LMFDB - Embedded newform 24.7.b.a.19.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [24,7,Mod(19,24)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("24.19"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(24, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 24 = 2^{3} \cdot 3 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	24.b (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.52129800688$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{26}\cdot 3^{11} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.3
Root			$-9.37784 - 8.67520i$ of defining polynomial
Character	$\chi$	$=$	24.19
Dual form			24.7.b.a.19.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.86506 - 6.35069i) q^{2} +15.5885 q^{3} +(-16.6624 + 61.7929i) q^{4} +100.822i q^{5} +(-75.8387 - 98.9974i) q^{6} +277.765i q^{7} +(473.491 - 194.808i) q^{8} +243.000 q^{9} +(640.287 - 490.503i) q^{10} +1922.36 q^{11} +(-259.742 + 963.256i) q^{12} +1721.01i q^{13} +(1764.00 - 1351.34i) q^{14} +1571.65i q^{15} +(-3540.73 - 2059.24i) q^{16} +1654.12 q^{17} +(-1182.21 - 1543.22i) q^{18} -9365.55 q^{19} +(-6230.07 - 1679.94i) q^{20} +4329.93i q^{21} +(-9352.39 - 12208.3i) q^{22} +15697.3i q^{23} +(7381.00 - 3036.76i) q^{24} +5459.98 q^{25} +(10929.6 - 8372.79i) q^{26} +3788.00 q^{27} +(-17163.9 - 4628.24i) q^{28} -28485.7i q^{29} +(9981.09 - 7646.19i) q^{30} +30249.4i q^{31} +(4148.24 + 32504.4i) q^{32} +29966.6 q^{33} +(-8047.37 - 10504.8i) q^{34} -28004.7 q^{35} +(-4048.97 + 15015.7i) q^{36} -72593.3i q^{37} +(45563.9 + 59477.7i) q^{38} +26827.8i q^{39} +(19640.9 + 47738.2i) q^{40} +34125.3 q^{41} +(27498.0 - 21065.3i) q^{42} -71200.1 q^{43} +(-32031.2 + 118788. i) q^{44} +24499.7i q^{45} +(99688.4 - 76368.1i) q^{46} -149872. i q^{47} +(-55194.5 - 32100.4i) q^{48} +40495.6 q^{49} +(-26563.1 - 34674.7i) q^{50} +25785.1 q^{51} +(-106346. - 28676.1i) q^{52} -235085. i q^{53} +(-18428.8 - 24056.4i) q^{54} +193816. i q^{55} +(54110.9 + 131519. i) q^{56} -145994. q^{57} +(-180904. + 138584. i) q^{58} -135778. q^{59} +(-97117.1 - 26187.6i) q^{60} +106714. i q^{61} +(192105. - 147165. i) q^{62} +67496.9i q^{63} +(186244. - 184480. i) q^{64} -173515. q^{65} +(-145789. - 190309. i) q^{66} +207500. q^{67} +(-27561.6 + 102213. i) q^{68} +244696. i q^{69} +(136245. + 177849. i) q^{70} -232520. i q^{71} +(115058. - 47338.4i) q^{72} +645892. q^{73} +(-461017. + 353170. i) q^{74} +85112.7 q^{75} +(156053. - 578725. i) q^{76} +533964. i q^{77} +(170375. - 130519. i) q^{78} +535360. i q^{79} +(207616. - 356982. i) q^{80} +59049.0 q^{81} +(-166021. - 216719. i) q^{82} +660358. q^{83} +(-267559. - 72147.2i) q^{84} +166771. i q^{85} +(346393. + 452170. i) q^{86} -444048. i q^{87} +(910220. - 374491. i) q^{88} -942878. q^{89} +(155590. - 119192. i) q^{90} -478035. q^{91} +(-969980. - 261555. i) q^{92} +471542. i q^{93} +(-951790. + 729136. i) q^{94} -944251. i q^{95} +(64664.7 + 506693. i) q^{96} -1.16254e6 q^{97} +(-197013. - 257175. i) q^{98} +467133. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 10 q^{2} + 24 q^{4} + 162 q^{6} + 796 q^{8} + 2916 q^{9} + 2172 q^{10} + 2720 q^{11} - 972 q^{12} - 6444 q^{14} + 11640 q^{16} - 4888 q^{17} + 2430 q^{18} + 3936 q^{19} - 31608 q^{20} - 60432 q^{22}+ \cdots + 660960 q^{99}+O(q^{100}) $ 12 * q + 10 * q^2 + 24 * q^4 + 162 * q^6 + 796 * q^8 + 2916 * q^9 + 2172 * q^10 + 2720 * q^11 - 972 * q^12 - 6444 * q^14 + 11640 * q^16 - 4888 * q^17 + 2430 * q^18 + 3936 * q^19 - 31608 * q^20 - 60432 * q^22 + 26244 * q^24 - 27204 * q^25 + 53952 * q^26 - 57072 * q^28 - 24300 * q^30 + 109480 * q^32 + 47388 * q^34 + 162336 * q^35 + 5832 * q^36 - 89080 * q^38 + 72120 * q^40 - 54280 * q^41 + 21060 * q^42 - 49824 * q^43 + 229184 * q^44 + 171864 * q^46 - 23328 * q^48 - 304644 * q^49 - 500078 * q^50 + 80352 * q^51 + 256848 * q^52 + 39366 * q^54 - 699816 * q^56 - 136080 * q^57 - 409524 * q^58 - 886144 * q^59 + 95904 * q^60 + 691356 * q^62 - 500640 * q^64 + 473376 * q^65 + 3888 * q^66 + 1565952 * q^67 + 669104 * q^68 + 473784 * q^70 + 193428 * q^72 + 555480 * q^73 - 753720 * q^74 - 1073088 * q^75 - 293136 * q^76 - 535248 * q^78 - 251616 * q^80 + 708588 * q^81 + 2317716 * q^82 + 2497760 * q^83 - 1168344 * q^84 + 476024 * q^86 + 971424 * q^88 + 367400 * q^89 + 527796 * q^90 - 4475808 * q^91 - 377376 * q^92 - 2642568 * q^94 + 2372328 * q^96 - 1165656 * q^97 + 182674 * q^98 + 660960 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/24\mathbb{Z}\right)^\times$.

$n$	$7$	$13$	$17$
$\chi(n)$	$-1$	$-1$	$1$

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
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	−16.6624	+	61.7929i	−0.260351	+	0.965514i
$5$			100.822i			0.806574i	0.915074	+	0.403287i	$0.132132\pi$
$5$			100.822i			0.806574i	−0.915074	+	0.403287i	$0.867868\pi$
$6$	−75.8387	−	98.9974i	−0.351105	−	0.458321i
$7$			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
$9$	243.000			0.333333
$10$	640.287	−	490.503i	0.640287	−	0.490503i
$11$	1922.36			1.44430			0.722149	−	0.691738i	$-0.243155\pi$
$11$	1922.36			1.44430			0.722149	+	0.691738i	$0.243155\pi$
$12$	−259.742	+	963.256i	−0.150313	+	0.557440i
$13$			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
$15$			1571.65i			0.465675i
$16$	−3540.73	−	2059.24i	−0.864435	−	0.502744i
$17$	1654.12			0.336681			0.168341	−	0.985729i	$-0.446159\pi$
$17$	1654.12			0.336681			0.168341	+	0.985729i	$0.446159\pi$
$18$	−1182.21	−	1543.22i	−0.202711	−	0.264612i
$19$	−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
$21$			4329.93i			0.467544i
$22$	−9352.39	−	12208.3i	−0.878324	−	1.14654i
$23$			15697.3i			1.29015i	0.764119	+	0.645076i	$0.223174\pi$
$23$			15697.3i			1.29015i	−0.764119	+	0.645076i	$0.776826\pi$
$24$	7381.00	−	3036.76i	0.533926	−	0.219673i
$25$	5459.98			0.349439
$26$	10929.6	−	8372.79i	0.621846	−	0.476376i
$27$	3788.00			0.192450
$28$	−17163.9	−	4628.24i	−0.781884	−	0.210835i
$29$		−	28485.7i		−	1.16797i	−0.811764	−	0.583986i	$-0.801492\pi$
$29$		−	28485.7i		−	1.16797i	0.811764	−	0.583986i	$-0.198508\pi$
$30$	9981.09	−	7646.19i	0.369670	−	0.283192i
$31$			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
$33$	29966.6			0.833865
$34$	−8047.37	−	10504.8i	−0.204747	−	0.267270i
$35$	−28004.7			−0.653172
$36$	−4048.97	+	15015.7i	−0.0867835	+	0.321838i
$37$		−	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
$39$			26827.8i			0.452263i
$40$	19640.9	+	47738.2i	0.306889	+	0.745909i
$41$	34125.3			0.495136			0.247568	−	0.968871i	$-0.420369\pi$
$41$	34125.3			0.495136			0.247568	+	0.968871i	$0.420369\pi$
$42$	27498.0	−	21065.3i	0.371153	−	0.284329i
$43$	−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
$45$			24499.7i			0.268858i
$46$	99688.4	−	76368.1i	1.02417	−	0.784582i
$47$		−	149872.i		−	1.44353i	−0.692136	−	0.721767i	$-0.743330\pi$
$47$		−	149872.i		−	1.44353i	0.692136	−	0.721767i	$-0.256670\pi$
$48$	−55194.5	−	32100.4i	−0.499082	−	0.290260i
$49$	40495.6			0.344207
$50$	−26563.1	−	34674.7i	−0.212505	−	0.277397i
$51$	25785.1			0.194383
$52$	−106346.	−	28676.1i	−0.756329	−	0.203944i
