LMFDB - Embedded newform 72.7.b.c.19.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [72,7,Mod(19,72)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(72, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("72.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 72 = 2^{3} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	72.b (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$16.5638940206$
Analytic rank:	$0$
Dimension:	$12$
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} - 2 x^{11} + 31 x^{10} - 1286 x^{9} + 7702 x^{8} - 174032 x^{7} + 1952056 x^{6} + \cdots + 767595744 $ x^12 - 2x^11 + 31x^10 - 1286x^9 + 7702x^8 - 174032x^7 + 1952056x^6 - 6345392x^5 + 7695616x^4 - 6850848x^3 - 19274256x^2 - 69390432*x + 767595744
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{30}\cdot 3^{11} $
Twist minimal:	no (minimal twist has level 24)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.10
Root			$-9.37784 + 8.67520i$ of defining polynomial
Character	$\chi$	$=$	72.19
Dual form			72.7.b.c.19.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.86506 + 6.35069i) q^{2} +(-16.6624 + 61.7929i) q^{4} -100.822i q^{5} +277.765i q^{7} +(-473.491 + 194.808i) q^{8} +O(q^{10})$	\(q+(4.86506 + 6.35069i) q^{2} +(-16.6624 + 61.7929i) q^{4} -100.822i q^{5} +277.765i q^{7} +(-473.491 + 194.808i) q^{8} +(640.287 - 490.503i) q^{10} -1922.36 q^{11} +1721.01i q^{13} +(-1764.00 + 1351.34i) q^{14} +(-3540.73 - 2059.24i) q^{16} -1654.12 q^{17} -9365.55 q^{19} +(6230.07 + 1679.94i) q^{20} +(-9352.39 - 12208.3i) q^{22} -15697.3i q^{23} +5459.98 q^{25} +(-10929.6 + 8372.79i) q^{26} +(-17163.9 - 4628.24i) q^{28} +28485.7i q^{29} +30249.4i q^{31} +(-4148.24 - 32504.4i) q^{32} +(-8047.37 - 10504.8i) q^{34} +28004.7 q^{35} -72593.3i q^{37} +(-45563.9 - 59477.7i) q^{38} +(19640.9 + 47738.2i) q^{40} -34125.3 q^{41} -71200.1 q^{43} +(32031.2 - 118788. i) q^{44} +(99688.4 - 76368.1i) q^{46} +149872. i q^{47} +40495.6 q^{49} +(26563.1 + 34674.7i) q^{50} +(-106346. - 28676.1i) q^{52} +235085. i q^{53} +193816. i q^{55} +(-54110.9 - 131519. i) q^{56} +(-180904. + 138584. i) q^{58} +135778. q^{59} +106714. i q^{61} +(-192105. + 147165. i) q^{62} +(186244. - 184480. i) q^{64} +173515. q^{65} +207500. q^{67} +(27561.6 - 102213. i) q^{68} +(136245. + 177849. i) q^{70} +232520. i q^{71} +645892. q^{73} +(461017. - 353170. i) q^{74} +(156053. - 578725. i) q^{76} -533964. i q^{77} +535360. i q^{79} +(-207616. + 356982. i) q^{80} +(-166021. - 216719. i) q^{82} -660358. q^{83} +166771. i q^{85} +(-346393. - 452170. i) q^{86} +(910220. - 374491. i) q^{88} +942878. q^{89} -478035. q^{91} +(969980. + 261555. i) q^{92} +(-951790. + 729136. i) q^{94} +944251. i q^{95} -1.16254e6 q^{97} +(197013. + 257175. i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{2} + 24 q^{4} - 796 q^{8}+O(q^{10}) $ 12 * q - 10 * q^2 + 24 * q^4 - 796 * q^8	$ 12 q - 10 q^{2} + 24 q^{4} - 796 q^{8} + 2172 q^{10} - 2720 q^{11} + 6444 q^{14} + 11640 q^{16} + 4888 q^{17} + 3936 q^{19} + 31608 q^{20} - 60432 q^{22} - 27204 q^{25} - 53952 q^{26} - 57072 q^{28} - 109480 q^{32} + 47388 q^{34} - 162336 q^{35} + 89080 q^{38} + 72120 q^{40} + 54280 q^{41} - 49824 q^{43} - 229184 q^{44} + 171864 q^{46} - 304644 q^{49} + 500078 q^{50} + 256848 q^{52} + 699816 q^{56} - 409524 q^{58} + 886144 q^{59} - 691356 q^{62} - 500640 q^{64} - 473376 q^{65} + 1565952 q^{67} - 669104 q^{68} + 473784 q^{70} + 555480 q^{73} + 753720 q^{74} - 293136 q^{76} + 251616 q^{80} + 2317716 q^{82} - 2497760 q^{83} - 476024 q^{86} + 971424 q^{88} - 367400 q^{89} - 4475808 q^{91} + 377376 q^{92} - 2642568 q^{94} - 1165656 q^{97} - 182674 q^{98}+O(q^{100}) $ 12 * q - 10 * q^2 + 24 * q^4 - 796 * q^8 + 2172 * q^10 - 2720 * q^11 + 6444 * q^14 + 11640 * q^16 + 4888 * q^17 + 3936 * q^19 + 31608 * q^20 - 60432 * q^22 - 27204 * q^25 - 53952 * q^26 - 57072 * q^28 - 109480 * q^32 + 47388 * q^34 - 162336 * q^35 + 89080 * q^38 + 72120 * q^40 + 54280 * q^41 - 49824 * q^43 - 229184 * q^44 + 171864 * q^46 - 304644 * q^49 + 500078 * q^50 + 256848 * q^52 + 699816 * q^56 - 409524 * q^58 + 886144 * q^59 - 691356 * q^62 - 500640 * q^64 - 473376 * q^65 + 1565952 * q^67 - 669104 * q^68 + 473784 * q^70 + 555480 * q^73 + 753720 * q^74 - 293136 * q^76 + 251616 * q^80 + 2317716 * q^82 - 2497760 * q^83 - 476024 * q^86 + 971424 * q^88 - 367400 * q^89 - 4475808 * q^91 + 377376 * q^92 - 2642568 * q^94 - 1165656 * q^97 - 182674 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/72\mathbb{Z}\right)^\times$.

$n$	$37$	$55$	$65$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	4.86506	+	6.35069i	0.608132	+	0.793836i
$2$	4.86506	+	6.35069i	0.608132	+	0.793836i
$3$		0			0
$3$		0			0
$4$	−16.6624	+	61.7929i	−0.260351	+	0.965514i
$5$		−	100.822i		−	0.806574i	−0.915074	−	0.403287i	$-0.867868\pi$
$5$		−	100.822i		−	0.806574i	0.915074	−	0.403287i	$-0.132132\pi$
$6$		0			0
$7$			277.765i			0.809811i	0.914359	+	0.404905i	$0.132696\pi$
$7$			277.765i			0.809811i	−0.914359	+	0.404905i	$0.867304\pi$
$8$	−473.491	+	194.808i	−0.924787	+	0.380485i
$9$		0			0
$10$	640.287	−	490.503i	0.640287	−	0.490503i
$11$	−1922.36			−1.44430			−0.722149	−	0.691738i	$-0.756845\pi$
$11$	−1922.36			−1.44430			−0.722149	+	0.691738i	$0.756845\pi$
$12$		0			0
$13$			1721.01i			0.783343i	0.920105	+	0.391672i	$0.128103\pi$
$13$			1721.01i			0.783343i	−0.920105	+	0.391672i	$0.871897\pi$
$14$	−1764.00	+	1351.34i	−0.642857	+	0.492472i
$15$		0			0
$16$	−3540.73	−	2059.24i	−0.864435	−	0.502744i
$17$	−1654.12			−0.336681			−0.168341	−	0.985729i	$-0.553841\pi$
$17$	−1654.12			−0.336681			−0.168341	+	0.985729i	$0.553841\pi$
$18$		0			0
$19$	−9365.55			−1.36544			−0.682720	−	0.730680i	$-0.739203\pi$
$19$	−9365.55			−1.36544			−0.682720	+	0.730680i	$0.739203\pi$
$20$	6230.07	+	1679.94i	0.778758	+	0.209992i
$21$		0			0
$22$	−9352.39	−	12208.3i	−0.878324	−	1.14654i
$23$		−	15697.3i		−	1.29015i	−0.764119	−	0.645076i	$-0.776826\pi$
$23$		−	15697.3i		−	1.29015i	0.764119	−	0.645076i	$-0.223174\pi$
$24$		0			0
$25$	5459.98			0.349439
$26$	−10929.6	+	8372.79i	−0.621846	+	0.476376i
$27$		0			0
$28$	−17163.9	−	4628.24i	−0.781884	−	0.210835i
$29$			28485.7i			1.16797i	0.811764	+	0.583986i	$0.198508\pi$
$29$			28485.7i			1.16797i	−0.811764	+	0.583986i	$0.801492\pi$
$30$		0			0
$31$			30249.4i			1.01539i	0.861537	+	0.507694i	$0.169502\pi$
$31$			30249.4i			1.01539i	−0.861537	+	0.507694i	$0.830498\pi$
$32$	−4148.24	−	32504.4i	−0.126594	−	0.991955i
$33$		0			0
$34$	−8047.37	−	10504.8i	−0.204747	−	0.267270i
$35$	28004.7			0.653172
$36$		0			0
$37$		−	72593.3i		−	1.43315i	−0.697511	−	0.716574i	$-0.745709\pi$
$37$		−	72593.3i		−	1.43315i	0.697511	−	0.716574i	$-0.254291\pi$
$38$	−45563.9	−	59477.7i	−0.830368	−	1.08393i
$39$		0			0
$40$	19640.9	+	47738.2i	0.306889	+	0.745909i
$41$	−34125.3			−0.495136			−0.247568	−	0.968871i	$-0.579631\pi$
$41$	−34125.3			−0.495136			−0.247568	+	0.968871i	$0.579631\pi$
$42$		0			0
$43$	−71200.1			−0.895520			−0.447760	−	0.894154i	$-0.647778\pi$
$43$	−71200.1			−0.895520			−0.447760	+	0.894154i	$0.647778\pi$
$44$	32031.2	−	118788.i	0.376024	−	1.39449i
$45$		0			0
$46$	99688.4	−	76368.1i	1.02417	−	0.784582i
