LMFDB - Embedded newform 81.7.d.b.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,7,Mod(26,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("81.26");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	81.d (of order $6$, degree $2$, not 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:	$18.6343807732$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	81.26
Dual form			81.7.d.b.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.19615 - 3.00000i) q^{2} +(-14.0000 - 24.2487i) q^{4} +(-207.846 + 120.000i) q^{5} +(-149.500 + 258.942i) q^{7} +552.000i q^{8} +1440.00 q^{10} +(540.400 + 312.000i) q^{11} +(-1247.50 - 2160.73i) q^{13} +(1553.65 - 897.000i) q^{14} +(760.000 - 1316.36i) q^{16} +1872.00i q^{17} -2509.00 q^{19} +(5819.69 + 3360.00i) q^{20} +(-1872.00 - 3242.40i) q^{22} +(-12429.2 + 7176.00i) q^{23} +(20987.5 - 36351.4i) q^{25} +14970.0i q^{26} +8372.00 q^{28} +(-20535.2 - 11856.0i) q^{29} +(-2665.00 - 4615.92i) q^{31} +(22696.8 - 13104.0i) q^{32} +(5616.00 - 9727.20i) q^{34} -71760.0i q^{35} +32591.0 q^{37} +(13037.1 + 7527.00i) q^{38} +(-66240.0 - 114731. i) q^{40} +(57282.4 - 33072.0i) q^{41} +(35315.0 - 61167.4i) q^{43} -17472.0i q^{44} +86112.0 q^{46} +(-3450.25 - 1992.00i) q^{47} +(14124.0 + 24463.5i) q^{49} +(-218108. + 125925. i) q^{50} +(-34930.0 + 60500.5i) q^{52} +190944. i q^{53} -149760. q^{55} +(-142936. - 82524.0i) q^{56} +(71136.0 + 123211. i) q^{58} +(205560. - 118680. i) q^{59} +(30900.5 - 53521.2i) q^{61} +31980.0i q^{62} -254528. q^{64} +(518576. + 299400. i) q^{65} +(215130. + 372617. i) q^{67} +(45393.6 - 26208.0i) q^{68} +(-215280. + 372876. i) q^{70} -251712. i q^{71} +251615. q^{73} +(-169348. - 97773.0i) q^{74} +(35126.0 + 60840.0i) q^{76} +(-161580. + 93288.0i) q^{77} +(-330414. + 572293. i) q^{79} +364800. i q^{80} -396864. q^{82} +(-690964. - 398928. i) q^{83} +(-224640. - 389088. i) q^{85} +(-367004. + 211890. i) q^{86} +(-172224. + 298301. i) q^{88} -270576. i q^{89} +746005. q^{91} +(348018. + 200928. i) q^{92} +(11952.0 + 20701.5i) q^{94} +(521486. - 301080. i) q^{95} +(-110364. + 191155. i) q^{97} -169488. i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 56 q^{4} - 598 q^{7} + 5760 q^{10} - 4990 q^{13} + 3040 q^{16} - 10036 q^{19} - 7488 q^{22} + 83950 q^{25} + 33488 q^{28} - 10660 q^{31} + 22464 q^{34} + 130364 q^{37} - 264960 q^{40} + 141260 q^{43}+ \cdots - 441454 q^{97}+O(q^{100}) $ 4 * q - 56 * q^4 - 598 * q^7 + 5760 * q^10 - 4990 * q^13 + 3040 * q^16 - 10036 * q^19 - 7488 * q^22 + 83950 * q^25 + 33488 * q^28 - 10660 * q^31 + 22464 * q^34 + 130364 * q^37 - 264960 * q^40 + 141260 * q^43 + 344448 * q^46 + 56496 * q^49 - 139720 * q^52 - 599040 * q^55 + 284544 * q^58 + 123602 * q^61 - 1018112 * q^64 + 860522 * q^67 - 861120 * q^70 + 1006460 * q^73 + 140504 * q^76 - 1321654 * q^79 - 1587456 * q^82 - 898560 * q^85 - 688896 * q^88 + 2984020 * q^91 + 47808 * q^94 - 441454 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−5.19615	−	3.00000i	−0.649519	−	0.375000i	0.138753	−	0.990327i	$-0.455691\pi$
$2$	−5.19615	−	3.00000i	−0.649519	−	0.375000i	−0.788272	+	0.615327i	$0.789024\pi$
$3$		0			0
$3$		0			0
$4$	−14.0000	−	24.2487i	−0.218750	−	0.378886i
$5$	−207.846	+	120.000i	−1.66277	+	0.960000i	−0.691384	+	0.722487i	$0.742999\pi$
$5$	−207.846	+	120.000i	−1.66277	+	0.960000i	−0.971384	+	0.237513i	$0.923668\pi$
$6$		0			0
$7$	−149.500	+	258.942i	−0.435860	+	0.754932i	−0.997365	−	0.0725413i	$-0.976889\pi$
$7$	−149.500	+	258.942i	−0.435860	+	0.754932i	0.561505	+	0.827473i	$0.310222\pi$
$8$			552.000i			1.07812i
$9$		0			0
$10$	1440.00			1.44000
$11$	540.400	+	312.000i	0.406010	+	0.234410i	0.689074	−	0.724691i	$-0.258017\pi$
$11$	540.400	+	312.000i	0.406010	+	0.234410i	−0.283064	+	0.959101i	$0.591351\pi$
$12$		0			0
$13$	−1247.50	−	2160.73i	−0.567820	−	0.983493i	−0.996781	−	0.0801699i	$-0.974454\pi$
$13$	−1247.50	−	2160.73i	−0.567820	−	0.983493i	0.428961	−	0.903323i	$-0.358880\pi$
$14$	1553.65	−	897.000i	0.566199	−	0.326895i
$15$		0			0
$16$	760.000	−	1316.36i	0.185547	−	0.321377i
$17$			1872.00i			0.381030i	0.981684	+	0.190515i	$0.0610158\pi$
$17$			1872.00i			0.381030i	−0.981684	+	0.190515i	$0.938984\pi$
$18$		0			0
$19$	−2509.00			−0.365797			−0.182898	−	0.983132i	$-0.558548\pi$
$19$	−2509.00			−0.365797			−0.182898	+	0.983132i	$0.558548\pi$
$20$	5819.69	+	3360.00i	0.727461	+	0.420000i
$21$		0			0
$22$	−1872.00	−	3242.40i	−0.175808	−	0.304508i
$23$	−12429.2	+	7176.00i	−1.02155	+	0.589792i	−0.914552	−	0.404467i	$-0.867457\pi$
$23$	−12429.2	+	7176.00i	−1.02155	+	0.589792i	−0.106997	+	0.994259i	$0.534124\pi$
$24$		0			0
$25$	20987.5	−	36351.4i	1.34320	−	2.32649i
$26$			14970.0i			0.851730i
$27$		0			0
$28$	8372.00			0.381378
$29$	−20535.2	−	11856.0i	−0.841986	−	0.486121i	0.0159529	−	0.999873i	$-0.494922\pi$
$29$	−20535.2	−	11856.0i	−0.841986	−	0.486121i	−0.857939	+	0.513752i	$0.828255\pi$
$30$		0			0
$31$	−2665.00	−	4615.92i	−0.0894565	−	0.154943i	0.817825	−	0.575467i	$-0.195180\pi$
$31$	−2665.00	−	4615.92i	−0.0894565	−	0.154943i	−0.907282	+	0.420524i	$0.861846\pi$
$32$	22696.8	−	13104.0i	0.692651	−	0.399902i
$33$		0			0
$34$	5616.00	−	9727.20i	0.142886	−	0.247486i
$35$		−	71760.0i		−	1.67370i
$36$		0			0
$37$	32591.0			0.643417			0.321708	−	0.946839i	$-0.395743\pi$
$37$	32591.0			0.643417			0.321708	+	0.946839i	$0.395743\pi$
$38$	13037.1	+	7527.00i	0.237592	+	0.137174i
$39$		0			0
$40$	−66240.0	−	114731.i	−1.03500	−	1.79267i
$41$	57282.4	−	33072.0i	0.831131	−	0.479854i	−0.0231087	−	0.999733i	$-0.507356\pi$
$41$	57282.4	−	33072.0i	0.831131	−	0.479854i	0.854240	+	0.519879i	$0.174023\pi$
$42$		0			0
$43$	35315.0	−	61167.4i	0.444175	−	0.769333i	−0.553820	−	0.832637i	$-0.686830\pi$
$43$	35315.0	−	61167.4i	0.444175	−	0.769333i	0.997994	+	0.0633035i	$0.0201636\pi$
$44$		−	17472.0i		−	0.205109i
$45$		0			0
$46$	86112.0			0.884688
$47$	−3450.25	−	1992.00i	−0.0332320	−	0.0191865i	0.483292	−	0.875459i	$-0.339441\pi$
$47$	−3450.25	−	1992.00i	−0.0332320	−	0.0191865i	−0.516524	+	0.856273i	$0.672774\pi$
$48$		0			0
$49$	14124.0	+	24463.5i	0.120052	+	0.207936i
$50$	−218108.	+	125925.i	−1.74487	+	1.00740i
$51$		0			0
$52$	−34930.0	+	60500.5i	−0.248421	+	0.430278i
$53$			190944.i			1.28256i	0.767306	+	0.641281i	$0.221597\pi$
$53$			190944.i			1.28256i	−0.767306	+	0.641281i	$0.778403\pi$
$54$		0			0
$55$	−149760.			−0.900135
$56$	−142936.	−	82524.0i	−0.813911	−	0.469912i
$57$		0			0
$58$	71136.0	+	123211.i	0.364591	+	0.631489i
$59$	205560.	−	118680.i	1.00088	−	0.577858i	0.0923717	−	0.995725i	$-0.470555\pi$
$59$	205560.	−	118680.i	1.00088	−	0.577858i	0.908509	+	0.417866i	$0.137222\pi$
$60$		0			0
$61$	30900.5	−	53521.2i	0.136137	−	0.235796i	−0.789894	−	0.613243i	$-0.789865\pi$
$61$	30900.5	−	53521.2i	0.136137	−	0.235796i	0.926031	+	0.377447i	$0.123198\pi$
$62$			31980.0i			0.134185i
$63$		0			0
$64$	−254528.			−0.970947
$65$	518576.	+	299400.i	1.88831	+	1.09021i
$66$		0			0
$67$	215130.	+	372617.i	0.715282	+	1.23891i	0.962850	+	0.270035i	$0.0870353\pi$
$67$	215130.	+	372617.i	0.715282	+	1.23891i	−0.247568	+	0.968871i	$0.579631\pi$
$68$	45393.6	−	26208.0i	0.144367	−	0.0833503i
$69$		0			0
$70$	−215280.	+	372876.i	−0.627638	+	1.08710i
$71$		−	251712.i		−	0.703281i	−0.936135	−	0.351640i	$-0.885624\pi$
$71$		−	251712.i		−	0.703281i	0.936135	−	0.351640i	$-0.114376\pi$
$72$		0			0
$73$	251615.			0.646797			0.323398	−	0.946263i	$-0.395175\pi$