$53$		−	235085.i		−	1.57906i	−0.613713	−	0.789529i	$-0.710325\pi$
$53$		−	235085.i		−	1.57906i	0.613713	−	0.789529i	$-0.289675\pi$
$54$	−18428.8	−	24056.4i	−0.117035	−	0.152774i
$55$			193816.i			1.16493i
$56$	54110.9	+	131519.i	0.308120	+	0.748903i
$57$	−145994.			−0.788337
$58$	−180904.	+	138584.i	−0.927178	+	0.710281i
$59$	−135778.			−0.661109			−0.330554	−	0.943787i	$-0.607236\pi$
$59$	−135778.			−0.661109			−0.330554	+	0.943787i	$0.607236\pi$
$60$	−97117.1	−	26187.6i	−0.449616	−	0.121239i
$61$			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
$63$			67496.9i			0.269937i
$64$	186244.	−	184480.i	0.710463	−	0.703735i
$65$	−173515.			−0.631824
$66$	−145789.	−	190309.i	−0.507100	−	0.661952i
$67$	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
$69$			244696.i			0.744869i
$70$	136245.	+	177849.i	0.397215	+	0.518511i
$71$		−	232520.i		−	0.649657i	−0.945773	−	0.324829i	$-0.894693\pi$
$71$		−	232520.i		−	0.649657i	0.945773	−	0.324829i	$-0.105307\pi$
$72$	115058.	−	47338.4i	0.308262	−	0.126828i
$73$	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
$75$	85112.7			0.201749
$76$	156053.	−	578725.i	0.355493	−	1.31835i
$77$			533964.i			1.16961i
$78$	170375.	−	130519.i	0.359023	−	0.275036i
$79$			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
$81$	59049.0			0.111111
$82$	−166021.	−	216719.i	−0.301108	−	0.393057i
$83$	660358.			1.15490			0.577451	−	0.816426i	$-0.304048\pi$
$83$	660358.			1.15490			0.577451	+	0.816426i	$0.304048\pi$
$84$	−267559.	−	72147.2i	−0.451421	−	0.121725i
$85$			166771.i			0.271558i
$86$	346393.	+	452170.i	0.544595	+	0.710896i
$87$		−	444048.i		−	0.674329i
$88$	910220.	−	374491.i	1.33567	−	0.549533i
$89$	−942878.			−1.33747			−0.668737	−	0.743499i	$-0.733165\pi$
$89$	−942878.			−1.33747			−0.668737	+	0.743499i	$0.733165\pi$
$90$	155590.	−	119192.i	0.213429	−	0.163501i
$91$	−478035.			−0.634360
$92$	−969980.	−	261555.i	−1.24566	−	0.335892i
$93$			471542.i			0.586235i
$94$	−951790.	+	729136.i	−1.14593	+	0.877860i
$95$		−	944251.i		−	1.10133i
$96$	64664.7	+	506693.i	0.0730892	+	0.572705i
$97$	−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
$99$	467133.			0.481432
$100$	−90976.7	+	337388.i	−0.0909767	+	0.337388i
$101$			327259.i			0.317635i	0.987308	+	0.158817i	$0.0507681\pi$
$101$			327259.i			0.317635i	−0.987308	+	0.158817i	$0.949232\pi$
$102$	−125446.	−	163753.i	−0.118211	−	0.154308i
$103$		−	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
$105$	−436551.			−0.377109
$106$	−1.49295e6	+	1.14370e6i	−1.25351	+	0.960276i
$107$	647520.			0.528569			0.264285	−	0.964445i	$-0.414864\pi$
$107$	647520.			0.528569			0.264285	+	0.964445i	$0.414864\pi$
$108$	−63117.2	+	234071.i	−0.0501045	+	0.185813i
$109$		−	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
$111$		−	1.13162e6i		−	0.827428i
$112$	571985.	−	983490.i	0.407128	−	0.700029i
$113$	767081.			0.531626			0.265813	−	0.964025i	$-0.414360\pi$
$113$	767081.			0.531626			0.265813	+	0.964025i	$0.414360\pi$
$114$	710272.	+	927165.i	0.479413	+	0.625810i
$115$	−1.58263e6			−1.04060
$116$	1.76021e6	+	474641.i	1.12769	+	0.304082i
$117$			418204.i			0.261114i
$118$	660567.	+	862282.i	0.402041	+	0.524812i
$119$			459455.i			0.272648i
$120$	306171.	+	744165.i	0.177182	+	0.430651i
$121$	1.92391e6			1.08599
$122$	677707.	−	519169.i	0.373218	−	0.285910i
$123$	531960.			0.285867
$124$	−1.86920e6	−	504029.i	−0.980372	−	0.264357i
$125$			2.12582e6i			1.08842i
$126$	428652.	−	328376.i	0.214286	−	0.164157i
$127$			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
$129$	−1.10990e6			−0.517029
$130$	844159.	+	1.10194e6i	0.384233	+	0.501565i
$131$	691211.			0.307466			0.153733	−	0.988112i	$-0.450870\pi$
$131$	691211.			0.307466			0.153733	+	0.988112i	$0.450870\pi$
$132$	−499317.	+	1.85172e6i	−0.217097	+	0.805109i
$133$		−	2.60142e6i		−	1.10575i
$134$	−1.00950e6	−	1.31777e6i	−0.419558	−	0.547677i
$135$			381912.i			0.155225i
$136$	783209.	−	322235.i	0.311359	−	0.128102i
$137$	1.64458e6			0.639577			0.319788	−	0.947489i	$-0.396388\pi$
$137$	1.64458e6			0.639577			0.319788	+	0.947489i	$0.396388\pi$
$138$	1.55399e6	−	1.19046e6i	0.591304	−	0.452979i
$139$	−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
$141$		−	2.33627e6i		−	0.833425i
$142$	−1.47666e6	+	1.13122e6i	−0.515721	+	0.395078i
$143$			3.30839e6i			1.13138i
$144$	−860396.	−	500396.i	−0.288145	−	0.167581i
$145$	2.87197e6			0.942055
$146$	−3.14230e6	−	4.10186e6i	−1.00969	−	1.31802i
$147$	631264.			0.198728
$148$	4.48575e6	+	1.20958e6i	1.38372	+	0.373121i
$149$			1.85074e6i			0.559483i	0.960075	+	0.279741i	$0.0902487\pi$
$149$			1.85074e6i			0.559483i	−0.960075	+	0.279741i	$0.909751\pi$
$150$	−414078.	−	540524.i	−0.122690	−	0.160155i
$151$			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
$153$	401950.			0.112227
$154$	3.39104e6	−	2.59777e6i	0.928476	−	0.711276i
$155$	−3.04980e6			−0.818985
$156$	−1.65777e6	−	447017.i	−0.436667	−	0.117747i
$157$		−	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
$159$		−	3.66462e6i		−	0.911670i
$160$	−3.27715e6	+	418233.i	−0.800084	+	0.102108i
$161$	−4.36015e6			−1.04478
$162$	−287277.	−	375002.i	−0.0675702	−	0.0882040i
$163$	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
$165$			3.02129e6i			0.672574i
$166$	−3.21268e6	−	4.19372e6i	−0.702333	−	0.916802i
$167$			2.36063e6i			0.506849i	0.967355	+	0.253425i	$0.0815569\pi$
$167$			2.36063e6i			0.506849i	−0.967355	+	0.253425i	$0.918443\pi$
$168$	843505.	+	2.05018e6i	0.177893	+	0.432379i
$169$	1.86495e6			0.386373
$170$	1.05911e6	−	811349.i	0.215573	−	0.165143i
$171$	−2.27583e6			−0.455147
$172$	1.18637e6	−	4.39966e6i	0.233149	−	0.864638i
$173$		−	1.45298e6i		−	0.280621i	−0.990108	−	0.140311i	$-0.955190\pi$
$173$		−	1.45298e6i		−	0.280621i	0.990108	−	0.140311i	$-0.0448101\pi$
$174$	−2.82001e6	+	2.16032e6i	−0.535306	+	0.410081i
$175$			1.51659e6i			0.282979i
$176$	−6.80655e6	−	3.95860e6i	−1.24850	−	0.726112i
$177$	−2.11657e6			−0.381691
$178$	4.58715e6	+	5.98792e6i	0.813361	+	1.06174i
$179$	1.42925e6			0.249201			0.124601	−	0.992207i	$-0.460235\pi$
$179$	1.42925e6			0.249201			0.124601	+	0.992207i	$0.460235\pi$
$180$	−1.51391e6	−	408224.i	−0.259586	−	0.0699973i
$181$			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
$183$			1.66351e6i			0.271438i
$184$	3.05795e6	+	7.43252e6i	0.490883	+	1.19312i
$185$	7.31898e6			1.15594
$186$	2.99462e6	−	2.29408e6i	0.465374	−	0.356508i
$187$	3.17981e6			0.486268
$188$	9.26103e6	+	2.49723e6i	1.39375	+	0.375825i
$189$			1.05217e6i			0.155848i
$190$	−5.99664e6	+	4.59383e6i	−0.874273	+	0.669753i
$191$		−	1.01412e7i		−	1.45543i	−0.685880	−	0.727715i	$-0.740582\pi$
$191$		−	1.01412e7i		−	1.45543i	0.685880	−	0.727715i	$-0.259418\pi$
$192$	2.90325e6	−	2.87576e6i	0.410186	−	0.406301i
$193$	−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
$195$	−2.70483e6			−0.364784
$196$	−674755.	+	2.50234e6i	−0.0896145	+	0.332337i
$197$		−	9.41343e6i		−	1.23126i	−0.788036	−	0.615629i	$-0.788902\pi$
$197$		−	9.41343e6i		−	1.23126i	0.788036	−	0.615629i	$-0.211098\pi$
$198$	−2.27263e6	−	2.96662e6i	−0.292775	−	0.382178i
$199$		−	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
