0.196960	−	0.358065i
$781$	−5.83602e7	−	1.01083e8i	−0.122508	−	0.212190i
$782$		−	5.00724e8i		−	1.04708i
$783$	2.69309e8	+	4.05978e8i	0.561004	+	0.845703i
$784$	−1.14201e7			−0.0236986
$785$	−5.43542e8	+	3.13814e8i	−1.12363	+	0.648730i
$786$	1.84816e8	+	1.01662e8i	0.380604	+	0.209358i
$787$	2.48419e8	−	4.30274e8i	0.509636	−	0.882716i	−0.490301	−	0.871553i	$-0.663113\pi$
$787$	2.48419e8	−	4.30274e8i	0.509636	−	0.882716i	0.999938	−	0.0111631i	$-0.00355339\pi$
$788$	−1.13132e8	−	6.53165e7i	−0.231209	−	0.133489i
$789$	−2.29214e8	+	4.74616e6i	−0.466670	+	0.00966298i
$790$	−3.95605e7	−	6.85208e7i	−0.0802380	−	0.138976i
$791$		−	4.36893e8i		−	0.882767i
$792$	3.82854e7	−	7.31474e7i	0.0770651	−	0.147239i
$793$	5.41442e8			1.08576
$794$	−1.79624e8	+	1.03706e8i	−0.358842	+	0.207177i
$795$	−4.23350e8	+	2.56251e8i	−0.842556	+	0.509993i
$796$	1.64502e7	−	2.84926e7i	0.0326161	−	0.0564927i
$797$	−9.18416e7	−	5.30248e7i	−0.181411	−	0.104738i	0.406544	−	0.913631i	$-0.366734\pi$
$797$	−9.18416e7	−	5.30248e7i	−0.181411	−	0.104738i	−0.587956	+	0.808893i	$0.700067\pi$
$798$	3.14739e8	+	5.19978e8i	0.619358	+	1.02324i
$799$	2.67751e8	+	4.63759e8i	0.524918	+	0.909184i
$800$			1.95516e7i			0.0381867i
$801$	2.54363e8	−	1.61252e8i	0.494944	−	0.313767i
$802$	−6.84894e8			−1.32770
$803$	−1.31175e8	+	7.57341e7i	−0.253341	+	0.146266i
$804$	7.28476e6	+	3.51815e8i	0.0140167	+	0.676934i
$805$	3.87380e8	−	6.70962e8i	0.742591	−	1.28621i
$806$	−4.02691e8	−	2.32494e8i	−0.769071	−	0.444023i
$807$	−1.15022e7	+	2.09105e7i	−0.0218857	+	0.0397873i
$808$	−1.01936e8	−	1.76558e8i	−0.193238	−	0.334698i
$809$		−	2.99505e8i		−	0.565664i	−0.959169	−	0.282832i	$-0.908726\pi$
$809$		−	2.99505e8i		−	0.565664i	0.959169	−	0.282832i	$-0.0912739\pi$
$810$	1.41960e8	−	3.00928e8i	0.267122	−	0.566248i
$811$	−4.31983e8			−0.809848			−0.404924	−	0.914350i	$-0.632702\pi$
$811$	−4.31983e8			−0.809848			−0.404924	+	0.914350i	$0.632702\pi$
$812$	2.23845e8	−	1.29237e8i	0.418100	−	0.241390i
$813$	1.46122e8	+	8.03768e7i	0.271921	+	0.149575i
$814$	−5.32529e7	+	9.22367e7i	−0.0987348	+	0.171014i
$815$	−5.35335e8	−	3.09076e8i	−0.988900	−	0.570942i
$816$	−1.14066e8	+	2.36188e6i	−0.209936	+	0.00434698i
$817$	5.36166e8	+	9.28667e8i	0.983180	+	1.70292i
$818$			2.25304e8i			0.411632i
$819$	−2.58321e8	−	4.07483e8i	−0.470228	−	0.741750i
$820$	−2.09775e8			−0.380463
$821$	2.29258e8	−	1.32362e8i	0.414282	−	0.239186i	−0.278346	−	0.960481i	$-0.589786\pi$