$73$	251615.			0.646797			0.323398	+	0.946263i	$0.395175\pi$
$74$	−169348.	−	97773.0i	−0.417912	−	0.241281i
$75$		0			0
$76$	35126.0	+	60840.0i	0.0800180	+	0.138595i
$77$	−161580.	+	93288.0i	−0.353927	+	0.204340i
$78$		0			0
$79$	−330414.	+	572293.i	−0.670157	+	1.16075i	0.307702	+	0.951483i	$0.400440\pi$
$79$	−330414.	+	572293.i	−0.670157	+	1.16075i	−0.977859	+	0.209263i	$0.932893\pi$
$80$			364800.i			0.712500i
$81$		0			0
$82$	−396864.			−0.719781
$83$	−690964.	−	398928.i	−1.20843	−	0.697686i	−0.246012	−	0.969267i	$-0.579120\pi$
$83$	−690964.	−	398928.i	−1.20843	−	0.697686i	−0.962416	+	0.271580i	$0.912454\pi$
$84$		0			0
$85$	−224640.	−	389088.i	−0.365789	−	0.633565i
$86$	−367004.	+	211890.i	−0.577000	+	0.333131i
$87$		0			0
$88$	−172224.	+	298301.i	−0.252724	+	0.437730i
$89$		−	270576.i		−	0.383813i	−0.981413	−	0.191906i	$-0.938533\pi$
$89$		−	270576.i		−	0.383813i	0.981413	−	0.191906i	$-0.0614670\pi$
$90$		0			0
$91$	746005.			0.989960
$92$	348018.	+	200928.i	0.446928	+	0.258034i
$93$		0			0
$94$	11952.0	+	20701.5i	0.0143899	+	0.0249240i
$95$	521486.	−	301080.i	0.608235	−	0.351165i
$96$		0			0
$97$	−110364.	+	191155.i	−0.120923	+	0.209445i	−0.920132	−	0.391608i	$-0.871919\pi$
$97$	−110364.	+	191155.i	−0.120923	+	0.209445i	0.799209	+	0.601054i	$0.205252\pi$
$98$		−	169488.i		−	0.180078i
$99$		0			0
$100$	−1.17530e6			−1.17530
$101$	−250746.	−	144768.i	−0.243371	−	0.140510i	0.373354	−	0.927689i	$-0.378208\pi$
$101$	−250746.	−	144768.i	−0.243371	−	0.140510i	−0.616725	+	0.787179i	$0.711541\pi$
$102$		0			0
$103$	297102.	+	514597.i	0.271891	+	0.470929i	0.969346	−	0.245700i	$-0.0790177\pi$
$103$	297102.	+	514597.i	0.271891	+	0.470929i	−0.697455	+	0.716628i	$0.745684\pi$
$104$	1.19272e6	−	688620.i	1.06033	−	0.612181i
$105$		0			0
$106$	572832.	−	992174.i	0.480961	−	0.833049i
$107$		−	1.99368e6i		−	1.62744i	−0.581259	−	0.813718i	$-0.697440\pi$
$107$		−	1.99368e6i		−	1.62744i	0.581259	−	0.813718i	$-0.302560\pi$
$108$		0			0
$109$	1.51135e6			1.16704			0.583521	−	0.812098i	$-0.301674\pi$
$109$	1.51135e6			1.16704			0.583521	+	0.812098i	$0.301674\pi$
$110$	778176.	+	449280.i	0.584655	+	0.337551i
$111$		0			0
$112$	227240.	+	393591.i	0.161745	+	0.280150i
$113$	−1.42936e6	+	825240.i	−0.990617	+	0.571933i	−0.905459	−	0.424435i	$-0.860473\pi$
$113$	−1.42936e6	+	825240.i	−0.990617	+	0.571933i	−0.0851580	+	0.996367i	$0.527140\pi$
$114$		0			0
$115$	1.72224e6	−	2.98301e6i	1.13240	−	1.96138i
$116$			663936.i			0.425356i
$117$		0			0
$118$	−1.42416e6			−0.866788
$119$	−484739.	−	279864.i	−0.287652	−	0.166076i
$120$		0			0
$121$	−691092.	−	1.19701e6i	−0.390104	−	0.675679i
$122$	−321127.	+	185403.i	−0.176847	+	0.102103i
$123$		0			0
$124$	−74620.0	+	129246.i	−0.0391372	+	0.0677877i
$125$			6.32400e6i			3.23789i
$126$		0			0
$127$	1.41135e6			0.689005			0.344502	−	0.938785i	$-0.388048\pi$
$127$	1.41135e6			0.689005			0.344502	+	0.938785i	$0.388048\pi$
$128$	−130029.	−	75072.0i	−0.0620024	−	0.0357971i
$129$		0			0
$130$	−1.79640e6	−	3.11146e6i	−0.817660	−	1.41623i
$131$	−279927.	+	161616.i	−0.124518	+	0.0718903i	−0.560965	−	0.827839i	$-0.689570\pi$
$131$	−279927.	+	161616.i	−0.124518	+	0.0718903i	0.436447	+	0.899730i	$0.356236\pi$
$132$		0			0
$133$	375096.	−	649684.i	0.159436	−	0.276152i
$134$		−	2.58157e6i		−	1.07292i
$135$		0			0
$136$	−1.03334e6			−0.410798
$137$	1.85195e6	+	1.06922e6i	0.720224	+	0.415822i	0.814835	−	0.579693i	$-0.196827\pi$
$137$	1.85195e6	+	1.06922e6i	0.720224	+	0.415822i	−0.0946111	+	0.995514i	$0.530161\pi$
$138$		0			0
$139$	55614.5	+	96327.1i	0.0207083	+	0.0358678i	0.876194	−	0.481959i	$-0.160075\pi$
$139$	55614.5	+	96327.1i	0.0207083	+	0.0358678i	−0.855486	+	0.517827i	$0.826741\pi$
$140$	−1.74009e6	+	1.00464e6i	−0.634143	+	0.366122i
$141$		0			0
$142$	−755136.	+	1.30793e6i	−0.263730	+	0.456794i
$143$		−	1.55688e6i		−	0.532411i
$144$		0			0
$145$	5.69088e6			1.86670
$146$	−1.30743e6	−	754845.i	−0.420107	−	0.242549i
$147$		0			0
$148$	−456274.	−	790290.i	−0.140747	−	0.243782i
$149$	2.97619e6	−	1.71830e6i	0.899708	−	0.519447i	0.0226029	−	0.999745i	$-0.492805\pi$
$149$	2.97619e6	−	1.71830e6i	0.899708	−	0.519447i	0.877106	+	0.480298i	$0.159471\pi$
$150$		0			0
$151$	1.96966e6	−	3.41156e6i	0.572086	−	0.990881i	−0.424266	−	0.905538i	$-0.639468\pi$
$151$	1.96966e6	−	3.41156e6i	0.572086	−	0.990881i	0.996352	−	0.0853436i	$-0.0271988\pi$
$152$		−	1.38497e6i		−	0.394375i
$153$		0			0
$154$	1.11946e6			0.306510
$155$	1.10782e6	+	639600.i	0.297491	+	0.171757i
$156$		0			0
$157$	−215533.	−	373314.i	−0.0556948	−	0.0964663i	0.836834	−	0.547457i	$-0.184404\pi$
$157$	−215533.	−	373314.i	−0.0556948	−	0.0964663i	−0.892529	+	0.450991i	$0.851071\pi$
$158$	3.43376e6	−	1.98248e6i	0.870559	−	0.502618i
$159$		0			0
$160$	−3.14496e6	+	5.44723e6i	−0.767813	+	1.32989i
$161$		−	4.29125e6i		−	1.02827i
$162$		0			0
$163$	−7.94353e6			−1.83422			−0.917109	−	0.398637i	$-0.869483\pi$
$163$	−7.94353e6			−1.83422			−0.917109	+	0.398637i	$0.869483\pi$
$164$	−1.60391e6	−	926016.i	−0.363620	−	0.209936i
$165$		0			0
$166$	2.39357e6	+	4.14578e6i	0.523265	+	0.906321i
$167$	−3.06428e6	+	1.76916e6i	−0.657928	+	0.379855i	−0.791487	−	0.611186i	$-0.790693\pi$
$167$	−3.06428e6	+	1.76916e6i	−0.657928	+	0.379855i	0.133559	+	0.991041i	$0.457359\pi$
$168$		0			0
$169$	−699108.	+	1.21089e6i	−0.144839	+	0.250868i
$170$			2.69568e6i			0.548683i
$171$		0			0
$172$	−1.97764e6			−0.388653
$173$	−1.53149e6	−	884208.i	−0.295785	−	0.170772i	0.344763	−	0.938690i	$-0.387959\pi$
$173$	−1.53149e6	−	884208.i	−0.295785	−	0.170772i	−0.640548	+	0.767918i	$0.721293\pi$
$174$		0			0
$175$	6.27526e6	+	1.08691e7i	1.17089	+	2.02805i
$176$	821408.	−	474240.i	0.150668	−	0.0869882i
$177$		0			0
$178$	−811728.	+	1.40595e6i	−0.143930	+	0.249294i
$179$			3.82637e6i			0.667156i	0.942722	+	0.333578i	$0.108256\pi$
$179$			3.82637e6i			0.667156i	−0.942722	+	0.333578i	$0.891744\pi$
$180$		0			0
$181$	−2.32721e6			−0.392464			−0.196232	−	0.980558i	$-0.562871\pi$
$181$	−2.32721e6			−0.392464			−0.196232	+	0.980558i	$0.562871\pi$
$182$	−3.87636e6	−	2.23802e6i	−0.642998	−	0.371235i
$183$		0			0
$184$	−3.96115e6	−	6.86092e6i	−0.635870	−	1.10136i
$185$	−6.77391e6	+	3.91092e6i	−1.06985	+	0.617680i
$186$		0			0
$187$	−584064.	+	1.01163e6i	−0.0893173	+	0.154702i
$188$			111552.i			0.0167882i
$189$		0			0
$190$	−3.61296e6			−0.526747
$191$	−4.47073e6	−	2.58118e6i	−0.641620	−	0.370440i	0.143618	−	0.989633i	$-0.454126\pi$
$191$	−4.47073e6	−	2.58118e6i	−0.641620	−	0.370440i	−0.785238	+	0.619193i	$0.787460\pi$
$192$		0			0
$193$	1.73777e6	+	3.00990e6i	0.241724	+	0.418678i	0.961205	−	0.275833i	$-0.0889538\pi$
$193$	1.73777e6	+	3.00990e6i	0.241724	+	0.418678i	−0.719481	+	0.694512i	$0.755620\pi$
$194$	1.14693e6	−	662181.i	0.157084	−	0.0906925i
$195$		0			0
$196$	395472.	−	684978.i	0.0525228	−	0.0909721i
$197$		−	7.36920e6i		−	0.963877i	−0.876205	−	0.481939i	$-0.839933\pi$
$197$		−	7.36920e6i		−	0.963877i	0.876205	−	0.481939i	$-0.160067\pi$
$198$		0			0
$199$	8.43100e6			1.06984			0.534921	−	0.844902i	$-0.320341\pi$
$199$	8.43100e6			1.06984			0.534921	+	0.844902i	$0.320341\pi$
$200$	2.00660e7	+	1.15851e7i	2.50825	+	1.44814i
$201$		0			0
$202$	868608.	+	1.50447e6i	0.105383	+	0.182528i
$203$	6.14002e6	−	3.54494e6i	0.733976	−	0.423761i
$204$		0			0
$205$	−7.93728e6	+	1.37478e7i	−0.921319	+	1.59577i
$206$		−	3.56523e6i		−	0.407836i
$207$		0			0
$208$	−3.79240e6			−0.421429
$209$	−1.35586e6	−	782808.i	−0.148517	−	0.0857465i