$201$	3.23461e6			0.398321
$202$	2.07832e6	−	1.59214e6i	0.252150	−	0.193164i
$203$	7.91232e6			0.945836
$204$	−429643.	+	1.59334e6i	−0.0506078	+	0.187680i
$205$			3.44057e6i			0.399363i
$206$	−6.17821e6	+	4.73293e6i	−0.706742	+	0.541413i
$207$			3.81444e6i			0.430050i
$208$	3.54396e6	−	6.09361e6i	0.393821	−	0.677149i
$209$	−1.80040e7			−1.97210
$210$	2.12384e6	+	2.77240e6i	0.229332	+	0.299363i
$211$	−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
$213$		−	3.62462e6i		−	0.375080i
$214$	−3.15022e6	−	4.11220e6i	−0.321440	−	0.419597i
$215$		−	7.17852e6i		−	0.722303i
$216$	1.79358e6	−	737932.i	0.177975	−	0.0732243i
$217$	−8.40223e6			−0.822272
$218$	−1.53331e7	+	1.17462e7i	−1.48000	+	1.13378i
$219$	1.00685e7			0.958586
$220$	−1.19764e7	−	3.22944e6i	−1.12476	−	0.303291i
$221$			2.84674e6i			0.263737i
$222$	−7.18654e6	+	5.50538e6i	−0.656842	+	0.503186i
$223$		−	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
$225$	1.32678e6			0.116480
$226$	−3.73189e6	−	4.87149e6i	−0.323299	−	0.422023i
$227$	−1.21128e7			−1.03554			−0.517772	−	0.855519i	$-0.673238\pi$
$227$	−1.21128e7			−1.03554			−0.517772	+	0.855519i	$0.673238\pi$
$228$	2.43262e6	−	9.02142e6i	0.205244	−	0.761150i
$229$			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
$231$			8.32368e6i			0.675273i
$232$	−5.54924e6	−	1.34877e7i	−0.444395	−	1.08013i
$233$	1.39434e7			1.10231			0.551153	−	0.834404i	$-0.314188\pi$
$233$	1.39434e7			1.10231			0.551153	+	0.834404i	$0.314188\pi$
$234$	2.65588e6	−	2.03459e6i	0.207282	−	0.158792i
$235$	1.51104e7			1.16432
$236$	2.26239e6	−	8.39011e6i	0.172120	−	0.638310i
$237$			8.34543e6i			0.626908i
$238$	2.91786e6	−	2.23528e6i	0.216438	−	0.165806i
$239$			828490.i			0.0606867i	0.999540	+	0.0303433i	$0.00966007\pi$
$239$			828490.i			0.0606867i	−0.999540	+	0.0303433i	$0.990340\pi$
$240$	3.23642e6	−	5.56480e6i	0.234116	−	0.402546i
$241$	−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
$243$	920483.			0.0641500
$244$	−6.59416e6	−	1.77811e6i	−0.453931	−	0.122402i
$245$			4.08283e6i			0.277628i
$246$	−2.58802e6	−	3.37831e6i	−0.173845	−	0.226931i
$247$		−	1.61182e7i		−	1.06961i
$248$	5.89283e6	+	1.43228e7i	0.386340	+	0.939018i
$249$	1.02940e7			0.666783
$250$	1.35004e7	−	1.03423e7i	0.864028	−	0.661904i
$251$	−4.68287e6			−0.296136			−0.148068	−	0.988977i	$-0.547305\pi$
$251$	−4.68287e6			−0.296136			−0.148068	+	0.988977i	$0.547305\pi$
$252$	−4.17083e6	−	1.12466e6i	−0.260628	−	0.0702782i
$253$			3.01758e7i			1.86336i
$254$	1.63703e7	−	1.25408e7i	0.998978	−	0.765285i
$255$			2.59970e6i			0.156784i
$256$	8.29627e6	+	1.45824e7i	0.494496	+	0.869180i
$257$	1.06513e7			0.627487			0.313743	−	0.949508i	$-0.398417\pi$
$257$	1.06513e7			0.627487			0.313743	+	0.949508i	$0.398417\pi$
$258$	5.39973e6	+	7.04863e6i	0.314422	+	0.410436i
$259$	2.01639e7			1.16058
$260$	2.89118e6	−	1.07220e7i	0.164496	−	0.610035i
$261$		−	6.92202e6i		−	0.389324i
$262$	−3.36278e6	−	4.38967e6i	−0.186980	−	0.244077i
$263$			1.08575e7i			0.596848i	0.954433	+	0.298424i	$0.0964609\pi$
$263$			1.08575e7i			0.596848i	−0.954433	+	0.298424i	$0.903539\pi$
$264$	1.41889e7	−	5.83774e6i	0.771148	−	0.317273i
$265$	2.37017e7			1.27363
$266$	−1.65208e7	+	1.26561e7i	−0.877782	+	0.672441i
$267$	−1.46980e7			−0.772191
$268$	−3.45746e6	+	1.28220e7i	−0.179619	+	0.666120i
$269$		−	1.27083e7i		−	0.652878i	−0.945218	−	0.326439i	$-0.894151\pi$
$269$		−	1.27083e7i		−	0.652878i	0.945218	−	0.326439i	$-0.105849\pi$
$270$	2.42540e6	−	1.85802e6i	0.123223	−	0.0943974i
$271$			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
$273$	−7.45183e6			−0.366248
$274$	−8.00097e6	−	1.04442e7i	−0.388947	−	0.507719i
$275$	1.04961e7			0.504694
$276$	−1.51205e7	−	4.07724e6i	−0.719182	−	0.193927i
$277$		−	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
$279$			7.35061e6i			0.338463i
$280$	−1.32600e7	+	5.45555e6i	−0.604045	+	0.248522i
$281$	623477.			0.0280997			0.0140498	−	0.999901i	$-0.495528\pi$
$281$	623477.			0.0280997			0.0140498	+	0.999901i	$0.495528\pi$
$282$	−1.48369e7	+	1.13661e7i	−0.661603	+	0.506832i
$283$	−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
$285$		−	1.47194e7i		−	0.635852i
$286$	2.10106e7	−	1.60955e7i	0.898131	−	0.688029i
$287$			9.47880e6i			0.400966i
$288$	1.00802e6	+	7.89856e6i	0.0421981	+	0.330652i
$289$	−2.14015e7			−0.886646
$290$	−1.39723e7	−	1.82390e7i	−0.572894	−	0.747837i
$291$	−1.81221e7			−0.735412
$292$	−1.07621e7	+	3.99116e7i	−0.432265	+	1.60306i
$293$		−	1.23605e7i		−	0.491398i	−0.969346	−	0.245699i	$-0.920983\pi$
$293$		−	1.23605e7i		−	0.491398i	0.969346	−	0.245699i	$-0.0790175\pi$
$294$	−3.07113e6	−	4.00896e6i	−0.120853	−	0.157757i
$295$		−	1.36894e7i		−	0.533233i
$296$	−1.41418e7	−	3.43723e7i	−0.545291	−	1.32536i
$297$	7.28189e6			0.277955
$298$	1.17535e7	−	9.00396e6i	0.444138	−	0.340240i
$299$	−2.70151e7			−1.01063
$300$	−1.41819e6	+	5.25936e6i	−0.0525254	+	0.194791i
$301$		−	1.97769e7i		−	0.725202i
$302$	2.42233e7	−	1.85567e7i	0.879451	−	0.673719i
$303$			5.10147e6i			0.183386i
$304$	3.31609e7	+	1.92859e7i	1.18033	+	0.686467i
$305$	−1.07591e7			−0.379206
$306$	−1.95551e6	−	2.55266e6i	−0.0682489	−	0.0890899i
$307$	−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
$309$		−	1.51651e7i		−	0.514008i
$310$	1.48374e7	+	1.93683e7i	0.498051	+	0.650140i
$311$			3.78807e7i			1.25932i	0.776869	+	0.629662i	$0.216807\pi$
$311$			3.78807e7i			1.25932i	−0.776869	+	0.629662i	$0.783193\pi$
$312$	5.22628e6	+	1.27027e7i	0.172079	+	0.418248i
$313$	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
$315$	−6.80515e6			−0.217724
$316$	−3.30814e7	−	8.92040e6i	−1.04839	−	0.282698i
$317$		−	4.24239e7i		−	1.33178i	−0.746049	−	0.665891i	$-0.768052\pi$
$317$		−	4.24239e7i		−	1.33178i	0.746049	−	0.665891i	$-0.231948\pi$
$318$	−2.32728e7	+	1.78286e7i	−0.723716	+	0.554416i
$319$		−	5.47597e7i		−	1.68690i
$320$	1.85996e7	+	1.87774e7i	0.567614	+	0.573041i
$321$	1.00938e7			0.305170
$322$	2.12124e7	+	2.76900e7i	0.635363	+	0.829382i
$323$	−1.54917e7			−0.459718
$324$	−983900.	+	3.64881e6i	−0.0289278	+	0.107279i
$325$			9.39666e6i			0.273731i
$326$	−1.08409e7	−	1.41513e7i	−0.312904	−	0.408454i
$327$		−	3.76368e7i		−	1.07639i
$328$	1.61580e7	−	6.64787e6i	0.457895	−	0.188391i
$329$	4.16292e7			1.16899
$330$	1.91872e7	−	1.46987e7i	0.533913	−	0.409014i
$331$	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
$333$		−	1.76402e7i		−	0.477716i
$334$	1.49916e7	−	1.14846e7i	0.402355	−	0.308231i
$335$			2.09205e7i			0.556465i
$336$	8.91637e6	−	1.53311e7i	0.235055	−	0.404162i
$337$	−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
$339$	1.19576e7			0.306934
$340$	−1.03052e7	−	2.77881e6i	−0.262193	−	0.0707004i
$341$			5.81503e7i			1.46652i
$342$	1.10720e7	+	1.44531e7i	0.276789	+	0.361312i
$343$			4.39270e7i			1.08855i
$344$	−3.37126e7	+	1.38704e7i	−0.828166	+	0.340732i
$345$	−2.46707e7			−0.600792
$346$	−9.22740e6	+	7.06882e6i	−0.222767	+	0.170655i
$347$	2.20906e7			0.528713			0.264356	−	0.964425i	$-0.414841\pi$
$347$	2.20906e7			0.528713			0.264356	+	0.964425i	$0.414841\pi$
$348$	2.74390e7	+	7.39891e6i	0.651074	+	0.175562i