$47$			149872.i			1.44353i	0.692136	+	0.721767i	$0.256670\pi$
$47$			149872.i			1.44353i	−0.692136	+	0.721767i	$0.743330\pi$
$48$		0			0
$49$	40495.6			0.344207
$50$	26563.1	+	34674.7i	0.212505	+	0.277397i
$51$		0			0
$52$	−106346.	−	28676.1i	−0.756329	−	0.203944i
$53$			235085.i			1.57906i	0.613713	+	0.789529i	$0.289675\pi$
$53$			235085.i			1.57906i	−0.613713	+	0.789529i	$0.710325\pi$
$54$		0			0
$55$			193816.i			1.16493i
$56$	−54110.9	−	131519.i	−0.308120	−	0.748903i
$57$		0			0
$58$	−180904.	+	138584.i	−0.927178	+	0.710281i
$59$	135778.			0.661109			0.330554	−	0.943787i	$-0.392764\pi$
$59$	135778.			0.661109			0.330554	+	0.943787i	$0.392764\pi$
$60$		0			0
$61$			106714.i			0.470145i	0.971978	+	0.235072i	$0.0755327\pi$
$61$			106714.i			0.470145i	−0.971978	+	0.235072i	$0.924467\pi$
$62$	−192105.	+	147165.i	−0.806052	+	0.617490i
$63$		0			0
$64$	186244.	−	184480.i	0.710463	−	0.703735i
$65$	173515.			0.631824
$66$		0			0
$67$	207500.			0.689912			0.344956	−	0.938619i	$-0.387894\pi$
$67$	207500.			0.689912			0.344956	+	0.938619i	$0.387894\pi$
$68$	27561.6	−	102213.i	0.0876552	−	0.325071i
$69$		0			0
$70$	136245.	+	177849.i	0.397215	+	0.518511i
$71$			232520.i			0.649657i	0.945773	+	0.324829i	$0.105307\pi$
$71$			232520.i			0.649657i	−0.945773	+	0.324829i	$0.894693\pi$
$72$		0			0
$73$	645892.			1.66032			0.830160	−	0.557526i	$-0.188249\pi$
$73$	645892.			1.66032			0.830160	+	0.557526i	$0.188249\pi$
$74$	461017.	−	353170.i	1.13768	−	0.871543i
$75$		0			0
$76$	156053.	−	578725.i	0.355493	−	1.31835i
$77$		−	533964.i		−	1.16961i
$78$		0			0
$79$			535360.i			1.08584i	0.839786	+	0.542918i	$0.182681\pi$
$79$			535360.i			1.08584i	−0.839786	+	0.542918i	$0.817319\pi$
$80$	−207616.	+	356982.i	−0.405500	+	0.697231i
$81$		0			0
$82$	−166021.	−	216719.i	−0.301108	−	0.393057i
$83$	−660358.			−1.15490			−0.577451	−	0.816426i	$-0.695952\pi$
$83$	−660358.			−1.15490			−0.577451	+	0.816426i	$0.695952\pi$
$84$		0			0
$85$			166771.i			0.271558i
$86$	−346393.	−	452170.i	−0.544595	−	0.710896i
$87$		0			0
$88$	910220.	−	374491.i	1.33567	−	0.549533i
$89$	942878.			1.33747			0.668737	−	0.743499i	$-0.266835\pi$
$89$	942878.			1.33747			0.668737	+	0.743499i	$0.266835\pi$
$90$		0			0
$91$	−478035.			−0.634360
$92$	969980.	+	261555.i	1.24566	+	0.335892i
$93$		0			0
$94$	−951790.	+	729136.i	−1.14593	+	0.877860i
$95$			944251.i			1.10133i
$96$		0			0
$97$	−1.16254e6			−1.27377			−0.636886	−	0.770958i	$-0.719778\pi$
$97$	−1.16254e6			−1.27377			−0.636886	+	0.770958i	$0.719778\pi$
$98$	197013.	+	257175.i	0.209323	+	0.273244i
$99$		0			0
$100$	−90976.7	+	337388.i	−0.0909767	+	0.337388i
$101$		−	327259.i		−	0.317635i	−0.987308	−	0.158817i	$-0.949232\pi$
$101$		−	327259.i		−	0.317635i	0.987308	−	0.158817i	$-0.0507681\pi$
$102$		0			0
$103$		−	972842.i		−	0.890288i	−0.895459	−	0.445144i	$-0.853153\pi$
$103$		−	972842.i		−	0.890288i	0.895459	−	0.445144i	$-0.146847\pi$
$104$	−335266.	−	814881.i	−0.298050	−	0.724426i
$105$		0			0
$106$	−1.49295e6	+	1.14370e6i	−1.25351	+	0.960276i
$107$	−647520.			−0.528569			−0.264285	−	0.964445i	$-0.585136\pi$
$107$	−647520.			−0.528569			−0.264285	+	0.964445i	$0.585136\pi$
$108$		0			0
$109$		−	2.41440e6i		−	1.86436i	−0.361992	−	0.932181i	$-0.617903\pi$
$109$		−	2.41440e6i		−	1.86436i	0.361992	−	0.932181i	$-0.382097\pi$
$110$	−1.23086e6	+	942924.i	−0.924765	+	0.708433i
$111$		0			0
$112$	571985.	−	983490.i	0.407128	−	0.700029i
$113$	−767081.			−0.531626			−0.265813	−	0.964025i	$-0.585640\pi$
$113$	−767081.			−0.531626			−0.265813	+	0.964025i	$0.585640\pi$
$114$		0			0
$115$	−1.58263e6			−1.04060
$116$	−1.76021e6	−	474641.i	−1.12769	−	0.304082i
$117$		0			0
$118$	660567.	+	862282.i	0.402041	+	0.524812i
$119$		−	459455.i		−	0.272648i
$120$		0			0
$121$	1.92391e6			1.08599
$122$	−677707.	+	519169.i	−0.373218	+	0.285910i
$123$		0			0
$124$	−1.86920e6	−	504029.i	−0.980372	−	0.264357i
$125$		−	2.12582e6i		−	1.08842i
$126$		0			0
$127$			2.57772e6i			1.25842i	0.777236	+	0.629209i	$0.216621\pi$
$127$			2.57772e6i			1.25842i	−0.777236	+	0.629209i	$0.783379\pi$
$128$	2.07766e6	+	285270.i	0.990705	+	0.136027i
$129$		0			0
$130$	844159.	+	1.10194e6i	0.384233	+	0.501565i
$131$	−691211.			−0.307466			−0.153733	−	0.988112i	$-0.549130\pi$
$131$	−691211.			−0.307466			−0.153733	+	0.988112i	$0.549130\pi$
$132$		0			0
$133$		−	2.60142e6i		−	1.10575i
$134$	1.00950e6	+	1.31777e6i	0.419558	+	0.547677i
$135$		0			0
$136$	783209.	−	322235.i	0.311359	−	0.128102i
$137$	−1.64458e6			−0.639577			−0.319788	−	0.947489i	$-0.603612\pi$
$137$	−1.64458e6			−0.639577			−0.319788	+	0.947489i	$0.603612\pi$
$138$		0			0
$139$	−2.97102e6			−1.10627			−0.553135	−	0.833092i	$-0.686569\pi$
$139$	−2.97102e6			−1.10627			−0.553135	+	0.833092i	$0.686569\pi$
$140$	−466627.	+	1.73049e6i	−0.170054	+	0.630647i
$141$		0			0
$142$	−1.47666e6	+	1.13122e6i	−0.515721	+	0.395078i
$143$		−	3.30839e6i		−	1.13138i
$144$		0			0
$145$	2.87197e6			0.942055
$146$	3.14230e6	+	4.10186e6i	1.00969	+	1.31802i
$147$		0			0
$148$	4.48575e6	+	1.20958e6i	1.38372	+	0.373121i
$149$		−	1.85074e6i		−	0.559483i	−0.960075	−	0.279741i	$-0.909751\pi$
$149$		−	1.85074e6i		−	0.559483i	0.960075	−	0.279741i	$-0.0902487\pi$
$150$		0			0
$151$			3.81427e6i			1.10785i	0.832567	+	0.553925i	$0.186871\pi$
$151$			3.81427e6i			1.10785i	−0.832567	+	0.553925i	$0.813129\pi$
$152$	4.43450e6	−	1.82448e6i	1.26274	−	0.519529i
$153$		0			0
$154$	3.39104e6	−	2.59777e6i	0.928476	−	0.711276i
$155$	3.04980e6			0.818985
$156$		0			0
$157$		−	2.53058e6i		−	0.653916i	−0.945039	−	0.326958i	$-0.893976\pi$
$157$		−	2.53058e6i		−	0.653916i	0.945039	−	0.326958i	$-0.106024\pi$
$158$	−3.39990e6	+	2.60455e6i	−0.861976	+	0.660332i
$159$		0			0
$160$	−3.27715e6	+	418233.i	−0.800084	+	0.102108i
$161$	4.36015e6			1.04478
$162$		0			0
$163$	2.22831e6			0.514533			0.257266	−	0.966341i	$-0.417178\pi$
$163$	2.22831e6			0.514533			0.257266	+	0.966341i	$0.417178\pi$
$164$	568610.	−	2.10870e6i	0.128909	−	0.478061i
$165$		0			0
$166$	−3.21268e6	−	4.19372e6i	−0.702333	−	0.916802i
$167$		−	2.36063e6i		−	0.506849i	−0.967355	−	0.253425i	$-0.918443\pi$
$167$		−	2.36063e6i		−	0.506849i	0.967355	−	0.253425i	$-0.0815569\pi$
$168$		0			0
$169$	1.86495e6			0.386373
$170$	−1.05911e6	+	811349.i	−0.215573	+	0.165143i
$171$		0			0
$172$	1.18637e6	−	4.39966e6i	0.233149	−	0.864638i
$173$			1.45298e6i			0.280621i	0.990108	+	0.140311i	$0.0448101\pi$
$173$			1.45298e6i			0.280621i	−0.990108	+	0.140311i	$0.955190\pi$
$174$		0			0
$175$			1.51659e6i			0.282979i
$176$	6.80655e6	+	3.95860e6i	1.24850	+	0.726112i
$177$		0			0
$178$	4.58715e6	+	5.98792e6i	0.813361	+	1.06174i
$179$	−1.42925e6			−0.249201			−0.124601	−	0.992207i	$-0.539765\pi$
$179$	−1.42925e6			−0.249201			−0.124601	+	0.992207i	$0.539765\pi$
$180$		0			0
$181$			3.01823e6i			0.508999i	0.967073	+	0.254500i	$0.0819107\pi$
$181$			3.01823e6i			0.508999i	−0.967073	+	0.254500i	$0.918089\pi$
$182$	−2.32567e6	−	3.03585e6i	−0.385775	−	0.503577i
$183$		0			0
$184$	3.05795e6	+	7.43252e6i	0.490883	+	1.19312i
$185$	−7.31898e6			−1.15594
$186$		0			0
$187$	3.17981e6			0.486268
$188$	−9.26103e6	−	2.49723e6i	−1.39375	−	0.375825i
$189$		0			0
$190$	−5.99664e6	+	4.59383e6i	−0.874273	+	0.669753i
