LMFDB - Embedded newform 18.7.d.a.11.2

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			11.2
Root			$-7.20150i$ of defining polynomial
Character	$\chi$	$=$	18.11
Dual form			18.7.d.a.5.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.89898 - 2.82843i) q^{2} +(-11.1983 - 24.5683i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-39.5602 + 22.8401i) q^{5} +(-14.6295 + 152.033i) q^{6} +(-245.097 + 424.521i) q^{7} -181.019i q^{8} +(-478.198 + 550.243i) q^{9} +O(q^{10})$	\(q+(-4.89898 - 2.82843i) q^{2} +(-11.1983 - 24.5683i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-39.5602 + 22.8401i) q^{5} +(-14.6295 + 152.033i) q^{6} +(-245.097 + 424.521i) q^{7} -181.019i q^{8} +(-478.198 + 550.243i) q^{9} +258.406 q^{10} +(-873.336 - 504.221i) q^{11} +(501.683 - 703.427i) q^{12} +(466.801 + 808.523i) q^{13} +(2401.45 - 1386.48i) q^{14} +(1004.15 + 716.156i) q^{15} +(-512.000 + 886.810i) q^{16} -8090.59i q^{17} +(3899.01 - 1343.08i) q^{18} -7727.36 q^{19} +(-1265.93 - 730.884i) q^{20} +(13174.4 + 1267.72i) q^{21} +(2852.30 + 4940.34i) q^{22} +(-11848.0 + 6840.45i) q^{23} +(-4447.33 + 2027.10i) q^{24} +(-6769.16 + 11724.5i) q^{25} -5281.25i q^{26} +(18873.5 + 5586.73i) q^{27} -15686.2 q^{28} +(-1964.70 - 1134.32i) q^{29} +(-2893.70 - 6348.59i) q^{30} +(-17062.6 - 29553.2i) q^{31} +(5016.55 - 2896.31i) q^{32} +(-2607.99 + 27102.7i) q^{33} +(-22883.6 + 39635.6i) q^{34} -22392.2i q^{35} +(-22900.0 - 4448.33i) q^{36} +92058.0 q^{37} +(37856.2 + 21856.3i) q^{38} +(14636.6 - 20522.5i) q^{39} +(4134.50 + 7161.17i) q^{40} +(-31021.6 + 17910.3i) q^{41} +(-60955.5 - 43473.4i) q^{42} +(34570.9 - 59878.5i) q^{43} -32270.1i q^{44} +(6350.01 - 32689.8i) q^{45} +77390.9 q^{46} +(13211.1 + 7627.46i) q^{47} +(27520.9 + 2648.22i) q^{48} +(-61321.0 - 106211. i) q^{49} +(66323.9 - 38292.1i) q^{50} +(-198772. + 90600.5i) q^{51} +(-14937.6 + 25872.7i) q^{52} +236591. i q^{53} +(-76659.2 - 80751.6i) q^{54} +46065.9 q^{55} +(76846.5 + 44367.4i) q^{56} +(86533.0 + 189848. i) q^{57} +(6416.70 + 11114.0i) q^{58} +(-221890. + 128108. i) q^{59} +(-3780.35 + 39286.2i) q^{60} +(-19919.6 + 34501.8i) q^{61} +193041. i q^{62} +(-116385. - 337868. i) q^{63} -32768.0 q^{64} +(-36933.5 - 21323.6i) q^{65} +(89434.6 - 125399. i) q^{66} +(-160204. - 277482. i) q^{67} +(224213. - 129449. i) q^{68} +(300735. + 214484. i) q^{69} +(-63334.7 + 109699. i) q^{70} -404593. i q^{71} +(99604.7 + 86563.1i) q^{72} +393719. q^{73} +(-450990. - 260379. i) q^{74} +(363854. + 35012.2i) q^{75} +(-123638. - 214147. i) q^{76} +(428105. - 247167. i) q^{77} +(-129751. + 59140.8i) q^{78} +(-449184. + 778010. i) q^{79} -46776.5i q^{80} +(-74094.1 - 526251. i) q^{81} +202632. q^{82} +(154916. + 89441.0i) q^{83} +(175658. + 385383. i) q^{84} +(184790. + 320066. i) q^{85} +(-338724. + 195562. i) q^{86} +(-5867.06 + 60971.8i) q^{87} +(-91273.8 + 158091. i) q^{88} -826458. i q^{89} +(-123569. + 142186. i) q^{90} -457647. q^{91} +(-379136. - 218894. i) q^{92} +(-535000. + 750142. i) q^{93} +(-43147.4 - 74733.5i) q^{94} +(305696. - 176494. i) q^{95} +(-127334. - 90814.4i) q^{96} +(-317981. + 550760. i) q^{97} +693768. i q^{98} +(695072. - 239430. 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
$3$	−11.1983	−	24.5683i	−0.414750	−	0.909935i
$3$	−11.1983	−	24.5683i	−0.414750	−	0.909935i
$4$	16.0000	+	27.7128i	0.250000	+	0.433013i
$5$	−39.5602	+	22.8401i	−0.316482	+	0.182721i	−0.649823	−	0.760085i	$-0.725157\pi$
$5$	−39.5602	+	22.8401i	−0.316482	+	0.182721i	0.333341	+	0.942806i	$0.391824\pi$
$6$	−14.6295	+	152.033i	−0.0677291	+	0.703856i
$7$	−245.097	+	424.521i	−0.714570	+	1.23767i	0.248556	+	0.968618i	$0.420044\pi$
$7$	−245.097	+	424.521i	−0.714570	+	1.23767i	−0.963125	+	0.269053i	$0.913289\pi$
$8$		−	181.019i		−	0.353553i
$9$	−478.198	+	550.243i	−0.655965	+	0.754792i
$10$	258.406			0.258406
$11$	−873.336	−	504.221i	−0.656151	−	0.378829i	0.134658	−	0.990892i	$-0.457006\pi$
$11$	−873.336	−	504.221i	−0.656151	−	0.378829i	−0.790809	+	0.612063i	$0.790340\pi$
$12$	501.683	−	703.427i	0.290326	−	0.407076i
$13$	466.801	+	808.523i	0.212472	+	0.368012i	0.952488	−	0.304577i	$-0.0985152\pi$
$13$	466.801	+	808.523i	0.212472	+	0.368012i	−0.740016	+	0.672590i	$0.765182\pi$
$14$	2401.45	−	1386.48i	0.875166	−	0.505277i
$15$	1004.15	+	716.156i	0.297525	+	0.212194i
$16$	−512.000	+	886.810i	−0.125000	+	0.216506i
$17$		−	8090.59i		−	1.64677i	−0.567482	−	0.823386i	$-0.692082\pi$
$17$		−	8090.59i		−	1.64677i	0.567482	−	0.823386i	$-0.307918\pi$
$18$	3899.01	−	1343.08i	0.668554	−	0.230295i
$19$	−7727.36			−1.12660			−0.563301	−	0.826252i	$-0.690469\pi$
$19$	−7727.36			−1.12660			−0.563301	+	0.826252i	$0.690469\pi$
$20$	−1265.93	−	730.884i	−0.158241	−	0.0913604i
$21$	13174.4	+	1267.72i	1.42257	+	0.136888i
$22$	2852.30	+	4940.34i	0.267872	+	0.463969i
$23$	−11848.0	+	6840.45i	−0.973782	+	0.562213i	−0.900387	−	0.435090i	$-0.856717\pi$
$23$	−11848.0	+	6840.45i	−0.973782	+	0.562213i	−0.0733950	+	0.997303i	$0.523383\pi$
$24$	−4447.33	+	2027.10i	−0.321711	+	0.146636i
$25$	−6769.16	+	11724.5i	−0.433226	+	0.750370i
$26$		−	5281.25i		−	0.300481i
$27$	18873.5	+	5586.73i	0.958873	+	0.283835i
$28$	−15686.2			−0.714570
$29$	−1964.70	−	1134.32i	−0.0805570	−	0.0465096i	0.459180	−	0.888343i	$-0.348143\pi$
$29$	−1964.70	−	1134.32i	−0.0805570	−	0.0465096i	−0.539737	+	0.841833i	$0.681476\pi$
$30$	−2893.70	−	6348.59i	−0.107174	−	0.235133i
$31$	−17062.6	−	29553.2i	−0.572742	−	0.992019i	−0.996283	−	0.0861417i	$-0.972546\pi$
$31$	−17062.6	−	29553.2i	−0.572742	−	0.992019i	0.423541	−	0.905877i	$-0.360787\pi$
$32$	5016.55	−	2896.31i	0.153093	−	0.0883883i
$33$	−2607.99	+	27102.7i	−0.0725710	+	0.754174i
$34$	−22883.6	+	39635.6i	−0.582222	+	1.00844i
$35$		−	22392.2i		−	0.522267i
$36$	−22900.0	−	4448.33i	−0.490826	−	0.0953430i
$37$	92058.0			1.81743			0.908713	−	0.417422i	$-0.137066\pi$
$37$	92058.0			1.81743			0.908713	+	0.417422i	$0.137066\pi$
$38$	37856.2	+	21856.3i	0.689900	+	0.398314i
$39$	14636.6	−	20522.5i	0.246745	−	0.345969i
$40$	4134.50	+	7161.17i	0.0646016	+	0.111893i
$41$	−31021.6	+	17910.3i	−0.450103	+	0.259867i	−0.707874	−	0.706339i	$-0.750345\pi$
$41$	−31021.6	+	17910.3i	−0.450103	+	0.259867i	0.257771	+	0.966206i	$0.417012\pi$
$42$	−60955.5	−	43473.4i	−0.822745	−	0.586780i
$43$	34570.9	−	59878.5i	0.434816	−	0.753123i	−0.562465	−	0.826821i	$-0.690147\pi$
$43$	34570.9	−	59878.5i	0.434816	−	0.753123i	0.997281	+	0.0736985i	$0.0234803\pi$
$44$		−	32270.1i		−	0.378829i
$45$	6350.01	−	32689.8i	0.0696847	−	0.358736i
$46$	77390.9			0.795090
$47$	13211.1	+	7627.46i	0.127247	+	0.0734659i	0.562272	−	0.826952i	$-0.309927\pi$
$47$	13211.1	+	7627.46i	0.127247	+	0.0734659i	−0.435025	+	0.900418i	$0.643261\pi$
$48$	27520.9	+	2648.22i	0.248851	+	0.0239459i
$49$	−61321.0	−	106211.i	−0.521220	−	0.902779i
$50$	66323.9	−	38292.1i	0.530592	−	0.306337i
$51$	−198772.	+	90600.5i	−1.49846	+	0.682999i
$52$	−14937.6	+	25872.7i	−0.106236	+	0.184006i
$53$			236591.i			1.58917i	0.607153	+	0.794585i	$0.292312\pi$
$53$			236591.i			1.58917i	−0.607153	+	0.794585i	$0.707688\pi$
$54$	−76659.2	−	80751.6i	−0.486837	−	0.512826i
$55$	46065.9			0.276880
$56$	76846.5	+	44367.4i	0.437583	+	0.252639i
$57$	86533.0	+	189848.i	0.467258	+	1.02513i
$58$	6416.70	+	11114.0i	0.0328873	+	0.0569624i
$59$	−221890.	+	128108.i	−1.08039	+	0.623766i	−0.931003	−	0.365012i	$-0.881065\pi$
$59$	−221890.	+	128108.i	−1.08039	+	0.623766i	−0.149392	+	0.988778i	$0.547732\pi$
$60$	−3780.35	+	39286.2i	−0.0175016	+	0.181881i
$61$	−19919.6	+	34501.8i	−0.0877589	+	0.152003i	−0.906563	−	0.422069i	$-0.861304\pi$
$61$	−19919.6	+	34501.8i	−0.0877589	+	0.152003i	0.818805	+	0.574072i	$0.194637\pi$
$62$			193041.i			0.809980i
$63$	−116385.	−	337868.i	−0.465451	−	1.35122i
$64$	−32768.0			−0.125000
$65$	−36933.5	−	21323.6i	−0.134487	−	0.0776462i
$66$	89434.6	−	125399.i	0.311081	−	0.436178i
$67$	−160204.	−	277482.i	−0.532660	−	0.922593i	−0.999273	−	0.0381319i	$-0.987859\pi$
$67$	−160204.	−	277482.i	−0.532660	−	0.922593i	0.466613	−	0.884461i	$-0.345474\pi$
$68$	224213.	−	129449.i	0.713073	−	0.411693i
$69$	300735.	+	214484.i	0.915454	+	0.652901i
$70$	−63334.7	+	109699.i	−0.184649	+	0.319822i
$71$		−	404593.i		−	1.13043i	−0.824944	−	0.565215i	$-0.808793\pi$
$71$		−	404593.i		−	1.13043i	0.824944	−	0.565215i	$-0.191207\pi$
$72$	99604.7	+	86563.1i	0.266859	+	0.231918i
$73$	393719.			1.01209			0.506044	−	0.862508i	$-0.331107\pi$
$73$	393719.			1.01209			0.506044	+	0.862508i	$0.331107\pi$
$74$	−450990.	−	260379.i	−1.11294	−	0.642557i
$75$	363854.	+	35012.2i	0.862469	+	0.0829918i
$76$	−123638.	−	214147.i	−0.281650	−	0.487833i
$77$	428105.	−	247167.i	0.937731	−	0.541399i
$78$	−129751.	+	59140.8i	−0.273418	+	0.124624i
$79$	−449184.	+	778010.i	−0.911052	+	1.57799i	−0.0984709	+	0.995140i	$0.531395\pi$
$79$	−449184.	+	778010.i	−0.911052	+	1.57799i	−0.812581	+	0.582848i	$0.801938\pi$
$80$		−	46776.5i		−	0.0913604i
$81$	−74094.1	−	526251.i	−0.139421	−	0.990233i
$82$	202632.			0.367508
$83$	154916.	+	89441.0i	0.270934	+	0.156424i	0.629312	−	0.777153i	$-0.283337\pi$
$83$	154916.	+	89441.0i	0.270934	+	0.156424i	−0.358378	+	0.933576i	$0.616670\pi$