$210$		0			0
$211$	−2.05006e6	−	3.55081e6i	−0.218233	−	0.377990i	0.736035	−	0.676943i	$-0.236696\pi$
$211$	−2.05006e6	−	3.55081e6i	−0.218233	−	0.377990i	−0.954268	+	0.298953i	$0.903362\pi$
$212$	4.63015e6	−	2.67322e6i	0.485945	−	0.280560i
$213$		0			0
$214$	−5.98104e6	+	1.03595e7i	−0.610289	+	1.05705i
$215$			1.69512e7i			1.70563i
$216$		0			0
$217$	1.59367e6			0.155962
$218$	−7.85323e6	−	4.53406e6i	−0.758016	−	0.437641i
$219$		0			0
$220$	2.09664e6	+	3.63149e6i	0.196905	+	0.341049i
$221$	4.04489e6	−	2.33532e6i	0.374740	−	0.216356i
$222$		0			0
$223$	7.26818e6	−	1.25889e7i	0.655407	−	1.13520i	−0.326384	−	0.945237i	$-0.605830\pi$
$223$	7.26818e6	−	1.25889e7i	0.655407	−	1.13520i	0.981792	−	0.189962i	$-0.0608363\pi$
$224$			7.83619e6i			0.697206i
$225$		0			0
$226$	9.90288e6			0.857899
$227$	5.12266e6	+	2.95757e6i	0.437943	+	0.252847i	0.702725	−	0.711462i	$-0.251967\pi$
$227$	5.12266e6	+	2.95757e6i	0.437943	+	0.252847i	−0.264782	+	0.964308i	$0.585300\pi$
$228$		0			0
$229$	−9.58496e6	−	1.66016e7i	−0.798149	−	1.38243i	−0.920820	−	0.389988i	$-0.872479\pi$
$229$	−9.58496e6	−	1.66016e7i	−0.798149	−	1.38243i	0.122671	−	0.992447i	$-0.460854\pi$
$230$	−1.78980e7	+	1.03334e7i	−1.47103	+	0.849301i
$231$		0			0
$232$	6.54451e6	−	1.13354e7i	0.524099	−	0.907766i
$233$		−	7.40563e6i		−	0.585456i	−0.956196	−	0.292728i	$-0.905437\pi$
$233$		−	7.40563e6i		−	0.585456i	0.956196	−	0.292728i	$-0.0945631\pi$
$234$		0			0
$235$	956160.			0.0736762
$236$	−5.75567e6	−	3.32304e6i	−0.437885	−	0.252813i
$237$		0			0
$238$	1.67918e6	+	2.90843e6i	0.124557	+	0.215739i
$239$	−1.28766e7	+	7.43434e6i	−0.943212	+	0.544563i	−0.890966	−	0.454071i	$-0.849971\pi$
$239$	−1.28766e7	+	7.43434e6i	−0.943212	+	0.544563i	−0.0522459	+	0.998634i	$0.516638\pi$
$240$		0			0
$241$	2.11498e6	−	3.66325e6i	0.151097	−	0.261707i	−0.780534	−	0.625113i	$-0.785053\pi$
$241$	2.11498e6	−	3.66325e6i	0.151097	−	0.261707i	0.931631	+	0.363406i	$0.118386\pi$
$242$			8.29311e6i			0.585156i
$243$		0			0
$244$	−1.73043e6			−0.119120
$245$	−5.87124e6	−	3.38976e6i	−0.399237	−	0.230500i
$246$		0			0
$247$	3.12998e6	+	5.42128e6i	0.207707	+	0.359758i
$248$	2.54799e6	−	1.47108e6i	0.167048	−	0.0964453i
$249$		0			0
$250$	1.89720e7	−	3.28605e7i	1.21421	−	2.10307i
$251$		−	1.32500e7i		−	0.837906i	−0.908008	−	0.418953i	$-0.862397\pi$
$251$		−	1.32500e7i		−	0.837906i	0.908008	−	0.418953i	$-0.137603\pi$
$252$		0			0
$253$	−8.95565e6			−0.553013
$254$	−7.33357e6	−	4.23404e6i	−0.447522	−	0.258377i
$255$		0			0
$256$	8.59533e6	+	1.48875e7i	0.512321	+	0.887367i
$257$	2.78576e7	−	1.60836e7i	1.64114	−	0.947510i	0.660705	−	0.750646i	$-0.270257\pi$
$257$	2.78576e7	−	1.60836e7i	1.64114	−	0.947510i	0.980431	−	0.196865i	$-0.0630760\pi$
$258$		0			0
$259$	−4.87235e6	+	8.43917e6i	−0.280440	+	0.485736i
$260$		−	1.67664e7i		−	0.953937i
$261$		0			0
$262$	1.93939e6			0.107835
$263$	2.52540e7	+	1.45804e7i	1.38823	+	0.801497i	0.993116	−	0.117134i	$-0.0373708\pi$
$263$	2.52540e7	+	1.45804e7i	1.38823	+	0.801497i	0.395117	+	0.918631i	$0.370704\pi$
$264$		0			0
$265$	−2.29133e7	−	3.96870e7i	−1.23126	−	2.13260i
$266$	−3.89811e6	+	2.25057e6i	−0.207114	+	0.119577i
$267$		0			0
$268$	6.02365e6	−	1.04333e7i	0.312936	−	0.542021i
$269$		−	1.84710e7i		−	0.948930i	−0.880274	−	0.474465i	$-0.842642\pi$
$269$		−	1.84710e7i		−	0.948930i	0.880274	−	0.474465i	$-0.157358\pi$
$270$		0			0
$271$	−2.27473e7			−1.14294			−0.571468	−	0.820624i	$-0.693626\pi$
$271$	−2.27473e7			−1.14294			−0.571468	+	0.820624i	$0.693626\pi$
$272$	2.46422e6	+	1.42272e6i	0.122454	+	0.0706989i
$273$		0			0
$274$	−6.41534e6	−	1.11117e7i	−0.311866	−	0.540168i
$275$	2.26833e7	−	1.30962e7i	1.09071	−	0.629720i
$276$		0			0
$277$	1.08882e7	−	1.88590e7i	0.512293	−	0.887317i	−0.487606	−	0.873064i	$-0.662130\pi$
$277$	1.08882e7	−	1.88590e7i	0.512293	−	0.887317i	0.999898	−	0.0142530i	$-0.00453704\pi$
$278$		−	667374.i		−	0.0310624i
$279$		0			0
$280$	3.96115e7			1.80446
$281$	−2.61503e7	−	1.50979e7i	−1.17858	−	0.680451i	−0.222891	−	0.974843i	$-0.571549\pi$
$281$	−2.61503e7	−	1.50979e7i	−1.17858	−	0.680451i	−0.955685	+	0.294393i	$0.904883\pi$
$282$		0			0
$283$	9.88938e6	+	1.71289e7i	0.436325	+	0.755736i	0.997403	−	0.0720265i	$-0.0229466\pi$
$283$	9.88938e6	+	1.71289e7i	0.436325	+	0.755736i	−0.561078	+	0.827763i	$0.689613\pi$
$284$	−6.10369e6	+	3.52397e6i	−0.266463	+	0.153843i
$285$		0			0
$286$	−4.67064e6	+	8.08979e6i	−0.199654	+	0.345811i
$287$			1.97771e7i			0.836596i
$288$		0			0
$289$	2.06332e7			0.854816
$290$	−2.95707e7	−	1.70726e7i	−1.21246	−	0.700014i
$291$		0			0
$292$	−3.52261e6	−	6.10134e6i	−0.141487	−	0.245062i
$293$	−1.72782e7	+	9.97558e6i	−0.686904	+	0.396584i	−0.802451	−	0.596718i	$-0.796471\pi$
$293$	−1.72782e7	+	9.97558e6i	−0.686904	+	0.396584i	0.115547	+	0.993302i	$0.463138\pi$
$294$		0			0
$295$	−2.84832e7	+	4.93343e7i	−1.10949	+	1.92169i
$296$			1.79902e7i			0.693684i
$297$		0			0
$298$	−2.06196e7			−0.779170
$299$	3.10108e7	+	1.79041e7i	1.16011	+	0.669791i
$300$		0			0
$301$	1.05592e7	+	1.82890e7i	0.387196	+	0.670643i
$302$	−2.04693e7	+	1.18180e7i	−0.743161	+	0.429064i
$303$		0			0
$304$	−1.90684e6	+	3.30274e6i	−0.0678724	+	0.117559i
$305$			1.48322e7i			0.522766i
$306$		0			0
$307$	2.43404e7			0.841226			0.420613	−	0.907240i	$-0.361815\pi$
$307$	2.43404e7			0.841226			0.420613	+	0.907240i	$0.361815\pi$
$308$	4.52423e6	+	2.61206e6i	0.154843	+	0.0893988i
$309$		0			0
$310$	−3.83760e6	−	6.64692e6i	−0.128817	−	0.223118i
$311$	−4.60253e7	+	2.65727e7i	−1.53009	+	0.883395i	−0.530728	+	0.847542i	$0.678081\pi$
$311$	−4.60253e7	+	2.65727e7i	−1.53009	+	0.883395i	−0.999357	+	0.0358529i	$0.988585\pi$
$312$		0			0
$313$	1.58934e6	−	2.75282e6i	0.0518303	−	0.0897728i	−0.838946	−	0.544214i	$-0.816828\pi$
$313$	1.58934e6	−	2.75282e6i	0.0518303	−	0.0897728i	0.890777	+	0.454442i	$0.150161\pi$
$314$			2.58640e6i			0.0835422i
$315$		0			0
$316$	1.85032e7			0.586387
$317$	3.20922e7	+	1.85284e7i	1.00745	+	0.581649i	0.910443	−	0.413635i	$-0.135741\pi$
$317$	3.20922e7	+	1.85284e7i	1.00745	+	0.581649i	0.0970027	+	0.995284i	$0.469074\pi$
$318$		0			0
$319$	−7.39814e6	−	1.28140e7i	−0.227903	−	0.394740i
$320$	5.29027e7	−	3.05434e7i	1.61446	−	0.932109i
$321$		0			0
$322$	−1.28737e7	+	2.22980e7i	−0.385600	+	0.667879i
$323$		−	4.69685e6i		−	0.139380i
$324$		0			0
$325$	−1.04728e8			−3.05078
$326$	4.12758e7	+	2.38306e7i	1.19136	+	0.687832i
$327$		0			0
$328$	1.82557e7	+	3.16199e7i	0.517342	+	0.896063i
$329$	1.03162e6	−	595608.i	0.0289690	−	0.0167253i
$330$		0			0
$331$	−2.73374e6	+	4.73497e6i	−0.0753829	+	0.130567i	−0.901253	−	0.433294i	$-0.857351\pi$
$331$	−2.73374e6	+	4.73497e6i	−0.0753829	+	0.130567i	0.825870	+	0.563861i	$0.190685\pi$
$332$			2.23400e7i			0.610476i
$333$		0			0
$334$	2.12299e7			0.569782
$335$	−8.94281e7	−	5.16313e7i	−2.37870	−	1.37334i
$336$		0			0
$337$	2.04610e7	+	3.54394e7i	0.534609	+	0.925971i	0.999182	+	0.0404357i	$0.0128746\pi$
$337$	2.04610e7	+	3.54394e7i	0.534609	+	0.925971i	−0.464573	+	0.885535i	$0.653792\pi$
$338$	7.26534e6	−	4.19465e6i	0.188151	−	0.108629i
$339$		0			0
$340$	−6.28992e6	+	1.08945e7i	−0.160033	+	0.277185i
$341$		−	3.32592e6i		−	0.0838781i
$342$		0			0
$343$	−4.36232e7			−1.08102
$344$	3.37644e7	+	1.94939e7i	0.829437	+	0.478876i
$345$		0			0
$346$	5.30525e6	+	9.18896e6i	0.128079	+	0.221839i
$347$	4.64593e7	−	2.68233e7i	1.11195	−	0.641983i	0.172614	−	0.984990i	$-0.444779\pi$
$347$	4.64593e7	−	2.68233e7i	1.11195	−	0.641983i	0.939333	+	0.343007i	$0.111446\pi$