$349$		−	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
$351$			6.51916e6i			0.150754i
$352$	7.97441e6	+	6.24851e7i	0.182840	+	1.43268i
$353$	−4.12066e7			−0.936790			−0.468395	−	0.883519i	$-0.655168\pi$
$353$	−4.12066e7			−0.936790			−0.468395	+	0.883519i	$0.655168\pi$
$354$	1.02972e7	+	1.34417e7i	0.232119	+	0.303000i
$355$	2.34430e7			0.523997
$356$	1.57106e7	−	5.82632e7i	0.348212	−	1.29135i
$357$			7.16220e6i			0.157413i
$358$	−6.95340e6	−	9.07674e6i	−0.151547	−	0.197825i
$359$		−	2.94445e6i		−	0.0636386i	−0.999494	−	0.0318193i	$-0.989870\pi$
$359$		−	2.94445e6i		−	0.0636386i	0.999494	−	0.0318193i	$-0.0101301\pi$
$360$	4.77273e6	+	1.16004e7i	0.102296	+	0.248636i
$361$	4.06677e7			0.864426
$362$	1.91679e7	−	1.46839e7i	0.404062	−	0.309539i
$363$	2.99907e7			0.626999
$364$	7.96523e6	−	2.95392e7i	0.165156	−	0.612483i
$365$			6.51200e7i			1.33917i
$366$	1.05644e7	−	8.09305e6i	0.215477	−	0.165070i
$367$		−	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
$369$	8.29244e6			0.165045
$370$	−3.56072e7	−	4.64805e7i	−0.702964	−	0.917626i
$371$	6.52985e7			1.27874
$372$	−2.91379e7	−	7.85704e6i	−0.566018	−	0.152627i
$373$		−	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
$375$			3.31383e7i			0.628401i
$376$	−2.91963e7	−	7.09631e7i	−0.549242	−	1.33496i
$377$	4.90240e7			0.914923
$378$	6.68202e6	−	5.11888e6i	0.123718	−	0.0947763i
$379$	−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
$381$			4.01827e7i			0.726548i
$382$	−6.44039e7	+	4.93377e7i	−1.15537	+	0.885093i
$383$		−	1.48851e7i		−	0.264945i	−0.991187	−	0.132472i	$-0.957708\pi$
$383$		−	1.48851e7i		−	0.264945i	0.991187	−	0.132472i	$-0.0422915\pi$
$384$	−3.23875e7	−	4.44692e6i	−0.571984	−	0.0785355i
$385$	−5.38352e7			−0.943374
$386$	4.32372e6	+	5.64404e6i	0.0751788	+	0.0981359i
$387$	−1.73016e7			−0.298507
$388$	1.93707e7	−	7.18365e7i	0.331627	−	1.22984i
$389$			6.56561e7i			1.11539i	0.830046	+	0.557694i	$0.188314\pi$
$389$			6.56561e7i			1.11539i	−0.830046	+	0.557694i	$0.811686\pi$
$390$	1.31591e7	+	1.71775e7i	0.221837	+	0.289578i
$391$			2.59651e7i			0.434370i
$392$	1.91743e7	−	7.88887e6i	0.318318	−	0.130965i
$393$	1.07749e7			0.177515
$394$	−5.97817e7	+	4.57969e7i	−0.977417	+	0.748767i
$395$	−5.39759e7			−0.875807
$396$	−7.78358e6	+	2.88655e7i	−0.125341	+	0.464830i
$397$			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
$399$		−	4.05522e7i		−	0.638404i
$400$	−1.93323e7	−	1.12434e7i	−0.302067	−	0.175679i
$401$	−5.25147e7			−0.814418			−0.407209	−	0.913335i	$-0.633498\pi$
$401$	−5.25147e7			−0.814418			−0.407209	+	0.913335i	$0.633498\pi$
$402$	−1.57365e7	−	2.05420e7i	−0.242232	−	0.316202i
$403$	−5.20594e7			−0.795398
$404$	−2.02223e7	−	5.45294e6i	−0.306681	−	0.0826964i
$405$			5.95342e6i			0.0896193i
$406$	−3.84939e7	−	5.02487e7i	−0.575193	−	0.750838i
$407$		−	1.39550e8i		−	2.06989i
$408$	1.22090e7	−	5.02315e6i	0.179763	−	0.0739598i
$409$	−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
$411$	2.56364e7			0.369260
$412$	6.01147e7	+	1.62099e7i	0.859586	+	0.231787i
$413$		−	3.77143e7i		−	0.535373i
$414$	2.42243e7	−	1.85575e7i	0.341389	−	0.261527i
$415$			6.65784e7i			0.931513i
$416$	−5.59402e7	+	7.13914e6i	−0.777041	+	0.0991668i
$417$	−4.63136e7			−0.638705
$418$	8.75903e7	+	1.14337e8i	1.19930	+	1.56552i
$419$	7.01771e7			0.954011			0.477006	−	0.878900i	$-0.341722\pi$
$419$	7.01771e7			0.954011			0.477006	+	0.878900i	$0.341722\pi$
$420$	7.27400e6	−	2.69757e7i	0.0981805	−	0.364104i
$421$			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
$423$		−	3.64189e7i		−	0.481178i
$424$	−4.57965e7	−	1.11311e8i	−0.600807	−	1.46029i
$425$	9.03145e6			0.117650
$426$	−2.30188e7	+	1.76340e7i	−0.297752	+	0.228098i
$427$	−2.96414e7			−0.380728
$428$	−1.07893e7	+	4.00122e7i	−0.137613	+	0.510341i
$429$			5.15727e7i			0.653203i
$430$	−4.55885e7	+	3.49239e7i	−0.573390	+	0.439256i
$431$			1.50713e7i			0.188243i	0.995561	+	0.0941215i	$0.0300042\pi$
$431$			1.50713e7i			0.188243i	−0.995561	+	0.0941215i	$0.969996\pi$
$432$	−1.34123e7	−	7.80040e6i	−0.166361	−	0.0967532i
$433$	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
$435$	4.47696e7			0.543896
$436$	1.49193e8	+	4.02298e7i	1.80007	+	0.485388i
$437$		−	1.47014e8i		−	1.76162i
$438$	−4.89837e7	−	6.39417e7i	−0.582947	−	0.760960i
$439$			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
$441$	9.84043e6			0.114736
$442$	1.80788e7	−	1.38496e7i	0.209364	−	0.160387i
$443$	1.75231e7			0.201558			0.100779	−	0.994909i	$-0.467867\pi$
$443$	1.75231e7			0.201558			0.100779	+	0.994909i	$0.467867\pi$
$444$	6.99259e7	+	1.88555e7i	0.798894	+	0.215422i
$445$		−	9.50626e7i		−	1.07877i
$446$	−1.93341e7	+	1.48113e7i	−0.217932	+	0.166950i
$447$			2.88502e7i			0.323018i
$448$	5.12420e7	+	5.17320e7i	0.569892	+	0.575341i
$449$	−1.08791e8			−1.20186			−0.600928	−	0.799303i	$-0.705202\pi$
$449$	−1.08791e8			−1.20186			−0.600928	+	0.799303i	$0.705202\pi$
$450$	−6.45484e6	−	8.42594e6i	−0.0708350	−	0.0924657i
$451$	6.56010e7			0.715123
$452$	−1.27814e7	+	4.74002e7i	−0.138409	+	0.513292i
$453$			5.94586e7i			0.639617i
$454$	5.89297e7	+	7.69249e7i	0.629748	+	0.822052i
$455$		−	4.81963e7i		−	0.511658i
$456$	−6.91271e7	+	2.84409e7i	−0.729044	+	0.299950i
$457$	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
$459$	6.26578e6			0.0647944
$460$	2.63704e7	−	9.77950e7i	0.270921	−	1.00472i
$461$			6.50970e7i			0.664444i	0.943201	+	0.332222i	$0.107798\pi$
$461$			6.50970e7i			0.664444i	−0.943201	+	0.332222i	$0.892202\pi$
$462$	5.28611e7	−	4.04952e7i	0.536056	−	0.410655i
$463$		−	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
$465$	−4.75417e7			−0.472841
$466$	−6.78357e7	−	8.85504e7i	−0.670348	−	0.875050i
$467$	−1.15723e7			−0.113624			−0.0568120	−	0.998385i	$-0.518094\pi$
$467$	−1.15723e7			−0.113624			−0.0568120	+	0.998385i	$0.518094\pi$
$468$	−2.58421e7	−	6.96830e6i	−0.252110	−	0.0679813i
$469$			5.76363e7i			0.558698i
$470$	−7.35127e7	−	9.59611e7i	−0.708058	−	0.924276i
$471$		−	3.94479e7i		−	0.377538i
$472$	−6.42896e7	+	2.64506e7i	−0.611385	+	0.251542i
$473$	−1.36872e8			−1.29340
$474$	5.29992e7	−	4.06010e7i	0.497662	−	0.381243i
$475$	−5.11358e7			−0.477138
$476$	−2.83911e7	−	7.65565e6i	−0.263246	−	0.0709841i
$477$		−	5.71258e7i		−	0.526353i
$478$	5.26148e6	−	4.03065e6i	0.0481753	−	0.0369055i
$479$		−	6.30807e7i		−	0.573971i	−0.957935	−	0.286985i	$-0.907347\pi$
$479$		−	6.30807e7i		−	0.573971i	0.957935	−	0.286985i	$-0.0926531\pi$
$480$	−5.10856e7	+	6.51960e6i	−0.461929	+	0.0589518i
$481$	1.24933e8			1.12265
$482$	1.26169e8	+	1.64698e8i	1.12671	+	1.47077i
$483$	−6.79681e7			−0.603203
$484$	−3.20570e7	+	1.18884e8i	−0.282739	+	1.04854i
$485$		−	1.17209e8i		−	1.02739i
$486$	−4.47820e6	−	5.84570e6i	−0.0390117	−	0.0509246i
$487$			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
$489$	3.47359e7			0.297066
$490$	2.59288e7	−	1.98632e7i	0.220391	−	0.168835i
$491$	−1.91695e8			−1.61944			−0.809721	−	0.586815i	$-0.800382\pi$
$491$	−1.91695e8			−1.61944			−0.809721	+	0.586815i	$0.800382\pi$
$492$	−8.86375e6	+	3.28714e7i	−0.0744256	+	0.276008i
$493$		−	4.71186e7i		−	0.393234i
$494$	−1.02361e8	+	7.84158e7i	−0.849093	+	0.650463i