$84$	175658.	+	385383.i	0.296368	+	0.650212i
$85$	184790.	+	320066.i	0.300900	+	0.521173i
$86$	−338724.	+	195562.i	−0.532538	+	0.307461i
$87$	−5867.06	+	60971.8i	−0.00890970	+	0.0925915i
$88$	−91273.8	+	158091.i	−0.133936	+	0.231984i
$89$		−	826458.i		−	1.17233i	−0.810191	−	0.586166i	$-0.800636\pi$
$89$		−	826458.i		−	1.17233i	0.810191	−	0.586166i	$-0.199364\pi$
$90$	−123569.	+	142186.i	−0.169505	+	0.195043i
$91$	−457647.			−0.607304
$92$	−379136.	−	218894.i	−0.486891	−	0.281107i
$93$	−535000.	+	750142.i	−0.665128	+	0.932599i
$94$	−43147.4	−	74733.5i	−0.0519483	−	0.0899770i
$95$	305696.	−	176494.i	0.356549	−	0.205854i
$96$	−127334.	−	90814.4i	−0.143923	−	0.102646i
$97$	−317981.	+	550760.i	−0.348406	+	0.603458i	−0.985967	−	0.166943i	$-0.946610\pi$
$97$	−317981.	+	550760.i	−0.348406	+	0.603458i	0.637560	+	0.770401i	$0.279944\pi$
$98$			693768.i			0.737116i
$99$	695072.	−	239430.i	0.716348	−	0.246759i
$100$	−433226.			−0.433226
$101$	−227301.	−	131232.i	−0.220616	−	0.127373i	0.385619	−	0.922658i	$-0.373988\pi$
$101$	−227301.	−	131232.i	−0.220616	−	0.127373i	−0.606236	+	0.795285i	$0.707321\pi$
$102$	1.23003e6	+	118361.i	1.15909	+	0.111534i
$103$	41238.0	+	71426.3i	0.0377386	+	0.0653652i	0.884278	−	0.466961i	$-0.154651\pi$
$103$	41238.0	+	71426.3i	0.0377386	+	0.0653652i	−0.846539	+	0.532326i	$0.821318\pi$
$104$	146358.	−	84500.0i	0.130112	−	0.0751202i
$105$	−550137.	+	250754.i	−0.475229	+	0.216610i
$106$	669180.	−	1.15905e6i	0.561857	−	0.973164i
$107$			1.03624e6i			0.845881i	0.906158	+	0.422940i	$0.139002\pi$
$107$			1.03624e6i			0.845881i	−0.906158	+	0.422940i	$0.860998\pi$
$108$	147152.	+	612425.i	0.116814	+	0.486163i
$109$	420018.			0.324331			0.162165	−	0.986764i	$-0.448152\pi$
$109$	420018.			0.324331			0.162165	+	0.986764i	$0.448152\pi$
$110$	−225676.	−	130294.i	−0.169553	−	0.0978918i
$111$	−1.03089e6	−	2.26171e6i	−0.753777	−	1.65374i
$112$	−250980.	−	434710.i	−0.178642	−	0.309418i
$113$	−1.32478e6	+	764860.i	−0.918136	+	0.530086i	−0.883040	−	0.469298i	$-0.844507\pi$
$113$	−1.32478e6	+	764860.i	−0.918136	+	0.530086i	−0.0350964	+	0.999384i	$0.511174\pi$
$114$	113047.	−	1.17481e6i	0.0763037	−	0.792965i
$115$	312473.	−	541220.i	0.205456	−	0.355861i
$116$		−	72596.7i		−	0.0465096i
$117$	−668108.	−	129780.i	−0.417147	−	0.0810309i
$118$	1.44938e6			0.882139
$119$	3.43463e6	+	1.98298e6i	2.03816	+	1.17673i
$120$	129638.	−	181770.i	0.0750221	−	0.105191i
$121$	−377303.	−	653508.i	−0.212978	−	0.368888i
$122$	195171.	−	112682.i	0.107482	−	0.0620549i
$123$	787412.	+	561581.i	0.423143	+	0.301785i
$124$	546002.	−	945703.i	0.286371	−	0.496009i
$125$		−	1.33219e6i		−	0.682080i
$126$	−385470.	+	1.98440e6i	−0.192699	+	0.992012i
$127$	−949267.			−0.463422			−0.231711	−	0.972785i	$-0.574432\pi$
$127$	−949267.			−0.463422			−0.231711	+	0.972785i	$0.574432\pi$
$128$	160530.	+	92681.9i	0.0765466	+	0.0441942i
$129$	−1.85824e6	−	178811.i	−0.865633	−	0.0832962i
$130$	120624.	+	208928.i	0.0549041	+	0.0950967i
$131$	−794197.	+	458530.i	−0.353276	+	0.203964i	−0.666127	−	0.745838i	$-0.732049\pi$
$131$	−794197.	+	458530.i	−0.353276	+	0.203964i	0.312851	+	0.949802i	$0.398716\pi$
$132$	−792821.	+	361369.i	−0.344710	+	0.157119i
$133$	1.89396e6	−	3.28043e6i	0.805035	−	1.39436i
$134$			1.81250e6i			0.753294i
$135$	−874242.	+	210060.i	−0.355329	+	0.0853774i
$136$	−1.46455e6			−0.582222
$137$	−413272.	−	238603.i	−0.160722	−	0.0927926i	0.417482	−	0.908685i	$-0.362913\pi$
$137$	−413272.	−	238603.i	−0.160722	−	0.0927926i	−0.578204	+	0.815893i	$0.696246\pi$
$138$	−866643.	−	1.90136e6i	−0.329764	−	0.723480i
$139$	2.04226e6	+	3.53730e6i	0.760443	+	1.31713i	0.942623	+	0.333860i	$0.108351\pi$
$139$	2.04226e6	+	3.53730e6i	0.760443	+	1.31713i	−0.182180	+	0.983265i	$0.558315\pi$
$140$	620551.	−	358275.i	0.226148	−	0.130567i
$141$	39451.5	−	409989.i	0.0140736	−	0.146256i
$142$	−1.14436e6	+	1.98209e6i	−0.399667	+	0.692244i
$143$		−	941484.i		−	0.321962i
$144$	−243124.	−	705795.i	−0.0814216	−	0.236369i
$145$	103632.			0.0339931
$146$	−1.92882e6	−	1.11361e6i	−0.619775	−	0.357827i
$147$	−1.92273e6	+	2.69593e6i	−0.605294	+	0.848704i
$148$	1.47293e6	+	2.55119e6i	0.454356	+	0.786968i
$149$	−3.18704e6	+	1.84004e6i	−0.963449	+	0.556248i	−0.897233	−	0.441558i	$-0.854426\pi$
$149$	−3.18704e6	+	1.84004e6i	−0.963449	+	0.556248i	−0.0662161	+	0.997805i	$0.521093\pi$
$150$	−1.68348e6	−	1.20066e6i	−0.498810	−	0.355751i
$151$	333742.	−	578059.i	0.0969350	−	0.167896i	−0.813480	−	0.581594i	$-0.802429\pi$
$151$	333742.	−	578059.i	0.0969350	−	0.167896i	0.910415	+	0.413697i	$0.135763\pi$
$152$			1.39880e6i			0.398314i
$153$	4.45179e6	+	3.86890e6i	1.24297	+	1.08022i
$154$	−2.79637e6			−0.765654
$155$	1.35000e6	+	779422.i	0.362525	+	0.209304i
$156$	802923.	+	77262.0i	0.211495	+	0.0203513i
$157$	753580.	+	1.30524e6i	0.194729	+	0.337280i	0.946812	−	0.321788i	$-0.104284\pi$
$157$	753580.	+	1.30524e6i	0.194729	+	0.337280i	−0.752083	+	0.659069i	$0.770951\pi$
$158$	4.40109e6	−	2.54097e6i	1.11581	−	0.644211i
$159$	5.81263e6	−	2.64941e6i	1.44604	−	0.659109i
$160$	−132304.	+	229157.i	−0.0323008	+	0.0559466i
$161$		−	6.70631e6i		−	1.60696i
$162$	−1.12548e6	+	2.78766e6i	−0.264723	+	0.655684i
$163$	−5.90805e6			−1.36421			−0.682105	−	0.731254i	$-0.738935\pi$
$163$	−5.90805e6			−1.36421			−0.682105	+	0.731254i	$0.738935\pi$
$164$	−992690.	−	573130.i	−0.225052	−	0.129934i
$165$	−515857.	−	1.13176e6i	−0.114836	−	0.251943i
$166$	−505955.	−	876339.i	−0.110608	−	0.191579i
$167$	2.33113e6	−	1.34588e6i	0.500515	−	0.288972i	−0.228411	−	0.973565i	$-0.573353\pi$
$167$	2.33113e6	−	1.34588e6i	0.500515	−	0.288972i	0.728926	+	0.684592i	$0.240020\pi$
$168$	229482.	−	2.38482e6i	0.0483972	−	0.502954i
$169$	1.97760e6	−	3.42530e6i	0.409711	−	0.709641i
$170$		−	2.09066e6i		−	0.425536i
$171$	3.69521e6	−	4.25193e6i	0.739011	−	0.850350i
$172$	2.21254e6			0.434816
$173$	−5.49562e6	−	3.17290e6i	−1.06140	−	0.612798i	−0.135579	−	0.990767i	$-0.543290\pi$
$173$	−5.49562e6	−	3.17290e6i	−1.06140	−	0.612798i	−0.925819	+	0.377968i	$0.876623\pi$
$174$	201197.	−	282105.i	0.0381921	−	0.0535504i
$175$	−3.31821e6	−	5.74730e6i	−0.619141	−	1.07238i
$176$	894297.	−	516322.i	0.164038	−	0.0947072i
$177$	5.63219e6	+	4.01687e6i	1.01568	+	0.724382i
$178$	−2.33758e6	+	4.04880e6i	−0.414482	+	0.717904i
$179$			9.31786e6i			1.62464i	0.583212	+	0.812320i	$0.301796\pi$
$179$			9.31786e6i			1.62464i	−0.583212	+	0.812320i	$0.698204\pi$
$180$	1.00753e6	−	347061.i	0.172759	−	0.0595097i
$181$	1.28997e6			0.217542			0.108771	−	0.994067i	$-0.465308\pi$
$181$	1.28997e6			0.217542			0.108771	+	0.994067i	$0.465308\pi$
$182$	2.24200e6	+	1.29442e6i	0.371896	+	0.214714i
$183$	1.07071e6	+	103030.i	0.174711	+	0.0168117i
$184$	1.23825e6	+	2.14472e6i	0.198772	+	0.344284i
$185$	−3.64184e6	+	2.10262e6i	−0.575182	+	0.332082i
$186$	4.74268e6	−	2.16172e6i	0.737029	−	0.335939i
$187$	−4.07944e6	+	7.06580e6i	−0.623844	+	1.08053i
$188$			488157.i			0.0734659i
$189$	−6.99753e6	+	6.64291e6i	−1.03648	+	0.983949i
$190$	−1.99680e6			−0.291121
$191$	−6.26560e6	−	3.61745e6i	−0.899214	−	0.519161i	−0.0222687	−	0.999752i	$-0.507089\pi$
$191$	−6.26560e6	−	3.61745e6i	−0.899214	−	0.519161i	−0.876945	+	0.480591i	$0.840422\pi$
$192$	366944.	+	805053.i	0.0518438	+	0.113742i
$193$	2.33819e6	+	4.04986e6i	0.325243	+	0.563337i	0.981561	−	0.191147i	$-0.0612207\pi$
$193$	2.33819e6	+	4.04986e6i	0.325243	+	0.563337i	−0.656319	+	0.754484i	$0.727887\pi$
$194$	3.11557e6	−	1.79877e6i	0.426709	−	0.246361i
$195$	−110292.	+	1.14618e6i	−0.0148744	+	0.154578i
$196$	1.96227e6	−	3.39875e6i	0.260610	−	0.451389i
$197$		−	2.50022e6i		−	0.327024i	−0.986541	−	0.163512i	$-0.947718\pi$
$197$		−	2.50022e6i		−	0.327024i	0.986541	−	0.163512i	$-0.0522822\pi$
$198$	−4.08235e6	−	792999.i	−0.525914	−	0.102159i
$199$	−3.28474e6			−0.416814			−0.208407	−	0.978042i	$-0.566828\pi$
$199$	−3.28474e6			−0.416814			−0.208407	+	0.978042i	$0.566828\pi$
$200$	2.12237e6	+	1.22535e6i	0.265296	+	0.153169i
$201$	−5.02324e6	+	7.04325e6i	−0.618580	+	0.867332i
$202$	742362.	+	1.28581e6i	0.0900662	+	0.155999i
$203$	963088.	−	556039.i	0.115127	−	0.0664687i
$204$	−5.69114e6	−	4.05891e6i	−0.670361	−	0.478100i
$205$	818147.	−	1.41707e6i	0.0949663	−	0.164486i
$206$		−	466555.i		−	0.0533704i
$207$	1.90178e6	−	9.79038e6i	0.214413	−	1.10379i
$208$	−956008.			−0.106236
$209$	6.74859e6	+	3.89630e6i	0.739220	+	0.426789i
$210$	3.40435e6	+	327587.i	0.367601	+	0.0353727i
$211$	−834440.	−	1.44529e6i	−0.0888276	−	0.153854i	0.818188	−	0.574950i	$-0.194979\pi$
$211$	−834440.	−	1.44529e6i	−0.0888276	−	0.153854i	−0.907016	+	0.421097i	$0.861645\pi$
$212$	−6.55660e6	+	3.78545e6i	−0.688131	+	0.397293i
$213$	−9.94014e6	+	4.53074e6i	−1.02862	+	0.468846i
$214$	2.93093e6	−	5.07652e6i	0.299064	−	0.517994i
$215$			3.15841e6i			0.317800i
$216$	1.01131e6	−	3.41647e6i	0.100351	−	0.339013i
$217$	1.67280e7			1.63706
$218$	−2.05766e6	−	1.18799e6i	−0.198611	−	0.114668i
$219$	−4.40897e6	−	9.67300e6i	−0.419764	−	0.920934i
$220$	737054.	+	1.27661e6i	0.0692199	+	0.119892i
$221$	6.54143e6	−	3.77669e6i	0.606032	−	0.349893i
$222$	−1.34676e6	+	1.39958e7i	−0.123093	+	1.27920i