$348$		0			0
$349$	−8.04437e6	+	1.39333e7i	−0.189241	+	0.327775i	−0.944997	−	0.327078i	$-0.893936\pi$
$349$	−8.04437e6	+	1.39333e7i	−0.189241	+	0.327775i	0.755756	+	0.654853i	$0.227269\pi$
$350$		−	7.53032e7i		−	1.75634i
$351$		0			0
$352$	1.63538e7			0.374965
$353$	−3.56049e6	−	2.05565e6i	−0.0809441	−	0.0467331i	0.458982	−	0.888446i	$-0.348214\pi$
$353$	−3.56049e6	−	2.05565e6i	−0.0809441	−	0.0467331i	−0.539926	+	0.841713i	$0.681548\pi$
$354$		0			0
$355$	3.02054e7	+	5.23174e7i	0.675150	+	1.16939i
$356$	−6.56112e6	+	3.78806e6i	−0.145421	+	0.0839590i
$357$		0			0
$358$	1.14791e7	−	1.98824e7i	0.250184	−	0.433331i
$359$			1.41496e7i			0.305816i	0.988240	+	0.152908i	$0.0488638\pi$
$359$			1.41496e7i			0.305816i	−0.988240	+	0.152908i	$0.951136\pi$
$360$		0			0
$361$	−4.07508e7			−0.866193
$362$	1.20925e7	+	6.98163e6i	0.254913	+	0.147174i
$363$		0			0
$364$	−1.04441e7	−	1.80897e7i	−0.216554	−	0.375082i
$365$	−5.22972e7	+	3.01938e7i	−1.07547	+	0.620925i
$366$		0			0
$367$	−2.06695e7	+	3.58006e7i	−0.418150	+	0.724257i	−0.995753	−	0.0920605i	$-0.970655\pi$
$367$	−2.06695e7	+	3.58006e7i	−0.418150	+	0.724257i	0.577603	+	0.816317i	$0.303988\pi$
$368$			2.18150e7i			0.437736i
$369$		0			0
$370$	4.69310e7			0.926520
$371$	−4.94433e7	−	2.85461e7i	−0.968247	−	0.559018i
$372$		0			0
$373$	−2.91690e7	−	5.05222e7i	−0.562076	−	0.973545i	−0.997315	−	0.0732299i	$-0.976669\pi$
$373$	−2.91690e7	−	5.05222e7i	−0.562076	−	0.973545i	0.435239	−	0.900315i	$-0.356664\pi$
$374$	6.06977e6	−	3.50438e6i	0.116027	−	0.0669880i
$375$		0			0
$376$	1.09958e6	−	1.90454e6i	0.0206854	−	0.0358282i
$377$			5.91614e7i			1.10412i
$378$		0			0
$379$	7.49065e7			1.37595			0.687974	−	0.725735i	$-0.258500\pi$
$379$	7.49065e7			1.37595			0.687974	+	0.725735i	$0.258500\pi$
$380$	−1.46016e7	−	8.43024e6i	−0.266103	−	0.153635i
$381$		0			0
$382$	1.54871e7	+	2.68244e7i	0.277830	+	0.481215i
$383$	−2.46336e7	+	1.42222e7i	−0.438461	+	0.253146i	−0.702945	−	0.711244i	$-0.748132\pi$
$383$	−2.46336e7	+	1.42222e7i	−0.438461	+	0.253146i	0.264483	+	0.964390i	$0.414799\pi$
$384$		0			0
$385$	2.23891e7	−	3.87791e7i	0.392333	−	0.679541i
$386$		−	2.08532e7i		−	0.362586i
$387$		0			0
$388$	6.18036e6			0.105808
$389$	5.29457e7	+	3.05682e7i	0.899460	+	0.519303i	0.877025	−	0.480445i	$-0.159525\pi$
$389$	5.29457e7	+	3.05682e7i	0.899460	+	0.519303i	0.0224348	+	0.999748i	$0.492858\pi$
$390$		0			0
$391$	−1.34335e7	−	2.32675e7i	−0.224728	−	0.389241i
$392$	−1.35038e7	+	7.79645e6i	−0.224181	+	0.129431i
$393$		0			0
$394$	−2.21076e7	+	3.82915e7i	−0.361454	+	0.626057i
$395$		−	1.58598e8i		−	2.57340i
$396$		0			0
$397$	−3.70144e7			−0.591561			−0.295780	−	0.955256i	$-0.595580\pi$
$397$	−3.70144e7			−0.591561			−0.295780	+	0.955256i	$0.595580\pi$
$398$	−4.38087e7	−	2.52930e7i	−0.694883	−	0.401191i
$399$		0			0
$400$	−3.19010e7	−	5.52542e7i	−0.498453	−	0.863346i
$401$	−1.80800e7	+	1.04385e7i	−0.280391	+	0.161884i	−0.633600	−	0.773660i	$-0.718424\pi$
$401$	−1.80800e7	+	1.04385e7i	−0.280391	+	0.161884i	0.353209	+	0.935544i	$0.385090\pi$
$402$		0			0
$403$	−6.64918e6	+	1.15167e7i	−0.101590	+	0.175960i
$404$			8.10701e6i			0.122947i
$405$		0			0
$406$	−4.25393e7			−0.635642
$407$	1.76122e7	+	1.01684e7i	0.261234	+	0.150824i
$408$		0			0
$409$	−4.55265e7	−	7.88542e7i	−0.665418	−	1.15254i	−0.979172	−	0.203033i	$-0.934920\pi$
$409$	−4.55265e7	−	7.88542e7i	−0.665418	−	1.15254i	0.313754	−	0.949504i	$-0.398413\pi$
$410$	8.24866e7	−	4.76237e7i	1.19683	−	0.690989i
$411$		0			0
$412$	8.31887e6	−	1.44087e7i	0.118952	−	0.206031i
$413$			7.09706e7i			1.00746i
$414$		0			0
$415$	1.91485e8			2.67912
$416$	−5.66285e7	−	3.26945e7i	−0.786602	−	0.454145i
$417$		0			0
$418$	4.69685e6	+	8.13518e6i	0.0643099	+	0.111388i
$419$	9.97756e7	−	5.76055e7i	1.35638	−	0.783108i	0.367249	−	0.930123i	$-0.380300\pi$
$419$	9.97756e7	−	5.76055e7i	1.35638	−	0.783108i	0.989134	+	0.147014i	$0.0469663\pi$
$420$		0			0
$421$	6.57948e7	−	1.13960e8i	0.881750	−	1.52724i	0.0323553	−	0.999476i	$-0.489699\pi$
$421$	6.57948e7	−	1.13960e8i	0.881750	−	1.52724i	0.849394	−	0.527759i	$-0.176967\pi$
$422$			2.46007e7i			0.327349i
$423$		0			0
$424$	−1.05401e8			−1.38276
$425$	6.80499e7	+	3.92886e7i	0.886463	+	0.511799i
$426$		0			0
$427$	9.23925e6	+	1.60028e7i	0.118673	+	0.205548i
$428$	−4.83442e7	+	2.79115e7i	−0.616613	+	0.356002i
$429$		0			0
$430$	5.08536e7	−	8.80810e7i	0.639612	−	1.10784i
$431$			7.15543e7i			0.893725i	0.894603	+	0.446863i	$0.147459\pi$
$431$			7.15543e7i			0.893725i	−0.894603	+	0.446863i	$0.852541\pi$
$432$		0			0
$433$	1.83937e7			0.226572			0.113286	−	0.993562i	$-0.463862\pi$
$433$	1.83937e7			0.226572			0.113286	+	0.993562i	$0.463862\pi$
$434$	−8.28095e6	−	4.78101e6i	−0.101300	−	0.0584858i
$435$		0			0
$436$	−2.11590e7	−	3.66484e7i	−0.255291	−	0.442176i
$437$	3.11849e7	−	1.80046e7i	0.373680	−	0.215744i
$438$		0			0
$439$	4.95305e7	−	8.57894e7i	0.585436	−	1.01400i	−0.409385	−	0.912362i	$-0.634257\pi$
$439$	4.95305e7	−	8.57894e7i	0.585436	−	1.01400i	0.994821	−	0.101643i	$-0.0324100\pi$
$440$		−	8.26675e7i		−	0.970458i
$441$		0			0
$442$	−2.80238e7			−0.324534
$443$	1.17257e8	+	6.76984e7i	1.34874	+	0.778695i	0.988071	−	0.154000i	$-0.0492155\pi$
$443$	1.17257e8	+	6.76984e7i	1.34874	+	0.778695i	0.360668	+	0.932694i	$0.382549\pi$
$444$		0			0
$445$	3.24691e7	+	5.62382e7i	0.368460	+	0.638192i
$446$	−7.55332e7	+	4.36091e7i	−0.851399	+	0.491555i
$447$		0			0
$448$	3.80519e7	−	6.59079e7i	0.423197	−	0.732999i
$449$			6.85948e7i			0.757796i	0.925438	+	0.378898i	$0.123697\pi$
$449$			6.85948e7i			0.757796i	−0.925438	+	0.378898i	$0.876303\pi$
$450$		0			0
$451$	4.12739e7			0.449930
$452$	4.00220e7	+	2.31067e7i	0.433395	+	0.250221i
$453$		0			0
$454$	−1.77454e7	−	3.07359e7i	−0.189635	−	0.328457i
$455$	−1.55054e8	+	8.95206e7i	−1.64607	+	0.950361i
$456$		0			0
$457$	−3.56324e7	+	6.17172e7i	−0.373334	+	0.646633i	−0.990076	−	0.140532i	$-0.955119\pi$
$457$	−3.56324e7	+	6.17172e7i	−0.373334	+	0.646633i	0.616743	+	0.787165i	$0.288452\pi$
$458$			1.15020e8i			1.19722i
$459$		0			0
$460$	−9.64454e7			−0.990851
$461$	−1.35584e8	−	7.82797e7i	−1.38391	−	0.798999i	−0.391287	−	0.920269i	$-0.627970\pi$
$461$	−1.35584e8	−	7.82797e7i	−1.38391	−	0.798999i	−0.992620	+	0.121270i	$0.961303\pi$
$462$		0			0
$463$	276906.	+	479616.i	0.00278991	+	0.00483227i	0.867417	−	0.497582i	$-0.165779\pi$
$463$	276906.	+	479616.i	0.00278991	+	0.00483227i	−0.864627	+	0.502414i	$0.832445\pi$
$464$	−3.12135e7	+	1.80211e7i	−0.312456	+	0.180396i
$465$		0			0
$466$	−2.22169e7	+	3.84808e7i	−0.219546	+	0.380265i
$467$		−	3.14739e7i		−	0.309030i	−0.987990	−	0.154515i	$-0.950619\pi$
$467$		−	3.14739e7i		−	0.309030i	0.987990	−	0.154515i	$-0.0493815\pi$
$468$		0			0
$469$	−1.28648e8			−1.24705
$470$	−4.96835e6	−	2.86848e6i	−0.0478541	−	0.0276286i
$471$		0			0
$472$	6.55114e7	+	1.13469e8i	0.623004	+	1.07907i
$473$	3.81684e7	−	2.20366e7i	0.360679	−	0.208238i
$474$		0			0
$475$	−5.26576e7	+	9.12057e7i	−0.491338	+	0.851023i
$476$			1.56724e7i			0.145316i
$477$		0			0
$478$	8.92120e7			0.816845
$479$	−5.78365e7	−	3.33919e7i	−0.526254	−	0.303833i	0.213236	−	0.977001i	$-0.431600\pi$
$479$	−5.78365e7	−	3.33919e7i	−0.526254	−	0.303833i	−0.739490	+	0.673168i	$0.764933\pi$
$480$		0			0
$481$	−4.06573e7	−	7.04205e7i	−0.365345	−	0.632796i
$482$	−2.19795e7	+	1.26899e7i	−0.196280	+	0.113322i
$483$		0			0
$484$	−1.93506e7	+	3.35162e7i	−0.170670	+	0.295610i
