LMFDB - Embedded newform 21.7.h.a.2.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(2,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 2]))

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

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

chi := DirichletCharacter("21.2");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2.1
Character	$\chi$	$=$	21.2
Dual form			21.7.h.a.11.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.1658 - 7.60129i) q^{2} +(23.2019 - 13.8084i) q^{3} +(83.5593 + 144.729i) q^{4} +(82.1651 + 47.4381i) q^{5} +(-410.434 + 5.43441i) q^{6} +(334.938 + 73.9300i) q^{7} -1567.67i q^{8} +(347.657 - 640.762i) q^{9} +O(q^{10})$	\(q+(-13.1658 - 7.60129i) q^{2} +(23.2019 - 13.8084i) q^{3} +(83.5593 + 144.729i) q^{4} +(82.1651 + 47.4381i) q^{5} +(-410.434 + 5.43441i) q^{6} +(334.938 + 73.9300i) q^{7} -1567.67i q^{8} +(347.657 - 640.762i) q^{9} +(-721.181 - 1249.12i) q^{10} +(-735.924 + 424.886i) q^{11} +(3937.21 + 2204.17i) q^{12} +1143.92 q^{13} +(-3847.77 - 3519.31i) q^{14} +(2561.43 - 33.9150i) q^{15} +(-6568.51 + 11377.0i) q^{16} +(2380.94 - 1374.64i) q^{17} +(-9447.80 + 5793.52i) q^{18} +(3551.65 - 6151.64i) q^{19} +15855.6i q^{20} +(8792.05 - 2909.64i) q^{21} +12918.7 q^{22} +(4815.31 + 2780.12i) q^{23} +(-21647.0 - 36372.9i) q^{24} +(-3311.76 - 5736.14i) q^{25} +(-15060.7 - 8695.28i) q^{26} +(-781.596 - 19667.5i) q^{27} +(17287.4 + 54652.7i) q^{28} +22700.1i q^{29} +(-33981.1 - 19023.7i) q^{30} +(-4260.11 - 7378.73i) q^{31} +(86070.7 - 49692.9i) q^{32} +(-11207.8 + 20020.1i) q^{33} -41796.1 q^{34} +(24013.1 + 21963.3i) q^{35} +(121787. - 3225.64i) q^{36} +(-35924.2 + 62222.6i) q^{37} +(-93520.8 + 53994.3i) q^{38} +(26541.2 - 15795.7i) q^{39} +(74367.1 - 128808. i) q^{40} -59009.1i q^{41} +(-137872. - 28523.2i) q^{42} -37766.3 q^{43} +(-122987. - 71006.3i) q^{44} +(58961.8 - 36156.1i) q^{45} +(-42265.0 - 73205.1i) q^{46} +(97600.2 + 56349.5i) q^{47} +(4696.04 + 354668. i) q^{48} +(106718. + 49523.9i) q^{49} +100695. i q^{50} +(36260.9 - 64771.2i) q^{51} +(95585.3 + 165559. i) q^{52} +(-175198. + 101151. i) q^{53} +(-139208. + 264880. i) q^{54} -80623.0 q^{55} +(115898. - 525071. i) q^{56} +(-2539.19 - 191772. i) q^{57} +(172550. - 298866. i) q^{58} +(-150163. + 86696.9i) q^{59} +(218940. + 367879. i) q^{60} +(24559.3 - 42538.0i) q^{61} +129529. i q^{62} +(163815. - 188913. i) q^{63} -670153. q^{64} +(93990.5 + 54265.4i) q^{65} +(299739. - 178387. i) q^{66} +(-156627. - 271286. i) q^{67} +(397900. + 229728. i) q^{68} +(150113. - 1987.60i) q^{69} +(-149203. - 471695. i) q^{70} +100708. i q^{71} +(-1.00450e6 - 545010. i) q^{72} +(141839. + 