$223$	5.65363e6	−	9.79237e6i	0.509815	−	0.883025i	−0.490121	−	0.871655i	$-0.663047\pi$
$223$	5.65363e6	−	9.79237e6i	0.509815	−	0.883025i	0.999935	−	0.0113705i	$-0.00361941\pi$
$224$			2.83951e6i			0.252639i
$225$	−3.21434e6	−	9.33133e6i	−0.282192	−	0.819211i
$226$	8.65340e6			0.749655
$227$	1.32731e7	+	7.66322e6i	1.13473	+	0.655139i	0.945121	−	0.326720i	$-0.105943\pi$
$227$	1.32731e7	+	7.66322e6i	1.13473	+	0.655139i	0.189613	+	0.981859i	$0.439277\pi$
$228$	−3.87669e6	+	5.43564e6i	−0.327082	+	0.458612i
$229$	−635525.	−	1.10076e6i	−0.0529208	−	0.0916615i	0.838351	−	0.545130i	$-0.183520\pi$
$229$	−635525.	−	1.10076e6i	−0.0529208	−	0.0916615i	−0.891272	+	0.453469i	$0.850186\pi$
$230$	−3.06160e6	+	1.76762e6i	−0.251632	+	0.145280i
$231$	−1.08665e7	−	7.74996e6i	−0.881562	−	0.628729i
$232$	−205334.	+	355650.i	−0.0164436	+	0.0284812i
$233$			1.45867e6i			0.115316i	0.998336	+	0.0576578i	$0.0183632\pi$
$233$			1.45867e6i			0.115316i	−0.998336	+	0.0576578i	$0.981637\pi$
$234$	2.90597e6	+	2.52548e6i	0.226800	+	0.197105i
$235$	−696848.			−0.0536951
$236$	−7.10049e6	−	4.09947e6i	−0.540197	−	0.311883i
$237$	2.41444e7	+	2.32332e6i	1.81373	+	0.174527i
$238$	−1.12174e7	−	1.94292e7i	−0.832076	−	1.44120i
$239$	4.35188e6	−	2.51256e6i	0.318774	−	0.184044i	−0.332072	−	0.943254i	$-0.607748\pi$
$239$	4.35188e6	−	2.51256e6i	0.318774	−	0.184044i	0.650846	+	0.759210i	$0.274414\pi$
$240$	−1.14922e6	+	523816.i	−0.0831321	+	0.0378918i
$241$	−2.56745e6	+	4.44695e6i	−0.183421	+	0.317695i	−0.943043	−	0.332670i	$-0.892051\pi$
$241$	−2.56745e6	+	4.44695e6i	−0.183421	+	0.317695i	0.759622	+	0.650365i	$0.225384\pi$
$242$			4.26869e6i			0.301196i
$243$	−1.20993e7	+	7.71345e6i	−0.843223	+	0.537564i
$244$	−1.27485e6			−0.0877589
$245$	4.85174e6	+	2.80116e6i	0.329913	+	0.190475i
$246$	−2.26912e6	−	4.97831e6i	−0.152424	−	0.334408i
$247$	−3.60714e6	−	6.24775e6i	−0.239371	−	0.414603i
$248$	−5.34971e6	+	3.08865e6i	−0.350732	+	0.202495i
$249$	462616.	−	4.80761e6i	0.0299656	−	0.311409i
$250$	−3.76799e6	+	6.52636e6i	−0.241152	+	0.417687i
$251$		−	1.72705e6i		−	0.109216i	−0.998508	−	0.0546078i	$-0.982609\pi$
$251$		−	1.72705e6i		−	0.109216i	0.998508	−	0.0546078i	$-0.0173909\pi$
$252$	7.50113e6	−	8.63124e6i	0.468732	−	0.539351i
$253$	1.37964e7			0.851930
$254$	4.65044e6	+	2.68493e6i	0.283787	+	0.163845i
$255$	5.79413e6	−	8.12414e6i	0.349436	−	0.489956i
$256$	−524288.	−	908093.i	−0.0312500	−	0.0541266i
$257$	−1.14470e7	+	6.60890e6i	−0.674358	+	0.389341i	−0.797726	−	0.603020i	$-0.793964\pi$
$257$	−1.14470e7	+	6.60890e6i	−0.674358	+	0.389341i	0.123368	+	0.992361i	$0.460631\pi$
$258$	8.59775e6	+	6.13190e6i	0.500640	+	0.357056i
$259$	−2.25632e7	+	3.90806e7i	−1.29868	+	2.24937i
$260$		−	1.36471e6i		−	0.0776462i
$261$	1.56367e6	−	538634.i	0.0879476	−	0.0302951i
$262$	5.18767e6			0.288449
$263$	−1.03590e7	−	5.98077e6i	−0.569444	−	0.328768i	0.187483	−	0.982268i	$-0.439967\pi$
$263$	−1.03590e7	−	5.98077e6i	−0.569444	−	0.328768i	−0.756927	+	0.653499i	$0.773300\pi$
$264$	4.90612e6	+	472096.i	0.266641	+	0.0256577i
$265$	−5.40376e6	−	9.35959e6i	−0.290375	−	0.502944i
$266$	−1.85569e7	+	1.07138e7i	−0.985963	+	0.569246i
$267$	−2.03046e7	+	9.25489e6i	−1.06675	+	0.486225i
$268$	5.12654e6	−	8.87942e6i	0.266330	−	0.461297i
$269$		−	210238.i		−	0.0108007i	−0.999985	−	0.00540037i	$-0.998281\pi$
$269$		−	210238.i		−	0.0108007i	0.999985	−	0.00540037i	$-0.00171900\pi$
$270$	4.87703e6	+	1.44365e6i	0.247779	+	0.0733448i
$271$	−1.71422e6			−0.0861309			−0.0430654	−	0.999072i	$-0.513712\pi$
$271$	−1.71422e6			−0.0861309			−0.0430654	+	0.999072i	$0.513712\pi$
$272$	7.17481e6	+	4.14238e6i	0.356536	+	0.205846i
$273$	5.12485e6	+	1.12436e7i	0.251880	+	0.552608i
$274$	1.34974e6	+	2.33782e6i	0.0656143	+	0.113647i
$275$	1.18235e7	−	6.82630e6i	0.568523	−	0.328237i
$276$	−1.13219e6	+	1.17660e7i	−0.0538507	+	0.559628i
$277$	−7.34449e6	+	1.27210e7i	−0.345559	+	0.598526i	−0.985455	−	0.169936i	$-0.945644\pi$
$277$	−7.34449e6	+	1.27210e7i	−0.345559	+	0.598526i	0.639896	+	0.768461i	$0.278977\pi$
$278$		−	2.31055e7i		−	1.07543i
$279$	2.44208e7	+	4.74374e6i	1.12447	+	0.218428i
$280$	−4.05342e6			−0.184649
$281$	−1.13328e7	−	6.54299e6i	−0.510761	−	0.294888i	0.222385	−	0.974959i	$-0.428616\pi$
$281$	−1.13328e7	−	6.54299e6i	−0.510761	−	0.294888i	−0.733147	+	0.680071i	$0.761949\pi$
$282$	−1.35290e6	+	1.89694e6i	−0.0603277	+	0.0845876i
$283$	−1.52840e6	−	2.64726e6i	−0.0674338	−	0.116799i	0.830337	−	0.557261i	$-0.188148\pi$
$283$	−1.52840e6	−	2.64726e6i	−0.0674338	−	0.116799i	−0.897771	+	0.440463i	$0.854814\pi$
$284$	1.12124e7	−	6.47349e6i	0.489490	−	0.282607i
$285$	−7.75941e6	−	5.53400e6i	−0.335192	−	0.239059i
$286$	−2.66292e6	+	4.61231e6i	−0.113831	+	0.197161i
$287$		−	1.75591e7i		−	0.742773i
$288$	−805233.	+	4.14533e6i	−0.0337089	+	0.173533i
$289$	−4.13200e7			−1.71186
$290$	−507692.	−	293116.i	−0.0208164	−	0.0120184i
$291$	1.70920e7	+	1.64470e6i	0.693609	+	0.0667431i
$292$	6.29951e6	+	1.09111e7i	0.253022	+	0.438247i
$293$	2.54752e7	−	1.47081e7i	1.01278	−	0.584729i	0.100776	−	0.994909i	$-0.467867\pi$
$293$	2.54752e7	−	1.47081e7i	1.01278	−	0.584729i	0.912005	+	0.410180i	$0.134534\pi$
$294$	1.70447e7	−	7.76899e6i	0.670728	−	0.305719i
$295$	5.85202e6	−	1.01360e7i	0.227950	−	0.394821i
$296$		−	1.66643e7i		−	0.642557i
$297$	−1.36660e7	−	1.43955e7i	−0.521640	−	0.549487i
$298$	2.08177e7			0.786653
$299$	−1.10613e7	−	6.38626e6i	−0.413803	−	0.238909i
$300$	4.85138e6	+	1.06436e7i	0.179681	+	0.394208i
$301$	1.69465e7	+	2.93521e7i	0.621412	+	1.07632i
$302$	−3.27000e6	+	1.88793e6i	−0.118721	+	0.0685434i
$303$	−678774.	+	7.05396e6i	−0.0244004	+	0.253574i
$304$	3.95641e6	−	6.85270e6i	0.140825	−	0.243916i
$305$		−	1.81986e6i		−	0.0641415i
$306$	−1.08663e7	−	3.15452e7i	−0.379243	−	1.10096i
$307$	3.82307e7			1.32129			0.660643	−	0.750700i	$-0.270284\pi$
$307$	3.82307e7			1.32129			0.660643	+	0.750700i	$0.270284\pi$
$308$	1.36994e7	+	7.90933e6i	0.468865	+	0.270700i
$309$	1.29303e6	−	1.81300e6i	0.0438260	−	0.0614499i
$310$	−4.40908e6	−	7.63674e6i	−0.148000	−	0.256344i
$311$	−638095.	+	368404.i	−0.0212131	+	0.0122474i	−0.510569	−	0.859837i	$-0.670565\pi$
$311$	−638095.	+	368404.i	−0.0212131	+	0.0122474i	0.489356	+	0.872084i	$0.337232\pi$
$312$	−3.71498e6	−	2.64952e6i	−0.122319	−	0.0872374i
$313$	7.12766e6	−	1.23455e7i	0.232442	−	0.402601i	−0.726084	−	0.687605i	$-0.758662\pi$
$313$	7.12766e6	−	1.23455e7i	0.232442	−	0.402601i	0.958526	+	0.285005i	$0.0919952\pi$
$314$		−	8.52579e6i		−	0.275388i
$315$	1.23212e7	+	1.07079e7i	0.394203	+	0.342589i
$316$	−2.87478e7			−0.911052
$317$	−4.59946e7	−	2.65550e7i	−1.44387	−	0.833621i	−0.445768	−	0.895149i	$-0.647069\pi$
$317$	−4.59946e7	−	2.65550e7i	−1.44387	−	0.833621i	−0.998105	+	0.0615279i	$0.980403\pi$
$318$	−3.59696e7	−	3.46120e6i	−1.11855	−	0.107633i
$319$	1.14390e6	+	1.98129e6i	0.0352383	+	0.0610346i
$320$	1.29631e6	−	748425.i	0.0395602	−	0.0228401i
$321$	2.54586e7	−	1.16041e7i	0.769697	−	0.350829i
$322$	−1.89683e7	+	3.28541e7i	−0.568147	+	0.984060i
$323$			6.25189e7i			1.85526i
$324$	1.33984e7	−	1.04734e7i	0.393928	−	0.307929i
$325$	−1.26394e7			−0.368194
$326$	2.89434e7	+	1.67105e7i	0.835405	+	0.482321i
$327$	−4.70347e6	−	1.03191e7i	−0.134516	−	0.295120i
$328$	3.24211e6	+	5.61550e6i	0.0918769	+	0.159135i
$329$	−6.47603e6	+	3.73894e6i	−0.181853	+	0.104993i
$330$	−673920.	+	7.00352e6i	−0.0187528	+	0.194883i
$331$	2.54781e7	−	4.41293e7i	0.702559	−	1.21687i	−0.265006	−	0.964247i	$-0.585374\pi$
$331$	2.54781e7	−	4.41293e7i	0.702559	−	1.21687i	0.967565	−	0.252621i	$-0.0812927\pi$
$332$			5.72422e6i			0.156424i
$333$	−4.40220e7	+	5.06543e7i	−1.19217	+	1.37178i
$334$	−1.52269e7			−0.408669
$335$	1.26754e7	+	7.31817e6i	0.337154	+	0.194656i
$336$	−7.86952e6	+	1.10341e7i	−0.207458	+	0.290884i
$337$	−2.71146e7	−	4.69638e7i	−0.708457	−	1.22708i	−0.965430	−	0.260664i	$-0.916058\pi$
$337$	−2.71146e7	−	4.69638e7i	−0.708457	−	1.22708i	0.256973	−	0.966419i	$-0.417275\pi$
$338$	−1.93764e7	+	1.11870e7i	−0.501792	+	0.289710i
$339$	3.36265e7	+	2.39823e7i	0.863142	+	0.615591i
$340$	−5.91328e6	+	1.02421e7i	−0.150450	+	0.260587i
$341$			3.44132e7i			0.867885i
$342$	−3.01290e7	+	1.03785e7i	−0.753194	+	0.259451i
$343$	2.44751e6			0.0606517
$344$	−1.08392e7	−	6.25800e6i	−0.266269	−	0.153730i
$345$	−1.67960e7	−	1.61621e6i	−0.409023	−	0.0393586i
$346$	1.79486e7	+	3.10879e7i	0.433314	+	0.750522i
$347$	−1.79173e7	+	1.03446e7i	−0.428829	+	0.247584i	−0.698848	−	0.715271i	$-0.746303\pi$
$347$	−1.79173e7	+	1.03446e7i	−0.428829	+	0.247584i	0.270019	+	0.962855i	$0.412970\pi$
$348$	−1.78357e6	+	812956.i	−0.0423207	+	0.0192899i
$349$	1.72770e7	−	2.99246e7i	0.406435	−	0.703967i	−0.588052	−	0.808823i	$-0.700105\pi$
$349$	1.72770e7	−	2.99246e7i	0.406435	−	0.703967i	0.994487	+	0.104857i	$0.0334383\pi$
$350$			3.75412e7i			0.875597i
$351$	4.29317e6	+	1.78675e7i	0.0992788	+	0.413184i
$352$	−5.84152e6			−0.133936
$353$	6.98774e7	+	4.03437e7i	1.58859	+	0.917174i	0.993539	+	0.113488i	$0.0362022\pi$
$353$	6.98774e7	+	4.03437e7i	1.58859	+	0.917174i	0.595053	+	0.803687i	$0.297131\pi$
$354$	−1.62306e7	−	3.56088e7i	−0.365867	−	0.802689i
$355$	9.24095e6	+	1.60058e7i	0.206553	+	0.357760i