$485$		−	5.29745e7i		−	0.464346i
$486$		0			0
$487$	2.00508e8			1.73598			0.867992	−	0.496579i	$-0.165411\pi$
$487$	2.00508e8			1.73598			0.867992	+	0.496579i	$0.165411\pi$
$488$	2.95437e7	+	1.70571e7i	0.254218	+	0.146773i
$489$		0			0
$490$	2.03386e7	+	3.52274e7i	0.172875	+	0.299428i
$491$	7.46373e7	−	4.30919e7i	0.630538	−	0.364042i	−0.150422	−	0.988622i	$-0.548063\pi$
$491$	7.46373e7	−	4.30919e7i	0.630538	−	0.364042i	0.780961	+	0.624580i	$0.214730\pi$
$492$		0			0
$493$	2.21944e7	−	3.84419e7i	0.185227	−	0.320822i
$494$		−	3.75597e7i		−	0.311560i
$495$		0			0
$496$	−8.10160e6			−0.0663935
$497$	6.51787e7	+	3.76309e7i	0.530929	+	0.306532i
$498$		0			0
$499$	−5.33365e6	−	9.23816e6i	−0.0429263	−	0.0743505i	0.843764	−	0.536714i	$-0.180335\pi$
$499$	−5.33365e6	−	9.23816e6i	−0.0429263	−	0.0743505i	−0.886690	+	0.462364i	$0.847001\pi$
$500$	1.53349e8	−	8.85360e7i	1.22679	−	0.708288i
$501$		0			0
$502$	−3.97500e7	+	6.88491e7i	−0.314215	+	0.544236i
$503$		−	1.07893e8i		−	0.847790i	−0.905711	−	0.423895i	$-0.860663\pi$
$503$		−	1.07893e8i		−	0.847790i	0.905711	−	0.423895i	$-0.139337\pi$
$504$		0			0
$505$	6.94886e7			0.539560
$506$	4.65349e7	+	2.68669e7i	0.359193	+	0.207380i
$507$		0			0
$508$	−1.97588e7	−	3.42233e7i	−0.150720	−	0.261054i
$509$	1.33397e8	−	7.70167e7i	1.01156	−	0.584025i	0.0999128	−	0.994996i	$-0.468144\pi$
$509$	1.33397e8	−	7.70167e7i	1.01156	−	0.584025i	0.911648	+	0.410971i	$0.134810\pi$
$510$		0			0
$511$	−3.76164e7	+	6.51536e7i	−0.281913	+	0.488288i
$512$		−	9.35347e7i		−	0.696888i
$513$		0			0
$514$	−1.93003e8			−1.42127
$515$	−1.23503e8	−	7.13046e7i	−0.904183	−	0.522030i
$516$		0			0
$517$	−1.24301e6	−	2.15295e6i	−0.00899502	−	0.0155798i
$518$	5.06350e7	−	2.92341e7i	0.364302	−	0.210330i
$519$		0			0
$520$	−1.65269e8	+	2.86254e8i	−1.17539	+	2.03583i
$521$		−	1.85442e8i		−	1.31128i	−0.755074	−	0.655640i	$-0.772399\pi$
$521$		−	1.85442e8i		−	1.31128i	0.755074	−	0.655640i	$-0.227601\pi$
$522$		0			0
$523$	−1.46950e7			−0.102723			−0.0513613	−	0.998680i	$-0.516356\pi$
$523$	−1.46950e7			−0.102723			−0.0513613	+	0.998680i	$0.516356\pi$
$524$	7.83796e6	+	4.52525e6i	0.0544765	+	0.0314520i
$525$		0			0
$526$	−8.74823e7	−	1.51524e8i	−0.601122	−	1.04117i
$527$	8.64099e6	−	4.98888e6i	0.0590380	−	0.0340856i
$528$		0			0
$529$	2.89720e7	−	5.01810e7i	0.195709	−	0.338979i
$530$			2.74959e8i			1.84689i
$531$		0			0
$532$	−2.10053e7			−0.139507
$533$	−1.42920e8	−	8.25146e7i	−0.943865	−	0.544941i
$534$		0			0
$535$	2.39242e8	+	4.14379e8i	1.56234	+	2.70605i
$536$	−2.05685e8	+	1.18752e8i	−1.33570	+	0.771164i
$537$		0			0
$538$	−5.54131e7	+	9.59783e7i	−0.355849	+	0.616348i
$539$			1.76268e7i			0.112566i
$540$		0			0
$541$	−1.03570e7			−0.0654098			−0.0327049	−	0.999465i	$-0.510412\pi$
$541$	−1.03570e7			−0.0654098			−0.0327049	+	0.999465i	$0.510412\pi$
$542$	1.18198e8	+	6.82419e7i	0.742359	+	0.428601i
$543$		0			0
$544$	2.45307e7	+	4.24884e7i	0.152375	+	0.263921i
$545$	−3.14129e8	+	1.81362e8i	−1.94052	+	1.12036i
$546$		0			0
$547$	−4.01598e7	+	6.95589e7i	−0.245375	+	0.425002i	−0.962237	−	0.272213i	$-0.912244\pi$
$547$	−4.01598e7	+	6.95589e7i	−0.245375	+	0.425002i	0.716862	+	0.697215i	$0.245578\pi$
$548$		−	5.98765e7i		−	0.363844i
$549$		0			0
$550$	−1.57154e8			−0.944579
$551$	5.15228e7	+	2.97467e7i	0.307996	+	0.177821i
$552$		0			0
$553$	−9.87936e7	−	1.71116e8i	−0.584189	−	1.01185i
$554$	−1.13154e8	+	6.53294e7i	−0.665488	+	0.384220i
$555$		0			0
$556$	1.55721e6	−	2.69716e6i	0.00905986	−	0.0156921i
$557$		−	3.87935e7i		−	0.224488i	−0.993681	−	0.112244i	$-0.964196\pi$
$557$		−	3.87935e7i		−	0.224488i	0.993681	−	0.112244i	$-0.0358038\pi$
$558$		0			0
$559$	−1.76222e8			−1.00884
$560$	−9.44619e7	−	5.45376e7i	−0.537889	−	0.310550i
$561$		0			0
$562$	9.05872e7	+	1.56902e8i	0.510338	+	0.883932i
$563$	2.12726e8	−	1.22818e8i	1.19205	−	0.688233i	0.233282	−	0.972409i	$-0.425054\pi$
$563$	2.12726e8	−	1.22818e8i	1.19205	−	0.688233i	0.958772	+	0.284177i	$0.0917202\pi$
$564$		0			0
$565$	1.98058e8	−	3.43046e8i	1.09811	−	1.90198i
$566$		−	1.18673e8i		−	0.654487i
$567$		0			0
$568$	1.38945e8			0.758225
$569$	2.91854e7	+	1.68502e7i	0.158427	+	0.0914677i	0.577117	−	0.816661i	$-0.304178\pi$
$569$	2.91854e7	+	1.68502e7i	0.158427	+	0.0914677i	−0.418691	+	0.908129i	$0.637511\pi$
$570$		0			0
$571$	1.18485e8	+	2.05222e8i	0.636435	+	1.10234i	0.986209	+	0.165504i	$0.0529250\pi$
$571$	1.18485e8	+	2.05222e8i	0.636435	+	1.10234i	−0.349774	+	0.936834i	$0.613742\pi$
$572$	−3.77523e7	+	2.17963e7i	−0.201723	+	0.116465i
$573$		0			0
$574$	5.93312e7	−	1.02765e8i	0.313724	−	0.543385i
$575$			6.02425e8i			3.16883i
$576$		0			0
$577$	4.09015e6			0.0212918			0.0106459	−	0.999943i	$-0.496611\pi$
$577$	4.09015e6			0.0212918			0.0106459	+	0.999943i	$0.496611\pi$
$578$	−1.07213e8	−	6.18996e7i	−0.555219	−	0.320556i
$579$		0			0
$580$	−7.96723e7	−	1.37997e8i	−0.408341	−	0.707268i
$581$	2.06598e8	−	1.19279e8i	1.05341	−	0.608187i
$582$		0			0
$583$	−5.95745e7	+	1.03186e8i	−0.300646	+	0.520734i
$584$			1.38891e8i			0.697328i
$585$		0			0
$586$	1.19707e8			0.594876
$587$	3.15888e8	+	1.82378e8i	1.56178	+	0.901692i	0.997078	+	0.0763950i	$0.0243410\pi$
$587$	3.15888e8	+	1.82378e8i	1.56178	+	0.901692i	0.564699	+	0.825297i	$0.308992\pi$
$588$		0			0
$589$	6.68648e6	+	1.15813e7i	0.0327229	+	0.0566778i
$590$	2.96006e8	−	1.70899e8i	1.44127	−	0.832116i
$591$		0			0
$592$	2.47692e7	−	4.29014e7i	0.119384	−	0.206779i
$593$		−	3.38297e8i		−	1.62231i	−0.584832	−	0.811154i	$-0.698840\pi$
$593$		−	3.38297e8i		−	1.62231i	0.584832	−	0.811154i	$-0.301160\pi$
$594$		0			0
$595$	1.34335e8			0.637731
$596$	−8.33333e7	−	4.81125e7i	−0.393622	−	0.227258i
$597$		0			0
$598$	−1.07425e8	−	1.86065e8i	−0.502343	−	0.870084i
$599$	−2.18701e8	+	1.26267e8i	−1.01758	+	0.587502i	−0.913403	−	0.407056i	$-0.866555\pi$
$599$	−2.18701e8	+	1.26267e8i	−1.01758	+	0.587502i	−0.104181	+	0.994558i	$0.533222\pi$
$600$		0			0
$601$	−1.33928e8	+	2.31971e8i	−0.616949	+	1.06859i	0.373090	+	0.927795i	$0.378298\pi$
$601$	−1.33928e8	+	2.31971e8i	−0.616949	+	1.06859i	−0.990039	+	0.140792i	$0.955035\pi$
$602$		−	1.26710e8i		−	0.580794i
$603$		0			0
$604$	−1.10301e8			−0.500575
$605$	2.87282e8	+	1.65862e8i	1.29730	+	0.748999i
$606$		0			0
$607$	1.36076e8	+	2.35691e8i	0.608438	+	1.05385i	0.991498	+	0.130122i	$0.0415370\pi$
$607$	1.36076e8	+	2.35691e8i	0.608438	+	1.05385i	−0.383060	+	0.923724i	$0.625130\pi$
$608$	−5.69463e7	+	3.28779e7i	−0.253370	+	0.146283i
$609$		0			0
$610$	4.44967e7	−	7.70706e7i	0.196037	−	0.339546i
$611$			9.94008e6i			0.0435779i
$612$		0			0
$613$	−4.91383e7			−0.213323			−0.106662	−	0.994295i	$-0.534016\pi$
$613$	−4.91383e7			−0.213323			−0.106662	+	0.994295i	$0.534016\pi$
$614$	−1.26476e8	−	7.30212e7i	−0.546392	−	0.315460i
$615$		0			0
$616$	−5.14950e7	−	8.91919e7i	−0.220304	−	0.381578i
$617$	1.07978e8	−	6.23412e7i	0.459706	−	0.265412i	−0.252214	−	0.967671i	$-0.581159\pi$
$617$	1.07978e8	−	6.23412e7i	0.459706	−	0.265412i	0.711921	+	0.702260i	$0.247826\pi$
$618$		0			0
$619$	2.26787e8	−	3.92806e8i	0.956193	−	1.65617i	0.224578	−	0.974456i	$-0.427900\pi$
$619$	2.26787e8	−	3.92806e8i	0.956193	−	1.65617i	0.731615	−	0.681718i	$-0.238767\pi$
$620$		−	3.58176e7i		−	0.150287i
$621$		0			0
$622$	3.18873e8			1.32509
$623$	7.00634e7	+	4.04511e7i	0.289752	+	0.167289i
$624$		0			0
$625$	−4.30950e8	−	7.46428e8i	−1.76517	−	3.05737i
$626$	−1.65169e7	+	9.53604e6i	−0.0673296	+	0.0388727i
$627$		0			0