245672. i) q^{73} +(945944. - 546141. i) q^{74} +(-156046. - 87359.2i) q^{75} +1.18709e6 q^{76} +(-277901. + 87903.5i) q^{77} +(-469504. + 6216.54i) q^{78} +(-186141. + 322406. i) q^{79} +(-1.07941e6 + 623195. i) q^{80} +(-289711. - 445530. i) q^{81} +(-448545. + 776903. i) q^{82} +243302. i q^{83} +(1.15577e6 + 1.02934e6i) q^{84} +260841. q^{85} +(497224. + 287073. i) q^{86} +(313452. + 526686. i) q^{87} +(666080. + 1.15368e6i) q^{88} +(-890049. - 513870. i) q^{89} +(-1.05111e6 + 27839.7i) q^{90} +(383143. + 84570.1i) q^{91} +929219. i q^{92} +(-200731. - 112375. i) q^{93} +(-856658. - 1.48377e6i) q^{94} +(583644. - 336967. i) q^{95} +(1.31082e6 - 2.34147e6i) q^{96} -1.64786e6 q^{97} +(-1.02858e6 - 1.46322e6i) q^{98} +(16401.9 + 619266. i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9}+O(q^{10}) $ 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9	$ 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9} - 930 q^{10} - 404 q^{12} + 3632 q^{13} + 5450 q^{15} - 13706 q^{16} + 1612 q^{18} + 6830 q^{19} - 11333 q^{21} - 27348 q^{22} - 54498 q^{24} - 7640 q^{25} + 13268 q^{27} + 88522 q^{28} + 32380 q^{30} + 69410 q^{31} - 85459 q^{33} - 31344 q^{34} + 399028 q^{36} - 71830 q^{37} + 104570 q^{39} + 230250 q^{40} - 467782 q^{42} - 498904 q^{43} - 85375 q^{45} - 342660 q^{46} - 324728 q^{48} + 395668 q^{49} + 42177 q^{51} + 218000 q^{52} - 402122 q^{54} + 231660 q^{55} + 786782 q^{57} + 459522 q^{58} + 1021150 q^{60} + 153158 q^{61} + 179011 q^{63} - 1399412 q^{64} + 80896 q^{66} - 977098 q^{67} - 1520742 q^{69} - 139650 q^{70} - 1001352 q^{72} - 488350 q^{73} + 1434610 q^{75} + 6196280 q^{76} + 245176 q^{78} + 380762 q^{79} + 893531 q^{81} - 3665004 q^{82} + 1231496 q^{84} - 912540 q^{85} + 1452416 q^{87} - 1522482 q^{88} - 11713820 q^{90} - 1529416 q^{91} - 1690071 q^{93} - 3034044 q^{94} + 7549346 q^{96} + 7212176 q^{97} + 435866 q^{99}+O(q^{100}) $ 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9 - 930 * q^10 - 404 * q^12 + 3632 * q^13 + 5450 * q^15 - 13706 * q^16 + 1612 * q^18 + 6830 * q^19 - 11333 * q^21 - 27348 * q^22 - 54498 * q^24 - 7640 * q^25 + 13268 * q^27 + 88522 * q^28 + 32380 * q^30 + 69410 * q^31 - 85459 * q^33 - 31344 * q^34 + 399028 * q^36 - 71830 * q^37 + 104570 * q^39 + 230250 * q^40 - 467782 * q^42 - 498904 * q^43 - 85375 * q^45 - 342660 * q^46 - 324728 * q^48 + 395668 * q^49 + 42177 * q^51 + 218000 * q^52 - 402122 * q^54 + 231660 * q^55 + 786782 * q^57 + 459522 * q^58 + 1021150 * q^60 + 153158 * q^61 + 179011 * q^63 - 1399412 * q^64 + 80896 * q^66 - 977098 * q^67 - 1520742 * q^69 - 139650 * q^70 - 1001352 * q^72 - 488350 * q^73 + 1434610 * q^75 + 6196280 * q^76 + 245176 * q^78 + 380762 * q^79 + 893531 * q^81 - 3665004 * q^82 + 1231496 * q^84 - 912540 * q^85 + 1452416 * q^87 - 1522482 * q^88 - 11713820 * q^90 - 1529416 * q^91 - 1690071 * q^93 - 3034044 * q^94 + 7549346 * q^96 + 7212176 * q^97 + 435866 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−13.1658	−	7.60129i	−1.64573	−	0.950161i	−0.978743	−	0.205090i	$-0.934251\pi$
$2$	−13.1658	−	7.60129i	−1.64573	−	0.950161i	−0.666985	−	0.745071i	$-0.732415\pi$
$3$	23.2019	−	13.8084i	0.859330	−	0.511422i
$3$	23.2019	−	13.8084i	0.859330	−	0.511422i
$4$	83.5593	+	144.729i	1.30561	+	2.26139i
$5$	82.1651	+	47.4381i	0.657321	+	0.379505i	0.791255	−	0.611486i	$-0.209428\pi$
$5$	82.1651	+	47.4381i	0.657321	+	0.379505i	−0.133934	+	0.990990i	$0.542761\pi$
$6$	−410.434	+	5.43441i	−1.90016	+	0.0251593i
$7$	334.938	+	73.9300i	0.976495	+	0.215539i
$7$	334.938	+	73.9300i	0.976495	+	0.215539i
$8$		−	1567.67i		−	3.06185i
$9$	347.657	−	640.762i	0.476895	−	0.878960i
$10$	−721.181	−	1249.12i	−0.721181	−	1.24912i
$11$	−735.924	+	424.886i	−0.552910	+	0.319223i	−0.750295	−	0.661103i	$-0.770089\pi$
$11$	−735.924	+	424.886i	−0.552910	+	0.319223i	0.197385	+	0.980326i	$0.436755\pi$
$12$	3937.21	+	2204.17i	2.27848	+	1.27556i
$13$	1143.92			0.520674			0.260337	−	0.965518i	$-0.416166\pi$
$13$	1143.92			0.520674			0.260337	+	0.965518i	$0.416166\pi$
$14$	−3847.77	−	3519.31i	−1.40225	−	1.28255i
$15$	2561.43	−	33.9150i	0.758942	−	0.0100489i
$16$	−6568.51	+	11377.0i	−1.60364	+	2.77759i
$17$	2380.94	−	1374.64i	0.484621	−	0.279796i	−0.237719	−	0.971334i	$-0.576400\pi$
$17$	2380.94	−	1374.64i	0.484621	−	0.279796i	0.722340	+	0.691538i	$0.243066\pi$
$18$	−9447.80	+	5793.52i	−1.61999	+	0.993402i
$19$	3551.65	−	6151.64i	0.517809	−	0.896871i	−0.481977	−	0.876184i	$-0.660081\pi$
$19$	3551.65	−	6151.64i	0.517809	−	0.896871i	0.999786	−	0.0206875i	$-0.00658549\pi$
$20$			15855.6i			1.98194i
$21$	8792.05	−	2909.64i	0.949363	−	0.314182i
$22$	12918.7			1.21325
$23$	4815.31	+	2780.12i	0.395768	+	0.228497i	0.684656	−	0.728866i	$-0.259952\pi$
$23$	4815.31	+	2780.12i	0.395768	+	0.228497i	−0.288888	+	0.957363i	$0.593286\pi$
$24$	−21647.0	−	36372.9i	−1.56590	−	2.63114i
$25$	−3311.76	−	5736.14i	−0.211953	−	0.367113i
$26$	−15060.7	−	8695.28i	−0.856888	−	0.494725i
$27$	−781.596	−	19667.5i	−0.0397092	−	0.999211i
$28$	17287.4	+	54652.7i	0.787507	+	2.48965i
$29$			22700.1i			0.930752i	0.885113	+	0.465376i	$0.154081\pi$
$29$			22700.1i			0.930752i	−0.885113	+	0.465376i	$0.845919\pi$
$30$	−33981.1	−	19023.7i	−1.25856	−	0.704580i
$31$	−4260.11	−	7378.73i	−0.143000	−	0.247683i	0.785625	−	0.618703i	$-0.212342\pi$