$356$	2.29035e7	−	1.32233e7i	0.507635	−	0.293083i
$357$	1.02566e7	−	1.06589e8i	0.225423	−	2.34264i
$358$	2.63549e7	−	4.56480e7i	0.574397	−	0.994885i
$359$			1.64156e7i			0.354792i	0.984140	+	0.177396i	$0.0567674\pi$
$359$			1.64156e7i			0.354792i	−0.984140	+	0.177396i	$0.943233\pi$
$360$	−5.91749e6	−	1.14948e6i	−0.126832	−	0.0246372i
$361$	1.26662e7			0.269231
$362$	−6.31954e6	−	3.64859e6i	−0.133217	−	0.0769129i
$363$	−1.18304e7	+	1.65878e7i	−0.247332	+	0.346792i
$364$	−7.32235e6	−	1.26827e7i	−0.151826	−	0.262970i
$365$	−1.55756e7	+	8.99259e6i	−0.320307	+	0.184930i
$366$	−4.95399e6	−	3.53318e6i	−0.101044	−	0.0720646i
$367$	2.52891e7	−	4.38021e7i	0.511606	−	0.886128i	−0.488303	−	0.872674i	$-0.662384\pi$
$367$	2.52891e7	−	4.38021e7i	0.511606	−	0.886128i	0.999909	−	0.0134538i	$-0.00428259\pi$
$368$		−	1.40092e7i		−	0.281107i
$369$	4.97943e6	−	2.56341e7i	0.0991061	−	0.510198i
$370$	2.37884e7			0.469634
$371$	−1.00438e8	−	5.79878e7i	−1.96687	−	1.13557i
$372$	−2.93486e7	−	2.82409e6i	−0.570109	−	0.0548592i
$373$	−7.01064e6	−	1.21428e7i	−0.135092	−	0.233987i	0.790540	−	0.612410i	$-0.209800\pi$
$373$	−7.01064e6	−	1.21428e7i	−0.135092	−	0.233987i	−0.925633	+	0.378423i	$0.876466\pi$
$374$	3.99702e7	−	2.30768e7i	0.764050	−	0.441124i
$375$	−3.27295e7	+	1.49182e7i	−0.620648	+	0.282893i
$376$	1.38072e6	−	2.39147e6i	0.0259741	−	0.0449885i
$377$		−	2.11801e6i		−	0.0395280i
$378$	5.30697e7	−	1.27515e7i	0.982588	−	0.236094i
$379$	−1.76705e7			−0.324587			−0.162294	−	0.986743i	$-0.551889\pi$
$379$	−1.76705e7			−0.324587			−0.162294	+	0.986743i	$0.551889\pi$
$380$	9.78228e6	+	5.64780e6i	0.178275	+	0.102927i
$381$	1.06301e7	+	2.33218e7i	0.192205	+	0.421684i
$382$	2.04634e7	+	3.54436e7i	0.367102	+	0.635840i
$383$	7.86852e7	−	4.54289e7i	1.40054	−	0.808605i	0.406096	−	0.913830i	$-0.366890\pi$
$383$	7.86852e7	−	4.54289e7i	1.40054	−	0.808605i	0.994448	+	0.105226i	$0.0335565\pi$
$384$	479379.	−	4.98181e6i	0.00846614	−	0.0879820i
$385$	−1.12906e7	+	1.95559e7i	−0.197850	+	0.342686i
$386$		−	2.64536e7i		−	0.459962i
$387$	1.64160e7	+	4.76562e7i	0.283227	+	0.822217i
$388$	−2.03508e7			−0.348406
$389$	7.01566e7	+	4.05049e7i	1.19184	+	0.688112i	0.958725	−	0.284336i	$-0.0917731\pi$
$389$	7.01566e7	+	4.05049e7i	1.19184	+	0.688112i	0.233120	+	0.972448i	$0.425106\pi$
$390$	3.78220e6	−	5.30315e6i	0.0637604	−	0.0894006i
$391$	5.53433e7	+	9.58573e7i	0.925837	+	1.60360i
$392$	−1.92263e7	+	1.11003e7i	−0.319181	+	0.184279i
$393$	2.01589e7	+	1.43773e7i	0.332115	+	0.236864i
$394$	−7.07169e6	+	1.22485e7i	−0.115620	+	0.200260i
$395$		−	4.10377e7i		−	0.665873i
$396$	1.77564e7	+	1.54315e7i	0.285937	+	0.248498i
$397$	−5.78058e7			−0.923846			−0.461923	−	0.886920i	$-0.652840\pi$
$397$	−5.78058e7			−0.923846			−0.461923	+	0.886920i	$0.652840\pi$
$398$	1.60919e7	+	9.29066e6i	0.255245	+	0.147366i
$399$	−1.01803e8	−	9.79612e6i	−1.60267	−	0.154218i
$400$	−6.93162e6	−	1.20059e7i	−0.108307	−	0.187592i
$401$	−1.06341e8	+	6.13960e7i	−1.64918	+	0.952153i	−0.671778	+	0.740753i	$0.734469\pi$
$401$	−1.06341e8	+	6.13960e7i	−1.64918	+	0.952153i	−0.977400	+	0.211400i	$0.932198\pi$
$402$	4.45301e7	−	2.02969e7i	0.685449	−	0.312429i
$403$	1.59296e7	−	2.75910e7i	0.243383	−	0.421552i
$404$		−	8.39887e6i		−	0.127373i
$405$	1.49508e7	+	1.91263e7i	0.225061	+	0.287916i
$406$	−6.29086e6			−0.0940009
$407$	−8.03976e7	−	4.64176e7i	−1.19250	−	0.688493i
$408$	1.64004e7	+	3.59815e7i	0.241477	+	0.529784i
$409$	9.03706e6	+	1.56527e7i	0.132086	+	0.228780i	0.924481	−	0.381229i	$-0.124499\pi$
$409$	9.03706e6	+	1.56527e7i	0.132086	+	0.228780i	−0.792394	+	0.610009i	$0.791166\pi$
$410$	−8.01617e6	+	4.62814e6i	−0.116309	+	0.0671513i
$411$	−1.23413e6	+	1.28253e7i	−0.0177760	+	0.184732i
$412$	−1.31962e6	+	2.28564e6i	−0.0188693	+	0.0326826i
$413$		−	1.25596e8i		−	1.78290i
$414$	−3.70082e7	+	4.25838e7i	−0.521551	+	0.600127i
$415$	−8.17137e6			−0.114327
$416$	4.68347e6	+	2.70400e6i	0.0650560	+	0.0375601i
$417$	6.40355e7	−	8.97863e7i	0.883105	−	1.23823i
$418$	−2.20408e7	−	3.81758e7i	−0.301785	−	0.522708i
$419$	−8.72440e6	+	5.03704e6i	−0.118602	+	0.0684751i	−0.558128	−	0.829755i	$-0.688480\pi$
$419$	−8.72440e6	+	5.03704e6i	−0.118602	+	0.0684751i	0.439525	+	0.898230i	$0.355147\pi$
$420$	−1.57513e7	−	1.12338e7i	−0.212602	−	0.151628i
$421$	−7.04278e7	+	1.21985e8i	−0.943839	+	1.63478i	−0.185780	+	0.982591i	$0.559481\pi$
$421$	−7.04278e7	+	1.21985e8i	−0.943839	+	1.63478i	−0.758059	+	0.652186i	$0.773852\pi$
$422$			9.44061e6i			0.125621i
$423$	−1.05145e7	+	3.62190e6i	−0.138921	+	0.0478537i
$424$	4.28275e7			0.561857
$425$	9.48583e7	+	5.47665e7i	1.23569	+	0.713424i
$426$	6.15114e7	+	5.91899e6i	0.795659	+	0.0765630i
$427$	−9.76448e6	−	1.69126e7i	−0.125420	−	0.217233i
$428$	−2.87171e7	+	1.65798e7i	−0.366277	+	0.211470i
$429$	−2.31306e7	+	1.05430e7i	−0.292965	+	0.133534i
$430$	8.93333e6	−	1.54730e7i	0.112359	−	0.194612i
$431$			6.81157e6i			0.0850777i	0.999095	+	0.0425388i	$0.0135446\pi$
$431$			6.81157e6i			0.0850777i	−0.999095	+	0.0425388i	$0.986455\pi$
$432$	−1.46176e7	+	1.38768e7i	−0.181311	+	0.172123i
$433$	−1.17807e8			−1.45113			−0.725566	−	0.688153i	$-0.758422\pi$
$433$	−1.17807e8			−1.45113			−0.725566	+	0.688153i	$0.758422\pi$
$434$	−8.19500e7	−	4.73138e7i	−1.00249	−	0.578787i
$435$	−1.16050e6	−	2.54606e6i	−0.0140986	−	0.0309315i
$436$	6.72029e6	+	1.16399e7i	0.0810827	+	0.140439i
$437$	9.15538e7	−	5.28586e7i	1.09706	−	0.633391i
$438$	−5.75991e6	+	5.98583e7i	−0.0685478	+	0.712364i
$439$	−3.55152e7	+	6.15142e7i	−0.419780	+	0.727079i	−0.995917	−	0.0902733i	$-0.971226\pi$
$439$	−3.55152e7	+	6.15142e7i	−0.419780	+	0.727079i	0.576137	+	0.817353i	$0.304559\pi$
$440$		−	8.33881e6i		−	0.0978918i
$441$	8.77655e7	+	1.70485e7i	1.02331	+	0.198779i
$442$	−4.27284e7			−0.494823
$443$	1.83090e7	+	1.05707e7i	0.210597	+	0.121588i	0.601589	−	0.798806i	$-0.294535\pi$
$443$	1.83090e7	+	1.05707e7i	0.210597	+	0.121588i	−0.390992	+	0.920394i	$0.627868\pi$
$444$	4.61840e7	−	6.47561e7i	0.527646	−	0.739830i
$445$	1.88764e7	+	3.26949e7i	0.214210	+	0.371022i
$446$	−5.53940e7	+	3.19817e7i	−0.624393	+	0.360493i
$447$	8.08958e7	+	5.76948e7i	0.905740	+	0.645972i
$448$	8.03135e6	−	1.39107e7i	0.0893212	−	0.154709i
$449$			5.48751e7i			0.606228i	0.952954	+	0.303114i	$0.0980263\pi$
$449$			5.48751e7i			0.606228i	−0.952954	+	0.303114i	$0.901974\pi$
$450$	−1.06460e7	+	5.48055e7i	−0.116828	+	0.601432i
$451$	3.61230e7			0.393780
$452$	−4.23928e7	−	2.44755e7i	−0.459068	−	0.265043i
$453$	−1.79392e7	−	1.72622e6i	−0.192979	−	0.0185695i
$454$	−4.33497e7	−	7.50839e7i	−0.463253	−	0.802378i
$455$	1.81046e7	−	1.04527e7i	0.192201	−	0.110967i
$456$	3.43661e7	−	1.56641e7i	0.362440	−	0.165201i
$457$	9.82826e6	−	1.70230e7i	0.102974	−	0.178356i	−0.809935	−	0.586520i	$-0.800497\pi$
$457$	9.82826e6	−	1.70230e7i	0.102974	−	0.178356i	0.912909	+	0.408164i	$0.133831\pi$
$458$			7.19015e6i			0.0748413i
$459$	4.51999e7	−	1.52698e8i	0.467412	−	1.57904i
$460$	1.99983e7			0.205456
$461$	4.97070e7	+	2.86983e7i	0.507358	+	0.292923i	0.731747	−	0.681576i	$-0.238705\pi$
$461$	4.97070e7	+	2.86983e7i	0.507358	+	0.292923i	−0.224389	+	0.974500i	$0.572039\pi$
$462$	3.13145e7	+	6.87019e7i	0.317555	+	0.696695i
$463$	−5.06076e7	−	8.76549e7i	−0.509885	−	0.883147i	−0.999934	−	0.0114526i	$-0.996354\pi$
$463$	−5.06076e7	−	8.76549e7i	−0.509885	−	0.883147i	0.490049	−	0.871695i	$-0.336979\pi$
$464$	2.01186e6	−	1.16155e6i	0.0201392	−	0.0116274i
$465$	4.03141e6	−	4.18953e7i	0.0400957	−	0.416683i
$466$	4.12573e6	−	7.14597e6i	0.0407702	−	0.0706161i
$467$		−	1.26426e8i		−	1.24133i	−0.784077	−	0.620663i	$-0.786863\pi$
$467$		−	1.26426e8i		−	1.24133i	0.784077	−	0.620663i	$-0.213137\pi$
$468$	−7.09315e6	−	2.05916e7i	−0.0691993	−	0.200888i
$469$	1.57063e8			1.52249
$470$	3.41384e6	+	1.97098e6i	0.0328814	+	0.0189841i
$471$	2.36287e7	−	3.31306e7i	0.226140	−	0.317078i
$472$	2.31901e7	+	4.01665e7i	0.220535	+	0.381977i
$473$	−6.03840e7	+	3.48627e7i	−0.570609	+	0.329441i
$474$	−1.11712e8	−	7.96726e7i	−1.04897	−	0.748125i
$475$	5.23077e7	−	9.05997e7i	0.488073	−	0.845368i
$476$			1.26911e8i			1.17673i
$477$	−1.30183e8	−	1.13137e8i	−1.19949	−	1.04244i
$478$	−2.84264e7			−0.260278
$479$	−5.77665e7	−	3.33515e7i	−0.525617	−	0.303465i	0.213613	−	0.976918i	$-0.431477\pi$
$479$	−5.77665e7	−	3.33515e7i	−0.525617	−	0.303465i	−0.739230	+	0.673453i	$0.764810\pi$
$480$	7.11157e6	+	684317.i	0.0643046	+	0.00618776i
$481$	4.29728e7	+	7.44310e7i	0.386152	+	0.668835i
$482$	2.51557e7	−	1.45237e7i	0.224644	−	0.129699i
$483$	−1.64762e8	+	7.50989e7i	−1.46223	+	0.666488i
$484$	1.20737e7	−	2.09122e7i	0.106489	−	0.184444i
$485$		−	2.90509e7i		−	0.254645i
$486$	8.10913e7	−	3.56595e6i	0.706424	−	0.0310647i
$487$	6.97650e7			0.604019			0.302009	−	0.953305i	$-0.402343\pi$
$487$	6.97650e7			0.604019			0.302009	+	0.953305i	$0.402343\pi$
$488$	6.24549e6	+	3.60583e6i	0.0537411	+	0.0310275i
$489$	6.61599e7	+	1.45151e8i	0.565807	+	1.24134i
$490$	−1.58457e7	−	2.74456e7i	−0.134686	−	0.233284i
$491$	9.22974e7	−	5.32879e7i	0.779731	−	0.450178i	−0.0566037	−	0.998397i	$-0.518027\pi$
$491$	9.22974e7	−	5.32879e7i	0.779731	−	0.450178i	0.836335	+	0.548219i	$0.184694\pi$