$628$	−6.03492e6	+	1.04528e7i	−0.0243665	+	0.0422040i
$629$			6.10104e7i			0.245161i
$630$		0			0
$631$	−5.31523e7			−0.211560			−0.105780	−	0.994390i	$-0.533734\pi$
$631$	−5.31523e7			−0.211560			−0.105780	+	0.994390i	$0.533734\pi$
$632$	−3.15906e8	−	1.82388e8i	−1.25143	−	0.722513i
$633$		0			0
$634$	−1.11171e8	−	1.92553e8i	−0.436237	−	0.755584i
$635$	−2.93343e8	+	1.69362e8i	−1.14566	+	0.661445i
$636$		0			0
$637$	3.52394e7	−	6.10364e7i	0.136336	−	0.236141i
$638$			8.87777e7i			0.341855i
$639$		0			0
$640$	3.60346e7			0.137461
$641$	−3.16482e8	−	1.82721e8i	−1.20164	−	0.693768i	−0.240721	−	0.970594i	$-0.577384\pi$
$641$	−3.16482e8	−	1.82721e8i	−1.20164	−	0.693768i	−0.960920	+	0.276826i	$0.910717\pi$
$642$		0			0
$643$	−7.62806e7	−	1.32122e8i	−0.286933	−	0.496983i	0.686143	−	0.727467i	$-0.259303\pi$
$643$	−7.62806e7	−	1.32122e8i	−0.286933	−	0.496983i	−0.973076	+	0.230484i	$0.925969\pi$
$644$	−1.04057e8	+	6.00775e7i	−0.389596	+	0.224933i
$645$		0			0
$646$	−1.40905e7	+	2.44055e7i	−0.0522673	+	0.0905296i
$647$		−	1.22990e7i		−	0.0454107i	−0.999742	−	0.0227054i	$-0.992772\pi$
$647$		−	1.22990e7i		−	0.0454107i	0.999742	−	0.0227054i	$-0.00722796\pi$
$648$		0			0
$649$	1.48113e8			0.541824
$650$	5.44181e8	+	3.14183e8i	1.98154	+	1.14404i
$651$		0			0
$652$	1.11209e8	+	1.92620e8i	0.401235	+	0.694960i
$653$	−4.95449e7	+	2.86048e7i	−0.177934	+	0.102730i	−0.586322	−	0.810078i	$-0.699425\pi$
$653$	−4.95449e7	+	2.86048e7i	−0.177934	+	0.102730i	0.408387	+	0.912809i	$0.366091\pi$
$654$		0			0
$655$	3.87878e7	−	6.71825e7i	0.138029	−	0.239074i
$656$		−	1.00539e8i		−	0.356141i
$657$		0			0
$658$	−7.14730e6			−0.0250879
$659$	−1.99266e8	−	1.15046e8i	−0.696269	−	0.401991i	0.109687	−	0.993966i	$-0.465015\pi$
$659$	−1.99266e8	−	1.15046e8i	−0.696269	−	0.401991i	−0.805956	+	0.591975i	$0.798348\pi$
$660$		0			0
$661$	−2.40523e7	−	4.16598e7i	−0.0832822	−	0.144249i	0.821376	−	0.570388i	$-0.193207\pi$
$661$	−2.40523e7	−	4.16598e7i	−0.0832822	−	0.144249i	−0.904658	+	0.426138i	$0.859874\pi$
$662$	2.84098e7	−	1.64024e7i	0.0979253	−	0.0565372i
$663$		0			0
$664$	2.20208e8	−	3.81412e8i	0.752193	−	1.30284i
$665$			1.80046e8i			0.612235i
$666$		0			0
$667$	3.40315e8			1.14684
$668$	8.57997e7	+	4.95365e7i	0.287843	+	0.166187i
$669$		0			0
$670$	3.09788e8	+	5.36568e8i	1.03001	+	1.78402i
$671$	3.33973e7	−	1.92819e7i	0.110546	−	0.0638238i
$672$		0			0
$673$	−1.15326e8	+	1.99751e8i	−0.378341	+	0.655305i	−0.990821	−	0.135181i	$-0.956839\pi$
$673$	−1.15326e8	+	1.99751e8i	−0.378341	+	0.655305i	0.612480	+	0.790486i	$0.290172\pi$
$674$		−	2.45532e8i		−	0.801914i
$675$		0			0
$676$	3.91500e7			0.126734
$677$	−4.88652e8	−	2.82123e8i	−1.57483	−	0.909228i	−0.995564	−	0.0940888i	$-0.970006\pi$
$677$	−4.88652e8	−	2.82123e8i	−1.57483	−	0.909228i	−0.579265	−	0.815139i	$-0.696660\pi$
$678$		0			0
$679$	−3.29987e7	−	5.71554e7i	−0.105411	−	0.182578i
$680$	2.14777e8	−	1.24001e8i	0.683062	−	0.394366i
$681$		0			0
$682$	−9.97776e6	+	1.72820e7i	−0.0314543	+	0.0544804i
$683$		−	2.05363e8i		−	0.644555i	−0.946645	−	0.322278i	$-0.895552\pi$
$683$		−	2.05363e8i		−	0.644555i	0.946645	−	0.322278i	$-0.104448\pi$
$684$		0			0
$685$	−5.13228e8			−1.59675
$686$	2.26673e8	+	1.30870e8i	0.702145	+	0.405384i
$687$		0			0
$688$	−5.36788e7	−	9.29744e7i	−0.164830	−	0.285495i
$689$	4.12579e8	−	2.38203e8i	1.26139	−	0.728264i
$690$		0			0
$691$	5.43345e7	−	9.41101e7i	0.164680	−	0.285234i	−0.771861	−	0.635791i	$-0.780674\pi$
$691$	5.43345e7	−	9.41101e7i	0.164680	−	0.285234i	0.936542	+	0.350556i	$0.114007\pi$
$692$			4.95156e7i			0.149425i
$693$		0			0
$694$	−3.21879e8			−0.962974
$695$	−2.31185e7	−	1.33475e7i	−0.0688661	−	0.0397599i
$696$		0			0
$697$	6.19108e7	+	1.07233e8i	0.182839	+	0.316686i
$698$	8.35995e7	−	4.82662e7i	0.245831	−	0.141931i
$699$		0			0
$700$	1.75707e8	−	3.04334e8i	0.512266	−	0.887271i
$701$			1.08271e8i			0.314310i	0.987574	+	0.157155i	$0.0502321\pi$
$701$			1.08271e8i			0.314310i	−0.987574	+	0.157155i	$0.949768\pi$
$702$		0			0
$703$	−8.17708e7			−0.235360
$704$	−1.37547e8	−	7.94127e7i	−0.394215	−	0.227600i
$705$		0			0
$706$	1.23339e7	+	2.13629e7i	0.0350498	+	0.0607081i
$707$	7.49729e7	−	4.32856e7i	0.212152	−	0.122486i
$708$		0			0
$709$	−8.42675e7	+	1.45956e8i	−0.236440	+	0.409527i	−0.959690	−	0.281060i	$-0.909314\pi$
$709$	−8.42675e7	+	1.45956e8i	−0.236440	+	0.409527i	0.723250	+	0.690586i	$0.242647\pi$
$710$		−	3.62465e8i		−	1.01272i
$711$		0			0
$712$	1.49358e8			0.413798
$713$	6.62476e7	+	3.82481e7i	0.182769	+	0.105522i
$714$		0			0
$715$	1.86826e8	+	3.23591e8i	0.511115	+	0.885276i
$716$	9.27845e7	−	5.35692e7i	0.252776	−	0.145940i
$717$		0			0
$718$	4.24488e7	−	7.35234e7i	0.114681	−	0.198633i
$719$		−	6.10328e8i		−	1.64201i	−0.570918	−	0.821007i	$-0.693413\pi$
$719$		−	6.10328e8i		−	1.64201i	0.570918	−	0.821007i	$-0.306587\pi$
$720$		0			0
$721$	−1.77667e8			−0.474025
$722$	2.11747e8	+	1.22252e8i	0.562609	+	0.324822i
$723$		0			0
$724$	3.25809e7	+	5.64318e7i	0.0858515	+	0.148699i
$725$	−8.61965e8	+	4.97656e8i	−2.26191	+	1.30591i
$726$		0			0
$727$	−3.07962e8	+	5.33407e8i	−0.801483	+	1.38821i	0.117156	+	0.993113i	$0.462622\pi$
$727$	−3.07962e8	+	5.33407e8i	−0.801483	+	1.38821i	−0.918640	+	0.395096i	$0.870711\pi$
$728$			4.11795e8i			1.06730i
$729$		0			0
$730$	3.62326e8			0.931388
$731$	1.14505e8	+	6.61097e7i	0.293139	+	0.169244i
$732$		0			0
$733$	−1.82521e8	−	3.16136e8i	−0.463449	−	0.802716i	0.535681	−	0.844420i	$-0.320055\pi$
$733$	−1.82521e8	−	3.16136e8i	−0.463449	−	0.802716i	−0.999130	+	0.0417037i	$0.986721\pi$
$734$	2.14804e8	−	1.24017e8i	0.543193	−	0.313612i
$735$		0			0
$736$	−1.88069e8	+	3.25744e8i	−0.471718	+	0.817040i
$737$			2.68483e8i			0.670678i
$738$		0			0
$739$	−7.10760e8			−1.76112			−0.880562	−	0.473931i	$-0.842835\pi$
$739$	−7.10760e8			−1.76112			−0.880562	+	0.473931i	$0.842835\pi$
$740$	1.89670e8	+	1.09506e8i	0.468061	+	0.270235i
$741$		0			0
$742$	1.71277e8	+	2.96660e8i	0.419263	+	0.726185i
$743$	−1.83073e8	+	1.05697e8i	−0.446331	+	0.257689i	−0.706279	−	0.707933i	$-0.749628\pi$
$743$	−1.83073e8	+	1.05697e8i	−0.446331	+	0.257689i	0.259949	+	0.965622i	$0.416294\pi$
$744$		0			0
$745$	−4.12393e8	+	7.14286e8i	−0.997338	+	1.72744i
$746$			3.50028e8i			0.843115i
$747$		0			0
$748$	3.27076e7			0.0781526
$749$	5.16247e8	+	2.98055e8i	1.22860	+	0.709335i
$750$		0			0
$751$	9.53126e7	+	1.65086e8i	0.225025	+	0.389754i	0.956327	−	0.292299i	$-0.0944203\pi$
$751$	9.53126e7	+	1.65086e8i	0.225025	+	0.389754i	−0.731302	+	0.682054i	$0.761087\pi$
$752$	−5.24437e6	+	3.02784e6i	−0.0123322	+	0.00711999i
$753$		0			0
$754$	1.77484e8	−	3.07412e8i	0.414043	−	0.717144i
$755$			9.45438e8i			2.19681i
$756$		0			0
$757$	6.27405e8			1.44631			0.723153	−	0.690688i	$-0.242692\pi$
$757$	6.27405e8			1.44631			0.723153	+	0.690688i	$0.242692\pi$
$758$	−3.89226e8	−	2.24720e8i	−0.893704	−	0.515980i
$759$		0			0
$760$	1.66196e8	+	2.87860e8i	0.378600	+	0.655754i
$761$	6.91991e7	−	3.99521e7i	0.157017	−	0.0906537i	−0.419433	−	0.907786i	$-0.637771\pi$
$761$	6.91991e7	−	3.99521e7i	0.157017	−	0.0906537i	0.576450	+	0.817133i	$0.304438\pi$
$762$		0			0
$763$	−2.25947e8	+	3.91352e8i	−0.508667	+	0.881038i
$764$			1.44546e8i			0.324135i
$765$		0			0
$766$	1.70666e8			0.379719
$767$	−5.12872e8	−	2.96107e8i	−1.13664	−	0.656239i
$768$		0			0
$769$	−3.32237e8	−	5.75452e8i	−0.730583	−	1.26541i	−0.956634	−	0.291291i	$-0.905915\pi$
$769$	−3.32237e8	−	5.75452e8i	−0.730583	−	1.26541i	0.226052	−	0.974115i	$-0.427418\pi$