$821$	2.29258e8	−	1.32362e8i	0.414282	−	0.239186i	0.692628	+	0.721295i	$0.256453\pi$
$822$	−4.63548e8	+	2.80582e8i	−0.834601	+	0.505178i
$823$	1.83269e8	−	3.17431e8i	0.328768	−	0.569443i	−0.653499	−	0.756927i	$-0.726700\pi$
$823$	1.83269e8	−	3.17431e8i	0.328768	−	0.569443i	0.982268	+	0.187484i	$0.0600332\pi$
$824$	1.65795e8	+	9.57215e7i	0.296339	+	0.171091i
$825$	2.95239e7	+	4.87762e7i	0.0525789	+	0.0868652i
$826$	−4.91511e7	−	8.51323e7i	−0.0872154	−	0.151062i
$827$			5.77816e8i			1.02158i	0.859705	+	0.510791i	$0.170647\pi$
$827$			5.77816e8i			1.02158i	−0.859705	+	0.510791i	$0.829353\pi$
$828$	−4.43341e8	−	2.32045e8i	−0.780993	−	0.408772i
$829$	−3.22169e8			−0.565484			−0.282742	−	0.959196i	$-0.591244\pi$
$829$	−3.22169e8			−0.565484			−0.282742	+	0.959196i	$0.591244\pi$
$830$	3.73973e7	−	2.15913e7i	0.0654042	−	0.0377611i
$831$	−3.24510e6	−	1.56721e8i	−0.00565491	−	0.273102i
$832$	−3.32269e7	+	5.75507e7i	−0.0576926	+	0.0999265i
$833$	3.98556e7	+	2.30106e7i	0.0689532	+	0.0398101i
$834$	2.37057e8	−	4.30959e8i	0.408653	−	0.742913i
$835$	3.28097e8	+	5.68280e8i	0.563563	+	0.976119i
$836$		−	2.44139e8i		−	0.417847i
$837$	−7.14331e8	−	3.55240e8i	−1.21821	−	0.605823i
$838$	3.06393e8			0.520650
$839$	−7.64777e8	+	4.41544e8i	−1.29494	+	0.747632i	−0.979525	−	0.201322i	$-0.935476\pi$
$839$	−7.64777e8	+	4.41544e8i	−1.29494	+	0.747632i	−0.315412	+	0.948955i	$0.602143\pi$
$840$	−1.54674e8	−	8.50815e7i	−0.260964	−	0.143548i
$841$	8.90391e6	−	1.54220e7i	0.0149690	−	0.0259271i
$842$	−2.65168e8	−	1.53095e8i	−0.444206	−	0.256463i
$843$	3.66580e8	−	7.59049e6i	0.611908	−	0.0126703i
$844$	2.47206e8	+	4.28173e8i	0.411180	+	0.712184i
$845$		−	7.90226e7i		−	0.130973i
$846$	5.34693e8	−	2.21525e7i	0.883067	−	0.0365857i
$847$	4.50392e8			0.741209
$848$	1.46855e8	−	8.47868e7i	0.240825	−	0.139040i
$849$	1.16924e8	−	7.07732e7i	0.191065	−	0.115650i
$850$	3.93948e7	−	6.82338e7i	0.0641479	−	0.111107i
$851$	5.59040e8	+	3.22762e8i	0.907098	+	0.523713i
$852$	8.34676e7	+	1.37896e8i	0.134958	+	0.222963i
$853$	−2.30927e8	−	3.99977e8i	−0.372073	−	0.644449i	0.617812	−	0.786326i	$-0.288019\pi$
$853$	−2.30927e8	−	3.99977e8i	−0.372073	−	0.644449i	−0.989884	+	0.141877i	$0.954686\pi$
$854$		−	4.92861e8i		−	0.791317i
$855$	−4.07286e7	−	9.83066e8i	−0.0651631	−	1.57284i
$856$	1.09923e8			0.175254
$857$	−3.69032e8	+	2.13061e8i	−0.586303	+	0.338502i	−0.763634	−	0.645649i	$-0.776587\pi$
$857$	−3.69032e8	+	2.13061e8i	−0.586303	+	0.338502i	0.177331	+	0.984151i	$0.443254\pi$