$492$	−2.96440e6	+	3.08067e7i	−0.0248910	+	0.258672i
$493$	−9.17734e6	+	1.58956e7i	−0.0765907	+	0.132659i
$494$			4.08101e7i			0.338522i
$495$	−2.20286e7	+	2.53474e7i	−0.181623	+	0.208986i
$496$	3.49441e7			0.286371
$497$	1.71758e8	+	9.91647e7i	1.39910	+	0.807770i
$498$	−1.58643e7	+	2.22439e7i	−0.128450	+	0.180104i
$499$	−6.75572e7	−	1.17012e8i	−0.543713	−	0.941739i	−0.998687	−	0.0512338i	$-0.983685\pi$
$499$	−6.75572e7	−	1.17012e8i	−0.543713	−	0.941739i	0.454974	−	0.890505i	$-0.349649\pi$
$500$	3.69186e7	−	2.13150e7i	0.295349	−	0.170520i
$501$	−5.91705e7	−	4.22003e7i	−0.470535	−	0.335585i
$502$	−4.88485e6	+	8.46080e6i	−0.0386136	+	0.0668806i
$503$			2.31473e8i			1.81885i	0.415869	+	0.909425i	$0.363477\pi$
$503$			2.31473e8i			1.81885i	−0.415869	+	0.909425i	$0.636523\pi$
$504$	−6.11607e7	+	2.10679e7i	−0.477728	+	0.164562i
$505$	1.19894e7			0.0930947
$506$	−6.75883e7	−	3.90221e7i	−0.521699	−	0.301203i
$507$	−1.06299e8	−	1.02287e7i	−0.815655	−	0.0784871i
$508$	−1.51883e7	−	2.63068e7i	−0.115856	−	0.200668i
$509$	−1.13698e8	+	6.56433e7i	−0.862179	+	0.497780i	−0.864742	−	0.502217i	$-0.832518\pi$
$509$	−1.13698e8	+	6.56433e7i	−0.862179	+	0.497780i	0.00256205	+	0.999997i	$0.499184\pi$
$510$	−5.13638e7	+	2.34117e7i	−0.387210	+	0.176491i
$511$	−9.64996e7	+	1.67142e8i	−0.723207	+	1.25263i
$512$			5.93164e6i			0.0441942i
$513$	−1.45842e8	−	4.31707e7i	−1.08027	−	0.319769i
$514$	7.47712e7			0.550611
$515$	−3.26277e6	−	1.88376e6i	−0.0238872	−	0.0137913i
$516$	−2.47765e7	−	5.43581e7i	−0.180340	−	0.395654i
$517$	−7.69185e6	−	1.33227e7i	−0.0556620	−	0.0964094i
$518$	2.21073e8	−	1.27637e8i	1.59055	−	0.918303i
$519$	−1.64112e7	+	1.70549e8i	−0.117392	+	1.21996i
$520$	−3.85998e6	+	6.68568e6i	−0.0274521	+	0.0475484i
$521$		−	1.14057e8i		−	0.806509i	−0.915088	−	0.403255i	$-0.867879\pi$
$521$		−	1.14057e8i		−	0.806509i	0.915088	−	0.403255i	$-0.132121\pi$
$522$	−9.18388e6	−	1.78397e6i	−0.0645676	−	0.0125423i
$523$	6.52785e7			0.456315			0.228158	−	0.973624i	$-0.426730\pi$
$523$	6.52785e7			0.456315			0.228158	+	0.973624i	$0.426730\pi$
$524$	−2.54143e7	−	1.46730e7i	−0.176638	−	0.101982i
$525$	−1.04043e8	+	1.45882e8i	−0.719010	+	1.00815i
$526$	3.38324e7	+	5.85994e7i	0.232474	+	0.402657i
$527$	−2.39103e8	+	1.38046e8i	−1.63363	+	0.943176i
$528$	−2.26997e7	−	1.61894e7i	−0.154212	−	0.109984i
$529$	1.95656e7	−	3.38886e7i	0.132168	−	0.228922i
$530$			6.11366e7i			0.410652i
$531$	3.56168e7	−	1.83355e8i	0.237887	−	1.22464i
$532$	1.21213e8			0.805035
$533$	−2.89618e7	−	1.67211e7i	−0.191269	−	0.110429i
$534$	1.25649e8	+	1.20907e7i	0.825153	+	0.0794011i
$535$	−2.36678e7	−	4.09939e7i	−0.154560	−	0.267706i
$536$	−5.02296e7	+	2.90001e7i	−0.326186	+	0.188324i
$537$	2.28924e8	−	1.04344e8i	1.47832	−	0.673820i
$538$	−594642.	+	1.02995e6i	−0.00381864	+	0.00661408i
$539$			1.23677e8i			0.789812i
$540$	−1.98092e7	−	2.08667e7i	−0.125802	−	0.132517i
$541$	1.71142e8			1.08085			0.540423	−	0.841394i	$-0.318264\pi$
$541$	1.71142e8			1.08085			0.540423	+	0.841394i	$0.318264\pi$
$542$	8.39793e6	+	4.84855e6i	0.0527442	+	0.0304519i
$543$	−1.44454e7	−	3.16923e7i	−0.0902258	−	0.197950i
$544$	−2.34328e7	−	4.05869e7i	−0.145555	−	0.252109i
$545$	−1.66160e7	+	9.59326e6i	−0.102645	+	0.0592620i
$546$	6.69514e6	−	6.95773e7i	0.0411322	−	0.427455i
$547$	−2.90478e7	+	5.03122e7i	−0.177481	+	0.307405i	−0.941017	−	0.338359i	$-0.890128\pi$
$547$	−2.90478e7	+	5.03122e7i	−0.177481	+	0.307405i	0.763536	+	0.645765i	$0.223461\pi$
$548$		−	1.52706e7i		−	0.0927926i
$549$	−9.45884e6	−	2.74593e7i	−0.0571638	−	0.165948i
$550$	−7.72308e7			−0.464197
$551$	1.51820e7	+	8.76532e6i	0.0907557	+	0.0523978i
$552$	3.88257e7	−	5.44388e7i	0.230835	−	0.323662i
$553$	−2.20188e8	−	3.81376e8i	−1.30202	−	2.25517i
$554$	7.19610e7	−	4.15467e7i	0.423221	−	0.244347i
$555$	9.24398e7	+	6.59280e7i	0.540730	+	0.385648i
$556$	−6.53523e7	+	1.13193e8i	−0.380221	+	0.658563i
$557$		−	1.36639e8i		−	0.790696i	−0.918532	−	0.395348i	$-0.870624\pi$
$557$		−	1.36639e8i		−	0.790696i	0.918532	−	0.395348i	$-0.129376\pi$
$558$	−1.06219e8	−	9.23118e7i	−0.611366	−	0.531318i
$559$	6.45509e7			0.369544
$560$	1.98576e7	+	1.14648e7i	0.113074	+	0.0652834i
$561$	2.19277e8	+	2.11001e7i	1.24195	+	0.119508i
$562$	3.70127e7	+	6.41079e7i	0.208517	+	0.361163i
$563$	2.39951e8	−	1.38536e8i	1.34461	−	0.776311i	0.357130	−	0.934055i	$-0.383755\pi$
$563$	2.39951e8	−	1.38536e8i	1.34461	−	0.776311i	0.987480	+	0.157743i	$0.0504218\pi$
$564$	1.19932e7	−	5.46651e6i	0.0668493	−	0.0304700i
$565$	3.49390e7	−	6.05161e7i	0.193716	−	0.335525i
$566$			1.72919e7i			0.0953657i
$567$	2.41565e8	+	9.75281e7i	1.32521	+	0.535033i
$568$	−7.32392e7			−0.399667
$569$	−2.10766e8	−	1.21686e8i	−1.14410	−	0.660546i	−0.196657	−	0.980472i	$-0.563009\pi$
$569$	−2.10766e8	−	1.21686e8i	−1.14410	−	0.660546i	−0.947443	+	0.319926i	$0.896342\pi$
$570$	2.23607e7	+	4.90579e7i	0.120743	+	0.264901i
$571$	6.95310e7	+	1.20431e8i	0.373483	+	0.646891i	0.990099	−	0.140373i	$-0.0448302\pi$
$571$	6.95310e7	+	1.20431e8i	0.373483	+	0.646891i	−0.616616	+	0.787264i	$0.711497\pi$
$572$	2.60912e7	−	1.50637e7i	0.139414	−	0.0804905i
$573$	−1.87105e7	+	1.94444e8i	−0.0994541	+	1.03355i
$574$	−4.96646e7	+	8.60215e7i	−0.262610	+	0.454853i
$575$		−	1.85216e8i		−	0.974262i
$576$	1.56696e7	−	1.80304e7i	0.0819956	−	0.0943490i
$577$	−3.45574e8			−1.79893			−0.899464	−	0.436994i	$-0.856043\pi$
$577$	−3.45574e8			−1.79893			−0.899464	+	0.436994i	$0.856043\pi$
$578$	2.02426e8	+	1.16871e8i	1.04829	+	0.605232i
$579$	7.33143e7	−	1.02797e8i	0.377705	−	0.529594i
$580$	1.65812e6	+	2.87194e6i	0.00849828	+	0.0147194i
$581$	−7.59392e7	+	4.38435e7i	−0.387202	+	0.223551i
$582$	−7.90816e7	−	5.64009e7i	−0.401150	−	0.286100i
$583$	1.19294e8	−	2.06623e8i	0.602023	−	1.04273i
$584$		−	7.12708e7i		−	0.357827i
$585$	2.93947e7	−	1.01255e7i	0.146825	−	0.0505766i
$586$	−1.66404e8			−0.826932
$587$	−1.43696e8	−	8.29627e7i	−0.710443	−	0.410174i	0.100782	−	0.994909i	$-0.467866\pi$
$587$	−1.43696e8	−	8.29627e7i	−0.710443	−	0.410174i	−0.811225	+	0.584734i	$0.801199\pi$
$588$	−1.05475e8	−	1.01495e7i	−0.518823	−	0.0499242i
$589$	1.31849e8	+	2.28369e8i	0.645253	+	1.11761i
$590$	−5.73379e7	+	3.31041e7i	−0.279181	+	0.161185i
$591$	−6.14260e7	+	2.79981e7i	−0.297571	+	0.135633i
$592$	−4.71337e7	+	8.16380e7i	−0.227178	+	0.393484i
$593$			2.87880e8i			1.38054i	0.723553	+	0.690268i	$0.242508\pi$
$593$			2.87880e8i			1.38054i	−0.723553	+	0.690268i	$0.757492\pi$
$594$	2.62326e7	+	1.09176e8i	0.125165	+	0.520919i
$595$	−1.81166e8			−0.860055
$596$	−1.01985e8	−	5.88812e7i	−0.481724	−	0.278124i
$597$	3.67834e7	+	8.07004e7i	0.172874	+	0.379274i
$598$	3.61261e7	+	6.25723e7i	0.168934	+	0.292603i
$599$	3.67511e7	−	2.12182e7i	0.170997	−	0.0987254i	−0.412059	−	0.911157i	$-0.635190\pi$
$599$	3.67511e7	−	2.12182e7i	0.170997	−	0.0987254i	0.583056	+	0.812432i	$0.301857\pi$
$600$	6.33788e6	−	6.58646e7i	0.0293420	−	0.304929i
$601$	8.90001e6	−	1.54153e7i	0.0409984	−	0.0710113i	−0.844798	−	0.535085i	$-0.820279\pi$
$601$	8.90001e6	−	1.54153e7i	0.0409984	−	0.0710113i	0.885796	+	0.464074i	$0.153613\pi$
$602$		−	1.91727e8i		−	0.878809i
$603$	2.29292e8	+	4.45400e7i	1.04577	+	0.203142i
$604$	2.13595e7			0.0969350
$605$	2.98524e7	+	1.72353e7i	0.134807	+	0.0778309i
$606$	2.32769e7	−	3.26374e7i	0.104594	−	0.146655i
$607$	1.72485e8	+	2.98753e8i	0.771232	+	1.33581i	0.936888	+	0.349629i	$0.113692\pi$
$607$	1.72485e8	+	2.98753e8i	0.771232	+	1.33581i	−0.165656	+	0.986184i	$0.552974\pi$
$608$	−3.87647e7	+	2.23808e7i	−0.172475	+	0.0995785i
$609$	−2.44458e7	−	1.74347e7i	−0.108231	−	0.0771904i
$610$	−5.14735e6	+	8.91547e6i	−0.0226775	+	0.0392785i
$611$			1.42420e7i			0.0624378i
$612$	−3.59896e7	+	1.85274e8i	−0.157008	+	0.808277i
$613$	1.15533e8			0.501562			0.250781	−	0.968044i	$-0.419313\pi$
$613$	1.15533e8			0.501562			0.250781	+	0.968044i	$0.419313\pi$
$614$	−1.87291e8	−	1.08133e8i	−0.809119	−	0.467145i
$615$	−4.39768e7	−	4.23170e6i	−0.189059	−	0.0181924i
$616$	−4.47419e7	−	7.74953e7i	−0.191413	−	0.331538i
$617$	−1.99692e8	+	1.15292e8i	−0.850168	+	0.490845i	−0.860707	−	0.509100i	$-0.829978\pi$
$617$	−1.99692e8	+	1.15292e8i	−0.850168	+	0.490845i	0.0105398	+	0.999944i	$0.496645\pi$
$618$	−1.14624e7	+	5.22460e6i	−0.0485637	+	0.0221354i
$619$	−1.43315e8	+	2.48228e8i	−0.604253	+	1.04660i	0.387916	+	0.921695i	$0.373195\pi$
$619$	−1.43315e8	+	2.48228e8i	−0.604253	+	1.04660i	−0.992169	+	0.124902i	$0.960138\pi$
$620$			4.98830e7i			0.209304i
$621$	−2.61829e8	+	6.29116e7i	−1.09331	+	0.262698i
$622$	4.16802e6			0.0173204
$623$	3.50849e8	+	2.02563e8i	1.45096	+	0.837713i
$624$	1.07056e7	+	2.34875e7i	0.0440614	+	0.0966679i
$625$	−7.53408e7	−	1.30494e8i	−0.308596	−	0.534504i
$626$	−6.98365e7	+	4.03201e7i	−0.284682	+	0.164361i
$627$	2.01528e7	−	2.09433e8i	0.0817586	−	0.849654i
$628$	−2.41146e7	+	4.17677e7i	−0.0973645	+	0.168640i
$629$		−	7.44804e8i		−	2.99288i
$630$	−3.00746e7	−	8.73073e7i	−0.120276	−	0.349164i
$631$	−2.03780e8			−0.811098			−0.405549	−	0.914073i	$-0.632920\pi$
$631$	−2.03780e8			−0.811098			−0.405549	+	0.914073i	$0.632920\pi$
$632$	1.40835e8	+	8.13110e7i	0.557903	+	0.322105i