$770$	−2.32675e8	+	1.34335e8i	−0.509656	+	0.294250i
$771$		0			0
$772$	4.86575e7	−	8.42773e7i	0.105754	−	0.183172i
$773$			6.85987e6i			0.0148517i	0.999972	+	0.00742587i	$0.00236375\pi$
$773$			6.85987e6i			0.0148517i	−0.999972	+	0.00742587i	$0.997636\pi$
$774$		0			0
$775$	−2.23727e8			−0.480632
$776$	−1.05518e8	−	6.09207e7i	−0.225808	−	0.130371i
$777$		0			0
$778$	−1.83409e8	−	3.17674e8i	−0.389477	−	0.674595i
$779$	−1.43722e8	+	8.29776e7i	−0.304025	+	0.175529i
$780$		0			0
$781$	7.85341e7	−	1.36025e8i	0.164856	−	0.285539i
$782$			1.61202e8i			0.337093i
$783$		0			0
$784$	4.29370e7			0.0891011
$785$	8.95954e7	+	5.17279e7i	0.185215	+	0.106934i
$786$		0			0
$787$	1.52795e8	+	2.64648e8i	0.313462	+	0.542932i	0.979109	−	0.203335i	$-0.0651779\pi$
$787$	1.52795e8	+	2.64648e8i	0.313462	+	0.542932i	−0.665648	+	0.746266i	$0.731845\pi$
$788$	−1.78694e8	+	1.03169e8i	−0.365200	+	0.210848i
$789$		0			0
$790$	−4.75795e8	+	8.24102e8i	−0.965026	+	1.67147i
$791$		−	4.93494e8i		−	0.997131i
$792$		0			0
$793$	−1.54193e8			−0.309205
$794$	1.92332e8	+	1.11043e8i	0.384230	+	0.221835i
$795$		0			0
$796$	−1.18034e8	−	2.04441e8i	−0.234028	−	0.405348i
$797$	1.74456e8	−	1.00722e8i	0.344597	−	0.198953i	−0.317706	−	0.948189i	$-0.602913\pi$
$797$	1.74456e8	−	1.00722e8i	0.344597	−	0.198953i	0.662303	+	0.749236i	$0.269579\pi$
$798$		0			0
$799$	3.72902e6	−	6.45886e6i	0.00731063	−	0.0126624i
$800$		−	1.10008e9i		−	2.14860i
$801$		0			0
$802$	1.25262e8			0.242826
$803$	1.35973e8	+	7.85039e7i	0.262606	+	0.151616i
$804$		0			0
$805$	5.14950e8	+	8.91919e8i	0.987137	+	1.70977i
$806$	6.91003e7	−	3.98950e7i	0.131970	−	0.0761928i
$807$		0			0
$808$	7.99119e7	−	1.38412e8i	0.151488	−	0.262385i
$809$			1.11534e8i			0.210650i	0.994438	+	0.105325i	$0.0335882\pi$
$809$			1.11534e8i			0.210650i	−0.994438	+	0.105325i	$0.966412\pi$
$810$		0			0
$811$	−1.72124e8			−0.322685			−0.161343	−	0.986898i	$-0.551582\pi$
$811$	−1.72124e8			−0.322685			−0.161343	+	0.986898i	$0.551582\pi$
$812$	−1.71921e8	−	9.92584e7i	−0.321115	−	0.185396i
$813$		0			0
$814$	−6.10104e7	−	1.05673e8i	−0.113118	−	0.195925i
$815$	1.65103e9	−	9.53224e8i	3.04988	−	1.76085i
$816$		0			0
$817$	−8.86053e7	+	1.53469e8i	−0.162478	+	0.281420i
$818$			5.46318e8i			0.998126i
$819$		0			0
$820$	4.44488e8			0.806154
$821$	7.46933e8	+	4.31242e8i	1.34975	+	0.779276i	0.988213	−	0.153084i	$-0.0489204\pi$
$821$	7.46933e8	+	4.31242e8i	1.34975	+	0.779276i	0.361532	+	0.932360i	$0.382254\pi$
$822$		0			0
$823$	2.94505e6	+	5.10097e6i	0.00528315	+	0.00915068i	0.868655	−	0.495418i	$-0.164985\pi$
$823$	2.94505e6	+	5.10097e6i	0.00528315	+	0.00915068i	−0.863372	+	0.504568i	$0.831652\pi$
$824$	−2.84057e8	+	1.64001e8i	−0.507720	+	0.293132i
$825$		0			0
$826$	2.12912e8	−	3.68774e8i	0.377798	−	0.654366i
$827$		−	7.60618e8i		−	1.34478i	−0.740199	−	0.672388i	$-0.765269\pi$
$827$		−	7.60618e8i		−	1.34478i	0.740199	−	0.672388i	$-0.234731\pi$
$828$		0			0
$829$	−1.06302e9			−1.86585			−0.932926	−	0.360067i	$-0.882754\pi$
$829$	−1.06302e9			−1.86585			−0.932926	+	0.360067i	$0.882754\pi$
$830$	−9.94988e8	−	5.74456e8i	−1.74014	−	1.00467i
$831$		0			0
$832$	3.17524e8	+	5.49967e8i	0.551323	+	0.954920i
$833$	−4.57956e7	+	2.64401e7i	−0.0792299	+	0.0457434i
$834$		0			0
$835$	4.24598e8	−	7.35426e8i	0.729321	−	1.26322i
$836$			4.38372e7i			0.0750282i
$837$		0			0
$838$	−6.91266e8			−1.17466
$839$	4.04427e8	+	2.33496e8i	0.684786	+	0.395361i	0.801656	−	0.597786i	$-0.203953\pi$
$839$	4.04427e8	+	2.33496e8i	0.684786	+	0.395361i	−0.116870	+	0.993147i	$0.537286\pi$
$840$		0			0
$841$	−1.62822e7	−	2.82016e7i	−0.0273732	−	0.0474117i
$842$	−6.83760e8	+	3.94769e8i	−1.14543	+	0.661312i
$843$		0			0
$844$	−5.74017e7	+	9.94227e7i	−0.0954767	+	0.165371i
$845$		−	3.35572e8i		−	0.556180i
$846$		0			0
$847$	4.13273e8			0.680122
$848$	2.51351e8	+	1.45117e8i	0.412185	+	0.237975i
$849$		0			0
$850$	−2.35732e8	−	4.08299e8i	−0.383850	−	0.664847i
$851$	−4.05080e8	+	2.33873e8i	−0.657282	+	0.379482i
$852$		0			0
$853$	5.10268e8	−	8.83809e8i	0.822150	−	1.42400i	−0.0819289	−	0.996638i	$-0.526108\pi$
$853$	5.10268e8	−	8.83809e8i	0.822150	−	1.42400i	0.904078	−	0.427367i	$-0.140559\pi$
$854$		−	1.10871e8i		−	0.178010i
$855$		0			0
$856$	1.10051e9			1.75458
$857$	5.46885e7	+	3.15744e7i	0.0868867	+	0.0501641i	0.542814	−	0.839853i	$-0.317359\pi$
$857$	5.46885e7	+	3.15744e7i	0.0868867	+	0.0501641i	−0.455927	+	0.890017i	$0.650692\pi$
$858$		0			0
$859$	−5.17778e8	−	8.96818e8i	−0.816892	−	1.41490i	−0.907962	−	0.419053i	$-0.862362\pi$
$859$	−5.17778e8	−	8.96818e8i	−0.816892	−	1.41490i	0.0910701	−	0.995844i	$-0.470971\pi$
$860$	4.11045e8	−	2.37317e8i	0.646240	−	0.373107i
$861$		0			0
$862$	2.14663e8	−	3.71807e8i	0.335147	−	0.580492i
$863$		−	4.60575e8i		−	0.716585i	−0.933609	−	0.358292i	$-0.883359\pi$
$863$		−	4.60575e8i		−	0.716585i	0.933609	−	0.358292i	$-0.116641\pi$
$864$		0			0
$865$	4.24420e8			0.655764
$866$	−9.55765e7	−	5.51811e7i	−0.147163	−	0.0849643i
$867$		0			0
$868$	−2.23114e7	−	3.86444e7i	−0.0341167	−	0.0590919i
$869$	−3.57111e8	+	2.06178e8i	−0.544181	+	0.314183i
$870$		0			0
$871$	5.36751e8	−	9.29679e8i	0.812303	−	1.40695i
$872$			8.34267e8i			1.25822i
$873$		0			0
$874$	−2.16055e8			−0.323616
$875$	−1.63755e9	−	9.45438e8i	−2.44438	−	1.41127i
$876$		0			0
$877$	4.52290e8	+	7.83389e8i	0.670530	+	1.16139i	0.977754	+	0.209754i	$0.0672664\pi$
$877$	4.52290e8	+	7.83389e8i	0.670530	+	1.16139i	−0.307224	+	0.951637i	$0.599400\pi$
$878$	−5.14736e8	+	2.97183e8i	−0.760504	+	0.439077i
$879$		0			0
$880$	−1.13818e8	+	1.97138e8i	−0.167017	+	0.289282i
$881$			1.06708e9i			1.56051i	0.625460	+	0.780257i	$0.284912\pi$
$881$			1.06708e9i			1.56051i	−0.625460	+	0.780257i	$0.715088\pi$
$882$		0			0
$883$	−8.52780e7			−0.123867			−0.0619334	−	0.998080i	$-0.519727\pi$
$883$	−8.52780e7			−0.123867			−0.0619334	+	0.998080i	$0.519727\pi$
$884$	−1.13257e8	−	6.53890e7i	−0.163949	−	0.0946559i
$885$		0			0
$886$	−4.06190e8	−	7.03542e8i	−0.584021	−	1.01155i
$887$	2.10625e8	−	1.21604e8i	0.301814	−	0.174252i	−0.341444	−	0.939902i	$-0.610916\pi$
$887$	2.10625e8	−	1.21604e8i	0.301814	−	0.174252i	0.643258	+	0.765650i	$0.277582\pi$
$888$		0			0
$889$	−2.10996e8	+	3.65456e8i	−0.300310	+	0.520152i
$890$		−	3.89629e8i		−	0.552690i
$891$		0			0
$892$	−4.07018e8			−0.573481
$893$	8.65667e6	+	4.99793e6i	0.0121562	+	0.00701836i
$894$		0			0
$895$	−4.59164e8	−	7.95296e8i	−0.640470	−	1.10933i
$896$	3.88785e7	−	2.24465e7i	0.0540488	−	0.0312051i
$897$		0			0
$898$	2.05784e8	−	3.56429e8i	0.284174	−	0.492203i
$899$			1.26385e8i			0.173947i
$900$		0			0
$901$	−3.57447e8			−0.488695
$902$	−2.14465e8	−	1.23822e8i	−0.292238	−	0.168724i
$903$		0			0
$904$	−4.55532e8	−	7.89005e8i	−0.616615	−	1.06801i
$905$	4.83701e8	−	2.79265e8i	0.652577	−	0.376765i
$906$		0			0
$907$	−4.31213e8	+	7.46882e8i	−0.577922	+	1.00099i	0.417795	+	0.908541i	$0.362803\pi$
$907$	−4.31213e8	+	7.46882e8i	−0.577922	+	1.00099i	−0.995717	+	0.0924497i	$0.970530\pi$
$908$		−	1.65624e8i		−	0.221241i
$909$		0			0
$910$	1.07425e9			1.42554
$911$	9.92770e8	+	5.73176e8i	1.31309	+	0.758111i	0.982606	−	0.185702i	$-0.0594559\pi$
$911$	9.92770e8	+	5.73176e8i	1.31309	+	0.758111i	0.330480	+	0.943813i	$0.392789\pi$
$912$		0			0
$913$	−2.48931e8	−	4.31161e8i	−0.327090	−	0.566536i
$914$	3.70303e8	−	2.13795e8i	0.484974	−	0.280000i
$915$		0			0
$916$	−2.68379e8	+	4.64846e8i	−0.349190	+	0.604815i
$917$		−	9.66464e7i		−	0.125336i
$918$		0			0