$858$	4.01180e6	+	1.93748e8i	0.00635152	+	0.306744i
$859$	1.54794e8	−	2.68110e8i	0.244216	−	0.422994i	−0.717695	−	0.696357i	$-0.754803\pi$
$859$	1.54794e8	−	2.68110e8i	0.244216	−	0.422994i	0.961911	+	0.273363i	$0.0881362\pi$
$860$	−2.69718e8	−	1.55722e8i	−0.424047	−	0.244824i
$861$	−2.51529e8	+	4.57268e8i	−0.394074	+	0.716410i
$862$	−2.28590e8	−	3.95929e8i	−0.356890	−	0.618152i
$863$			3.39614e8i			0.528388i	0.964470	+	0.264194i	$0.0851059\pi$
$863$			3.39614e8i			0.528388i	−0.964470	+	0.264194i	$0.914894\pi$
$864$	−5.07693e7	+	1.02089e8i	−0.0787154	+	0.158284i
$865$	2.48396e8			0.383792
$866$	−6.55083e7	+	3.78212e7i	−0.100865	+	0.0582347i
$867$	−1.68183e8	−	9.25121e7i	−0.258062	−	0.141952i
$868$	−2.11633e8	+	3.66559e8i	−0.323612	+	0.560512i
$869$	6.84709e7	+	3.95317e7i	0.104339	+	0.0602402i
$870$	−4.18320e8	+	8.66183e6i	−0.635259	+	0.0131538i
$871$	−4.12984e8	−	7.15310e8i	−0.624999	−	1.08253i
$872$		−	1.74015e8i		−	0.262444i
$873$	3.30766e8	−	6.31956e8i	0.497140	−	0.949827i
$874$	−1.47971e9			−2.21636
$875$	5.94321e8	−	3.43132e8i	0.887150	−	0.512196i
$876$	1.78948e8	−	1.08316e8i	0.266204	−	0.161131i
$877$	−2.91464e8	+	5.04830e8i	−0.432101	+	0.748422i	−0.997054	−	0.0767016i	$-0.975561\pi$
$877$	−2.91464e8	+	5.04830e8i	−0.432101	+	0.748422i	0.564953	+	0.825123i	$0.308894\pi$
$878$	3.74089e8	+	2.15980e8i	0.552703	+	0.319103i
$879$	−5.26625e8	−	8.70034e8i	−0.775416	−	1.28106i
$880$	3.54532e7	+	6.14068e7i	0.0520245	+	0.0901090i
$881$			5.04493e8i			0.737781i	0.929473	+	0.368890i	$0.120262\pi$
$881$			5.04493e8i			0.737781i	−0.929473	+	0.368890i	$0.879738\pi$
$882$	3.88435e7	−	2.46246e7i	0.0566125	−	0.0358892i
$883$	−5.92257e8			−0.860256			−0.430128	−	0.902768i	$-0.641532\pi$
$883$	−5.92257e8			−0.860256			−0.430128	+	0.902768i	$0.641532\pi$
$884$	2.31920e8	−	1.33899e8i	0.335723	−	0.193830i
$885$	3.29425e6	+	1.59094e8i	0.00475254	+	0.229522i
$886$	−3.14533e8	+	5.44786e8i	−0.452235	+	0.783295i
$887$	3.30070e8	+	1.90566e8i	0.472972	+	0.273071i	0.717483	−	0.696576i	$-0.245294\pi$
$887$	3.30070e8	+	1.90566e8i	0.472972	+	0.273071i	−0.244511	+	0.969647i	$0.578627\pi$
$888$	7.08891e7	−	1.28873e8i	0.101237	−	0.184045i
$889$	2.65677e8	+	4.60165e8i	0.378136	+	0.654951i
$890$			2.58655e8i			0.366903i
$891$	2.75030e7	+	3.31350e8i	0.0388818	+	0.468439i
$892$	8.99614e7			0.126754
$893$	1.37047e9	−	7.91241e8i	1.92449	−	1.11110i
$894$	1.22297e8	+	6.72717e7i	0.171160	+	0.0941498i