$191$			1.01412e7i			1.45543i	0.685880	+	0.727715i	$0.259418\pi$
$191$			1.01412e7i			1.45543i	−0.685880	+	0.727715i	$0.740582\pi$
$192$		0			0
$193$	−888729.			−0.123622			−0.0618112	−	0.998088i	$-0.519688\pi$
$193$	−888729.			−0.123622			−0.0618112	+	0.998088i	$0.519688\pi$
$194$	−5.65581e6	−	7.38290e6i	−0.774621	−	1.01117i
$195$		0			0
$196$	−674755.	+	2.50234e6i	−0.0896145	+	0.332337i
$197$			9.41343e6i			1.23126i	0.788036	+	0.615629i	$0.211098\pi$
$197$			9.41343e6i			1.23126i	−0.788036	+	0.615629i	$0.788902\pi$
$198$		0			0
$199$		−	9.47494e6i		−	1.20231i	−0.799132	−	0.601156i	$-0.794707\pi$
$199$		−	9.47494e6i		−	1.20231i	0.799132	−	0.601156i	$-0.205293\pi$
$200$	−2.58525e6	+	1.06365e6i	−0.323157	+	0.132956i
$201$		0			0
$202$	2.07832e6	−	1.59214e6i	0.252150	−	0.193164i
$203$	−7.91232e6			−0.945836
$204$		0			0
$205$			3.44057e6i			0.399363i
$206$	6.17821e6	−	4.73293e6i	0.706742	−	0.541413i
$207$		0			0
$208$	3.54396e6	−	6.09361e6i	0.393821	−	0.677149i
$209$	1.80040e7			1.97210
$210$		0			0
$211$	−7.65737e6			−0.815140			−0.407570	−	0.913174i	$-0.633624\pi$
$211$	−7.65737e6			−0.815140			−0.407570	+	0.913174i	$0.633624\pi$
$212$	−1.45266e7	−	3.91710e6i	−1.52460	−	0.411109i
$213$		0			0
$214$	−3.15022e6	−	4.11220e6i	−0.321440	−	0.419597i
$215$			7.17852e6i			0.722303i
$216$		0			0
$217$	−8.40223e6			−0.822272
$218$	1.53331e7	−	1.17462e7i	1.48000	−	1.13378i
$219$		0			0
$220$	−1.19764e7	−	3.22944e6i	−1.12476	−	0.303291i
$221$		−	2.84674e6i		−	0.263737i
$222$		0			0
$223$		−	3.04442e6i		−	0.274530i	−0.990534	−	0.137265i	$-0.956169\pi$
$223$		−	3.04442e6i		−	0.274530i	0.990534	−	0.137265i	$-0.0438311\pi$
$224$	9.02858e6	−	1.15224e6i	0.803295	−	0.102517i
$225$		0			0
$226$	−3.73189e6	−	4.87149e6i	−0.323299	−	0.422023i
$227$	1.21128e7			1.03554			0.517772	−	0.855519i	$-0.326762\pi$
$227$	1.21128e7			1.03554			0.517772	+	0.855519i	$0.326762\pi$
$228$		0			0
$229$			1.06343e7i			0.885528i	0.896638	+	0.442764i	$0.146002\pi$
$229$			1.06343e7i			0.885528i	−0.896638	+	0.442764i	$0.853998\pi$
$230$	−7.69956e6	−	1.00508e7i	−0.632823	−	0.826067i
$231$		0			0
$232$	−5.54924e6	−	1.34877e7i	−0.444395	−	1.08013i
$233$	−1.39434e7			−1.10231			−0.551153	−	0.834404i	$-0.685812\pi$
$233$	−1.39434e7			−1.10231			−0.551153	+	0.834404i	$0.685812\pi$
$234$		0			0
$235$	1.51104e7			1.16432
$236$	−2.26239e6	+	8.39011e6i	−0.172120	+	0.638310i
$237$		0			0
$238$	2.91786e6	−	2.23528e6i	0.216438	−	0.165806i
$239$		−	828490.i		−	0.0606867i	−0.999540	−	0.0303433i	$-0.990340\pi$
$239$		−	828490.i		−	0.0606867i	0.999540	−	0.0303433i	$-0.00966007\pi$
$240$		0			0
$241$	−2.59338e7			−1.85274			−0.926372	−	0.376611i	$-0.877089\pi$
$241$	−2.59338e7			−1.85274			−0.926372	+	0.376611i	$0.877089\pi$
$242$	9.35991e6	+	1.22181e7i	0.660428	+	0.862102i
$243$		0			0
$244$	−6.59416e6	−	1.77811e6i	−0.453931	−	0.122402i
$245$		−	4.08283e6i		−	0.277628i
$246$		0			0
$247$		−	1.61182e7i		−	1.06961i
$248$	−5.89283e6	−	1.43228e7i	−0.386340	−	0.939018i
$249$		0			0
$250$	1.35004e7	−	1.03423e7i	0.864028	−	0.661904i
$251$	4.68287e6			0.296136			0.148068	−	0.988977i	$-0.452695\pi$
$251$	4.68287e6			0.296136			0.148068	+	0.988977i	$0.452695\pi$
$252$		0			0
$253$			3.01758e7i			1.86336i
$254$	−1.63703e7	+	1.25408e7i	−0.998978	+	0.765285i
$255$		0			0
$256$	8.29627e6	+	1.45824e7i	0.494496	+	0.869180i
$257$	−1.06513e7			−0.627487			−0.313743	−	0.949508i	$-0.601583\pi$
$257$	−1.06513e7			−0.627487			−0.313743	+	0.949508i	$0.601583\pi$
$258$		0			0
$259$	2.01639e7			1.16058
$260$	−2.89118e6	+	1.07220e7i	−0.164496	+	0.610035i
$261$		0			0
$262$	−3.36278e6	−	4.38967e6i	−0.186980	−	0.244077i
$263$		−	1.08575e7i		−	0.596848i	−0.954433	−	0.298424i	$-0.903539\pi$
$263$		−	1.08575e7i		−	0.596848i	0.954433	−	0.298424i	$-0.0964609\pi$
$264$		0			0
$265$	2.37017e7			1.27363
$266$	1.65208e7	−	1.26561e7i	0.877782	−	0.672441i
$267$		0			0
$268$	−3.45746e6	+	1.28220e7i	−0.179619	+	0.666120i
$269$			1.27083e7i			0.652878i	0.945218	+	0.326439i	$0.105849\pi$
$269$			1.27083e7i			0.652878i	−0.945218	+	0.326439i	$0.894151\pi$
$270$		0			0
$271$			2.24450e7i			1.12775i	0.825861	+	0.563874i	$0.190690\pi$
$271$			2.24450e7i			1.12775i	−0.825861	+	0.563874i	$0.809310\pi$
$272$	5.85677e6	+	3.40622e6i	0.291039	+	0.169265i
$273$		0			0
$274$	−8.00097e6	−	1.04442e7i	−0.388947	−	0.507719i
$275$	−1.04961e7			−0.504694
$276$		0			0
$277$		−	1.32124e7i		−	0.621646i	−0.950468	−	0.310823i	$-0.899395\pi$
$277$		−	1.32124e7i		−	0.621646i	0.950468	−	0.310823i	$-0.100605\pi$
$278$	−1.44542e7	−	1.88680e7i	−0.672758	−	0.878197i
$279$		0			0
$280$	−1.32600e7	+	5.45555e6i	−0.604045	+	0.248522i
$281$	−623477.			−0.0280997			−0.0140498	−	0.999901i	$-0.504472\pi$
$281$	−623477.			−0.0280997			−0.0140498	+	0.999901i	$0.504472\pi$
$282$		0			0
$283$	−484240.			−0.0213649			−0.0106825	−	0.999943i	$-0.503400\pi$
$283$	−484240.			−0.0213649			−0.0106825	+	0.999943i	$0.503400\pi$
$284$	−1.43681e7	−	3.87434e6i	−0.627253	−	0.169139i
$285$		0			0
$286$	2.10106e7	−	1.60955e7i	0.898131	−	0.688029i
$287$		−	9.47880e6i		−	0.400966i
$288$		0			0
$289$	−2.14015e7			−0.886646
$290$	1.39723e7	+	1.82390e7i	0.572894	+	0.747837i
$291$		0			0
$292$	−1.07621e7	+	3.99116e7i	−0.432265	+	1.60306i
$293$			1.23605e7i			0.491398i	0.969346	+	0.245699i	$0.0790175\pi$
$293$			1.23605e7i			0.491398i	−0.969346	+	0.245699i	$0.920983\pi$
$294$		0			0
$295$		−	1.36894e7i		−	0.533233i
$296$	1.41418e7	+	3.43723e7i	0.545291	+	1.32536i
$297$		0			0
$298$	1.17535e7	−	9.00396e6i	0.444138	−	0.340240i
$299$	2.70151e7			1.01063
$300$		0			0
$301$		−	1.97769e7i		−	0.725202i
$302$	−2.42233e7	+	1.85567e7i	−0.879451	+	0.673719i
$303$		0			0
$304$	3.31609e7	+	1.92859e7i	1.18033	+	0.686467i
$305$	1.07591e7			0.379206
$306$		0			0
$307$	−2.59925e7			−0.898323			−0.449161	−	0.893451i	$-0.648277\pi$
$307$	−2.59925e7			−0.898323			−0.449161	+	0.893451i	$0.648277\pi$
$308$	3.29952e7	+	8.89715e6i	1.12927	+	0.304508i
$309$		0			0
$310$	1.48374e7	+	1.93683e7i	0.498051	+	0.650140i
$311$		−	3.78807e7i		−	1.25932i	−0.776869	−	0.629662i	$-0.783193\pi$
$311$		−	3.78807e7i		−	1.25932i	0.776869	−	0.629662i	$-0.216807\pi$
$312$		0			0
$313$	5.00119e7			1.63095			0.815474	−	0.578794i	$-0.196476\pi$
$313$	5.00119e7			1.63095			0.815474	+	0.578794i	$0.196476\pi$
$314$	1.60709e7	−	1.23114e7i	0.519102	−	0.397667i
$315$		0			0
$316$	−3.30814e7	−	8.92040e6i	−1.04839	−	0.282698i
$317$			4.24239e7i			1.33178i	0.746049	+	0.665891i	$0.231948\pi$
$317$			4.24239e7i			1.33178i	−0.746049	+	0.665891i	$0.768052\pi$
$318$		0			0
$319$		−	5.47597e7i		−	1.68690i
$320$	−1.85996e7	−	1.87774e7i	−0.567614	−	0.573041i
$321$		0			0
$322$	2.12124e7	+	2.76900e7i	0.635363	+	0.829382i
$323$	1.54917e7			0.459718
$324$		0			0
$325$			9.39666e6i			0.273731i
$326$	1.08409e7	+	1.41513e7i	0.312904	+	0.408454i
$327$		0			0
$328$	1.61580e7	−	6.64787e6i	0.457895	−	0.188391i
$329$	−4.16292e7			−1.16899
$330$		0			0
$331$	7.44447e6			0.205282			0.102641	−	0.994718i	$-0.467271\pi$
$331$	7.44447e6			0.205282			0.102641	+	0.994718i	$0.467271\pi$
$332$	1.10032e7	−	4.08054e7i	0.300679	−	1.11507i
$333$		0			0
$334$	1.49916e7	−	1.14846e7i	0.402355	−	0.308231i
$335$		−	2.09205e7i		−	0.556465i
$336$		0			0