$31$	−4260.11	−	7378.73i	−0.143000	−	0.247683i	−0.928625	+	0.371020i	$0.879008\pi$
$32$	86070.7	−	49692.9i	2.62667	−	1.51651i
$33$	−11207.8	+	20020.1i	−0.311875	+	0.557088i
$34$	−41796.1			−1.06341
$35$	24013.1	+	21963.3i	0.560073	+	0.512263i
$36$	121787.	−	3225.64i	2.61031	−	0.0691366i
$37$	−35924.2	+	62222.6i	−0.709222	+	1.22841i	0.255924	+	0.966697i	$0.417620\pi$
$37$	−35924.2	+	62222.6i	−0.709222	+	1.22841i	−0.965146	+	0.261712i	$0.915713\pi$
$38$	−93520.8	+	53994.3i	−1.70435	+	0.984004i
$39$	26541.2	−	15795.7i	0.447431	−	0.266284i
$40$	74367.1	−	128808.i	1.16199	−	2.01262i
$41$		−	59009.1i		−	0.856184i	−0.903735	−	0.428092i	$-0.859186\pi$
$41$		−	59009.1i		−	0.856184i	0.903735	−	0.428092i	$-0.140814\pi$
$42$	−137872.	−	28523.2i	−1.86092	−	0.384991i
$43$	−37766.3			−0.475006			−0.237503	−	0.971387i	$-0.576329\pi$
$43$	−37766.3			−0.475006			−0.237503	+	0.971387i	$0.576329\pi$
$44$	−122987.	−	71006.3i	−1.44377	−	0.833564i
$45$	58961.8	−	36156.1i	0.647043	−	0.396775i
$46$	−42265.0	−	73205.1i	−0.434218	−	0.752087i
$47$	97600.2	+	56349.5i	0.940063	+	0.542746i	0.889980	−	0.455999i	$-0.150718\pi$
$47$	97600.2	+	56349.5i	0.940063	+	0.542746i	0.0500830	+	0.998745i	$0.484051\pi$
$48$	4696.04	+	354668.i	0.0424627	+	3.20700i
$49$	106718.	+	49523.9i	0.907086	+	0.420946i
$50$			100695.i			0.805557i
$51$	36260.9	−	64771.2i	0.273355	−	0.488283i
$52$	95585.3	+	165559.i	0.679800	+	1.17745i
$53$	−175198.	+	101151.i	−1.17680	+	0.679426i	−0.955272	−	0.295728i	$-0.904438\pi$
$53$	−175198.	+	101151.i	−1.17680	+	0.679426i	−0.221528	+	0.975154i	$0.571104\pi$
$54$	−139208.	+	264880.i	−0.884062	+	1.68216i
$55$	−80623.0			−0.484586
$56$	115898.	−	525071.i	0.659950	−	2.98988i
$57$	−2539.19	−	191772.i	−0.0137110	−	1.03553i
$58$	172550.	−	298866.i	0.884364	−	1.53176i
$59$	−150163.	+	86696.9i	−0.731153	+	0.422131i	−0.818844	−	0.574017i	$-0.805385\pi$
$59$	−150163.	+	86696.9i	−0.731153	+	0.422131i	0.0876910	+	0.996148i	$0.472051\pi$
$60$	218940.	+	367879.i	1.01361	+	1.70314i
$61$	24559.3	−	42538.0i	0.108200	−	0.187408i	−0.806841	−	0.590768i	$-0.798825\pi$
$61$	24559.3	−	42538.0i	0.108200	−	0.187408i	0.915041	+	0.403361i	$0.132158\pi$
$62$			129529.i			0.543492i
$63$	163815.	−	188913.i	0.655136	−	0.755511i
$64$	−670153.			−2.55643
$65$	93990.5	+	54265.4i	0.342250	+	0.197598i
$66$	299739.	−	178387.i	1.04258	−	0.620484i
$67$	−156627.	−	271286.i	−0.520765	−	0.901992i	−0.999708	−	0.0241460i	$-0.992313\pi$
$67$	−156627.	−	271286.i	−0.520765	−	0.901992i	0.478943	−	0.877846i	$-0.341020\pi$
$68$	397900.	+	229728.i	1.26546	+	0.730611i
$69$	150113.	−	1987.60i	0.456953	−	0.00605036i
$70$	−149203.	−	471695.i	−0.434995	−	1.37520i