$895$	−4.30235e7	+	7.45189e7i	−0.0600118	+	0.103944i
$896$	5.23870e7	+	3.02456e7i	0.0728281	+	0.0420473i
$897$	1.17430e9	−	2.43152e7i	1.62705	−	0.0336900i
$898$	3.86123e8	+	6.68785e8i	0.533209	+	0.923545i
$899$			1.00322e9i			1.38075i
$900$	−4.21580e7	−	6.65011e7i	−0.0578299	−	0.0912223i
$901$	−6.83353e8			−0.934267
$902$	1.81539e8	−	1.04811e8i	0.247371	−	0.142820i
$903$	−6.62844e8	+	4.01214e8i	−0.900218	+	0.544895i
$904$	1.21172e8	−	2.09876e8i	0.164020	−	0.284091i
$905$	−3.93654e8	−	2.27276e8i	−0.531091	−	0.306625i
$906$	1.26456e8	+	2.08917e8i	0.170042	+	0.280925i
$907$	6.63839e8	+	1.14980e9i	0.889695	+	1.54100i	0.840237	+	0.542220i	$0.182416\pi$
$907$	6.63839e8	+	1.14980e9i	0.889695	+	1.54100i	0.0494580	+	0.998776i	$0.484251\pi$
$908$		−	2.38630e8i		−	0.318762i
$909$	7.27417e8	+	3.80730e8i	0.968482	+	0.506904i
$910$	4.14359e8			0.549860
$911$	9.77428e8	−	5.64318e8i	1.29280	−	0.746396i	0.313646	−	0.949540i	$-0.398449\pi$
$911$	9.77428e8	−	5.64318e8i	1.29280	−	0.746396i	0.979149	+	0.203144i	$0.0651161\pi$
$912$	6.97969e6	+	3.37081e8i	0.00920135	+	0.444376i
$913$	−2.15756e7	+	3.73701e7i	−0.0283499	+	0.0491034i
$914$	5.31094e8	+	3.06627e8i	0.695557	+	0.401580i
$915$	−3.84524e8	+	6.99048e8i	−0.501950	+	0.912523i
$916$	2.01994e8	+	3.49864e8i	0.262816	+	0.455211i
$917$			4.50683e8i			0.584471i
$918$	3.82882e8	−	2.53988e8i	0.494922	−	0.328311i
$919$	−1.60932e8			−0.207347			−0.103673	−	0.994611i	$-0.533060\pi$
$919$	−1.60932e8			−0.207347			−0.103673	+	0.994611i	$0.533060\pi$
$920$	3.72182e8	−	2.14879e8i	0.477960	−	0.275951i
$921$	−1.08927e9	−	5.99174e8i	−1.39430	−	0.766962i
$922$	4.64265e8	−	8.04131e8i	0.592343	−	1.02597i
$923$	−3.27661e8	−	1.89175e8i	−0.416697	−	0.240580i
$924$	1.76364e8	−	3.65184e6i	0.223560	−	0.00462909i
$925$	5.07871e7	+	8.79658e7i	0.0641694	+	0.111145i
$926$			2.11549e8i			0.266427i
$927$	−7.70318e8	+	3.19144e7i	−0.967009	+	0.0400634i
$928$	1.43375e8			0.179403
$929$	−1.99102e8	+	1.14952e8i	−0.248330	+	0.143373i	−0.618999	−	0.785392i	$-0.712462\pi$
$929$	−1.99102e8	+	1.14952e8i	−0.248330	+	0.143373i	0.370669	+	0.928765i	$0.379128\pi$
$930$	5.86155e8	−	3.54795e8i	0.728725	−	0.441092i
$931$	6.79995e7	−	1.17779e8i	0.0842669	−	0.145955i
$932$	4.55275e8	+	2.62853e8i	0.562375	+	0.324687i
$933$	−3.98897e8	−	6.59015e8i	−0.491152	−	0.811429i
$934$	−4.12812e8	−	7.15012e8i	−0.506654	−	0.877551i
$935$		−	2.85741e8i		−	0.349573i
$936$	−1.10782e7	−	2.67393e8i	−0.0135095	−	0.326079i