$495$			4.70972e7i			0.388311i
$496$	6.22909e7	−	1.07105e8i	0.510481	−	0.877737i
$497$	6.45858e7			0.526099
$498$	−5.00807e7	−	6.53737e7i	−0.405492	−	0.529316i
$499$	−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
$501$			3.67986e7i			0.292629i
$502$	2.27824e7	+	2.97395e7i	0.180090	+	0.235083i
$503$			1.07931e7i			0.0848087i	0.999101	+	0.0424044i	$0.0135018\pi$
$503$			1.07931e7i			0.0848087i	−0.999101	+	0.0424044i	$0.986498\pi$
$504$	1.31489e7	+	3.19592e7i	0.102707	+	0.249634i
$505$	−3.29948e7			−0.256196
$506$	1.91637e8	−	1.46807e8i	1.47920	−	1.13317i
$507$	2.90717e7			0.223073
$508$	−1.59285e8	−	4.29512e7i	−1.21502	−	0.327630i
$509$			4.84357e7i			0.367293i	0.982992	+	0.183646i	$0.0587901\pi$
$509$			4.84357e7i			0.367293i	−0.982992	+	0.183646i	$0.941210\pi$
$510$	1.65099e7	−	1.26477e7i	0.124461	−	0.0953455i
$511$			1.79406e8i			1.34454i
$512$	5.22465e7	−	1.23631e8i	0.389267	−	0.921125i
$513$	−3.54767e7			−0.262779
$514$	−5.18193e7	−	6.76432e7i	−0.381595	−	0.498121i
$515$	9.80835e7			0.718083
$516$	1.84936e7	−	6.85840e7i	0.134609	−	0.499199i
$517$		−	2.88108e8i		−	2.08489i
$518$	−9.80984e7	−	1.28054e8i	−0.705785	−	0.921309i
$519$		−	2.26497e7i		−	0.162017i
$520$	−8.21577e7	+	3.38021e7i	−0.584303	+	0.240399i
$521$	2.16291e8			1.52941			0.764706	−	0.644379i	$-0.222884\pi$
$521$	2.16291e8			1.52941			0.764706	+	0.644379i	$0.222884\pi$
$522$	−4.39596e7	+	3.36760e7i	−0.309059	+	0.236760i
$523$	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
$525$			2.36413e7i			0.163378i
$526$	6.89527e7	−	5.28225e7i	0.473799	−	0.362962i
$527$			5.00361e7i			0.341862i
$528$	−1.06104e8	−	6.17085e7i	−0.720823	−	0.419221i
$529$	−9.83684e7			−0.664490
$530$	−1.15310e8	−	1.50522e8i	−0.774533	−	1.01105i
$531$	−3.29940e7			−0.220370
$532$	1.60749e8	+	4.33460e7i	1.06761	+	0.287882i
$533$			5.87297e7i			0.387861i
$534$	7.15067e7	+	9.33425e7i	0.469594	+	0.612993i
$535$			6.52841e7i			0.426330i
$536$	9.82495e7	−	4.04227e7i	0.638022	−	0.262501i
$537$	2.22799e7			0.143876
$538$	−8.07067e7	+	6.18268e7i	−0.518278	+	0.397036i
$539$	7.78471e7			0.497137
$540$	−2.35995e7	−	6.36359e6i	−0.149872	−	0.0404130i
$541$			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
$543$			4.70496e7i			0.293871i
$544$	6.86167e6	+	5.37660e7i	0.0426219	+	0.333973i
$545$	2.43424e8			1.50375
$546$	3.62536e7	+	4.73242e7i	0.222727	+	0.290741i
$547$	−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
$549$			2.59315e7i			0.156715i
$550$	−5.10639e7	−	6.66572e7i	−0.306921	−	0.400644i
$551$			2.66784e8i			1.59479i
$552$	4.76688e7	+	1.15861e8i	0.283411	+	0.688845i
$553$	−1.48704e8			−0.879322
$554$	−8.39080e7	+	6.42792e7i	−0.493485	+	0.378043i
$555$	1.14092e8			0.667382
$556$	4.95044e7	−	1.83588e8i	0.288018	−	1.06812i
$557$		−	1.22171e7i		−	0.0706971i	−0.999375	−	0.0353486i	$-0.988746\pi$
$557$		−	1.22171e7i		−	0.0706971i	0.999375	−	0.0353486i	$-0.0112541\pi$
$558$	4.66814e7	−	3.57611e7i	0.268684	−	0.205830i
$559$		−	1.22536e8i		−	0.701500i
$560$	9.91571e7	+	5.76685e7i	0.564625	+	0.328378i
$561$	4.95683e7			0.280747
$562$	−3.03325e6	−	3.95951e6i	−0.0170883	−	0.0223065i
$563$	−8.96182e7			−0.502193			−0.251097	−	0.967962i	$-0.580791\pi$
$563$	−8.96182e7			−0.502193			−0.251097	+	0.967962i	$0.580791\pi$
$564$	1.44365e8	+	3.89280e7i	0.804684	+	0.216983i
$565$			7.73384e7i			0.428795i
$566$	2.35586e6	+	3.07526e6i	0.0129927	+	0.0169602i
$567$			1.64017e7i			0.0899790i
$568$	−4.52967e7	−	1.10096e8i	−0.247185	−	0.600795i
$569$	−1.36856e8			−0.742894			−0.371447	−	0.928454i	$-0.621138\pi$
$569$	−1.36856e8			−0.742894			−0.371447	+	0.928454i	$0.621138\pi$
$570$	−9.34784e7	+	7.16108e7i	−0.504762	+	0.386682i
$571$	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
$573$		−	1.58086e8i		−	0.840293i
$574$	6.01969e7	−	4.61149e7i	0.318301	−	0.243840i
$575$			8.57069e7i			0.450829i
$576$	4.52572e7	−	4.48286e7i	0.236821	−	0.234578i
$577$	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
$579$	−1.38539e7			−0.0713735
$580$	−4.78541e7	+	1.77468e8i	−0.245265	+	0.909568i
$581$			1.83424e8i			0.935251i
$582$	8.81653e7	+	1.15088e8i	0.447228	+	0.583796i
$583$		−	4.51919e8i		−	2.28063i
$584$	3.05824e8	−	1.25825e8i	1.53544	−	0.631726i
$585$	−4.21641e7			−0.210608
$586$	−7.84977e7	+	6.01346e7i	−0.390089	+	0.298835i
$587$	1.63395e7			0.0807839			0.0403920	−	0.999184i	$-0.487139\pi$
$587$	1.63395e7			0.0807839			0.0403920	+	0.999184i	$0.487139\pi$
$588$	−1.05184e7	+	3.90076e7i	−0.0517389	+	0.191875i
$589$		−	2.83303e8i		−	1.38645i
$590$	−8.69368e7	+	6.65995e7i	−0.423299	+	0.324276i
$591$		−	1.46741e8i		−	0.710867i
$592$	−1.49487e8	+	2.57033e8i	−0.720507	+	1.23886i
$593$	−1.22802e8			−0.588898			−0.294449	−	0.955667i	$-0.595136\pi$
$593$	−1.22802e8			−0.588898			−0.294449	+	0.955667i	$0.595136\pi$
$594$	−3.54268e7	−	4.62450e7i	−0.169033	−	0.220651i
$595$	−4.63231e7			−0.219911
$596$	−1.14363e8	−	3.08379e7i	−0.540189	−	0.145662i
$597$		−	1.47700e8i		−	0.694155i
$598$	1.31430e8	+	1.71564e8i	0.614597	+	0.802275i
$599$		−	1.70436e8i		−	0.793016i	−0.918031	−	0.396508i	$-0.870222\pi$
$599$		−	1.70436e8i		−	0.793016i	0.918031	−	0.396508i	$-0.129778\pi$
$600$	4.03001e7	−	1.65806e7i	0.186575	−	0.0767623i
$601$	−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
$603$	5.04225e7			0.229971
$604$	−2.35695e8	−	6.35551e7i	−1.06964	−	0.288429i
$605$			1.93972e8i			0.875935i
$606$	3.23978e7	−	2.48189e7i	0.145579	−	0.111523i
$607$		−	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
$609$	1.23341e8			0.546079
$610$	5.23435e7	+	6.83275e7i	0.230608	+	0.301028i
$611$	2.57931e8			1.13078
$612$	−6.69747e6	+	2.48377e7i	−0.0292184	+	0.108357i
$613$			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
$615$			5.36331e7i			0.230573i
$616$	1.04021e8	+	2.52827e8i	0.445017	+	1.08164i
$617$	−3.50474e8			−1.49211			−0.746055	−	0.665885i	$-0.768054\pi$
$617$	−3.50474e8			−1.49211			−0.746055	+	0.665885i	$0.768054\pi$
$618$	−9.63088e7	+	7.37791e7i	−0.408038	+	0.312585i
$619$	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
$621$			5.94612e7i			0.248290i
$622$	2.40569e8	−	1.84292e8i	0.999696	−	0.765835i
$623$		−	2.61899e8i		−	1.08310i
$624$	5.52449e7	−	9.49900e7i	0.227373	−	0.390952i
$625$	−1.29017e8			−0.528453
$626$	−2.43311e8	−	3.17610e8i	−0.991832	−	1.29471i
$627$	−2.80654e8			−1.13859
$628$	1.56372e8	+	4.21657e7i	0.631365	+	0.170247i
$629$		−	1.20078e8i		−	0.482514i
$630$	3.31075e7	+	4.32174e7i	0.132405	+	0.172837i
$631$		−	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
$633$	−1.19367e8			−0.470621
$634$	−2.69421e8	+	2.06395e8i	−1.05722	+	0.809899i
$635$	−2.59890e8			−1.01501
$636$	2.26447e8	+	6.10615e7i	0.880230	+	0.237354i
$637$			6.96931e7i			0.269632i
$638$	−3.47762e8	+	2.66409e8i	−1.33912	+	1.02586i
$639$		−	5.65022e7i		−	0.216552i
$640$	2.87614e7	−	2.09473e8i	0.109716	−	0.799077i
$641$	1.45116e8			0.550987			0.275494	−	0.961303i	$-0.411159\pi$
$641$	1.45116e8			0.550987			0.275494	+	0.961303i	$0.411159\pi$
$642$	−4.91071e7	−	6.41028e7i	−0.185583	−	0.242255i
$643$	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