$919$	8.23240e8			1.06067			0.530335	−	0.847788i	$-0.322066\pi$
$919$	8.23240e8			1.06067			0.530335	+	0.847788i	$0.322066\pi$
$920$	1.64662e9	+	9.50676e8i	2.11461	+	1.22087i
$921$		0			0
$922$	4.69678e8	+	8.13506e8i	0.599249	+	1.03793i
$923$	−5.43883e8	+	3.14011e8i	−0.691672	+	0.399337i
$924$		0			0
$925$	6.84004e8	−	1.18473e9i	0.864238	−	1.49690i
$926$		−	3.32288e6i		−	0.00418486i
$927$		0			0
$928$	−6.21444e8			−0.777603
$929$	−6.31105e8	−	3.64369e8i	−0.787144	−	0.454458i	0.0518119	−	0.998657i	$-0.483500\pi$
$929$	−6.31105e8	−	3.64369e8i	−0.787144	−	0.454458i	−0.838956	+	0.544199i	$0.816834\pi$
$930$		0			0
$931$	−3.54371e7	−	6.13789e7i	−0.0439146	−	0.0760624i
$932$	−1.79577e8	+	1.03679e8i	−0.221821	+	0.128069i
$933$		0			0
$934$	−9.44218e7	+	1.63543e8i	−0.115886	+	0.200721i
$935$		−	2.80351e8i		−	0.342978i
$936$		0			0
$937$	5.88557e8			0.715434			0.357717	−	0.933830i	$-0.383555\pi$
$937$	5.88557e8			0.715434			0.357717	+	0.933830i	$0.383555\pi$
$938$	6.68475e8	+	3.85944e8i	0.809984	+	0.467645i
$939$		0			0
$940$	−1.33862e7	−	2.31856e7i	−0.0161167	−	0.0279149i
$941$	8.43199e8	−	4.86821e8i	1.01196	−	0.584253i	0.100192	−	0.994968i	$-0.468054\pi$
$941$	8.43199e8	−	4.86821e8i	1.01196	−	0.584253i	0.911764	+	0.410715i	$0.134721\pi$
$942$		0			0
$943$	−4.74649e8	+	8.22117e8i	−0.566028	+	0.980389i
$944$		−	3.60787e8i		−	0.428879i
$945$		0			0
$946$	−2.64439e8			−0.312357
$947$	3.38266e8	+	1.95298e8i	0.398299	+	0.229958i	0.685750	−	0.727838i	$-0.259475\pi$
$947$	3.38266e8	+	1.95298e8i	0.398299	+	0.229958i	−0.287451	+	0.957795i	$0.592808\pi$
$948$		0			0
$949$	−3.13890e8	−	5.43673e8i	−0.367264	−	0.636120i
$950$	5.47234e8	−	3.15946e8i	0.638267	−	0.368504i
$951$		0			0
$952$	1.54485e8	−	2.67576e8i	0.179050	−	0.310124i
$953$			4.41062e7i			0.0509590i	0.999675	+	0.0254795i	$0.00811125\pi$
$953$			4.41062e7i			0.0509590i	−0.999675	+	0.0254795i	$0.991889\pi$
$954$		0			0
$955$	1.23896e9			1.42249
$956$	3.60546e8	+	2.08161e8i	0.412655	+	0.238247i
$957$		0			0
$958$	2.00352e8	+	3.47019e8i	0.227875	+	0.394691i
$959$	−5.53733e8	+	3.19698e8i	−0.627834	+	0.362480i
$960$		0			0
$961$	4.29547e8	−	7.43998e8i	0.483995	−	0.838304i
$962$			4.87887e8i			0.548017i
$963$		0			0
$964$	−1.18439e8			−0.132209
$965$	−7.22377e8	−	4.17064e8i	−0.803863	−	0.464110i
$966$		0			0
$967$	4.81689e8	+	8.34310e8i	0.532705	+	0.922673i	0.999271	+	0.0381861i	$0.0121580\pi$
$967$	4.81689e8	+	8.34310e8i	0.532705	+	0.922673i	−0.466565	+	0.884487i	$0.654509\pi$
$968$	6.60748e8	−	3.81483e8i	0.728467	−	0.420581i
$969$		0			0
$970$	−1.58923e8	+	2.75263e8i	−0.174130	+	0.301601i
$971$			7.36207e8i			0.804160i	0.915605	+	0.402080i	$0.131713\pi$
$971$			7.36207e8i			0.804160i	−0.915605	+	0.402080i	$0.868287\pi$
$972$		0			0
$973$	−3.32575e7			−0.0361036
$974$	−1.04187e9	−	6.01525e8i	−1.12755	−	0.650994i
$975$		0			0
$976$	−4.69688e7	−	8.13523e7i	−0.0505196	−	0.0875025i
$977$	−1.39341e9	+	8.04484e8i	−1.49415	+	0.862648i	−0.999977	−	0.00671600i	$-0.997862\pi$
$977$	−1.39341e9	+	8.04484e8i	−1.49415	+	0.862648i	−0.494172	+	0.869364i	$0.664529\pi$
$978$		0			0
$979$	8.44197e7	−	1.46219e8i	0.0899696	−	0.155832i
$980$			1.89827e8i			0.201687i
$981$		0			0
$982$	−5.17103e8			−0.546062
$983$	−3.87093e8	−	2.23488e8i	−0.407526	−	0.235285i	0.282200	−	0.959356i	$-0.408936\pi$
$983$	−3.87093e8	−	2.23488e8i	−0.407526	−	0.235285i	−0.689726	+	0.724070i	$0.742269\pi$
$984$		0			0
$985$	8.84304e8	+	1.53166e9i	0.925322	+	1.60270i
$986$	−2.30651e8	+	1.33167e8i	−0.240616	+	0.138920i
$987$		0			0
$988$	8.76394e7	−	1.51796e8i	0.0908716	−	0.157394i
$989$			1.01368e9i			1.04788i
$990$		0			0
$991$	−1.40384e9			−1.44244			−0.721220	−	0.692706i	$-0.756418\pi$
$991$	−1.40384e9			−1.44244			−0.721220	+	0.692706i	$0.756418\pi$
$992$	−1.20974e8	−	6.98443e7i	−0.123924	−	0.0715478i
$993$		0			0
$994$	−2.25786e8	−	3.91072e8i	−0.229899	−	0.398197i
$995$	−1.75235e9	+	1.01172e9i	−1.77890	+	1.02705i
$996$		0			0
$997$	−6.65711e8	+	1.15304e9i	−0.671738	+	1.16348i	0.305673	+	0.952137i	$0.401119\pi$
$997$	−6.65711e8	+	1.15304e9i	−0.671738	+	1.16348i	−0.977411	+	0.211348i	$0.932215\pi$
$998$			6.40038e7i			0.0643894i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.7.d.b.26.1		4
3.2	odd	2	inner	81.7.d.b.26.2		4
9.2	odd	6		27.7.b.b.26.1	✓	2
9.4	even	3	inner	81.7.d.b.53.2		4
9.5	odd	6	inner	81.7.d.b.53.1		4
9.7	even	3		27.7.b.b.26.2	yes	2
36.7	odd	6		432.7.e.d.161.1		2
36.11	even	6		432.7.e.d.161.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.7.b.b.26.1	✓	2	9.2	odd	6
27.7.b.b.26.2	yes	2	9.7	even	3
81.7.d.b.26.1		4	1.1	even	1	trivial
81.7.d.b.26.2		4	3.2	odd	2	inner
81.7.d.b.53.1		4	9.5	odd	6	inner
81.7.d.b.53.2		4	9.4	even	3	inner
432.7.e.d.161.1		2	36.7	odd	6
432.7.e.d.161.2		2	36.11	even	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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	81.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-5.19615 - 3.00000i) q^{2} +(-14.0000 - 24.2487i) q^{4} +(-207.846 + 120.000i) q^{5} +(-149.500 + 258.942i) q^{7} +552.000i q^{8} +1440.00 q^{10} +(540.400 + 312.000i) q^{11} +(-1247.50 - 2160.73i) q^{13} +(1553.65 - 897.000i) q^{14} +(760.000 - 1316.36i) q^{16} +1872.00i q^{17} -2509.00 q^{19} +(5819.69 + 3360.00i) q^{20} +(-1872.00 - 3242.40i) q^{22} +(-12429.2 + 7176.00i) q^{23} +(20987.5 - 36351.4i) q^{25} +14970.0i q^{26} +8372.00 q^{28} +(-20535.2 - 11856.0i) q^{29} +(-2665.00 - 4615.92i) q^{31} +(22696.8 - 13104.0i) q^{32} +(5616.00 - 9727.20i) q^{34} -71760.0i q^{35} +32591.0 q^{37} +(13037.1 + 7527.00i) q^{38} +(-66240.0 - 114731. i) q^{40} +(57282.4 - 33072.0i) q^{41} +(35315.0 - 61167.4i) q^{43} -17472.0i q^{44} +86112.0 q^{46} +(-3450.25 - 1992.00i) q^{47} +(14124.0 + 24463.5i) q^{49} +(-218108. + 125925. i) q^{50} +(-34930.0 + 60500.5i) q^{52} +190944. i q^{53} -149760. q^{55} +(-142936. - 82524.0i) q^{56} +(71136.0 + 123211. i) q^{58} +(205560. - 118680. i) q^{59} +(30900.5 - 53521.2i) q^{61} +31980.0i q^{62} -254528. q^{64} +(518576. + 299400. i) q^{65} +(215130. + 372617. i) q^{67} +(45393.6 - 26208.0i) q^{68} +(-215280. + 372876. i) q^{70} -251712. i q^{71} +251615. q^{73} +(-169348. - 97773.0i) q^{74} +(35126.0 + 60840.0i) q^{76} +(-161580. + 93288.0i) q^{77} +(-330414. + 572293. i) q^{79} +364800. i q^{80} -396864. q^{82} +(-690964. - 398928. i) q^{83} +(-224640. - 389088. i) q^{85} +(-367004. + 211890. i) q^{86} +(-172224. + 298301. i) q^{88} -270576. i q^{89} +746005. q^{91} +(348018. + 200928. i) q^{92} +(11952.0 + 20701.5i) q^{94} +(521486. - 301080. i) q^{95} +(-110364. + 191155. i) q^{97} -169488. i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 56 q^{4} - 598 q^{7} + 5760 q^{10} - 4990 q^{13} + 3040 q^{16} - 10036 q^{19} - 7488 q^{22} + 83950 q^{25} + 33488 q^{28} - 10660 q^{31} + 22464 q^{34} + 130364 q^{37} - 264960 q^{40} + 141260 q^{43}+ \cdots - 441454 q^{97}+O(q^{100}) \) 4 * q - 56 * q^4 - 598 * q^7 + 5760 * q^10 - 4990 * q^13 + 3040 * q^16 - 10036 * q^19 - 7488 * q^22 + 83950 * q^25 + 33488 * q^28 - 10660 * q^31 + 22464 * q^34 + 130364 * q^37 - 264960 * q^40 + 141260 * q^43 + 344448 * q^46 + 56496 * q^49 - 139720 * q^52 - 599040 * q^55 + 284544 * q^58 + 123602 * q^61 - 1018112 * q^64 + 860522 * q^67 - 861120 * q^70 + 1006460 * q^73 + 140504 * q^76 - 1321654 * q^79 - 1587456 * q^82 - 898560 * q^85 - 688896 * q^88 + 2984020 * q^91 + 47808 * q^94 - 441454 * q^97

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