$937$	−7.89016e8			−0.959107			−0.479553	−	0.877513i	$-0.659201\pi$
$937$	−7.89016e8			−0.959107			−0.479553	+	0.877513i	$0.659201\pi$
$938$	−6.51129e8	+	3.75929e8i	−0.788966	+	0.455510i
$939$	1.23255e7	+	5.95258e8i	0.0148871	+	0.718966i
$940$	−2.29804e8	+	3.98033e8i	−0.276678	+	0.479220i
$941$	2.11650e8	+	1.22196e8i	0.254009	+	0.146652i	0.621599	−	0.783336i	$-0.286484\pi$
$941$	2.11650e8	+	1.22196e8i	0.254009	+	0.146652i	−0.367590	+	0.929988i	$0.619817\pi$
$942$	−4.17439e8	+	7.58887e8i	−0.499391	+	0.907871i
$943$	−6.35254e8	−	1.10029e9i	−0.757552	−	1.31212i
$944$		−	5.45282e7i		−	0.0648194i
$945$	7.09552e8	−	4.41269e7i	0.840792	−	0.0522887i
$946$	3.11216e8			0.367612
$947$	−4.13601e8	+	2.38793e8i	−0.487004	+	0.281172i	−0.723331	−	0.690502i	$-0.757390\pi$
$947$	−4.13601e8	+	2.38793e8i	−0.487004	+	0.281172i	0.236327	+	0.971674i	$0.424056\pi$
$948$	−9.56677e7	−	5.26238e7i	−0.112290	−	0.0617671i
$949$	−2.45493e8	+	4.25206e8i	−0.287237	+	0.497509i
$950$	−2.01640e8	−	1.16417e8i	−0.235183	−	0.135783i
$951$	−4.67519e8	+	9.68055e6i	−0.543572	+	0.0112553i
$952$	−1.21885e8	−	2.11111e8i	−0.141266	−	0.244680i
$953$		−	1.14002e9i		−	1.31715i	−0.752517	−	0.658573i	$-0.771160\pi$
$953$		−	1.14002e9i		−	1.31715i	0.752517	−	0.658573i	$-0.228840\pi$
$954$	−3.16679e8	+	6.05041e8i	−0.364732	+	0.696851i
$955$	4.72370e8			0.542341
$956$	−2.70419e8	+	1.56127e8i	−0.309502	+	0.178691i
$957$	3.57684e8	−	2.16504e8i	0.408098	−	0.247019i
$958$	3.76102e8	−	6.51428e8i	0.427769	−	0.740917i
$959$	−1.00263e9	−	5.78867e8i	−1.13680	−	0.656332i
$960$	−5.07057e7	−	8.37706e7i	−0.0573117	−	0.0946843i
$961$	−3.77661e8	−	6.54128e8i	−0.425532	−	0.737043i
$962$			3.45240e8i			0.387789i
$963$	−3.73882e8	+	2.37020e8i	−0.418654	+	0.265404i
$964$	4.71691e8			0.526534
$965$	−7.76400e8	+	4.48255e8i	−0.863980	+	0.498819i
$966$	−2.21335e7	−	1.06893e9i	−0.0245538	−	1.18582i
$967$	−1.51397e8	+	2.62227e8i	−0.167431	+	0.290000i	−0.937516	−	0.347942i	$-0.886881\pi$
$967$	−1.51397e8	+	2.62227e8i	−0.167431	+	0.290000i	0.770085	+	0.637942i	$0.220214\pi$
$968$	2.16361e8	+	1.24916e8i	0.238535	+	0.137718i
$969$	6.54832e8	−	1.19046e9i	0.719712	−	1.30840i
$970$	3.06298e8	+	5.30523e8i	0.335605	+	0.581285i
$971$		−	2.05629e8i		−	0.224608i	−0.993674	−	0.112304i	$-0.964177\pi$
$971$		−	2.05629e8i		−	0.224608i	0.993674	−	0.112304i	$-0.0358231\pi$
$972$	−4.74462e7	−	4.56707e8i	−0.0516658	−	0.497323i
$973$	1.05091e9			1.14085
$974$	−2.26426e8	+	1.30727e8i	−0.245047	+	0.141478i