$633$	−2.61640e7	+	3.66855e7i	−0.103156	+	0.144638i
$634$	1.50218e8	+	2.60185e8i	0.589459	+	1.02097i
$635$	3.75532e7	−	2.16814e7i	0.146665	−	0.0846770i
$636$	1.66424e8	+	1.18694e8i	0.646913	+	0.461377i
$637$	5.72494e7	−	9.91588e7i	0.221489	−	0.383631i
$638$		−	1.29417e7i		−	0.0498345i
$639$	2.22625e8	+	1.93476e8i	0.853239	+	0.741521i
$640$	−8.46746e6			−0.0323008
$641$	−4.12801e8	−	2.38331e8i	−1.56735	−	0.904910i	−0.996476	−	0.0838727i	$-0.973271\pi$
$641$	−4.12801e8	−	2.38331e8i	−1.56735	−	0.904910i	−0.570874	−	0.821038i	$-0.693396\pi$
$642$	−1.57543e8	−	1.51597e7i	−0.595378	−	0.0572908i
$643$	−8.05937e7	−	1.39592e8i	−0.303157	−	0.525084i	0.673692	−	0.739012i	$-0.264707\pi$
$643$	−8.05937e7	−	1.39592e8i	−0.303157	−	0.525084i	−0.976849	+	0.213928i	$0.931374\pi$
$644$	1.85851e8	−	1.07301e8i	0.695835	−	0.401741i
$645$	7.75966e7	−	3.53687e7i	0.289177	−	0.131807i
$646$	1.76830e8	−	3.06279e8i	0.655932	−	1.13611i
$647$			3.18171e8i			1.17476i	0.809313	+	0.587378i	$0.199840\pi$
$647$			3.18171e8i			1.17476i	−0.809313	+	0.587378i	$0.800160\pi$
$648$	−9.52615e7	+	1.34125e7i	−0.350100	+	0.0492928i
$649$	2.58380e8			0.945202
$650$	6.19202e7	+	3.57496e7i	0.225472	+	0.130176i
$651$	−1.87324e8	−	4.10977e8i	−0.678970	−	1.48962i
$652$	−9.45288e7	−	1.63729e8i	−0.341053	−	0.590721i
$653$	1.55040e8	−	8.95121e7i	0.556805	−	0.321471i	−0.195057	−	0.980792i	$-0.562489\pi$
$653$	1.55040e8	−	8.95121e7i	0.556805	−	0.321471i	0.751862	+	0.659321i	$0.229156\pi$
$654$	−6.14465e6	+	6.38565e7i	−0.0219666	+	0.228282i
$655$	2.09457e7	−	3.62791e7i	0.0745370	−	0.129102i
$656$		−	3.66803e7i		−	0.129934i
$657$	−1.88276e8	+	2.16641e8i	−0.663894	+	0.763915i
$658$	4.23013e7			0.148483
$659$	2.74307e8	+	1.58371e8i	0.958475	+	0.553376i	0.895703	−	0.444652i	$-0.146673\pi$
$659$	2.74307e8	+	1.58371e8i	0.958475	+	0.553376i	0.0627716	+	0.998028i	$0.480006\pi$
$660$	2.31105e7	−	3.24040e7i	0.0803854	−	0.112711i
$661$	1.88046e8	+	3.25706e8i	0.651119	+	1.12777i	0.982852	+	0.184398i	$0.0590334\pi$
$661$	1.88046e8	+	3.25706e8i	0.651119	+	1.12777i	−0.331733	+	0.943373i	$0.607633\pi$
$662$	−2.49633e8	+	1.44126e8i	−0.860456	+	0.496784i
$663$	−1.66039e8	−	1.18419e8i	−0.569732	−	0.406332i
$664$	1.61906e7	−	2.80429e7i	0.0553041	−	0.0957895i
$665$			1.73033e8i			0.588387i
$666$	3.58935e8	−	1.23641e8i	1.21505	−	0.418544i
$667$	3.10371e7			0.104593
$668$	7.45961e7	+	4.30681e7i	0.250257	+	0.144486i
$669$	−3.03892e8	−	2.92423e7i	−1.01494	−	0.0976636i
$670$	−4.13978e7	−	7.17031e7i	−0.137643	−	0.238404i
$671$	3.47930e7	−	2.00878e7i	0.115166	−	0.0664912i
$672$	6.97618e7	−	3.17976e7i	0.229885	−	0.104782i
$673$	1.18840e8	−	2.05836e8i	0.389867	−	0.675269i	−0.602564	−	0.798070i	$-0.705854\pi$
$673$	1.18840e8	−	2.05836e8i	0.389867	−	0.675269i	0.992431	+	0.122801i	$0.0391877\pi$
$674$			3.06767e8i			1.00191i
$675$	−1.93259e8	+	1.83465e8i	−0.628390	+	0.596544i
$676$	1.26566e8			0.409711
$677$	3.37474e8	+	1.94841e8i	1.08761	+	0.627933i	0.932940	−	0.360033i	$-0.117234\pi$
$677$	3.37474e8	+	1.94841e8i	1.08761	+	0.627933i	0.154672	+	0.987966i	$0.450568\pi$
$678$	−9.69030e7	−	2.12599e8i	−0.310920	−	0.682138i
$679$	−1.55873e8	−	2.69979e8i	−0.497921	−	0.862425i
$680$	5.79380e7	−	3.34505e7i	0.184263	−	0.106384i
$681$	3.96365e7	−	4.11911e8i	0.125503	−	1.30425i
$682$	9.73353e7	−	1.68590e8i	0.306844	−	0.531469i
$683$			3.91877e8i			1.22995i	0.788546	+	0.614975i	$0.210834\pi$
$683$			3.91877e8i			1.22995i	−0.788546	+	0.614975i	$0.789166\pi$
$684$	1.76956e8	+	3.43738e7i	0.552965	+	0.107414i
$685$	2.17988e7			0.0678206
$686$	−1.19903e7	−	6.92261e6i	−0.0371414	−	0.0214436i
$687$	−1.99270e7	+	2.79404e7i	−0.0614571	+	0.0861711i
$688$	3.54006e7	+	6.13156e7i	0.108704	+	0.188281i
$689$	−1.91289e8	+	1.10441e8i	−0.584834	+	0.337654i
$690$	7.77118e7	+	5.54240e7i	0.236559	+	0.168714i
$691$	1.26455e8	−	2.19026e8i	0.383267	−	0.663838i	−0.608260	−	0.793738i	$-0.708132\pi$
$691$	1.26455e8	−	2.19026e8i	0.383267	−	0.663838i	0.991527	+	0.129900i	$0.0414655\pi$
$692$		−	2.03065e8i		−	0.612798i
$693$	−6.87173e7	+	3.53756e8i	−0.206475	+	1.06293i
$694$	1.17035e8			0.350137
$695$	−1.61584e8	−	9.32908e7i	−0.481333	−	0.277897i
$696$	1.10371e7	+	1.06205e6i	0.0327360	+	0.00315005i
$697$	1.44905e8	+	2.50983e8i	0.427942	+	0.741217i
$698$	−1.69279e8	+	9.77333e7i	−0.497780	+	0.287393i
$699$	3.58369e7	−	1.63345e7i	0.104930	−	0.0478272i
$700$	1.06183e8	−	1.83914e8i	0.309570	−	0.536191i
$701$		−	2.15054e8i		−	0.624299i	−0.950033	−	0.312150i	$-0.898951\pi$
$701$		−	2.15054e8i		−	0.624299i	0.950033	−	0.312150i	$-0.101049\pi$
$702$	2.95049e7	−	9.96757e7i	0.0852870	−	0.288123i
$703$	−7.11366e8			−2.04751
$704$	2.86175e7	+	1.65223e7i	0.0820188	+	0.0473536i
$705$	7.80348e6	+	1.71203e7i	0.0222700	+	0.0488590i
$706$	−2.28219e8	−	3.95286e8i	−0.648540	−	1.12330i
$707$	1.11422e8	−	6.43294e7i	0.315291	−	0.182033i
$708$	−2.12037e7	+	2.20354e8i	−0.0597465	+	0.620898i
$709$	7.04509e7	−	1.22025e8i	0.197673	−	0.342380i	−0.750100	−	0.661324i	$-0.769995\pi$
$709$	7.04509e7	−	1.22025e8i	0.197673	−	0.342380i	0.947774	+	0.318944i	$0.103328\pi$
$710$		−	1.04549e8i		−	0.292110i
$711$	−2.13296e8	−	6.19203e8i	−0.593435	−	1.72276i
$712$	−1.49605e8			−0.414482
$713$	4.04315e8	+	2.33431e8i	1.11545	+	0.644007i
$714$	−3.51725e8	+	4.93166e8i	−0.966293	+	1.35487i
$715$	2.15036e7	+	3.72453e7i	0.0588292	+	0.101895i
$716$	−2.58224e8	+	1.49086e8i	−0.703490	+	0.406160i
$717$	−1.10463e8	−	7.87818e7i	−0.299680	−	0.213731i
$718$	4.64304e7	−	8.04198e7i	0.125438	−	0.217265i
$719$			4.59075e8i			1.23508i	0.786538	+	0.617542i	$0.211872\pi$
$719$			4.59075e8i			1.23508i	−0.786538	+	0.617542i	$0.788128\pi$
$720$	2.57385e7	+	2.23685e7i	0.0689581	+	0.0599292i
$721$	−4.04293e7			−0.107867
$722$	−6.20516e7	−	3.58255e7i	−0.164870	−	0.0951877i
$723$	1.38005e8	+	1.32796e7i	0.365156	+	0.0351375i
$724$	2.06395e7	+	3.57487e7i	0.0543856	+	0.0941986i
$725$	2.65988e7	−	1.53568e7i	0.0697988	−	0.0402984i
$726$	1.04874e8	−	4.78019e7i	0.274069	−	0.124921i
$727$	−2.26267e8	+	3.91905e8i	−0.588867	+	1.01995i	0.405514	+	0.914089i	$0.367092\pi$
$727$	−2.26267e8	+	3.91905e8i	−0.588867	+	1.01995i	−0.994381	+	0.105859i	$0.966241\pi$
$728$			8.28429e7i			0.214714i
$729$	3.24997e8	+	2.10882e8i	0.838875	+	0.544324i
$730$	1.01740e8			0.261530
$731$	−4.84452e8	−	2.79699e8i	−1.24022	−	0.716042i
$732$	1.42761e7	+	3.13209e7i	0.0363980	+	0.0798549i
$733$	2.37788e8	+	4.11861e8i	0.603779	+	1.04578i	0.992243	+	0.124312i	$0.0396725\pi$
$733$	2.37788e8	+	4.11861e8i	0.603779	+	1.04578i	−0.388464	+	0.921464i	$0.626994\pi$
$734$	−2.47782e8	+	1.43057e8i	−0.626587	+	0.361760i
$735$	1.44884e7	−	1.50567e8i	0.0364888	−	0.379199i
$736$	−3.96241e7	+	6.86310e7i	−0.0993862	+	0.172142i
$737$			3.23113e8i			0.807147i
$738$	−9.68982e7	+	1.11497e8i	−0.241072	+	0.277392i
$739$	8.91913e7			0.220999			0.110499	−	0.993876i	$-0.464755\pi$
$739$	8.91913e7			0.220999			0.110499	+	0.993876i	$0.464755\pi$
$740$	−1.16539e8	−	6.72837e7i	−0.287591	−	0.166041i
$741$	−1.13103e8	+	1.58585e8i	−0.277983	+	0.389769i
$742$	3.28029e8	+	5.68162e8i	0.802971	+	1.39079i
$743$	6.30917e8	−	3.64260e8i	1.53818	−	0.888066i	0.539230	−	0.842158i	$-0.318715\pi$
$743$	6.30917e8	−	3.64260e8i	1.53818	−	0.888066i	0.998946	−	0.0459081i	$-0.0146182\pi$
$744$	1.35790e8	+	9.68454e7i	0.329723	+	0.235158i
$745$	8.40534e7	−	1.45585e8i	0.203276	−	0.352085i
$746$			7.93163e7i			0.191049i
$747$	−1.23295e8	+	4.24711e7i	−0.295790	+	0.101890i
$748$	−2.61084e8			−0.623844
$749$	−4.39906e8	−	2.53980e8i	−1.04692	−	0.604441i
$750$	2.02536e8	+	1.94892e7i	0.480086	+	0.0461967i
$751$	1.79422e8	+	3.10769e8i	0.423601	+	0.733698i	0.996289	−	0.0860756i	$-0.0274327\pi$
$751$	1.79422e8	+	3.10769e8i	0.423601	+	0.733698i	−0.572688	+	0.819773i	$0.694099\pi$
$752$	−1.35282e7	+	7.81051e6i	−0.0318117	+	0.0183665i
$753$	−4.24307e7	+	1.93400e7i	−0.0993791	+	0.0452972i
$754$	−5.99064e6	+	1.03761e7i	−0.0139752	+	0.0242058i
$755$			3.04909e7i			0.0708482i
$756$	−2.96054e8	−	8.76347e7i	−0.685182	−	0.202820i
$757$	3.38232e8			0.779700			0.389850	−	0.920878i	$-0.372527\pi$
$757$	3.38232e8			0.779700			0.389850	+	0.920878i	$0.372527\pi$
$758$	8.65675e7	+	4.99798e7i	0.198768	+	0.114759i
$759$	−1.54496e8	−	3.38953e8i	−0.353338	−	0.775202i
$760$	−3.19488e7	−	5.53369e7i	−0.0727803	−	0.126059i
$761$	5.84127e8	−	3.37246e8i	1.32542	−	0.765232i	0.340833	−	0.940124i	$-0.389291\pi$
$761$	5.84127e8	−	3.37246e8i	1.32542	−	0.765232i	0.984588	+	0.174892i	$0.0559577\pi$
$762$	1.38873e7	−	1.44320e8i	0.0313872	−	0.326182i
$763$	−1.02945e8	+	1.78306e8i	−0.231757	+	0.401415i
$764$		−	2.31517e8i		−	0.519161i
$765$	−2.64480e8	−	5.13753e7i	−0.590757	−	0.114755i
$766$	−5.13970e8			−1.14354
$767$	−2.07157e8	−	1.19602e8i	−0.459107	−	0.265066i
$768$	−1.64392e7	+	2.30499e7i	−0.0362907	+	0.0508845i
$769$	−3.81386e8	−	6.60580e8i	−0.838660	−	1.45260i	−0.891016	−	0.453973i	$-0.850006\pi$
$769$	−3.81386e8	−	6.60580e8i	−0.838660	−	1.45260i	0.0523561	−	0.998628i	$-0.483327\pi$
$770$	1.10625e8	−	6.38694e7i	0.242316	−	0.139901i
$771$	2.90555e8	+	2.07224e8i	0.633965	+	0.452143i
$772$	−7.48220e7	+	1.29595e8i	−0.162621	+	0.281668i