$71$			100708.i			0.281378i	0.990054	+	0.140689i	$0.0449317\pi$
$71$			100708.i			0.281378i	−0.990054	+	0.140689i	$0.955068\pi$
$72$	−1.00450e6	−	545010.i	−2.69125	−	1.46018i
$73$	141839.	+	245672.i	0.364608	+	0.631519i	0.988713	−	0.149821i	$-0.0478697\pi$
$73$	141839.	+	245672.i	0.364608	+	0.631519i	−0.624105	+	0.781340i	$0.714536\pi$
$74$	945944.	−	546141.i	2.33437	−	1.34775i
$75$	−156046.	−	87359.2i	−0.369887	−	0.207074i
$76$	1.18709e6			2.70423
$77$	−277901.	+	87903.5i	−0.608720	+	0.192546i
$78$	−469504.	+	6216.54i	−0.989363	+	0.0130998i
$79$	−186141.	+	322406.i	−0.377539	+	0.653916i	−0.990703	−	0.136039i	$-0.956563\pi$
$79$	−186141.	+	322406.i	−0.377539	+	0.653916i	0.613165	+	0.789955i	$0.289896\pi$
$80$	−1.07941e6	+	623195.i	−2.10821	+	1.21718i
$81$	−289711.	−	445530.i	−0.545142	−	0.838344i
$82$	−448545.	+	776903.i	−0.813513	+	1.40905i
$83$			243302.i			0.425511i	0.977105	+	0.212756i	$0.0682438\pi$
$83$			243302.i			0.425511i	−0.977105	+	0.212756i	$0.931756\pi$
$84$	1.15577e6	+	1.02934e6i	1.94999	+	1.73668i
$85$	260841.			0.424736
$86$	497224.	+	287073.i	0.781730	+	0.451332i
$87$	313452.	+	526686.i	0.476007	+	0.799823i
$88$	666080.	+	1.15368e6i	0.977414	+	1.69293i
$89$	−890049.	−	513870.i	−1.26254	−	0.728926i	−0.288972	−	0.957338i	$-0.593313\pi$
$89$	−890049.	−	513870.i	−1.26254	−	0.728926i	−0.973565	+	0.228412i	$0.926647\pi$
$90$	−1.05111e6	+	27839.7i	−1.44186	+	0.0381889i
$91$	383143.	+	84570.1i	0.508436	+	0.112226i
$92$			929219.i			1.19331i
$93$	−200731.	−	112375.i	−0.249555	−	0.139708i
$94$	−856658.	−	1.48377e6i	−1.03139	−	1.78642i
$95$	583644.	−	336967.i	0.680733	−	0.393022i
$96$	1.31082e6	−	2.34147e6i	1.48160	−	2.64652i
$97$	−1.64786e6			−1.80553			−0.902767	−	0.430131i	$-0.858467\pi$
$97$	−1.64786e6			−1.80553			−0.902767	+	0.430131i	$0.858467\pi$
$98$	−1.02858e6	−	1.46322e6i	−1.09285	−	1.55464i
$99$	16401.9	+	619266.i	0.0169039	+	0.638222i
$100$	553457.	−	958615.i	0.553457	−	0.958615i
$101$	18331.9	−	10583.9i	0.0177927	−	0.0102726i	−0.491077	−	0.871116i	$-0.663397\pi$
$101$	18331.9	−	10583.9i	0.0177927	−	0.0102726i	0.508870	+	0.860843i	$0.330063\pi$
$102$	−969749.	+	577137.i	−0.913816	+	0.543849i
$103$	−832919.	+	1.44266e6i	−0.762239	+	1.32024i	0.179455	+	0.983766i	$0.442567\pi$
$103$	−832919.	+	1.44266e6i	−0.762239	+	1.32024i	−0.941694	+	0.336470i	$0.890767\pi$
$104$		−	1.79329e6i		−	1.59423i
$105$	860427.	+	178007.i	0.743270	+	0.153769i
$106$	3.07551e6			2.58226
$107$	901153.	+	520281.i	0.735609	+	0.424704i	0.820471	−	0.571689i	$-0.193711\pi$
$107$	901153.	+	520281.i	0.735609	+	0.424704i	−0.0848615	+	0.996393i	$0.527045\pi$
$108$	2.78114e6	−	1.75652e6i	2.20776	−	1.39438i