$337$	−5.96814e7			−1.55937			−0.779686	−	0.626171i	$-0.784621\pi$
$337$	−5.96814e7			−1.55937			−0.779686	+	0.626171i	$0.784621\pi$
$338$	9.07309e6	+	1.18437e7i	0.234966	+	0.306717i
$339$		0			0
$340$	−1.03052e7	−	2.77881e6i	−0.262193	−	0.0707004i
$341$		−	5.81503e7i		−	1.46652i
$342$		0			0
$343$			4.39270e7i			1.08855i
$344$	3.37126e7	−	1.38704e7i	0.828166	−	0.340732i
$345$		0			0
$346$	−9.22740e6	+	7.06882e6i	−0.222767	+	0.170655i
$347$	−2.20906e7			−0.528713			−0.264356	−	0.964425i	$-0.585159\pi$
$347$	−2.20906e7			−0.528713			−0.264356	+	0.964425i	$0.585159\pi$
$348$		0			0
$349$		−	5.69624e6i		−	0.134002i	−0.997753	−	0.0670011i	$-0.978657\pi$
$349$		−	5.69624e6i		−	0.134002i	0.997753	−	0.0670011i	$-0.0213431\pi$
$350$	−9.63141e6	+	7.37831e6i	−0.224639	+	0.172089i
$351$		0			0
$352$	7.97441e6	+	6.24851e7i	0.182840	+	1.43268i
$353$	4.12066e7			0.936790			0.468395	−	0.883519i	$-0.344832\pi$
$353$	4.12066e7			0.936790			0.468395	+	0.883519i	$0.344832\pi$
$354$		0			0
$355$	2.34430e7			0.523997
$356$	−1.57106e7	+	5.82632e7i	−0.348212	+	1.29135i
$357$		0			0
$358$	−6.95340e6	−	9.07674e6i	−0.151547	−	0.197825i
$359$			2.94445e6i			0.0636386i	0.999494	+	0.0318193i	$0.0101301\pi$
$359$			2.94445e6i			0.0636386i	−0.999494	+	0.0318193i	$0.989870\pi$
$360$		0			0
$361$	4.06677e7			0.864426
$362$	−1.91679e7	+	1.46839e7i	−0.404062	+	0.309539i
$363$		0			0
$364$	7.96523e6	−	2.95392e7i	0.165156	−	0.612483i
$365$		−	6.51200e7i		−	1.33917i
$366$		0			0
$367$		−	2.64356e7i		−	0.534800i	−0.963586	−	0.267400i	$-0.913836\pi$
$367$		−	2.64356e7i		−	0.534800i	0.963586	−	0.267400i	$-0.0861645\pi$
$368$	−3.23245e7	+	5.55797e7i	−0.648616	+	1.11525i
$369$		0			0
$370$	−3.56072e7	−	4.64805e7i	−0.702964	−	0.917626i
$371$	−6.52985e7			−1.27874
$372$		0			0
$373$		−	2.13360e7i		−	0.411136i	−0.978643	−	0.205568i	$-0.934096\pi$
$373$		−	2.13360e7i		−	0.411136i	0.978643	−	0.205568i	$-0.0659042\pi$
$374$	1.54699e7	+	2.01939e7i	0.295715	+	0.386017i
$375$		0			0
$376$	−2.91963e7	−	7.09631e7i	−0.549242	−	1.33496i
$377$	−4.90240e7			−0.914923
$378$		0			0
$379$	−1.21237e7			−0.222698			−0.111349	−	0.993781i	$-0.535517\pi$
$379$	−1.21237e7			−0.222698			−0.111349	+	0.993781i	$0.535517\pi$
$380$	−5.83480e7	−	1.57335e7i	−1.06335	−	0.286731i
$381$		0			0
$382$	−6.44039e7	+	4.93377e7i	−1.15537	+	0.885093i
$383$			1.48851e7i			0.264945i	0.991187	+	0.132472i	$0.0422915\pi$
$383$			1.48851e7i			0.264945i	−0.991187	+	0.132472i	$0.957708\pi$
$384$		0			0
$385$	−5.38352e7			−0.943374
$386$	−4.32372e6	−	5.64404e6i	−0.0751788	−	0.0981359i
$387$		0			0
$388$	1.93707e7	−	7.18365e7i	0.331627	−	1.22984i
$389$		−	6.56561e7i		−	1.11539i	−0.830046	−	0.557694i	$-0.811686\pi$
$389$		−	6.56561e7i		−	1.11539i	0.830046	−	0.557694i	$-0.188314\pi$
$390$		0			0
$391$			2.59651e7i			0.434370i
$392$	−1.91743e7	+	7.88887e6i	−0.318318	+	0.130965i
$393$		0			0
$394$	−5.97817e7	+	4.57969e7i	−0.977417	+	0.748767i
$395$	5.39759e7			0.875807
$396$		0			0
$397$			1.53950e7i			0.246042i	0.992404	+	0.123021i	$0.0392582\pi$
$397$			1.53950e7i			0.246042i	−0.992404	+	0.123021i	$0.960742\pi$
$398$	6.01724e7	−	4.60961e7i	0.954439	−	0.731165i
$399$		0			0
$400$	−1.93323e7	−	1.12434e7i	−0.302067	−	0.175679i
$401$	5.25147e7			0.814418			0.407209	−	0.913335i	$-0.366502\pi$
$401$	5.25147e7			0.814418			0.407209	+	0.913335i	$0.366502\pi$
$402$		0			0
$403$	−5.20594e7			−0.795398
$404$	2.02223e7	+	5.45294e6i	0.306681	+	0.0826964i
$405$		0			0
$406$	−3.84939e7	−	5.02487e7i	−0.575193	−	0.750838i
$407$			1.39550e8i			2.06989i
$408$		0			0
$409$	−5.65258e7			−0.826184			−0.413092	−	0.910689i	$-0.635551\pi$
$409$	−5.65258e7			−0.826184			−0.413092	+	0.910689i	$0.635551\pi$
$410$	−2.18500e7	+	1.67385e7i	−0.317029	+	0.242866i
$411$		0			0
$412$	6.01147e7	+	1.62099e7i	0.859586	+	0.231787i
$413$			3.77143e7i			0.535373i
$414$		0			0
$415$			6.65784e7i			0.931513i
$416$	5.59402e7	−	7.13914e6i	0.777041	−	0.0991668i
$417$		0			0
$418$	8.75903e7	+	1.14337e8i	1.19930	+	1.56552i
$419$	−7.01771e7			−0.954011			−0.477006	−	0.878900i	$-0.658278\pi$
$419$	−7.01771e7			−0.954011			−0.477006	+	0.878900i	$0.658278\pi$
$420$		0			0
$421$			9.23872e6i			0.123813i	0.998082	+	0.0619064i	$0.0197180\pi$
$421$			9.23872e6i			0.123813i	−0.998082	+	0.0619064i	$0.980282\pi$
$422$	−3.72535e7	−	4.86295e7i	−0.495713	−	0.647087i
$423$		0			0
$424$	−4.57965e7	−	1.11311e8i	−0.600807	−	1.46029i
$425$	−9.03145e6			−0.117650
$426$		0			0
$427$	−2.96414e7			−0.380728
$428$	1.07893e7	−	4.00122e7i	0.137613	−	0.510341i
$429$		0			0
$430$	−4.55885e7	+	3.49239e7i	−0.573390	+	0.439256i
$431$		−	1.50713e7i		−	0.188243i	−0.995561	−	0.0941215i	$-0.969996\pi$
$431$		−	1.50713e7i		−	0.188243i	0.995561	−	0.0941215i	$-0.0300042\pi$
$432$		0			0
$433$	1.18653e8			1.46156			0.730779	−	0.682614i	$-0.239157\pi$
$433$	1.18653e8			1.46156			0.730779	+	0.682614i	$0.239157\pi$
$434$	−4.08773e7	−	5.33600e7i	−0.500050	−	0.652749i
$435$		0			0
$436$	1.49193e8	+	4.02298e7i	1.80007	+	0.485388i
$437$			1.47014e8i			1.76162i
$438$		0			0
$439$			8.40011e6i			0.0992868i	0.998767	+	0.0496434i	$0.0158085\pi$
$439$			8.40011e6i			0.0992868i	−0.998767	+	0.0496434i	$0.984192\pi$
$440$	−3.77568e7	−	9.17700e7i	−0.443239	−	1.07731i
$441$		0			0
$442$	1.80788e7	−	1.38496e7i	0.209364	−	0.160387i
$443$	−1.75231e7			−0.201558			−0.100779	−	0.994909i	$-0.532133\pi$
$443$	−1.75231e7			−0.201558			−0.100779	+	0.994909i	$0.532133\pi$
$444$		0			0
$445$		−	9.50626e7i		−	1.07877i
$446$	1.93341e7	−	1.48113e7i	0.217932	−	0.166950i
$447$		0			0
$448$	5.12420e7	+	5.17320e7i	0.569892	+	0.575341i
$449$	1.08791e8			1.20186			0.600928	−	0.799303i	$-0.294798\pi$
$449$	1.08791e8			1.20186			0.600928	+	0.799303i	$0.294798\pi$
$450$		0			0
$451$	6.56010e7			0.715123
$452$	1.27814e7	−	4.74002e7i	0.138409	−	0.513292i
$453$		0			0
$454$	5.89297e7	+	7.69249e7i	0.629748	+	0.822052i
$455$			4.81963e7i			0.511658i
$456$		0			0
$457$	1.35491e8			1.41959			0.709795	−	0.704409i	$-0.248788\pi$
$457$	1.35491e8			1.41959			0.709795	+	0.704409i	$0.248788\pi$
$458$	−6.75351e7	+	5.17365e7i	−0.702964	+	0.538518i
$459$		0			0
$460$	2.63704e7	−	9.77950e7i	0.270921	−	1.00472i
$461$		−	6.50970e7i		−	0.664444i	−0.943201	−	0.332222i	$-0.892202\pi$
$461$		−	6.50970e7i		−	0.664444i	0.943201	−	0.332222i	$-0.107798\pi$
$462$		0			0
$463$		−	4.98070e7i		−	0.501819i	−0.968011	−	0.250910i	$-0.919270\pi$
$463$		−	4.98070e7i		−	0.501819i	0.968011	−	0.250910i	$-0.0807297\pi$
$464$	5.86588e7	−	1.00860e8i	0.587191	−	1.00964i
$465$		0			0
$466$	−6.78357e7	−	8.85504e7i	−0.670348	−	0.875050i
$467$	1.15723e7			0.113624			0.0568120	−	0.998385i	$-0.481906\pi$
$467$	1.15723e7			0.113624			0.0568120	+	0.998385i	$0.481906\pi$
$468$		0			0
$469$			5.76363e7i			0.558698i
$470$	7.35127e7	+	9.59611e7i	0.708058	+	0.924276i
$471$		0			0
$472$	−6.42896e7	+	2.64506e7i	−0.611385	+	0.251542i
$473$	1.36872e8			1.29340
$474$		0			0
$475$	−5.11358e7			−0.477138
$476$	2.83911e7	+	7.65565e6i	0.263246	+	0.0709841i
$477$		0			0
$478$	5.26148e6	−	4.03065e6i	0.0481753	−	0.0369055i
$479$			6.30807e7i			0.573971i	0.957935	+	0.286985i	$0.0926531\pi$
$479$			6.30807e7i			0.573971i	−0.957935	+	0.286985i	$0.907347\pi$
$480$		0			0