$773$		−	6.42100e8i		−	1.39016i	−0.718933	−	0.695080i	$-0.755369\pi$
$773$		−	6.42100e8i		−	1.39016i	0.718933	−	0.695080i	$-0.244631\pi$
$774$	5.43703e7	−	2.79898e8i	0.117257	−	0.603639i
$775$	4.61997e8			0.992508
$776$	9.96981e7	+	5.75607e7i	0.213355	+	0.123180i
$777$	1.21281e9	+	1.16704e8i	2.58541	+	0.248783i
$778$	−2.29131e8	−	3.96866e8i	−0.486569	−	0.842762i
$779$	2.39715e8	−	1.38399e8i	0.507087	−	0.292767i
$780$	−3.35285e7	+	1.52824e7i	−0.0706530	+	0.0322038i
$781$	−2.04004e8	+	3.53346e8i	−0.428239	+	0.741732i
$782$		−	6.26138e8i		−	1.30933i
$783$	−3.07437e7	−	3.23849e7i	−0.0640429	−	0.0674617i
$784$	1.25585e8			0.260610
$785$	−5.96236e7	−	3.44237e7i	−0.123256	−	0.0711621i
$786$	−5.80929e7	−	1.27452e8i	−0.119634	−	0.262470i
$787$	−1.70763e8	−	2.95770e8i	−0.350323	−	0.606777i	0.635983	−	0.771703i	$-0.280595\pi$
$787$	−1.70763e8	−	2.95770e8i	−0.350323	−	0.606777i	−0.986306	+	0.164926i	$0.947262\pi$
$788$	6.92881e7	−	4.00035e7i	0.141606	−	0.0817560i
$789$	−3.09344e7	+	3.21477e8i	−0.0629811	+	0.654514i
$790$	−1.16072e8	+	2.01043e8i	−0.235422	+	0.407762i
$791$		−	7.49861e8i		−	1.51513i
$792$	−4.33414e7	−	1.25821e8i	−0.0872424	−	0.253267i
$793$	−3.71940e7			−0.0745852
$794$	2.83189e8	+	1.63499e8i	0.565738	+	0.326629i
$795$	−1.69436e8	+	2.37572e8i	−0.337213	+	0.472818i
$796$	−5.25559e7	−	9.10295e7i	−0.104204	−	0.180486i
$797$	−4.58166e8	+	2.64522e8i	−0.904998	+	0.522501i	−0.878818	−	0.477156i	$-0.841667\pi$
$797$	−4.58166e8	+	2.64522e8i	−0.904998	+	0.522501i	−0.0261795	+	0.999657i	$0.508334\pi$
$798$	4.71025e8	+	3.35934e8i	0.926905	+	0.661068i
$799$	6.17106e7	−	1.06886e8i	0.120982	−	0.209546i
$800$			7.84223e7i			0.153169i
$801$	4.54753e8	+	3.95211e8i	0.884867	+	0.769009i
$802$	6.94616e8			1.34655
$803$	−3.43849e8	−	1.98522e8i	−0.664082	−	0.383408i
$804$	−2.75560e8	−	2.65160e7i	−0.530210	−	0.0510200i
$805$	1.53173e8	+	2.65303e8i	0.293626	+	0.508575i
$806$	−1.56078e8	+	9.01117e7i	−0.298083	+	0.172098i
$807$	−5.16517e6	+	2.35430e6i	−0.00982798	+	0.00447961i
$808$	−2.37556e7	+	4.11459e7i	−0.0450331	+	0.0779996i
$809$			7.38055e8i			1.39394i	0.717102	+	0.696968i	$0.245468\pi$
$809$			7.38055e8i			1.39394i	−0.717102	+	0.696968i	$0.754532\pi$
$810$	−1.91464e7	−	1.35986e8i	−0.0360273	−	0.255883i
$811$	−4.57151e8			−0.857031			−0.428516	−	0.903534i	$-0.640963\pi$
$811$	−4.57151e8			−0.857031			−0.428516	+	0.903534i	$0.640963\pi$
$812$	3.08188e7	+	1.77933e7i	0.0575636	+	0.0332344i
$813$	1.91963e7	+	4.21154e7i	0.0357228	+	0.0783735i
$814$	2.62578e8	+	4.54798e8i	0.486838	+	0.843228i
$815$	2.33724e8	−	1.34941e8i	0.431748	−	0.249270i
$816$	2.14257e7	−	2.22660e8i	0.0394334	−	0.409800i
$817$	−2.67142e8	+	4.62703e8i	−0.489864	+	0.848469i
$818$		−	1.02243e8i		−	0.186798i
$819$	2.18846e8	−	2.51817e8i	0.398370	−	0.458388i
$820$	5.23614e7			0.0949663
$821$	−1.21939e8	−	7.04014e7i	−0.220350	−	0.127219i	0.385762	−	0.922598i	$-0.373938\pi$
$821$	−1.21939e8	−	7.04014e7i	−0.220350	−	0.127219i	−0.606112	+	0.795379i	$0.707272\pi$
$822$	4.23214e7	−	5.93403e7i	0.0761982	−	0.106840i
$823$	−1.48682e8	−	2.57524e8i	−0.266721	−	0.461975i	0.701292	−	0.712874i	$-0.252607\pi$
$823$	−1.48682e8	−	2.57524e8i	−0.266721	−	0.461975i	−0.968013	+	0.250899i	$0.919274\pi$
$824$	1.29295e7	−	7.46487e6i	0.0231101	−	0.0133426i
$825$	−3.00113e8	−	2.14040e8i	−0.534470	−	0.381183i
$826$	−3.55240e8	+	6.15293e8i	−0.630350	+	1.09180i
$827$			6.71385e8i			1.18701i	0.804830	+	0.593506i	$0.202257\pi$
$827$			6.71385e8i			1.18701i	−0.804830	+	0.593506i	$0.797743\pi$
$828$	3.01747e8	−	1.03942e8i	0.531560	−	0.183105i
$829$	−4.09596e8			−0.718939			−0.359470	−	0.933157i	$-0.617042\pi$
$829$	−4.09596e8			−0.718939			−0.359470	+	0.933157i	$0.617042\pi$
$830$	4.00314e7	+	2.31121e7i	0.0700110	+	0.0404209i
$831$	3.94779e8	+	3.79879e7i	0.687940	+	0.0661976i
$832$	−1.52961e7	−	2.64937e7i	−0.0265590	−	0.0460015i
$833$	−8.59310e8	+	4.96123e8i	−1.48667	+	0.858329i
$834$	−5.67662e8	+	2.58742e8i	−0.978570	+	0.446034i
$835$	−6.14800e7	+	1.06487e8i	−0.105603	+	0.182909i
$836$			2.49363e8i			0.426789i
$837$	−1.56924e8	−	6.53097e8i	−0.267617	−	1.11378i
$838$	5.69876e7			0.0968385
$839$	−2.60725e8	−	1.50530e8i	−0.441466	−	0.254881i	0.262753	−	0.964863i	$-0.415370\pi$
$839$	−2.60725e8	−	1.50530e8i	−0.441466	−	0.254881i	−0.704219	+	0.709982i	$0.748703\pi$
$840$	4.53913e7	+	9.95855e7i	0.0765834	+	0.168019i
$841$	−2.94838e8	−	5.10675e8i	−0.495674	−	0.858532i
$842$	6.90049e8	−	3.98400e8i	1.15596	−	0.667395i
$843$	−3.38423e7	+	3.51697e8i	−0.0564908	+	0.587065i
$844$	2.67021e7	−	4.62494e7i	0.0444138	−	0.0769269i
$845$			1.80674e8i			0.299451i
$846$	6.17546e7	+	1.19959e7i	0.101990	+	0.0198116i
$847$	3.69904e8			0.608749
$848$	−2.09811e8	−	1.21135e8i	−0.344065	−	0.198646i
$849$	−4.79233e7	+	6.71948e7i	−0.0783111	+	0.109803i
$850$	−3.09806e8	−	5.36600e8i	−0.504467	−	0.873763i
$851$	−1.09070e9	+	6.29718e8i	−1.76978	+	1.02178i
$852$	−2.84602e8	−	2.02978e8i	−0.460171	−	0.328193i
$853$	1.65403e8	−	2.86486e8i	0.266499	−	0.461590i	−0.701456	−	0.712713i	$-0.747466\pi$
$853$	1.65403e8	−	2.86486e8i	0.266499	−	0.461590i	0.967955	+	0.251122i	$0.0807997\pi$
$854$			1.10473e8i			0.177370i
$855$	−4.90689e7	+	2.52606e8i	−0.0785069	+	0.404153i
$856$	1.87580e8			0.299064
$857$	6.31284e8	+	3.64472e8i	1.00296	+	0.579057i	0.909122	−	0.416530i	$-0.136754\pi$
$857$	6.31284e8	+	3.64472e8i	1.00296	+	0.579057i	0.0938349	+	0.995588i	$0.470087\pi$
$858$	1.43136e8	+	1.37734e7i	0.226615	+	0.0218062i
$859$	1.68202e7	+	2.91334e7i	0.0265370	+	0.0459634i	0.878989	−	0.476842i	$-0.158219\pi$
$859$	1.68202e7	+	2.91334e7i	0.0265370	+	0.0459634i	−0.852452	+	0.522806i	$0.824885\pi$
$860$	−8.75284e7	+	5.05346e7i	−0.137611	+	0.0794499i
$861$	−4.31396e8	+	1.96631e8i	−0.675875	+	0.308065i
$862$	1.92660e7	−	3.33698e7i	0.0300795	−	0.0520992i
$863$		−	3.65765e8i		−	0.569075i	−0.958665	−	0.284537i	$-0.908160\pi$
$863$		−	3.65765e8i		−	0.569075i	0.958665	−	0.284537i	$-0.0918400\pi$
$864$	1.10861e8	−	2.66374e7i	0.171885	−	0.0413000i
$865$	2.89877e8			0.447884
$866$	5.77133e8	+	3.33208e8i	0.888633	+	0.513052i
$867$	4.62712e8	+	1.01516e9i	0.709992	+	1.55768i
$868$	2.67647e8	+	4.63579e8i	0.409264	+	0.708867i
$869$	7.84578e8	−	4.52976e8i	1.19557	−	0.690265i
$870$	−1.51609e6	+	1.57555e7i	−0.00230232	+	0.0239262i
$871$	1.49567e8	−	2.59058e8i	0.226350	−	0.392051i
$872$		−	7.60314e7i		−	0.114668i
$873$	−1.50994e8	−	4.38339e8i	−0.226943	−	0.658821i
$874$	−5.98027e8			−0.895750
$875$	5.65541e8	+	3.26516e8i	0.844190	+	0.487393i
$876$	1.97522e8	−	2.76953e8i	0.293835	−	0.411997i
$877$	−3.66627e8	−	6.35017e8i	−0.543533	−	0.941426i	−0.998698	−	0.0510192i	$-0.983753\pi$
$877$	−3.66627e8	−	6.35017e8i	−0.543533	−	0.941426i	0.455165	−	0.890407i	$-0.349580\pi$
$878$	3.47977e8	−	2.00905e8i	0.514123	−	0.296829i
$879$	−6.46632e8	−	4.61177e8i	−0.952117	−	0.679048i
$880$	−2.35857e7	+	4.08517e7i	−0.0346100	+	0.0599462i
$881$		−	1.64762e8i		−	0.240951i	−0.992716	−	0.120475i	$-0.961558\pi$
$881$		−	1.64762e8i		−	0.240951i	0.992716	−	0.120475i	$-0.0384419\pi$
$882$	−3.81741e8	−	3.31758e8i	−0.556369	−	0.483522i
$883$	4.55533e8			0.661665			0.330832	−	0.943690i	$-0.392671\pi$
$883$	4.55533e8			0.661665			0.330832	+	0.943690i	$0.392671\pi$
$884$	2.09326e8	+	1.20854e8i	0.303016	+	0.174946i
$885$	−3.14556e8	−	3.02685e7i	−0.453804	−	0.0436677i
$886$	−5.97969e7	−	1.03571e8i	−0.0859760	−	0.148915i
$887$	−9.00541e8	+	5.19928e8i	−1.29043	+	0.745027i	−0.978730	−	0.205155i	$-0.934230\pi$
$887$	−9.00541e8	+	5.19928e8i	−1.29043	+	0.745027i	−0.311696	+	0.950182i	$0.600897\pi$
$888$	−4.09412e8	+	1.86611e8i	−0.584685	+	0.266501i
$889$	2.32663e8	−	4.02984e8i	0.331148	−	0.573564i
$890$		−	2.13562e8i		−	0.302938i
$891$	−2.00638e8	+	4.96954e8i	−0.283648	+	0.702559i
$892$	3.61832e8			0.509815
$893$	−1.02087e8	−	5.89401e7i	−0.143356	−	0.0827669i
$894$	−2.33121e8	−	5.11453e8i	−0.326264	−	0.715803i
$895$	−2.12821e8	−	3.68617e8i	−0.296856	−	0.514169i
$896$	−7.86909e7	+	4.54322e7i	−0.109396	+	0.0631596i
$897$	−3.30317e7	+	3.43272e8i	−0.0457671	+	0.475622i
$898$	1.55210e8	−	2.68832e8i	0.214334	−	0.371237i
$899$			7.74178e7i			0.106552i
$900$	2.07168e8	−	2.38380e8i	0.284181	−	0.326996i
$901$	1.91416e9			2.61700
$902$	−1.76966e8	−	1.02171e8i	−0.241140	−	0.139222i
$903$	5.31360e8	−	7.45038e8i	0.721648	−	1.01185i
$904$	1.38454e8	+	2.39810e8i	0.187414	+	0.324610i
$905$	−5.10315e7	+	2.94631e7i	−0.0688482	+	0.0397495i
$906$	8.30014e7	+	5.91965e7i	0.111609	+	0.0795997i
$907$	3.58121e8	−	6.20284e8i	0.479963	−	0.831321i	−0.519773	−	0.854305i	$-0.673983\pi$
$907$	3.58121e8	−	6.20284e8i	0.479963	−	0.831321i	0.999736	+	0.0229839i	$0.00731665\pi$
$908$			4.90446e8i			0.655139i
$909$	1.80905e8	−	6.23158e7i	0.240856	−	0.0829672i
$910$	−1.18259e8			−0.156931
$911$	7.52640e8	+	4.34537e8i	0.995479	+	0.574740i	0.906907	−	0.421330i	$-0.138437\pi$
$911$	7.52640e8	+	4.34537e8i	0.995479	+	0.574740i	0.0885714	+	0.996070i	$0.471770\pi$
$912$	−2.12664e8	−	2.04638e7i	−0.280355	−	0.0269774i
$913$	−9.01961e7	−	1.56224e8i	−0.118516	−	0.205275i
$914$	−9.62968e7	+	5.55970e7i	−0.126117	+	0.0728137i
$915$	−4.47109e7	+	2.03793e7i	−0.0583646	+	0.0266027i
$916$	2.03368e7	−	3.52244e7i	0.0264604	−	0.0458308i