$109$	−801880.	−	1.38890e6i	−0.619199	−	1.07248i	−0.989632	−	0.143625i	$-0.954124\pi$
$109$	−801880.	−	1.38890e6i	−0.619199	−	1.07248i	0.370434	−	0.928859i	$-0.379209\pi$
$110$	1.06147e6	+	612839.i	0.797497	+	0.460435i
$111$	25683.4	+	1.93974e6i	0.0187795	+	1.41832i
$112$	−3.04114e6	+	3.32498e6i	−2.16463	+	2.36665i
$113$		−	2.10378e6i		−	1.45803i	−0.684500	−	0.729013i	$-0.739979\pi$
$113$		−	2.10378e6i		−	1.45803i	0.684500	−	0.729013i	$-0.260021\pi$
$114$	−1.42429e6	+	2.54414e6i	−0.961353	+	1.71722i
$115$	263767.	+	456858.i	0.173431	+	0.300391i
$116$	−3.28536e6	+	1.89680e6i	−2.10479	+	1.21520i
$117$	397692.	−	732981.i	0.248307	−	0.457652i
$118$	2.63603e6			1.60437
$119$	899095.	−	284395.i	0.533537	−	0.168765i
$120$	−53167.5	−	4.01547e6i	−0.0307682	−	2.32377i
$121$	−524725.	+	908850.i	−0.296193	+	0.513022i
$122$	−646687.	+	373365.i	−0.356135	+	0.205615i
$123$	−814820.	−	1.36912e6i	−0.437871	−	0.735745i
$124$	711943.	−	1.23312e6i	0.373405	−	0.646757i
$125$		−	2.11085e6i		−	1.08076i
$126$	−3.59274e6	+	1.24199e6i	−1.79603	+	0.620879i
$127$	2.32058e6			1.13288			0.566441	−	0.824102i	$-0.308320\pi$
$127$	2.32058e6			1.13288			0.566441	+	0.824102i	$0.308320\pi$
$128$	3.31459e6	+	1.91368e6i	1.58052	+	0.912513i
$129$	−876250.	+	521492.i	−0.408187	+	0.242928i
$130$	−824975.	−	1.42890e6i	−0.375501	−	0.650386i
$131$	2.82139e6	+	1.62893e6i	1.25502	+	0.724585i	0.972102	−	0.234560i	$-0.0753650\pi$
$131$	2.82139e6	+	1.62893e6i	1.25502	+	0.724585i	0.282916	+	0.959145i	$0.408698\pi$
$132$	−3.83400e6	+	50764.7i	−1.66698	+	0.0220719i
$133$	1.64437e6	−	1.79784e6i	0.698949	−	0.764182i
$134$			4.76227e6i			1.97924i
$135$	868767.	−	1.65306e6i	0.353103	−	0.671872i
$136$	−2.15498e6	−	3.73253e6i	−0.856694	−	1.48384i
$137$	304223.	−	175643.i	0.118312	−	0.0683077i	−0.439676	−	0.898156i	$-0.644907\pi$
$137$	304223.	−	175643.i	0.118312	−	0.0683077i	0.557988	+	0.829849i	$0.311573\pi$
$138$	−1.99147e6	−	1.11489e6i	−0.757770	−	0.424222i
$139$	−324850.			−0.120959			−0.0604795	−	0.998169i	$-0.519263\pi$
$139$	−324850.			−0.120959			−0.0604795	+	0.998169i	$0.519263\pi$
$140$	−1.17220e6	+	5.31063e6i	−0.427187	+	1.93536i
$141$	3.04261e6	−	40286.1i	1.08540	−	0.0143713i
$142$	765512.	−	1.32591e6i	0.267354	−	0.463071i
$143$	−841839.	+	486036.i	−0.287886	+	0.166211i
$144$	5.00636e6	+	8.16414e6i	1.67662	+	2.73415i
$145$	−1.07685e6	+	1.86516e6i	−0.353224	+	0.611803i
$146$		−	4.31263e6i		−	1.38575i
$147$	3.15990e6	−	324551.i	0.994767	−	0.102172i
$148$	−1.20072e7			−3.70388
$149$	−844141.	−	487365.i	−0.255186	−	0.147331i	0.366951	−	0.930240i	$-0.380402\pi$
$149$	−844141.	−	487365.i	−0.255186	−	0.147331i	−0.622136	+	0.782909i	$0.713735\pi$