$481$	1.24933e8			1.12265
$482$	−1.26169e8	−	1.64698e8i	−1.12671	−	1.47077i
$483$		0			0
$484$	−3.20570e7	+	1.18884e8i	−0.282739	+	1.04854i
$485$			1.17209e8i			1.02739i
$486$		0			0
$487$			2.05406e8i			1.77839i	0.457530	+	0.889194i	$0.348734\pi$
$487$			2.05406e8i			1.77839i	−0.457530	+	0.889194i	$0.651266\pi$
$488$	−2.07887e7	−	5.05281e7i	−0.178883	−	0.434784i
$489$		0			0
$490$	2.59288e7	−	1.98632e7i	0.220391	−	0.168835i
$491$	1.91695e8			1.61944			0.809721	−	0.586815i	$-0.199618\pi$
$491$	1.91695e8			1.61944			0.809721	+	0.586815i	$0.199618\pi$
$492$		0			0
$493$		−	4.71186e7i		−	0.393234i
$494$	1.02361e8	−	7.84158e7i	0.849093	−	0.650463i
$495$		0			0
$496$	6.22909e7	−	1.07105e8i	0.510481	−	0.877737i
$497$	−6.45858e7			−0.526099
$498$		0			0
$499$	−1.17889e8			−0.948792			−0.474396	−	0.880312i	$-0.657333\pi$
$499$	−1.17889e8			−0.948792			−0.474396	+	0.880312i	$0.657333\pi$
$500$	1.31361e8	+	3.54214e7i	1.05089	+	0.283371i
$501$		0			0
$502$	2.27824e7	+	2.97395e7i	0.180090	+	0.235083i
$503$		−	1.07931e7i		−	0.0848087i	−0.999101	−	0.0424044i	$-0.986498\pi$
$503$		−	1.07931e7i		−	0.0848087i	0.999101	−	0.0424044i	$-0.0135018\pi$
$504$		0			0
$505$	−3.29948e7			−0.256196
$506$	−1.91637e8	+	1.46807e8i	−1.47920	+	1.13317i
$507$		0			0
$508$	−1.59285e8	−	4.29512e7i	−1.21502	−	0.327630i
$509$		−	4.84357e7i		−	0.367293i	−0.982992	−	0.183646i	$-0.941210\pi$
$509$		−	4.84357e7i		−	0.367293i	0.982992	−	0.183646i	$-0.0587901\pi$
$510$		0			0
$511$			1.79406e8i			1.34454i
$512$	−5.22465e7	+	1.23631e8i	−0.389267	+	0.921125i
$513$		0			0
$514$	−5.18193e7	−	6.76432e7i	−0.381595	−	0.498121i
$515$	−9.80835e7			−0.718083
$516$		0			0
$517$		−	2.88108e8i		−	2.08489i
$518$	9.80984e7	+	1.28054e8i	0.705785	+	0.921309i
$519$		0			0
$520$	−8.21577e7	+	3.38021e7i	−0.584303	+	0.240399i
$521$	−2.16291e8			−1.52941			−0.764706	−	0.644379i	$-0.777116\pi$
$521$	−2.16291e8			−1.52941			−0.764706	+	0.644379i	$0.777116\pi$
$522$		0			0
$523$	9.01442e7			0.630134			0.315067	−	0.949069i	$-0.397973\pi$
$523$	9.01442e7			0.630134			0.315067	+	0.949069i	$0.397973\pi$
$524$	1.15173e7	−	4.27119e7i	0.0800489	−	0.296863i
$525$		0			0
$526$	6.89527e7	−	5.28225e7i	0.473799	−	0.362962i
$527$		−	5.00361e7i		−	0.341862i
$528$		0			0
$529$	−9.83684e7			−0.664490
$530$	1.15310e8	+	1.50522e8i	0.774533	+	1.01105i
$531$		0			0
$532$	1.60749e8	+	4.33460e7i	1.06761	+	0.287882i
$533$		−	5.87297e7i		−	0.387861i
$534$		0			0
$535$			6.52841e7i			0.426330i
$536$	−9.82495e7	+	4.04227e7i	−0.638022	+	0.262501i
$537$		0			0
$538$	−8.07067e7	+	6.18268e7i	−0.518278	+	0.397036i
$539$	−7.78471e7			−0.497137
$540$		0			0
$541$			2.37875e8i			1.50230i	0.660130	+	0.751151i	$0.270501\pi$
$541$			2.37875e8i			1.50230i	−0.660130	+	0.751151i	$0.729499\pi$
$542$	−1.42541e8	+	1.09196e8i	−0.895247	+	0.685820i
$543$		0			0
$544$	6.86167e6	+	5.37660e7i	0.0426219	+	0.333973i
$545$	−2.43424e8			−1.50375
$546$		0			0
$547$	−2.03235e8			−1.24176			−0.620878	−	0.783908i	$-0.713224\pi$
$547$	−2.03235e8			−1.24176			−0.620878	+	0.783908i	$0.713224\pi$
$548$	2.74027e7	−	1.01623e8i	0.166514	−	0.617520i
$549$		0			0
$550$	−5.10639e7	−	6.66572e7i	−0.306921	−	0.400644i
$551$		−	2.66784e8i		−	1.59479i
$552$		0			0
$553$	−1.48704e8			−0.879322
$554$	8.39080e7	−	6.42792e7i	0.493485	−	0.378043i
$555$		0			0
$556$	4.95044e7	−	1.83588e8i	0.288018	−	1.06812i
$557$			1.22171e7i			0.0706971i	0.999375	+	0.0353486i	$0.0112541\pi$
$557$			1.22171e7i			0.0706971i	−0.999375	+	0.0353486i	$0.988746\pi$
$558$		0			0
$559$		−	1.22536e8i		−	0.701500i
$560$	−9.91571e7	−	5.76685e7i	−0.564625	−	0.328378i
$561$		0			0
$562$	−3.03325e6	−	3.95951e6i	−0.0170883	−	0.0223065i
$563$	8.96182e7			0.502193			0.251097	−	0.967962i	$-0.419209\pi$
$563$	8.96182e7			0.502193			0.251097	+	0.967962i	$0.419209\pi$
$564$		0			0
$565$			7.73384e7i			0.428795i
$566$	−2.35586e6	−	3.07526e6i	−0.0129927	−	0.0169602i
$567$		0			0
$568$	−4.52967e7	−	1.10096e8i	−0.247185	−	0.600795i
$569$	1.36856e8			0.742894			0.371447	−	0.928454i	$-0.378862\pi$
$569$	1.36856e8			0.742894			0.371447	+	0.928454i	$0.378862\pi$
$570$		0			0
$571$	2.26109e8			1.21453			0.607266	−	0.794498i	$-0.292266\pi$
$571$	2.26109e8			1.21453			0.607266	+	0.794498i	$0.292266\pi$
$572$	2.04435e8	+	5.51259e7i	1.09236	+	0.294556i
$573$		0			0
$574$	6.01969e7	−	4.61149e7i	0.318301	−	0.243840i
$575$		−	8.57069e7i		−	0.450829i
$576$		0			0
$577$	7.81285e7			0.406707			0.203354	−	0.979105i	$-0.434816\pi$
$577$	7.81285e7			0.406707			0.203354	+	0.979105i	$0.434816\pi$
$578$	−1.04119e8	−	1.35914e8i	−0.539198	−	0.703851i
$579$		0			0
$580$	−4.78541e7	+	1.77468e8i	−0.245265	+	0.909568i
$581$		−	1.83424e8i		−	0.935251i
$582$		0			0
$583$		−	4.51919e8i		−	2.28063i
$584$	−3.05824e8	+	1.25825e8i	−1.53544	+	0.631726i
$585$		0			0
$586$	−7.84977e7	+	6.01346e7i	−0.390089	+	0.298835i
$587$	−1.63395e7			−0.0807839			−0.0403920	−	0.999184i	$-0.512861\pi$
$587$	−1.63395e7			−0.0807839			−0.0403920	+	0.999184i	$0.512861\pi$
$588$		0			0
$589$		−	2.83303e8i		−	1.38645i
$590$	8.69368e7	−	6.65995e7i	0.423299	−	0.324276i
$591$		0			0
$592$	−1.49487e8	+	2.57033e8i	−0.720507	+	1.23886i
$593$	1.22802e8			0.588898			0.294449	−	0.955667i	$-0.404864\pi$
$593$	1.22802e8			0.588898			0.294449	+	0.955667i	$0.404864\pi$
$594$		0			0
$595$	−4.63231e7			−0.219911
$596$	1.14363e8	+	3.08379e7i	0.540189	+	0.145662i
$597$		0			0
$598$	1.31430e8	+	1.71564e8i	0.614597	+	0.802275i
$599$			1.70436e8i			0.793016i	0.918031	+	0.396508i	$0.129778\pi$
$599$			1.70436e8i			0.793016i	−0.918031	+	0.396508i	$0.870222\pi$
$600$		0			0
$601$	−1.40236e8			−0.646005			−0.323003	−	0.946398i	$-0.604692\pi$
$601$	−1.40236e8			−0.646005			−0.323003	+	0.946398i	$0.604692\pi$
$602$	1.25597e8	−	9.62158e7i	0.575691	−	0.441019i
$603$		0			0
$604$	−2.35695e8	−	6.35551e7i	−1.06964	−	0.288429i
$605$		−	1.93972e8i		−	0.875935i
$606$		0			0
$607$		−	3.57258e8i		−	1.59741i	−0.601723	−	0.798705i	$-0.705519\pi$
$607$		−	3.57258e8i		−	1.59741i	0.601723	−	0.798705i	$-0.294481\pi$
$608$	3.88506e7	+	3.04421e8i	0.172857	+	1.35445i
$609$		0			0
$610$	5.23435e7	+	6.83275e7i	0.230608	+	0.301028i
$611$	−2.57931e8			−1.13078
$612$		0			0
$613$			3.35039e8i			1.45450i	0.686372	+	0.727250i	$0.259202\pi$
$613$			3.35039e8i			1.45450i	−0.686372	+	0.727250i	$0.740798\pi$
$614$	−1.26455e8	−	1.65070e8i	−0.546299	−	0.713121i
$615$		0			0
$616$	1.04021e8	+	2.52827e8i	0.445017	+	1.08164i
$617$	3.50474e8			1.49211			0.746055	−	0.665885i	$-0.231946\pi$
$617$	3.50474e8			1.49211			0.746055	+	0.665885i	$0.231946\pi$
$618$		0			0
$619$	4.73998e7			0.199850			0.0999252	−	0.994995i	$-0.468140\pi$
$619$	4.73998e7			0.199850			0.0999252	+	0.994995i	$0.468140\pi$
$620$	−5.08171e7	+	1.88456e8i	−0.213223	+	0.790742i
$621$		0			0
$622$	2.40569e8	−	1.84292e8i	0.999696	−	0.765835i
$623$			2.61899e8i			1.08310i
$624$		0			0
$625$	−1.29017e8			−0.528453
$626$	2.43311e8	+	3.17610e8i	0.991832	+	1.29471i
$627$		0			0
$628$	1.56372e8	+	4.21657e7i	0.631365	+	0.170247i
$629$			1.20078e8i			0.482514i
$630$		0			0
$631$		−	6.31596e7i		−	0.251392i	−0.992069	−	0.125696i	$-0.959884\pi$
$631$		−	6.31596e7i		−	0.251392i	0.992069	−	0.125696i	$-0.0401164\pi$
$632$	−1.04292e8	−	2.53488e8i	−0.413144	−	1.00417i