$917$		−	4.49538e8i		−	0.582986i
$918$	−6.53328e8	+	6.20218e8i	−0.844507	+	0.801708i
$919$	6.50303e8			0.837855			0.418928	−	0.908020i	$-0.362406\pi$
$919$	6.50303e8			0.837855			0.418928	+	0.908020i	$0.362406\pi$
$920$	−9.79712e7	−	5.65637e7i	−0.125816	−	0.0726398i
$921$	−4.28117e8	−	9.39261e8i	−0.548004	−	1.20229i
$922$	−1.62342e8	−	2.81185e8i	−0.207128	−	0.358756i
$923$	3.27123e8	−	1.88864e8i	0.416012	−	0.240185i
$924$	4.09095e7	−	4.25140e8i	0.0518571	−	0.538910i
$925$	−6.23155e8	+	1.07934e9i	−0.787356	+	1.36374i
$926$			5.72559e8i			0.721087i
$927$	−5.90218e7	−	1.14650e7i	−0.0740923	−	0.0143925i
$928$	−1.31414e7			−0.0164436
$929$	−2.94052e8	−	1.69771e8i	−0.366755	−	0.211746i	0.305285	−	0.952261i	$-0.401248\pi$
$929$	−2.94052e8	−	1.69771e8i	−0.366755	−	0.211746i	−0.672040	+	0.740515i	$0.734582\pi$
$930$	−1.38247e8	+	1.93842e8i	−0.171873	+	0.240989i
$931$	4.73849e8	+	8.20731e8i	0.587207	+	1.01707i
$932$	−4.04237e7	+	2.33387e7i	−0.0499331	+	0.0288289i
$933$	1.61966e7	+	1.15514e7i	0.0199425	+	0.0142229i
$934$	−3.57587e8	+	6.19359e8i	−0.438875	+	0.760154i
$935$		−	3.72700e8i		−	0.455957i
$936$	−2.34927e7	+	1.20940e8i	−0.0286488	+	0.147484i
$937$	−1.59228e9			−1.93554			−0.967769	−	0.251838i	$-0.918965\pi$
$937$	−1.59228e9			−1.93554			−0.967769	+	0.251838i	$0.918965\pi$
$938$	−7.69446e8	−	4.44240e8i	−0.932331	−	0.538281i
$939$	−3.83124e8	−	3.68664e7i	−0.462746	−	0.0445281i
$940$	−1.11496e7	−	1.93116e7i	−0.0134238	−	0.0232506i
$941$	1.17773e9	−	6.79964e8i	1.41344	−	0.816051i	0.417730	−	0.908571i	$-0.362826\pi$
$941$	1.17773e9	−	6.79964e8i	1.41344	−	0.816051i	0.995711	+	0.0925206i	$0.0294924\pi$
$942$	−2.09464e8	+	9.54739e7i	−0.250586	+	0.114217i
$943$	2.45029e8	−	4.24403e8i	0.292202	−	0.506108i
$944$		−	2.62366e8i		−	0.311883i
$945$	1.25099e8	−	4.22619e8i	0.148238	−	0.500788i
$946$	3.94427e8			0.465900
$947$	2.77528e8	+	1.60231e8i	0.326781	+	0.188667i	0.654411	−	0.756139i	$-0.272917\pi$
$947$	2.77528e8	+	1.60231e8i	0.326781	+	0.188667i	−0.327630	+	0.944806i	$0.606250\pi$
$948$	3.21925e8	+	7.06283e8i	0.377859	+	0.828998i
$949$	1.83789e8	+	3.18331e8i	0.215040	+	0.372461i
$950$	−5.12509e8	+	2.95897e8i	−0.597765	+	0.345120i
$951$	−1.37351e8	+	1.42738e9i	−0.159694	+	1.65958i
$952$	3.58958e8	−	6.21734e8i	0.416038	−	0.720599i
$953$			6.65905e8i			0.769367i	0.923049	+	0.384683i	$0.125689\pi$
$953$			6.65905e8i			0.769367i	−0.923049	+	0.384683i	$0.874311\pi$
$954$	3.17761e8	+	9.22469e8i	0.365978	+	1.06245i
$955$	3.30492e8			0.379446
$956$	1.39260e8	+	8.04019e7i	0.159387	+	0.0920222i
$957$	3.58672e7	−	5.02906e7i	0.0409224	−	0.0573787i
$958$	1.88665e8	+	3.26777e8i	0.214582	+	0.371668i
$959$	2.02584e8	−	1.16962e8i	0.229694	−	0.132614i
$960$	−3.29039e7	−	2.34670e7i	−0.0371906	−	0.0265243i
$961$	−1.38511e8	+	2.39907e8i	−0.156068	+	0.270317i
$962$		−	4.86182e8i		−	0.546101i
$963$	−5.70184e8	−	4.95528e8i	−0.638464	−	0.554868i
$964$	−1.64316e8			−0.183421
$965$	−1.84998e8	−	1.06809e8i	−0.205867	−	0.118857i
$966$	1.01958e9	+	9.81098e7i	1.13107	+	0.108838i
$967$	−1.79185e8	−	3.10357e8i	−0.198163	−	0.343228i	0.749770	−	0.661698i	$-0.230164\pi$
$967$	−1.79185e8	−	3.10357e8i	−0.198163	−	0.343228i	−0.947933	+	0.318471i	$0.896831\pi$
$968$	−1.18298e8	+	6.82991e7i	−0.130422	+	0.0752990i
$969$	1.53598e9	−	7.00102e8i	1.68816	−	0.769467i
$970$	−8.21684e7	+	1.42320e8i	−0.0900304	+	0.155937i
$971$		−	3.10565e8i		−	0.339230i	−0.985510	−	0.169615i	$-0.945748\pi$
$971$		−	3.10565e8i		−	0.339230i	0.985510	−	0.169615i	$-0.0542525\pi$
$972$	−4.07351e8	−	2.11891e8i	−0.443578	−	0.230735i
$973$	−2.00221e9			−2.17356
$974$	−3.41777e8	−	1.97325e8i	−0.369884	−	0.213553i
$975$	1.41539e8	+	3.10528e8i	0.152708	+	0.335032i
$976$	−2.03977e7	−	3.53298e7i	−0.0219397	−	0.0380007i
$977$	−1.19157e9	+	6.87955e8i	−1.27772	+	0.737694i	−0.976430	−	0.215837i	$-0.930752\pi$
$977$	−1.19157e9	+	6.87955e8i	−1.27772	+	0.737694i	−0.301295	+	0.953531i	$0.597419\pi$
$978$	8.64318e7	−	8.98218e8i	0.0923968	−	0.960207i
$979$	−4.16718e8	+	7.21776e8i	−0.444113	+	0.769227i
$980$			1.79274e8i			0.190475i
$981$	−2.00852e8	+	2.31112e8i	−0.212750	+	0.244802i
$982$	−6.02884e8			−0.636648
$983$	−4.88903e8	−	2.82268e8i	−0.514709	−	0.297168i	0.220058	−	0.975487i	$-0.429375\pi$
$983$	−4.88903e8	−	2.82268e8i	−0.514709	−	0.297168i	−0.734767	+	0.678319i	$0.762709\pi$
$984$	1.01657e8	−	1.42537e8i	0.106697	−	0.149603i
$985$	5.71053e7	+	9.89093e7i	0.0597541	+	0.103497i
$986$	8.99192e7	−	5.19149e7i	0.0938040	−	0.0541578i
$987$	1.64379e8	+	1.17235e8i	0.170961	+	0.121929i
$988$	1.15428e8	−	1.99928e8i	0.119686	−	0.207302i
$989$			9.45922e8i			0.977836i
$990$	1.79611e8	−	6.18702e7i	0.185109	−	0.0637641i
$991$	1.94100e8			0.199436			0.0997182	−	0.995016i	$-0.468206\pi$
$991$	1.94100e8			0.199436			0.0997182	+	0.995016i	$0.468206\pi$
$992$	−1.71191e8	−	9.88369e7i	−0.175366	−	0.101248i
$993$	−1.36949e9	−	1.31780e8i	−1.39866	−	0.134587i
$994$	−5.60960e8	−	9.71612e8i	−0.571180	−	0.989313i
$995$	1.29945e8	−	7.50239e7i	0.131914	−	0.0761606i
$996$	1.40634e8	−	6.41013e7i	0.142335	−	0.0648767i
$997$	−2.08285e7	+	3.60761e7i	−0.0210171	+	0.0364027i	−0.876343	−	0.481688i	$-0.840024\pi$
$997$	−2.08285e7	+	3.60761e7i	−0.0210171	+	0.0364027i	0.855326	+	0.518091i	$0.173357\pi$
$998$			7.64322e8i			0.768926i
$999$	1.73746e9	+	5.14303e8i	1.74268	+	0.515849i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	18.7.d.a.11.2	yes	12
3.2	odd	2		54.7.d.a.35.6		12
4.3	odd	2		144.7.q.c.65.3		12
9.2	odd	6		162.7.b.c.161.5		12
9.4	even	3		54.7.d.a.17.6		12
9.5	odd	6	inner	18.7.d.a.5.2	✓	12
9.7	even	3		162.7.b.c.161.8		12
12.11	even	2		432.7.q.b.305.5		12
36.23	even	6		144.7.q.c.113.3		12
36.31	odd	6		432.7.q.b.17.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
18.7.d.a.5.2	✓	12	9.5	odd	6	inner
18.7.d.a.11.2	yes	12	1.1	even	1	trivial
54.7.d.a.17.6		12	9.4	even	3
54.7.d.a.35.6		12	3.2	odd	2
144.7.q.c.65.3		12	4.3	odd	2
144.7.q.c.113.3		12	36.23	even	6
162.7.b.c.161.5		12	9.2	odd	6
162.7.b.c.161.8		12	9.7	even	3
432.7.q.b.17.5		12	36.31	odd	6
432.7.q.b.305.5		12	12.11	even	2

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)

\(f(q)\)	\(=\)	\(q+(-4.89898 - 2.82843i) q^{2} +(-11.1983 - 24.5683i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-39.5602 + 22.8401i) q^{5} +(-14.6295 + 152.033i) q^{6} +(-245.097 + 424.521i) q^{7} -181.019i q^{8} +(-478.198 + 550.243i) q^{9} +O(q^{10})\)	\(q+(-4.89898 - 2.82843i) q^{2} +(-11.1983 - 24.5683i) q^{3} +(16.0000 + 27.7128i) q^{4} +(-39.5602 + 22.8401i) q^{5} +(-14.6295 + 152.033i) q^{6} +(-245.097 + 424.521i) q^{7} -181.019i q^{8} +(-478.198 + 550.243i) q^{9} +258.406 q^{10} +(-873.336 - 504.221i) q^{11} +(501.683 - 703.427i) q^{12} +(466.801 + 808.523i) q^{13} +(2401.45 - 1386.48i) q^{14} +(1004.15 + 716.156i) q^{15} +(-512.000 + 886.810i) q^{16} -8090.59i q^{17} +(3899.01 - 1343.08i) q^{18} -7727.36 q^{19} +(-1265.93 - 730.884i) q^{20} +(13174.4 + 1267.72i) q^{21} +(2852.30 + 4940.34i) q^{22} +(-11848.0 + 6840.45i) q^{23} +(-4447.33 + 2027.10i) q^{24} +(-6769.16 + 11724.5i) q^{25} -5281.25i q^{26} +(18873.5 + 5586.73i) q^{27} -15686.2 q^{28} +(-1964.70 - 1134.32i) q^{29} +(-2893.70 - 6348.59i) q^{30} +(-17062.6 - 29553.2i) q^{31} +(5016.55 - 2896.31i) q^{32} +(-2607.99 + 27102.7i) q^{33} +(-22883.6 + 39635.6i) q^{34} -22392.2i q^{35} +(-22900.0 - 4448.33i) q^{36} +92058.0 q^{37} +(37856.2 + 21856.3i) q^{38} +(14636.6 - 20522.5i) q^{39} +(4134.50 + 7161.17i) q^{40} +(-31021.6 + 17910.3i) q^{41} +(-60955.5 - 43473.4i) q^{42} +(34570.9 - 59878.5i) q^{43} -32270.1i q^{44} +(6350.01 - 32689.8i) q^{45} +77390.9 q^{46} +(13211.1 + 7627.46i) q^{47} +(27520.9 + 2648.22i) q^{48} +(-61321.0 - 106211. i) q^{49} +(66323.9 - 38292.1i) q^{50} +(-198772. + 90600.5i) q^{51} +(-14937.6 + 25872.7i) q^{52} +236591. i q^{53} +(-76659.2 - 80751.6i) q^{54} +46065.9 q^{55} +(76846.5 + 44367.4i) q^{56} +(86533.0 + 189848. i) q^{57} +(6416.70 + 11114.0i) q^{58} +(-221890. + 128108. i) q^{59} +(-3780.35 + 39286.2i) q^{60} +(-19919.6 + 34501.8i) q^{61} +193041. i q^{62} +(-116385. - 337868. i) q^{63} -32768.0 q^{64} +(-36933.5 - 21323.6i) q^{65} +(89434.6 - 125399. i) q^{66} +(-160204. - 277482. i) q^{67} +(224213. - 129449. i) q^{68} +(300735. + 214484. i) q^{69} +(-63334.7 + 109699. i) q^{70} -404593. i q^{71} +(99604.7 + 86563.1i) q^{72} +393719. q^{73} +(-450990. - 260379. i) q^{74} +(363854. + 35012.2i) q^{75} +(-123638. - 214147. i) q^{76} +(428105. - 247167. i) q^{77} +(-129751. + 59140.8i) q^{78} +(-449184. + 778010. i) q^{79} -46776.5i q^{80} +(-74094.1 - 526251. i) q^{81} +202632. q^{82} +(154916. + 89441.0i) q^{83} +(175658. + 385383. i) q^{84} +(184790. + 320066. i) q^{85} +(-338724. + 195562. i) q^{86} +(-5867.06 + 60971.8i) q^{87} +(-91273.8 + 158091. i) q^{88} -826458. i q^{89} +(-123569. + 142186. i) q^{90} -457647. q^{91} +(-379136. - 218894. i) q^{92} +(-535000. + 750142. i) q^{93} +(-43147.4 - 74733.5i) q^{94} +(305696. - 176494. i) q^{95} +(-127334. - 90814.4i) q^{96} +(-317981. + 550760. i) q^{97} +693768. i q^{98} +(695072. - 239430. 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