$150$	1.39043e6	+	2.33631e6i	0.411980	+	0.692239i
$151$	−1.06605e6	−	1.84645e6i	−0.309633	−	0.536299i	0.668649	−	0.743578i	$-0.266873\pi$
$151$	−1.06605e6	−	1.84645e6i	−0.309633	−	0.536299i	−0.978282	+	0.207278i	$0.933539\pi$
$152$	−9.64373e6	−	5.56781e6i	−2.74609	−	1.58545i
$153$	−53065.1	−	2.00352e6i	−0.0148161	−	0.559396i
$154$	4.32697e6	+	955081.i	1.18474	+	0.261504i
$155$		−	808365.i		−	0.217076i
$156$	4.50386e6	+	2.52139e6i	1.18634	+	0.664151i
$157$	1.84492e6	+	3.19549e6i	0.476736	+	0.825731i	0.999645	−	0.0266577i	$-0.00848640\pi$
$157$	1.84492e6	+	3.19549e6i	0.476736	+	0.825731i	−0.522909	+	0.852389i	$0.675153\pi$
$158$	4.90140e6	−	2.82983e6i	1.24265	−	0.717445i
$159$	−2.66821e6	+	4.76610e6i	−0.663786	+	1.18569i
$160$	9.42935e6			2.30209
$161$	1.40729e6	+	1.28716e6i	0.337215	+	0.308429i
$162$	427674.	+	8.06795e6i	0.100593	+	1.89766i
$163$	−113443.	+	196489.i	−0.0261947	+	0.0453706i	−0.878826	−	0.477143i	$-0.841672\pi$
$163$	−113443.	+	196489.i	−0.0261947	+	0.0453706i	0.852631	+	0.522514i	$0.175006\pi$
$164$	8.54032e6	−	4.93076e6i	1.93617	−	1.11785i
$165$	−1.87061e6	+	1.11327e6i	−0.416419	+	0.247828i
$166$	1.84941e6	−	3.20327e6i	0.404304	−	0.700276i
$167$			3.40177e6i			0.730392i	0.930931	+	0.365196i	$0.118998\pi$
$167$			3.40177e6i			0.730392i	−0.930931	+	0.365196i	$0.881002\pi$
$168$	−4.56134e6	−	1.37830e7i	−0.961978	−	2.90681i
$169$	−3.51825e6			−0.728898
$170$	−3.43418e6	−	1.98273e6i	−0.698999	−	0.403567i
$171$	−2.70698e6	−	4.41442e6i	−0.541373	−	0.882847i
$172$	−3.15572e6	−	5.46587e6i	−0.620174	−	1.07417i
$173$	−3.78125e6	−	2.18310e6i	−0.730293	−	0.421635i	0.0882366	−	0.996100i	$-0.471877\pi$
$173$	−3.78125e6	−	2.18310e6i	−0.730293	−	0.421635i	−0.818529	+	0.574465i	$0.805210\pi$
$174$	−123362.	−	9.31689e6i	−0.0234171	−	1.76857i
$175$	−685161.	−	2.16609e6i	−0.127843	−	0.404168i
$176$		−	1.11635e7i		−	2.04768i
$177$	−2.28693e6	+	4.08505e6i	−0.412414	+	0.736677i
$178$	7.81215e6	+	1.35310e7i	1.38519	+	2.39923i
$179$	−4.86130e6	+	2.80668e6i	−0.847605	+	0.489365i	−0.859842	−	0.510560i	$-0.829438\pi$
$179$	−4.86130e6	+	2.80668e6i	−0.847605	+	0.489365i	0.0122367	+	0.999925i	$0.496105\pi$
$180$	1.01596e7	+	5.51229e6i	1.74205	+	0.945180i
$181$	−2.54526e6			−0.429237			−0.214618	−	0.976698i	$-0.568851\pi$
$181$	−2.54526e6			−0.429237			−0.214618	+	0.976698i	$0.568851\pi$
$182$	−4.40155e6	−	4.02581e6i	−0.730115	−	0.667789i
$183$	−17558.2	−	1.32609e6i	−0.00286502	−	0.216381i
$184$	4.35830e6	−	7.54881e6i	0.699623	−	1.21178i
$185$	−5.90344e6	+	3.40835e6i	−0.932373	+	0.538306i
$186$	1.78859e6	+	3.00533e6i	0.277954	+	0.467039i