$633$		0			0
$634$	−2.69421e8	+	2.06395e8i	−1.05722	+	0.809899i
$635$	2.59890e8			1.01501
$636$		0			0
$637$			6.96931e7i			0.269632i
$638$	3.47762e8	−	2.66409e8i	1.33912	−	1.02586i
$639$		0			0
$640$	2.87614e7	−	2.09473e8i	0.109716	−	0.799077i
$641$	−1.45116e8			−0.550987			−0.275494	−	0.961303i	$-0.588841\pi$
$641$	−1.45116e8			−0.550987			−0.275494	+	0.961303i	$0.588841\pi$
$642$		0			0
$643$	8.95736e7			0.336936			0.168468	−	0.985707i	$-0.446118\pi$
$643$	8.95736e7			0.336936			0.168468	+	0.985707i	$0.446118\pi$
$644$	−7.26508e7	+	2.69426e8i	−0.272009	+	1.00875i
$645$		0			0
$646$	7.53680e7	+	9.83829e7i	0.279569	+	0.364941i
$647$		−	4.79942e8i		−	1.77205i	−0.463638	−	0.886025i	$-0.653456\pi$
$647$		−	4.79942e8i		−	1.77205i	0.463638	−	0.886025i	$-0.346544\pi$
$648$		0			0
$649$	−2.61014e8			−0.954837
$650$	−5.96753e7	+	4.57153e7i	−0.217297	+	0.166464i
$651$		0			0
$652$	−3.71291e7	+	1.37694e8i	−0.133959	+	0.496789i
$653$			2.92267e8i			1.04964i	0.851213	+	0.524820i	$0.175867\pi$
$653$			2.92267e8i			1.04964i	−0.851213	+	0.524820i	$0.824133\pi$
$654$		0			0
$655$			6.96891e7i			0.247994i
$656$	1.20828e8	+	7.02721e7i	0.428013	+	0.248927i
$657$		0			0
$658$	−2.02529e8	−	2.64374e8i	−0.710900	−	0.927986i
$659$	−4.27588e8			−1.49406			−0.747032	−	0.664788i	$-0.768522\pi$
$659$	−4.27588e8			−1.49406			−0.747032	+	0.664788i	$0.768522\pi$
$660$		0			0
$661$			3.87743e8i			1.34258i	0.741196	+	0.671288i	$0.234259\pi$
$661$			3.87743e8i			1.34258i	−0.741196	+	0.671288i	$0.765741\pi$
$662$	3.62178e7	+	4.72775e7i	0.124838	+	0.162960i
$663$		0			0
$664$	3.12673e8	−	1.28643e8i	1.06804	−	0.439422i
$665$	−2.62280e8			−0.891867
$666$		0			0
$667$	4.47147e8			1.50686
$668$	1.45870e8	+	3.93339e7i	0.489370	+	0.131958i
$669$		0			0
$670$	1.32860e8	−	1.01779e8i	0.441742	−	0.338404i
$671$		−	2.05143e8i		−	0.679029i
$672$		0			0
$673$	1.03450e8			0.339381			0.169690	−	0.985497i	$-0.445723\pi$
$673$	1.03450e8			0.339381			0.169690	+	0.985497i	$0.445723\pi$
$674$	−2.90354e8	−	3.79018e8i	−0.948304	−	1.23788i
$675$		0			0
$676$	−3.10746e7	+	1.15241e8i	−0.100593	+	0.373049i
$677$		−	2.13601e8i		−	0.688395i	−0.938897	−	0.344197i	$-0.888151\pi$
$677$		−	2.13601e8i		−	0.688395i	0.938897	−	0.344197i	$-0.111849\pi$
$678$		0			0
$679$		−	3.22912e8i		−	1.03151i
$680$	−3.24883e7	−	7.89645e7i	−0.103324	−	0.251134i
$681$		0			0
$682$	3.69294e8	−	2.82904e8i	1.16418	−	0.891840i
$683$	5.14381e8			1.61444			0.807222	−	0.590248i	$-0.200970\pi$
$683$	5.14381e8			1.61444			0.807222	+	0.590248i	$0.200970\pi$
$684$		0			0
$685$			1.65809e8i			0.515866i
$686$	−2.78967e8	+	2.13708e8i	−0.864132	+	0.661984i
$687$		0			0
$688$	2.52100e8	+	1.46618e8i	0.774119	+	0.450218i
$689$	−4.04583e8			−1.23694
$690$		0			0
$691$	3.80607e8			1.15357			0.576783	−	0.816897i	$-0.304308\pi$
$691$	3.80607e8			1.15357			0.576783	+	0.816897i	$0.304308\pi$
$692$	−8.97837e7	−	2.42101e7i	−0.270944	−	0.0730599i
$693$		0			0
$694$	−1.07472e8	−	1.40291e8i	−0.321527	−	0.419711i
$695$			2.99543e8i			0.892288i
$696$		0			0
$697$	5.64471e7			0.166703
$698$	3.61750e7	−	2.77125e7i	0.106376	−	0.0814910i
$699$		0			0
$700$	−9.37147e7	−	2.52701e7i	−0.273221	−	0.0736739i
$701$			2.83744e8i			0.823707i	0.911250	+	0.411854i	$0.135119\pi$
$701$			2.83744e8i			0.823707i	−0.911250	+	0.411854i	$0.864881\pi$
$702$		0			0
$703$			6.79876e8i			1.95688i
$704$	−3.58027e8	+	3.54637e8i	−1.02612	+	1.01640i
$705$		0			0
$706$	2.00472e8	+	2.61690e8i	0.569692	+	0.743658i
$707$	9.09012e7			0.257224
$708$		0			0
$709$		−	1.29996e8i		−	0.364746i	−0.983229	−	0.182373i	$-0.941622\pi$
$709$		−	1.29996e8i		−	0.364746i	0.983229	−	0.182373i	$-0.0583778\pi$
$710$	1.14052e8	+	1.48879e8i	0.318659	+	0.415967i
$711$		0			0
$712$	−4.46444e8	+	1.83680e8i	−1.23688	+	0.508888i
$713$	4.74833e8			1.31000
$714$		0			0
$715$	−3.33558e8			−0.912542
$716$	2.38149e7	−	8.83178e7i	0.0648797	−	0.240607i
$717$		0			0
$718$	−1.86993e7	+	1.43249e7i	−0.0505186	+	0.0387007i
$719$		−	1.93158e8i		−	0.519669i	−0.965653	−	0.259834i	$-0.916332\pi$
$719$		−	1.93158e8i		−	0.519669i	0.965653	−	0.259834i	$-0.0836679\pi$
$720$		0			0
$721$	2.70221e8			0.720965
$722$	1.97850e8	+	2.58268e8i	0.525685	+	0.686212i
$723$		0			0
$724$	−1.86505e8	−	5.02911e7i	−0.491446	−	0.132518i
$725$			1.55531e8i			0.408135i
$726$		0			0
$727$			1.11756e8i			0.290849i	0.989369	+	0.145425i	$0.0464548\pi$
$727$			1.11756e8i			0.290849i	−0.989369	+	0.145425i	$0.953545\pi$
$728$	2.26345e8	−	9.31251e7i	0.586648	−	0.241364i
$729$		0			0
$730$	4.13557e8	−	3.16812e8i	1.06308	−	0.814392i
$731$	1.17773e8			0.301505
$732$		0			0
$733$			5.01654e8i			1.27377i	0.770957	+	0.636887i	$0.219778\pi$
$733$			5.01654e8i			1.27377i	−0.770957	+	0.636887i	$0.780222\pi$
$734$	1.67884e8	−	1.28611e8i	0.424543	−	0.325229i
$735$		0			0
$736$	−5.10230e8	+	6.51160e7i	−1.27977	+	0.163326i
$737$	−3.98890e8			−0.996439
$738$		0			0
$739$	−3.98842e8			−0.988252			−0.494126	−	0.869390i	$-0.664512\pi$
$739$	−3.98842e8			−0.988252			−0.494126	+	0.869390i	$0.664512\pi$
$740$	1.21952e8	−	4.52261e8i	0.300950	−	1.11608i
$741$		0			0
$742$	−3.17681e8	−	4.14690e8i	−0.777642	−	1.01511i
$743$			3.10665e8i			0.757400i	0.925519	+	0.378700i	$0.123629\pi$
$743$			3.10665e8i			0.757400i	−0.925519	+	0.378700i	$0.876371\pi$
$744$		0			0
$745$	−1.86595e8			−0.451264
$746$	1.35498e8	−	1.03801e8i	0.326375	−	0.250025i
$747$		0			0
$748$	−5.29833e7	+	1.96489e8i	−0.126600	+	0.469499i
$749$		−	1.79858e8i		−	0.428041i
$750$		0			0
$751$		−	2.28649e8i		−	0.539820i	−0.962885	−	0.269910i	$-0.913006\pi$
$751$		−	2.28649e8i		−	0.539820i	0.962885	−	0.269910i	$-0.0869940\pi$
$752$	3.08623e8	−	5.30656e8i	0.725729	−	1.24784i
$753$		0			0
$754$	−2.38504e8	−	3.11336e8i	−0.556394	−	0.726299i
$755$	3.84561e8			0.893562
$756$		0			0
$757$		−	5.50703e8i		−	1.26949i	−0.772721	−	0.634746i	$-0.781105\pi$
$757$		−	5.50703e8i		−	1.26949i	0.772721	−	0.634746i	$-0.218895\pi$
$758$	−5.89824e7	−	7.69936e7i	−0.135430	−	0.176786i
$759$		0			0
$760$	−1.83948e8	−	4.47094e8i	−0.419038	−	1.01849i
$761$	4.86110e8			1.10301			0.551507	−	0.834170i	$-0.314053\pi$
$761$	4.86110e8			1.10301			0.551507	+	0.834170i	$0.314053\pi$
$762$		0			0
$763$	6.70637e8			1.50978
$764$	−6.26657e8	−	1.68978e8i	−1.40524	−	0.378922i
$765$		0			0
$766$	−9.45305e7	+	7.24168e7i	−0.210322	+	0.161121i
$767$			2.33674e8i			0.517875i
$768$		0			0
$769$	−6.00550e7			−0.132060			−0.0660298	−	0.997818i	$-0.521033\pi$
$769$	−6.00550e7			−0.132060			−0.0660298	+	0.997818i	$0.521033\pi$
$770$	−2.61911e8	−	3.41890e8i	−0.573696	−	0.748884i
$771$		0			0
$772$	1.48084e7	−	5.49171e7i	0.0321852	−	0.119359i
$773$			5.19835e8i			1.12545i	0.826644	+	0.562726i	$0.190247\pi$
$773$			5.19835e8i			1.12545i	−0.826644	+	0.562726i	$0.809753\pi$
$774$		0			0
$775$			1.65161e8i			0.354816i
$776$	5.50451e8	−	2.26471e8i	1.17797	−	0.484650i
$777$		0			0
$778$	4.16961e8	−	3.19421e8i	0.885436	−	0.678304i
$779$	3.19602e8			0.676078
$780$		0			0
$781$		−	4.46986e8i		−	0.938299i
$782$	−1.64896e8	+	1.26322e8i	−0.344818	+	0.264154i
$783$		0			0
$784$	−1.43384e8	−	8.33902e7i	−0.297544	−	0.173048i
$785$	−2.55138e8			−0.527431
$786$		0			0
$787$	−6.57660e8			−1.34920			−0.674601	−	0.738182i	$-0.735684\pi$