$645$		−	1.11902e8i		−	0.417022i
$646$	7.53680e7	+	9.83829e7i	0.279569	+	0.364941i
$647$			4.79942e8i			1.77205i	0.463638	+	0.886025i	$0.346544\pi$
$647$			4.79942e8i			1.77205i	−0.463638	+	0.886025i	$0.653456\pi$
$648$	2.79592e7	−	1.15032e7i	0.102754	−	0.0422761i
$649$	−2.61014e8			−0.954837
$650$	5.96753e7	−	4.57153e7i	0.217297	−	0.166464i
$651$	−1.30978e8			−0.474739
$652$	−3.71291e7	+	1.37694e8i	−0.133959	+	0.496789i
$653$		−	2.92267e8i		−	1.04964i	−0.851213	−	0.524820i	$-0.824133\pi$
$653$		−	2.92267e8i		−	1.04964i	0.851213	−	0.524820i	$-0.175867\pi$
$654$	−2.39020e8	+	1.83105e8i	−0.854477	+	0.654587i
$655$			6.96891e7i			0.247994i
$656$	−1.20828e8	−	7.02721e7i	−0.428013	−	0.248927i
$657$	1.56952e8			0.553440
$658$	−2.02529e8	−	2.64374e8i	−0.710900	−	0.927986i
$659$	4.27588e8			1.49406			0.747032	−	0.664788i	$-0.231478\pi$
$659$	4.27588e8			1.49406			0.747032	+	0.664788i	$0.231478\pi$
$660$	−1.86694e8	−	5.03420e7i	−0.649380	−	0.175105i
$661$			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
$663$			4.43763e7i			0.152269i
$664$	3.12673e8	−	1.28643e8i	1.06804	−	0.439422i
$665$	2.62280e8			0.891867
$666$	−1.12027e8	+	8.58204e7i	−0.379228	+	0.290514i
$667$	4.47147e8			1.50686
$668$	−1.45870e8	−	3.93339e7i	−0.489370	−	0.131958i
$669$		−	4.74577e7i		−	0.158500i
$670$	1.32860e8	−	1.01779e8i	0.441742	−	0.338404i
$671$			2.05143e8i			0.679029i
$672$	−1.40742e8	+	1.79616e7i	−0.463783	+	0.0591884i
$673$	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
$675$	2.06824e7			0.0672496
$676$	−3.10746e7	+	1.15241e8i	−0.100593	+	0.373049i
$677$			2.13601e8i			0.688395i	0.938897	+	0.344197i	$0.111849\pi$
$677$			2.13601e8i			0.688395i	−0.938897	+	0.344197i	$0.888151\pi$
$678$	−5.81745e7	−	7.59390e7i	−0.186657	−	0.243655i
$679$		−	3.22912e8i		−	1.03151i
$680$	3.24883e7	+	7.89645e7i	0.103324	+	0.251134i
$681$	−1.88821e8			−0.597872
$682$	3.69294e8	−	2.82904e8i	1.16418	−	0.891840i
$683$	−5.14381e8			−1.61444			−0.807222	−	0.590248i	$-0.799030\pi$
$683$	−5.14381e8			−1.61444			−0.807222	+	0.590248i	$0.799030\pi$
$684$	3.79209e7	−	1.40630e8i	0.118498	−	0.439450i
$685$			1.65809e8i			0.515866i
$686$	2.78967e8	−	2.13708e8i	0.864132	−	0.661984i
$687$			1.65772e8i			0.511260i
$688$	2.52100e8	+	1.46618e8i	0.774119	+	0.450218i
$689$	4.04583e8			1.23694
$690$	1.20024e8	+	1.56676e8i	0.365361	+	0.476930i
$691$	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
$693$			1.29753e8i			0.389869i
$694$	−1.07472e8	−	1.40291e8i	−0.321527	−	0.419711i
$695$		−	2.99543e8i		−	0.892288i
$696$	−8.65040e7	−	2.10253e8i	−0.256572	−	0.623611i
$697$	5.64471e7			0.166703
$698$	−3.61750e7	+	2.77125e7i	−0.106376	+	0.0814910i
$699$	2.17357e8			0.636417
$700$	−9.37147e7	−	2.52701e7i	−0.273221	−	0.0736739i
$701$		−	2.83744e8i		−	0.823707i	−0.911250	−	0.411854i	$-0.864881\pi$
$701$		−	2.83744e8i		−	0.823707i	0.911250	−	0.411854i	$-0.135119\pi$
$702$	4.14011e7	−	3.17161e7i	0.119674	−	0.0916787i
$703$			6.79876e8i			1.95688i
$704$	3.58027e8	−	3.54637e8i	1.02612	−	1.01640i
$705$	2.35547e8			0.672219
$706$	2.00472e8	+	2.61690e8i	0.569692	+	0.743658i
$707$	−9.09012e7			−0.257224
$708$	3.52672e7	−	1.30789e8i	0.0993735	−	0.368528i
$709$		−	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
$711$			1.30092e8i			0.361945i
$712$	−4.46444e8	+	1.83680e8i	−1.23688	+	0.508888i
$713$	−4.74833e8			−1.31000
$714$	4.54849e7	−	3.48445e7i	0.124960	−	0.0957282i
$715$	−3.33558e8			−0.912542
$716$	−2.38149e7	+	8.83178e7i	−0.0648797	+	0.240607i
$717$			1.29149e7i			0.0350375i
$718$	−1.86993e7	+	1.43249e7i	−0.0505186	+	0.0387007i
$719$			1.93158e8i			0.519669i	0.965653	+	0.259834i	$0.0836679\pi$
$719$			1.93158e8i			0.519669i	−0.965653	+	0.259834i	$0.916332\pi$
$720$	5.04507e7	−	8.67466e7i	0.135167	−	0.232410i
$721$	2.70221e8			0.720965
$722$	−1.97850e8	−	2.58268e8i	−0.525685	−	0.686212i
$723$	−4.04268e8			−1.06968
$724$	−1.86505e8	−	5.02911e7i	−0.491446	−	0.132518i
$725$		−	1.55531e8i		−	0.408135i
$726$	−1.45907e8	−	1.90462e8i	−0.381299	−	0.497735i
$727$			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
$729$	1.43489e7			0.0370370
$730$	4.13557e8	−	3.16812e8i	1.06308	−	0.814392i
$731$	−1.17773e8			−0.301505
$732$	−1.02793e8	−	2.77181e7i	−0.262077	−	0.0706691i
$733$			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
$735$			6.36451e7i			0.160289i
$736$	−5.10230e8	+	6.51160e7i	−1.27977	+	0.163326i
$737$	3.98890e8			0.996439
$738$	−4.03432e7	−	5.26627e7i	−0.100369	−	0.131019i
$739$	−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
$741$		−	2.51257e8i		−	0.617539i
$742$	−3.17681e8	−	4.14690e8i	−0.777642	−	1.01511i
$743$		−	3.10665e8i		−	0.757400i	−0.925519	−	0.378700i	$-0.876371\pi$
$743$		−	3.10665e8i		−	0.757400i	0.925519	−	0.378700i	$-0.123629\pi$
$744$	9.18602e7	+	2.23271e8i	0.223053	+	0.542142i
$745$	−1.86595e8			−0.451264
$746$	−1.35498e8	+	1.03801e8i	−0.326375	+	0.250025i
$747$	1.60467e8			0.384967
$748$	−5.29833e7	+	1.96489e8i	−0.126600	+	0.469499i
$749$			1.79858e8i			0.428041i
$750$	2.10451e8	−	1.61220e8i	0.498847	−	0.382151i
$751$		−	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
$753$	−7.29988e7			−0.170974
$754$	−2.38504e8	−	3.11336e8i	−0.556394	−	0.726299i
$755$	−3.84561e8			−0.893562
$756$	−6.50168e7	−	1.75318e7i	−0.150474	−	0.0405752i
$757$		−	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
$759$			4.70394e8i			1.07581i
$760$	−1.83948e8	−	4.47094e8i	−0.419038	−	1.01849i
$761$	−4.86110e8			−1.10301			−0.551507	−	0.834170i	$-0.685947\pi$
$761$	−4.86110e8			−1.10301			−0.551507	+	0.834170i	$0.685947\pi$
$762$	2.55188e8	−	1.95491e8i	0.576760	−	0.441837i
$763$	6.70637e8			1.50978
$764$	6.26657e8	+	1.68978e8i	1.40524	+	0.378922i
$765$			4.05253e7i			0.0905194i
$766$	−9.45305e7	+	7.24168e7i	−0.210322	+	0.161121i
$767$		−	2.33674e8i		−	0.517875i
$768$	1.29326e8	+	2.27317e8i	0.285497	+	0.501821i
$769$	−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
$771$	1.66038e8			0.362280
$772$	1.48084e7	−	5.49171e7i	0.0321852	−	0.119359i
$773$		−	5.19835e8i		−	1.12545i	−0.826644	−	0.562726i	$-0.809753\pi$
$773$		−	5.19835e8i		−	1.12545i	0.826644	−	0.562726i	$-0.190247\pi$
$774$	8.41734e7	+	1.09877e8i	0.181532	+	0.236965i
$775$			1.65161e8i			0.354816i
$776$	−5.50451e8	+	2.26471e8i	−1.17797	+	0.484650i
$777$	3.14324e8			0.670060
$778$	4.16961e8	−	3.19421e8i	0.885436	−	0.678304i
$779$	−3.19602e8			−0.676078
$780$	4.50690e7	−	1.67139e8i	0.0949717	−	0.352204i
$781$		−	4.46986e8i		−	0.938299i
$782$	1.64896e8	−	1.26322e8i	0.344818	−	0.264154i
$783$		−	1.07904e8i		−	0.224776i
$784$	−1.43384e8	−	8.33902e7i	−0.297544	−	0.173048i
$785$	2.55138e8			0.527431
$786$	−5.24206e7	−	6.84281e7i	−0.107953	−	0.140918i
$787$	−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
$789$			1.69252e8i			0.344590i
$790$	2.62596e8	+	3.42784e8i	0.532606	+	0.695247i
$791$			2.13068e8i			0.430516i
$792$	2.21184e8	−	9.10014e7i	0.445223	−	0.183178i
$793$	−1.83655e8			−0.368285
$794$	9.77689e7	−	7.48976e7i	0.195317	−	0.149626i
$795$	3.69473e8			0.735329
$796$	5.85484e8	+	1.57876e8i	1.16085	+	0.313023i
$797$		−	8.87902e8i		−	1.75384i	−0.480637	−	0.876920i	$-0.659594\pi$