$975$	1.61935e8	+	8.90751e7i	0.174713	+	0.0961042i
$976$	1.36695e8	−	2.36762e8i	0.147029	−	0.254661i
$977$	−5.08949e7	−	2.93842e7i	−0.0545746	−	0.0315087i	0.472464	−	0.881350i	$-0.343365\pi$
$977$	−5.08949e7	−	2.93842e7i	−0.0545746	−	0.0315087i	−0.527039	+	0.849841i	$0.676698\pi$
$978$	−8.52858e8	+	1.76595e7i	−0.911718	+	0.0188782i
$979$	−1.29233e8	−	2.23839e8i	−0.137729	−	0.238554i
$980$			3.94989e7i			0.0419669i
$981$	3.75218e8	+	5.91878e8i	0.397444	+	0.626939i
$982$	−5.18050e8			−0.547063
$983$	7.03441e7	−	4.06132e7i	0.0740572	−	0.0427569i	−0.462514	−	0.886612i	$-0.653053\pi$
$983$	7.03441e7	−	4.06132e7i	0.0740572	−	0.0427569i	0.536571	+	0.843855i	$0.319719\pi$
$984$	−2.47653e8	+	1.49903e8i	−0.259931	+	0.157335i
$985$	−2.25911e8	+	3.91289e8i	−0.236389	+	0.409438i
$986$	−5.00371e8	−	2.88889e8i	−0.521989	−	0.301370i
$987$	5.92088e8	+	9.78184e8i	0.615793	+	1.01735i
$988$	−3.95689e8	−	6.85354e8i	−0.410283	−	0.710631i
$989$		−	1.88626e9i		−	1.94990i
$990$	−2.52995e8	−	1.32418e8i	−0.260740	−	0.136471i
$991$	2.17703e8			0.223688			0.111844	−	0.993726i	$-0.464324\pi$
$991$	2.17703e8			0.223688			0.111844	+	0.993726i	$0.464324\pi$
$992$	−2.03330e8	+	1.17393e8i	−0.208289	+	0.120256i
$993$	7.91469e6	+	3.82237e8i	0.00808325	+	0.390378i
$994$	−1.72202e8	+	2.98262e8i	−0.175339	+	0.303696i
$995$	−9.85474e7	−	5.68964e7i	−0.100041	−	0.0577584i
$996$	2.87210e7	−	5.22136e7i	0.0290684	−	0.0528452i
$997$	−1.09951e8	−	1.90441e8i	−0.110947	−	0.192166i	0.805205	−	0.592996i	$-0.202055\pi$
$997$	−1.09951e8	−	1.90441e8i	−0.110947	−	0.192166i	−0.916152	+	0.400830i	$0.868722\pi$
$998$		−	3.23515e8i		−	0.325464i
$999$	3.67662e7	+	5.91193e8i	0.0368767	+	0.592970i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.7.d.a.5.4	✓	12
3.2	odd	2		54.7.d.a.17.3		12
4.3	odd	2		144.7.q.c.113.6		12
9.2	odd	6	inner	18.7.d.a.11.4	yes	12
9.4	even	3		162.7.b.c.161.11		12
9.5	odd	6		162.7.b.c.161.2		12
9.7	even	3		54.7.d.a.35.3		12
12.11	even	2		432.7.q.b.17.6		12
36.7	odd	6		432.7.q.b.305.6		12
36.11	even	6		144.7.q.c.65.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.7.d.a.5.4	✓	12	1.1	even	1	trivial
18.7.d.a.11.4	yes	12	9.2	odd	6	inner
54.7.d.a.17.3		12	3.2	odd	2
54.7.d.a.35.3		12	9.7	even	3
144.7.q.c.65.6		12	36.11	even	6
144.7.q.c.113.6		12	4.3	odd	2
162.7.b.c.161.2		12	9.5	odd	6
162.7.b.c.161.11		12	9.4	even	3
432.7.q.b.17.6		12	12.11	even	2
432.7.q.b.305.6		12	36.7	odd	6

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more