$787$	−6.57660e8			−1.34920			−0.674601	+	0.738182i	$0.735684\pi$
$788$	−5.81683e8	−	1.56851e8i	−1.18880	−	0.320559i
$789$		0			0
$790$	2.62596e8	+	3.42784e8i	0.532606	+	0.695247i
$791$		−	2.13068e8i		−	0.430516i
$792$		0			0
$793$	−1.83655e8			−0.368285
$794$	−9.77689e7	+	7.48976e7i	−0.195317	+	0.149626i
$795$		0			0
$796$	5.85484e8	+	1.57876e8i	1.16085	+	0.313023i
$797$			8.87902e8i			1.75384i	0.480637	+	0.876920i	$0.340406\pi$
$797$			8.87902e8i			1.75384i	−0.480637	+	0.876920i	$0.659594\pi$
$798$		0			0
$799$		−	2.47906e8i		−	0.486011i
$800$	−2.26493e7	−	1.77473e8i	−0.0442370	−	0.346628i
$801$		0			0
$802$	2.55487e8	+	3.33504e8i	0.495274	+	0.646514i
$803$	−1.24164e9			−2.39800
$804$		0			0
$805$		−	4.39598e8i		−	0.842690i
$806$	−2.53272e8	−	3.30613e8i	−0.483707	−	0.631415i
$807$		0			0
$808$	6.37528e7	+	1.54954e8i	0.120855	+	0.293745i
$809$	−2.61371e8			−0.493641			−0.246821	−	0.969061i	$-0.579386\pi$
$809$	−2.61371e8			−0.493641			−0.246821	+	0.969061i	$0.579386\pi$
$810$		0			0
$811$	−8.91041e8			−1.67046			−0.835228	−	0.549904i	$-0.814664\pi$
$811$	−8.91041e8			−1.67046			−0.835228	+	0.549904i	$0.814664\pi$
$812$	1.31839e8	−	4.88925e8i	0.246249	−	0.913218i
$813$		0			0
$814$	−8.86241e8	+	6.78920e8i	−1.64315	+	1.25877i
$815$		−	2.24662e8i		−	0.415008i
$816$		0			0
$817$	6.66828e8			1.22278
$818$	−2.75001e8	−	3.58978e8i	−0.502429	−	0.655854i
$819$		0			0
$820$	−2.12603e8	−	5.73282e7i	−0.385591	−	0.103975i
$821$		−	1.91855e8i		−	0.346693i	−0.984861	−	0.173346i	$-0.944542\pi$
$821$		−	1.91855e8i		−	0.346693i	0.984861	−	0.173346i	$-0.0554580\pi$
$822$		0			0
$823$			9.88312e7i			0.177294i	0.996063	+	0.0886471i	$0.0282543\pi$
$823$			9.88312e7i			0.177294i	−0.996063	+	0.0886471i	$0.971746\pi$
$824$	1.89517e8	+	4.60632e8i	0.338741	+	0.823327i
$825$		0			0
$826$	−2.39512e8	+	1.83482e8i	−0.424998	+	0.325577i
$827$	8.06273e8			1.42549			0.712747	−	0.701421i	$-0.247451\pi$
$827$	8.06273e8			1.42549			0.712747	+	0.701421i	$0.247451\pi$
$828$		0			0
$829$			6.07971e8i			1.06713i	0.845758	+	0.533567i	$0.179149\pi$
$829$			6.07971e8i			1.06713i	−0.845758	+	0.533567i	$0.820851\pi$
$830$	−4.22818e8	+	3.23908e8i	−0.739468	+	0.566483i
$831$		0			0
$832$	3.17491e8	+	3.20526e8i	0.551266	+	0.556537i
$833$	−6.69844e7			−0.115888
$834$		0			0
$835$	−2.38003e8			−0.408811
$836$	−2.99990e8	+	1.11252e9i	−0.513438	+	1.90409i
$837$		0			0
$838$	−3.41416e8	−	4.45673e8i	−0.580165	−	0.757328i
$839$			5.33468e8i			0.903280i	0.892200	+	0.451640i	$0.149161\pi$
$839$			5.33468e8i			0.903280i	−0.892200	+	0.451640i	$0.850839\pi$
$840$		0			0
$841$	−2.16610e8			−0.364158
$842$	−5.86722e7	+	4.49469e7i	−0.0982870	+	0.0752945i
$843$		0			0
$844$	1.27590e8	−	4.73171e8i	0.212222	−	0.787029i
$845$		−	1.88027e8i		−	0.311638i
$846$		0			0
$847$			5.34394e8i			0.879450i
$848$	4.84098e8	−	8.32373e8i	0.793863	−	1.36499i
$849$		0			0
$850$	−4.39385e7	−	5.73559e7i	−0.0715465	−	0.0933945i
$851$	−1.13952e9			−1.84898
$852$		0			0
$853$			2.10766e8i			0.339589i	0.985480	+	0.169794i	$0.0543104\pi$
$853$			2.10766e8i			0.339589i	−0.985480	+	0.169794i	$0.945690\pi$
$854$	−1.44207e8	−	1.88243e8i	−0.231533	−	0.302236i
$855$		0			0
$856$	3.06595e8	−	1.26142e8i	0.488814	−	0.201112i
$857$	3.39277e8			0.539030			0.269515	−	0.962996i	$-0.413137\pi$
$857$	3.39277e8			0.539030			0.269515	+	0.962996i	$0.413137\pi$
$858$		0			0
$859$	6.89905e8			1.08845			0.544227	−	0.838938i	$-0.316823\pi$
$859$	6.89905e8			1.08845			0.544227	+	0.838938i	$0.316823\pi$
$860$	−4.43582e8	−	1.19612e8i	−0.697394	−	0.188052i
$861$		0			0
$862$	9.57130e7	−	7.33227e7i	0.149434	−	0.114477i
$863$			7.15874e8i			1.11379i	0.830582	+	0.556896i	$0.188008\pi$
$863$			7.15874e8i			1.11379i	−0.830582	+	0.556896i	$0.811992\pi$
$864$		0			0
$865$	1.46492e8			0.226342
$866$	5.77255e8	+	7.53530e8i	0.888821	+	1.16024i
$867$		0			0
$868$	1.40002e8	−	5.19198e8i	0.214079	−	0.793915i
$869$		−	1.02915e9i		−	1.56827i
$870$		0			0
$871$			3.57109e8i			0.540438i
$872$	4.70345e8	+	1.14320e9i	0.709361	+	1.72414i
$873$		0			0
$874$	−9.33637e8	+	7.15229e8i	−1.39844	+	1.07130i
$875$	5.90480e8			0.881416
$876$		0			0
$877$		−	5.18679e8i		−	0.768952i	−0.923135	−	0.384476i	$-0.874382\pi$
$877$		−	5.18679e8i		−	0.768952i	0.923135	−	0.384476i	$-0.125618\pi$
$878$	−5.33465e7	+	4.08670e7i	−0.0788174	+	0.0603795i
$879$		0			0
$880$	3.99113e8	−	6.86248e8i	0.585663	−	1.00701i
$881$	6.17449e8			0.902971			0.451485	−	0.892279i	$-0.350894\pi$
$881$	6.17449e8			0.902971			0.451485	+	0.892279i	$0.350894\pi$
$882$		0			0
$883$	6.73125e8			0.977718			0.488859	−	0.872363i	$-0.337413\pi$
$883$	6.73125e8			0.977718			0.488859	+	0.872363i	$0.337413\pi$
$884$	1.75908e8	+	4.74337e7i	0.254642	+	0.0686641i
$885$		0			0
$886$	−8.52509e7	−	1.11284e8i	−0.122574	−	0.160004i
$887$		−	1.13085e9i		−	1.62045i	−0.586119	−	0.810225i	$-0.699345\pi$
$887$		−	1.13085e9i		−	1.62045i	0.586119	−	0.810225i	$-0.300655\pi$
$888$		0			0
$889$	−7.16001e8			−1.01908
$890$	6.03712e8	−	4.62485e8i	0.856367	−	0.656036i
$891$		0			0
$892$	1.88123e8	+	5.07274e7i	0.265062	+	0.0714740i
$893$		−	1.40363e9i		−	1.97106i
$894$		0			0
$895$			1.44100e8i			0.200999i
$896$	−7.92381e7	+	5.77101e8i	−0.110156	+	0.802283i
$897$		0			0
$898$	5.29272e8	+	6.90895e8i	0.730887	+	0.954076i
$899$	−8.61675e8			−1.18594
$900$		0			0
$901$		−	3.88858e8i		−	0.531639i
$902$	3.19153e8	+	4.16611e8i	0.434889	+	0.567690i
$903$		0			0
$904$	3.63206e8	−	1.49434e8i	0.491641	−	0.202275i
$905$	3.04303e8			0.410545
$906$		0			0
$907$	−1.74361e8			−0.233683			−0.116842	−	0.993151i	$-0.537277\pi$
$907$	−1.74361e8			−0.233683			−0.116842	+	0.993151i	$0.537277\pi$
$908$	−2.01830e8	+	7.48488e8i	−0.269605	+	0.999832i
$909$		0			0
$910$	−3.06080e8	+	2.34478e8i	−0.406172	+	0.311156i
$911$			8.56397e8i			1.13271i	0.824160	+	0.566356i	$0.191647\pi$
$911$			8.56397e8i			1.13271i	−0.824160	+	0.566356i	$0.808353\pi$
$912$		0			0
$913$	1.26945e9			1.66802
$914$	6.59173e8	+	8.60463e8i	0.863298	+	1.12692i
$915$		0			0
$916$	−6.57124e8	−	1.77193e8i	−0.854990	−	0.230548i
$917$		−	1.91994e8i		−	0.248989i
$918$		0			0
$919$		−	9.29130e8i		−	1.19710i	−0.801086	−	0.598550i	$-0.795744\pi$
$919$		−	9.29130e8i		−	1.19710i	0.801086	−	0.598550i	$-0.204256\pi$
$920$	7.49359e8	−	3.08308e8i	0.962335	−	0.395933i
$921$		0			0
$922$	4.13411e8	−	3.16701e8i	0.527459	−	0.404070i
$923$	−4.00167e8			−0.508905
$924$		0			0
$925$		−	3.96358e8i		−	0.500798i
$926$	3.16308e8	−	2.42314e8i	0.398362	−	0.305172i
$927$		0			0
$928$	9.25908e8	−	1.18165e8i	1.15857	−	0.147859i
$929$	1.46510e9			1.82734			0.913672	−	0.406451i	$-0.133234\pi$
$929$	1.46510e9			1.82734			0.913672	+	0.406451i	$0.133234\pi$
$930$		0			0
$931$	−3.79263e8			−0.469994
$932$	2.32332e8	−	8.61606e8i	0.286986	−	1.06429i
$933$		0			0
$934$	5.63001e7	+	7.34923e7i	0.0690984	+	0.0901988i
$935$		−	3.20593e8i		−	0.392211i
$936$		0			0
$937$	4.26387e8			0.518305			0.259152	−	0.965836i	$-0.416557\pi$
$937$	4.26387e8			0.518305			0.259152	+	0.965836i	$0.416557\pi$
$938$	−3.66030e8	+	2.80404e8i	−0.443515	+	0.339762i
$939$		0			0
$940$	−2.51775e8	+	9.33713e8i	−0.303131	+	1.12416i
$941$		−	1.14292e9i		−	1.37166i	−0.727763	−	0.685828i	$-0.759440\pi$