$797$		−	8.87902e8i		−	1.75384i	0.480637	−	0.876920i	$-0.340406\pi$
$798$	−2.57534e8	+	1.97289e8i	−0.506788	+	0.388234i
$799$		−	2.47906e8i		−	0.486011i
$800$	2.26493e7	+	1.77473e8i	0.0442370	+	0.346628i
$801$	−2.29119e8			−0.445825
$802$	2.55487e8	+	3.33504e8i	0.495274	+	0.646514i
$803$	1.24164e9			2.39800
$804$	−5.38964e7	+	1.99876e8i	−0.103703	+	0.384585i
$805$		−	4.39598e8i		−	0.842690i
$806$	2.53272e8	+	3.30613e8i	0.483707	+	0.631415i
$807$		−	1.98103e8i		−	0.376939i
$808$	6.37528e7	+	1.54954e8i	0.120855	+	0.293745i
$809$	2.61371e8			0.493641			0.246821	−	0.969061i	$-0.420614\pi$
$809$	2.61371e8			0.493641			0.246821	+	0.969061i	$0.420614\pi$
$810$	3.78083e7	−	2.89637e7i	0.0711430	−	0.0545004i
$811$	−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
$813$			3.49883e8i			0.651106i
$814$	−8.86241e8	+	6.78920e8i	−1.64315	+	1.25877i
$815$			2.24662e8i			0.415008i
$816$	−9.12980e7	−	5.30978e7i	−0.168032	−	0.0977250i
$817$	6.66828e8			1.22278
$818$	2.75001e8	+	3.58978e8i	0.502429	+	0.655854i
$819$	−1.16163e8			−0.211453
$820$	−2.12603e8	−	5.73282e7i	−0.385591	−	0.103975i
$821$			1.91855e8i			0.346693i	0.984861	+	0.173346i	$0.0554580\pi$
$821$			1.91855e8i			0.346693i	−0.984861	+	0.173346i	$0.944542\pi$
$822$	−1.24723e8	−	1.62809e8i	−0.224559	−	0.293132i
$823$			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
$825$	1.63617e8			0.291385
$826$	−2.39512e8	+	1.83482e8i	−0.424998	+	0.325577i
$827$	−8.06273e8			−1.42549			−0.712747	−	0.701421i	$-0.752549\pi$
$827$	−8.06273e8			−1.42549			−0.712747	+	0.701421i	$0.752549\pi$
$828$	−2.35705e8	−	6.35578e7i	−0.415220	−	0.111964i
$829$			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
$831$		−	2.05961e8i		−	0.358907i
$832$	3.17491e8	+	3.20526e8i	0.551266	+	0.556537i
$833$	6.69844e7			0.115888
$834$	2.25318e8	+	2.94123e8i	0.388417	+	0.507027i
$835$	−2.38003e8			−0.408811
$836$	2.99990e8	−	1.11252e9i	0.513438	−	1.90409i
$837$			1.14585e8i			0.195412i
$838$	−3.41416e8	−	4.45673e8i	−0.580165	−	0.757328i
$839$		−	5.33468e8i		−	0.903280i	−0.892200	−	0.451640i	$-0.850839\pi$
$839$		−	5.33468e8i		−	0.903280i	0.892200	−	0.451640i	$-0.149161\pi$
$840$	−2.06703e8	+	8.50436e7i	−0.348746	+	0.143484i
$841$	−2.16610e8			−0.364158
$842$	5.86722e7	−	4.49469e7i	0.0982870	−	0.0752945i
$843$	9.71905e6			0.0162234
$844$	1.27590e8	−	4.73171e8i	0.212222	−	0.787029i
$845$			1.88027e8i			0.311638i
$846$	−2.31285e8	+	1.77180e8i	−0.381976	+	0.292620i
$847$			5.34394e8i			0.879450i
$848$	−4.84098e8	+	8.32373e8i	−0.793863	+	1.36499i
$849$	−7.54855e6			−0.0123350
$850$	−4.39385e7	−	5.73559e7i	−0.0715465	−	0.0933945i
$851$	1.13952e9			1.84898
$852$	2.23976e8	+	6.03950e7i	0.362145	+	0.0976523i
$853$			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
$855$		−	2.29453e8i		−	0.367109i
$856$	3.06595e8	−	1.26142e8i	0.488814	−	0.201112i
$857$	−3.39277e8			−0.539030			−0.269515	−	0.962996i	$-0.586863\pi$
$857$	−3.39277e8			−0.539030			−0.269515	+	0.962996i	$0.586863\pi$
$858$	3.27522e8	−	2.50904e8i	0.518536	−	0.397234i
$859$	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
$861$			1.47760e8i			0.231498i
$862$	9.57130e7	−	7.33227e7i	0.149434	−	0.114477i
$863$		−	7.15874e8i		−	1.11379i	−0.830582	−	0.556896i	$-0.811992\pi$
$863$		−	7.15874e8i		−	1.11379i	0.830582	−	0.556896i	$-0.188008\pi$
$864$	1.57135e7	+	1.23126e8i	0.0243631	+	0.190902i
$865$	1.46492e8			0.226342
$866$	−5.77255e8	−	7.53530e8i	−0.888821	−	1.16024i
$867$	−3.33616e8			−0.511905
$868$	1.40002e8	−	5.19198e8i	0.214079	−	0.793915i
$869$			1.02915e9i			1.56827i
$870$	−2.17807e8	−	2.84318e8i	−0.330760	−	0.431764i
$871$			3.57109e8i			0.540438i
$872$	−4.70345e8	−	1.14320e9i	−0.709361	−	1.72414i
$873$	−2.82496e8			−0.424590
$874$	−9.33637e8	+	7.15229e8i	−1.39844	+	1.07130i
$875$	−5.90480e8			−0.881416
$876$	−1.67765e8	+	6.22160e8i	−0.249568	+	0.925528i
$877$		−	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
$879$		−	1.92681e8i		−	0.283709i
$880$	3.99113e8	−	6.86248e8i	0.585663	−	1.00701i
$881$	−6.17449e8			−0.902971			−0.451485	−	0.892279i	$-0.649106\pi$
$881$	−6.17449e8			−0.902971			−0.451485	+	0.892279i	$0.649106\pi$
$882$	−4.78742e7	−	6.24935e7i	−0.0697744	−	0.0910812i
$883$	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
$885$		−	2.13396e8i		−	0.307862i
$886$	−8.52509e7	−	1.11284e8i	−0.122574	−	0.160004i
$887$			1.13085e9i			1.62045i	0.586119	+	0.810225i	$0.300655\pi$
$887$			1.13085e9i			1.62045i	−0.586119	+	0.810225i	$0.699345\pi$
$888$	−2.20448e8	−	5.35810e8i	−0.314824	−	0.765195i
$889$	−7.16001e8			−1.01908
$890$	−6.03712e8	+	4.62485e8i	−0.856367	+	0.656036i
$891$	1.13513e8			0.160477
$892$	1.88123e8	+	5.07274e7i	0.265062	+	0.0714740i
$893$			1.40363e9i			1.97106i
$894$	1.83219e8	−	1.40358e8i	0.256423	−	0.196437i
$895$			1.44100e8i			0.200999i
$896$	7.92381e7	−	5.77101e8i	0.110156	−	0.802283i
$897$	−4.21123e8			−0.583488
$898$	5.29272e8	+	6.90895e8i	0.730887	+	0.954076i
$899$	8.61675e8			1.18594
$900$	−2.21073e7	+	8.19854e7i	−0.0303256	+	0.112463i
$901$		−	3.88858e8i		−	0.531639i
$902$	−3.19153e8	−	4.16611e8i	−0.434889	−	0.567690i
$903$		−	3.08291e8i		−	0.418695i
$904$	3.63206e8	−	1.49434e8i	0.491641	−	0.202275i
$905$	−3.04303e8			−0.410545
$906$	3.77603e8	−	2.89270e8i	0.507751	−	0.388972i
$907$	−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
$909$			7.95240e7i			0.105878i
$910$	−3.06080e8	+	2.34478e8i	−0.406172	+	0.311156i
$911$		−	8.56397e8i		−	1.13271i	−0.824160	−	0.566356i	$-0.808353\pi$
$911$		−	8.56397e8i		−	1.13271i	0.824160	−	0.566356i	$-0.191647\pi$
$912$	5.16927e8	+	3.00638e8i	0.681466	+	0.396332i
$913$	1.26945e9			1.66802
$914$	−6.59173e8	−	8.60463e8i	−0.863298	−	1.12692i
$915$	−1.67717e8			−0.218935
$916$	−6.57124e8	−	1.77193e8i	−0.854990	−	0.230548i
$917$			1.91994e8i			0.248989i
$918$	−3.04834e7	−	3.97920e7i	−0.0394035	−	0.0514361i
$919$		−	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
$921$	−4.05182e8			−0.518647
$922$	4.13411e8	−	3.16701e8i	0.527459	−	0.404070i
$923$	4.00167e8			0.508905
$924$	−5.14344e8	−	1.38693e8i	−0.651986	−	0.175808i
$925$		−	3.96358e8i		−	0.500798i
$926$	−3.16308e8	+	2.42314e8i	−0.398362	+	0.305172i
$927$		−	2.36401e8i		−	0.296763i
$928$	9.25908e8	−	1.18165e8i	1.15857	−	0.147859i
$929$	−1.46510e9			−1.82734			−0.913672	−	0.406451i	$-0.866766\pi$
$929$	−1.46510e9			−1.82734			−0.913672	+	0.406451i	$0.866766\pi$
$930$	2.31293e8	+	3.01922e8i	0.287550	+	0.375358i
$931$	−3.79263e8			−0.469994
$932$	−2.32332e8	+	8.61606e8i	−0.286986	+	1.06429i
$933$			5.90502e8i			0.727071i
$934$	5.63001e7	+	7.34923e7i	0.0690984	+	0.0901988i
$935$			3.20593e8i			0.392211i
$936$	8.14696e7	+	1.98016e8i	0.0993500	+	0.241475i
$937$	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
$939$	7.79608e8			0.941628
$940$	−2.51775e8	+	9.33713e8i	−0.303131	+	1.12416i
$941$			1.14292e9i			1.37166i	0.727763	+	0.685828i	$0.240560\pi$
$941$			1.14292e9i			1.37166i	−0.727763	+	0.685828i	$0.759440\pi$
$942$	−2.50521e8	+	1.91916e8i	−0.299704	+	0.229593i
$943$			5.35673e8i			0.638800i
$944$	4.80752e8	+	2.79599e8i	0.571485	+	0.332369i
$945$	−1.06082e8			−0.125703
$946$	6.65891e8	+	8.69233e8i	0.786557	+	1.02675i
$947$	−3.04615e8			−0.358675			−0.179338	−	0.983788i	$-0.557395\pi$
$947$	−3.04615e8			−0.358675			−0.179338	+	0.983788i	$0.557395\pi$
$948$	−5.15688e8	−	1.39055e8i	−0.605288	−	0.163216i
$949$			1.11158e9i			1.30060i
$950$	2.48778e8	+	3.24747e8i	0.290163	+	0.378769i
$951$		−	6.61323e8i		−	0.768904i
$952$	8.95056e7	+	2.17548e8i	0.103738	+	0.252142i
$953$	1.45008e9			1.67538			0.837692	−	0.546143i	$-0.183905\pi$
$953$	1.45008e9			1.67538			0.837692	+	0.546143i	$0.183905\pi$
$954$	−3.62788e8	+	2.77920e8i	−0.417838	+	0.320092i
$955$	1.02246e9			1.17391
$956$	−5.11948e7	−	1.38047e7i	−0.0585939	−	0.0157998i
$957$		−	8.53619e8i		−	0.973931i
$958$	−4.00606e8	+	3.06891e8i	−0.455639	+	0.349050i
$959$			4.56806e8i			0.517936i
$960$	2.89939e8	+	2.92711e8i	0.327712	+	0.330845i
$961$	−2.75244e7			−0.0310133
$962$	−6.07808e8	−	7.93413e8i	−0.682718	−	0.891197i
$963$	1.57347e8			0.176190
$964$	4.32121e8	−	1.60253e9i	0.482363	−	1.78885i
$965$		−	8.96032e7i		−	0.0997106i
$966$	3.30668e8	+	4.31644e8i	0.366827	+	0.478844i
$967$			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
$969$	−2.41492e8			−0.265418
$970$	−7.44357e8	+	5.70228e8i	−0.815579	+	0.624789i
$971$	−1.58886e9			−1.73552			−0.867759	−	0.496986i	$-0.834440\pi$
$971$	−1.58886e9			−1.73552			−0.867759	+	0.496986i	$0.834440\pi$
$972$	−1.53375e7	+	5.68793e7i	−0.0167015	+	0.0619378i
$973$		−	8.25246e8i		−	0.895869i
$974$	1.30447e9	−	9.99313e8i	1.41175	−	1.08150i
$975$			1.46479e8i			0.158039i
$976$	2.19750e8	−	3.77845e8i	0.236363	−	0.406410i
$977$	1.43593e9			1.53975			0.769875	−	0.638194i	$-0.220318\pi$
$977$	1.43593e9			1.53975			0.769875	+	0.638194i	$0.220318\pi$
$978$	−1.68992e8	−	2.20597e8i	−0.180655	−	0.235821i
$979$	−1.81255e9			−1.93171
$980$	−2.52290e8	−	6.80300e7i	−0.268054	−	0.0722807i
$981$		−	5.86700e8i		−	0.621454i
$982$	9.32605e8	+	1.21739e9i	0.984835	+	1.28557i
$983$		−	1.10373e9i		−	1.16199i	−0.813906	−	0.580997i	$-0.802663\pi$
$983$		−	1.10373e9i		−	1.16199i	0.813906	−	0.580997i	$-0.197337\pi$
$984$	2.51878e8	−	1.03630e8i	0.264366	−	0.108768i
$985$	9.49078e8			0.993100
$986$	−2.99235e8	+	2.29235e8i	−0.312163	+	0.239138i
$987$	6.48935e8			0.674916
$988$	9.95988e8	+	2.68568e8i	1.03272	+	0.278473i
$989$		−	1.11765e9i		−	1.15536i
$990$	2.99099e8	−	2.29131e8i	0.308255	−	0.236144i
$991$		−	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
$993$	1.16048e8			0.118519
$994$	−3.14214e8	−	4.10164e8i	−0.319938	−	0.417637i
$995$	9.55280e8			0.969753
$996$	−1.71522e8	+	6.36094e8i	−0.173597	+	0.643788i
$997$		−	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
$999$		−	2.74983e8i		−	0.275809i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
24.7.b.a.19.3	✓	12	1.1	even	1	trivial
24.7.b.a.19.4	yes	12	8.3	odd	2	inner
72.7.b.c.19.9		12	24.11	even	2
72.7.b.c.19.10		12	3.2	odd	2
96.7.b.a.79.2		12	8.5	even	2
96.7.b.a.79.5		12	4.3	odd	2
288.7.b.d.271.4		12	12.11	even	2
288.7.b.d.271.9		12	24.5	odd	2
768.7.g.l.511.5		24	16.5	even	4
768.7.g.l.511.6		24	16.3	odd	4
768.7.g.l.511.7		24	16.11	odd	4
768.7.g.l.511.8		24	16.13	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 24 = 2^{3} \cdot 3 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	24.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.86506 - 6.35069i) q^{2} +15.5885 q^{3} +(-16.6624 + 61.7929i) q^{4} +100.822i q^{5} +(-75.8387 - 98.9974i) q^{6} +277.765i q^{7} +(473.491 - 194.808i) q^{8} +243.000 q^{9} +(640.287 - 490.503i) q^{10} +1922.36 q^{11} +(-259.742 + 963.256i) q^{12} +1721.01i q^{13} +(1764.00 - 1351.34i) q^{14} +1571.65i q^{15} +(-3540.73 - 2059.24i) q^{16} +1654.12 q^{17} +(-1182.21 - 1543.22i) q^{18} -9365.55 q^{19} +(-6230.07 - 1679.94i) q^{20} +4329.93i q^{21} +(-9352.39 - 12208.3i) q^{22} +15697.3i q^{23} +(7381.00 - 3036.76i) q^{24} +5459.98 q^{25} +(10929.6 - 8372.79i) q^{26} +3788.00 q^{27} +(-17163.9 - 4628.24i) q^{28} -28485.7i q^{29} +(9981.09 - 7646.19i) q^{30} +30249.4i q^{31} +(4148.24 + 32504.4i) q^{32} +29966.6 q^{33} +(-8047.37 - 10504.8i) q^{34} -28004.7 q^{35} +(-4048.97 + 15015.7i) q^{36} -72593.3i q^{37} +(45563.9 + 59477.7i) q^{38} +26827.8i q^{39} +(19640.9 + 47738.2i) q^{40} +34125.3 q^{41} +(27498.0 - 21065.3i) q^{42} -71200.1 q^{43} +(-32031.2 + 118788. i) q^{44} +24499.7i q^{45} +(99688.4 - 76368.1i) q^{46} -149872. i q^{47} +(-55194.5 - 32100.4i) q^{48} +40495.6 q^{49} +(-26563.1 - 34674.7i) q^{50} +25785.1 q^{51} +(-106346. - 28676.1i) q^{52} -235085. i q^{53} +(-18428.8 - 24056.4i) q^{54} +193816. i q^{55} +(54110.9 + 131519. i) q^{56} -145994. q^{57} +(-180904. + 138584. i) q^{58} -135778. q^{59} +(-97117.1 - 26187.6i) q^{60} +106714. i q^{61} +(192105. - 147165. i) q^{62} +67496.9i q^{63} +(186244. - 184480. i) q^{64} -173515. q^{65} +(-145789. - 190309. i) q^{66} +207500. q^{67} +(-27561.6 + 102213. i) q^{68} +244696. i q^{69} +(136245. + 177849. i) q^{70} -232520. i q^{71} +(115058. - 47338.4i) q^{72} +645892. q^{73} +(-461017. + 353170. i) q^{74} +85112.7 q^{75} +(156053. - 578725. i) q^{76} +533964. i q^{77} +(170375. - 130519. i) q^{78} +535360. i q^{79} +(207616. - 356982. i) q^{80} +59049.0 q^{81} +(-166021. - 216719. i) q^{82} +660358. q^{83} +(-267559. - 72147.2i) q^{84} +166771. i q^{85} +(346393. + 452170. i) q^{86} -444048. i q^{87} +(910220. - 374491. i) q^{88} -942878. q^{89} +(155590. - 119192. i) q^{90} -478035. q^{91} +(-969980. - 261555. i) q^{92} +471542. i q^{93} +(-951790. + 729136. i) q^{94} -944251. i q^{95} +(64664.7 + 506693. i) q^{96} -1.16254e6 q^{97} +(-197013. - 257175. i) q^{98} +467133. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 10 q^{2} + 24 q^{4} + 162 q^{6} + 796 q^{8} + 2916 q^{9} + 2172 q^{10} + 2720 q^{11} - 972 q^{12} - 6444 q^{14} + 11640 q^{16} - 4888 q^{17} + 2430 q^{18} + 3936 q^{19} - 31608 q^{20} - 60432 q^{22}+ \cdots + 660960 q^{99}+O(q^{100}) \) 12 * q + 10 * q^2 + 24 * q^4 + 162 * q^6 + 796 * q^8 + 2916 * q^9 + 2172 * q^10 + 2720 * q^11 - 972 * q^12 - 6444 * q^14 + 11640 * q^16 - 4888 * q^17 + 2430 * q^18 + 3936 * q^19 - 31608 * q^20 - 60432 * q^22 + 26244 * q^24 - 27204 * q^25 + 53952 * q^26 - 57072 * q^28 - 24300 * q^30 + 109480 * q^32 + 47388 * q^34 + 162336 * q^35 + 5832 * q^36 - 89080 * q^38 + 72120 * q^40 - 54280 * q^41 + 21060 * q^42 - 49824 * q^43 + 229184 * q^44 + 171864 * q^46 - 23328 * q^48 - 304644 * q^49 - 500078 * q^50 + 80352 * q^51 + 256848 * q^52 + 39366 * q^54 - 699816 * q^56 - 136080 * q^57 - 409524 * q^58 - 886144 * q^59 + 95904 * q^60 + 691356 * q^62 - 500640 * q^64 + 473376 * q^65 + 3888 * q^66 + 1565952 * q^67 + 669104 * q^68 + 473784 * q^70 + 193428 * q^72 + 555480 * q^73 - 753720 * q^74 - 1073088 * q^75 - 293136 * q^76 - 535248 * q^78 - 251616 * q^80 + 708588 * q^81 + 2317716 * q^82 + 2497760 * q^83 - 1168344 * q^84 + 476024 * q^86 + 971424 * q^88 + 367400 * q^89 + 527796 * q^90 - 4475808 * q^91 - 377376 * q^92 - 2642568 * q^94 + 2372328 * q^96 - 1165656 * q^97 + 182674 * q^98 + 660960 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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