$941$		−	1.14292e9i		−	1.37166i	0.727763	−	0.685828i	$-0.240560\pi$
$942$		0			0
$943$			5.35673e8i			0.638800i
$944$	−4.80752e8	−	2.79599e8i	−0.571485	−	0.332369i
$945$		0			0
$946$	6.65891e8	+	8.69233e8i	0.786557	+	1.02675i
$947$	3.04615e8			0.358675			0.179338	−	0.983788i	$-0.442605\pi$
$947$	3.04615e8			0.358675			0.179338	+	0.983788i	$0.442605\pi$
$948$		0			0
$949$			1.11158e9i			1.30060i
$950$	−2.48778e8	−	3.24747e8i	−0.290163	−	0.378769i
$951$		0			0
$952$	8.95056e7	+	2.17548e8i	0.103738	+	0.252142i
$953$	−1.45008e9			−1.67538			−0.837692	−	0.546143i	$-0.816095\pi$
$953$	−1.45008e9			−1.67538			−0.837692	+	0.546143i	$0.816095\pi$
$954$		0			0
$955$	1.02246e9			1.17391
$956$	5.11948e7	+	1.38047e7i	0.0585939	+	0.0157998i
$957$		0			0
$958$	−4.00606e8	+	3.06891e8i	−0.455639	+	0.349050i
$959$		−	4.56806e8i		−	0.517936i
$960$		0			0
$961$	−2.75244e7			−0.0310133
$962$	6.07808e8	+	7.93413e8i	0.682718	+	0.891197i
$963$		0			0
$964$	4.32121e8	−	1.60253e9i	0.482363	−	1.78885i
$965$			8.96032e7i			0.0997106i
$966$		0			0
$967$			1.10779e9i			1.22512i	0.790423	+	0.612561i	$0.209861\pi$
$967$			1.10779e9i			1.22512i	−0.790423	+	0.612561i	$0.790139\pi$
$968$	−9.10953e8	+	3.74793e8i	−1.00431	+	0.413204i
$969$		0			0
$970$	−7.44357e8	+	5.70228e8i	−0.815579	+	0.624789i
$971$	1.58886e9			1.73552			0.867759	−	0.496986i	$-0.165560\pi$
$971$	1.58886e9			1.73552			0.867759	+	0.496986i	$0.165560\pi$
$972$		0			0
$973$		−	8.25246e8i		−	0.895869i
$974$	−1.30447e9	+	9.99313e8i	−1.41175	+	1.08150i
$975$		0			0
$976$	2.19750e8	−	3.77845e8i	0.236363	−	0.406410i
$977$	−1.43593e9			−1.53975			−0.769875	−	0.638194i	$-0.779682\pi$
$977$	−1.43593e9			−1.53975			−0.769875	+	0.638194i	$0.779682\pi$
$978$		0			0
$979$	−1.81255e9			−1.93171
$980$	2.52290e8	+	6.80300e7i	0.268054	+	0.0722807i
$981$		0			0
$982$	9.32605e8	+	1.21739e9i	0.984835	+	1.28557i
$983$			1.10373e9i			1.16199i	0.813906	+	0.580997i	$0.197337\pi$
$983$			1.10373e9i			1.16199i	−0.813906	+	0.580997i	$0.802663\pi$
$984$		0			0
$985$	9.49078e8			0.993100
$986$	2.99235e8	−	2.29235e8i	0.312163	−	0.239138i
$987$		0			0
$988$	9.95988e8	+	2.68568e8i	1.03272	+	0.278473i
$989$			1.11765e9i			1.15536i
$990$		0			0
$991$		−	1.81704e9i		−	1.86700i	−0.358581	−	0.933499i	$-0.616739\pi$
$991$		−	1.81704e9i		−	1.86700i	0.358581	−	0.933499i	$-0.383261\pi$
$992$	9.83239e8	−	1.25482e8i	1.00722	−	0.128542i
$993$		0			0
$994$	−3.14214e8	−	4.10164e8i	−0.319938	−	0.417637i
$995$	−9.55280e8			−0.969753
$996$		0			0
$997$		−	3.61159e8i		−	0.364430i	−0.983259	−	0.182215i	$-0.941673\pi$
$997$		−	3.61159e8i		−	0.364430i	0.983259	−	0.182215i	$-0.0583266\pi$
$998$	−5.73536e8	−	7.48675e8i	−0.576991	−	0.753185i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	72.7.b.c.19.10		12
3.2	odd	2		24.7.b.a.19.3	✓	12
4.3	odd	2		288.7.b.d.271.4		12
8.3	odd	2	inner	72.7.b.c.19.9		12
8.5	even	2		288.7.b.d.271.9		12
12.11	even	2		96.7.b.a.79.5		12
24.5	odd	2		96.7.b.a.79.2		12
24.11	even	2		24.7.b.a.19.4	yes	12
48.5	odd	4		768.7.g.l.511.5		24
48.11	even	4		768.7.g.l.511.7		24
48.29	odd	4		768.7.g.l.511.8		24
48.35	even	4		768.7.g.l.511.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.7.b.a.19.3	✓	12	3.2	odd	2
24.7.b.a.19.4	yes	12	24.11	even	2
72.7.b.c.19.9		12	8.3	odd	2	inner
72.7.b.c.19.10		12	1.1	even	1	trivial
96.7.b.a.79.2		12	24.5	odd	2
96.7.b.a.79.5		12	12.11	even	2
288.7.b.d.271.4		12	4.3	odd	2
288.7.b.d.271.9		12	8.5	even	2
768.7.g.l.511.5		24	48.5	odd	4
768.7.g.l.511.6		24	48.35	even	4
768.7.g.l.511.7		24	48.11	even	4
768.7.g.l.511.8		24	48.29	odd	4

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:	\( N \)	\(=\)	\( 72 = 2^{3} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	72.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(4.86506 + 6.35069i) q^{2} +(-16.6624 + 61.7929i) q^{4} -100.822i q^{5} +277.765i q^{7} +(-473.491 + 194.808i) q^{8} +O(q^{10})\)	\(q+(4.86506 + 6.35069i) q^{2} +(-16.6624 + 61.7929i) q^{4} -100.822i q^{5} +277.765i q^{7} +(-473.491 + 194.808i) q^{8} +(640.287 - 490.503i) q^{10} -1922.36 q^{11} +1721.01i q^{13} +(-1764.00 + 1351.34i) q^{14} +(-3540.73 - 2059.24i) q^{16} -1654.12 q^{17} -9365.55 q^{19} +(6230.07 + 1679.94i) q^{20} +(-9352.39 - 12208.3i) q^{22} -15697.3i q^{23} +5459.98 q^{25} +(-10929.6 + 8372.79i) q^{26} +(-17163.9 - 4628.24i) q^{28} +28485.7i q^{29} +30249.4i q^{31} +(-4148.24 - 32504.4i) q^{32} +(-8047.37 - 10504.8i) q^{34} +28004.7 q^{35} -72593.3i q^{37} +(-45563.9 - 59477.7i) q^{38} +(19640.9 + 47738.2i) q^{40} -34125.3 q^{41} -71200.1 q^{43} +(32031.2 - 118788. i) q^{44} +(99688.4 - 76368.1i) q^{46} +149872. i q^{47} +40495.6 q^{49} +(26563.1 + 34674.7i) q^{50} +(-106346. - 28676.1i) q^{52} +235085. i q^{53} +193816. i q^{55} +(-54110.9 - 131519. i) q^{56} +(-180904. + 138584. i) q^{58} +135778. q^{59} +106714. i q^{61} +(-192105. + 147165. i) q^{62} +(186244. - 184480. i) q^{64} +173515. q^{65} +207500. q^{67} +(27561.6 - 102213. i) q^{68} +(136245. + 177849. i) q^{70} +232520. i q^{71} +645892. q^{73} +(461017. - 353170. i) q^{74} +(156053. - 578725. i) q^{76} -533964. i q^{77} +535360. i q^{79} +(-207616. + 356982. i) q^{80} +(-166021. - 216719. i) q^{82} -660358. q^{83} +166771. i q^{85} +(-346393. - 452170. i) q^{86} +(910220. - 374491. i) q^{88} +942878. q^{89} -478035. q^{91} +(969980. + 261555. i) q^{92} +(-951790. + 729136. i) q^{94} +944251. i q^{95} -1.16254e6 q^{97} +(197013. + 257175. i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{2} + 24 q^{4} - 796 q^{8}+O(q^{10}) \) 12 * q - 10 * q^2 + 24 * q^4 - 796 * q^8	\( 12 q - 10 q^{2} + 24 q^{4} - 796 q^{8} + 2172 q^{10} - 2720 q^{11} + 6444 q^{14} + 11640 q^{16} + 4888 q^{17} + 3936 q^{19} + 31608 q^{20} - 60432 q^{22} - 27204 q^{25} - 53952 q^{26} - 57072 q^{28} - 109480 q^{32} + 47388 q^{34} - 162336 q^{35} + 89080 q^{38} + 72120 q^{40} + 54280 q^{41} - 49824 q^{43} - 229184 q^{44} + 171864 q^{46} - 304644 q^{49} + 500078 q^{50} + 256848 q^{52} + 699816 q^{56} - 409524 q^{58} + 886144 q^{59} - 691356 q^{62} - 500640 q^{64} - 473376 q^{65} + 1565952 q^{67} - 669104 q^{68} + 473784 q^{70} + 555480 q^{73} + 753720 q^{74} - 293136 q^{76} + 251616 q^{80} + 2317716 q^{82} - 2497760 q^{83} - 476024 q^{86} + 971424 q^{88} - 367400 q^{89} - 4475808 q^{91} + 377376 q^{92} - 2642568 q^{94} - 1165656 q^{97} - 182674 q^{98}+O(q^{100}) \) 12 * q - 10 * q^2 + 24 * q^4 - 796 * q^8 + 2172 * q^10 - 2720 * q^11 + 6444 * q^14 + 11640 * q^16 + 4888 * q^17 + 3936 * q^19 + 31608 * q^20 - 60432 * q^22 - 27204 * q^25 - 53952 * q^26 - 57072 * q^28 - 109480 * q^32 + 47388 * q^34 - 162336 * q^35 + 89080 * q^38 + 72120 * q^40 + 54280 * q^41 - 49824 * q^43 - 229184 * q^44 + 171864 * q^46 - 304644 * q^49 + 500078 * q^50 + 256848 * q^52 + 699816 * q^56 - 409524 * q^58 + 886144 * q^59 - 691356 * q^62 - 500640 * q^64 - 473376 * q^65 + 1565952 * q^67 - 669104 * q^68 + 473784 * q^70 + 555480 * q^73 + 753720 * q^74 - 293136 * q^76 + 251616 * q^80 + 2317716 * q^82 - 2497760 * q^83 - 476024 * q^86 + 971424 * q^88 - 367400 * q^89 - 4475808 * q^91 + 377376 * q^92 - 2642568 * q^94 - 1165656 * q^97 - 182674 * q^98

Introduction

L-functions

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