$187$	−1.16813e6	+	2.02326e6i	−0.178635	+	0.309404i
$188$			1.88341e7i			2.83446i
$189$	1.19223e6	−	6.64517e6i	0.176594	−	0.984284i
$190$	−1.02455e7			−1.49374
$191$	4.74984e6	+	2.74232e6i	0.681677	+	0.393566i	0.800487	−	0.599351i	$-0.204574\pi$
$191$	4.74984e6	+	2.74232e6i	0.681677	+	0.393566i	−0.118810	+	0.992917i	$0.537908\pi$
$192$	−1.55488e7	+	9.25373e6i	−2.19682	+	1.30741i
$193$	2.64818e6	+	4.58678e6i	0.368362	+	0.638022i	0.989310	−	0.145830i	$-0.0465853\pi$
$193$	2.64818e6	+	4.58678e6i	0.368362	+	0.638022i	−0.620948	+	0.783852i	$0.713252\pi$
$194$	2.16955e7	+	1.25259e7i	2.97142	+	1.71555i
$195$	2.93008e6	−	38796.1i	0.395162	−	0.00523220i
$196$	1.74971e6	+	1.95833e7i	0.232380	+	2.60087i
$197$		−	6.77574e6i		−	0.886254i	−0.896459	−	0.443127i	$-0.853869\pi$
$197$		−	6.77574e6i		−	0.886254i	0.896459	−	0.443127i	$-0.146131\pi$
$198$	4.49128e6	−	8.27783e6i	0.578595	−	1.06640i
$199$	−3.18804e6	−	5.52185e6i	−0.404543	−	0.700689i	0.589725	−	0.807604i	$-0.299236\pi$
$199$	−3.18804e6	−	5.52185e6i	−0.404543	−	0.700689i	−0.994268	+	0.106915i	$0.965903\pi$
$200$	−8.99236e6	+	5.19174e6i	−1.12405	+	0.648968i
$201$	−7.38006e6	−	4.13158e6i	−0.908808	−	0.508778i
$202$	−321806.			−0.0390427
$203$	−1.67822e6	+	7.60312e6i	−0.200614	+	0.908875i
$204$	1.24042e7	−	164240.i	1.46109	−	0.0193458i
$205$	2.79928e6	−	4.84849e6i	0.324926	−	0.562788i
$206$	2.19321e7	−	1.26625e7i	2.50888	−	1.44850i
$207$	3.45547e6	−	2.11894e6i	0.389579	−	0.238895i
$208$	−7.51386e6	+	1.30144e7i	−0.834974	+	1.44622i
$209$			6.03618e6i			0.661186i
$210$	−9.97515e6	−	8.88397e6i	−1.07711	−	0.959289i
$211$	9.79434e6			1.04262			0.521312	−	0.853366i	$-0.325443\pi$
$211$	9.79434e6			1.04262			0.521312	+	0.853366i	$0.325443\pi$
$212$	−2.92789e7	−	1.69042e7i	−3.07289	−	1.77414i
$213$	1.39062e6	+	2.33662e6i	0.143903	+	0.241796i
$214$	−7.90961e6	−	1.36999e7i	−0.807075	−	1.39789i
$215$	−3.10307e6	−	1.79156e6i	−0.312231	−	0.180267i
$216$	−3.08321e7	+	1.22528e6i	−3.05944	+	0.121584i
$217$	−881363.	−	2.78636e6i	−0.0862533	−	0.272683i
$218$			2.43813e7i			2.35336i
$219$	6.68326e6	+	3.74149e6i	0.636291	+	0.356215i
$220$	−6.73680e6	−	1.16685e7i	−0.632682	−	1.09584i
$221$	2.72361e6	−	1.57248e6i	0.252330	−	0.145683i
$222$	1.44064e7	−	2.57335e7i	1.31673	−	2.35201i
$223$	1.24725e7			1.12471			0.562353	−	0.826897i	$-0.309896\pi$
$223$	1.24725e7			1.12471			0.562353	+	0.826897i	$0.309896\pi$
$224$	3.25021e7	−	1.02808e7i	2.89180	−	0.914712i
$225$	−4.82685e6	+	127844.i	−0.423757	+	0.0112236i
$226$	−1.59915e7	+	2.76980e7i	−1.38536	+	2.39951i
$227$	−8.65703e6	+	4.99814e6i	−0.740101	+	0.427298i	−0.822106	−	0.569334i	$-0.807201\pi$
$227$	−8.65703e6	+	4.99814e6i	−0.740101	+	0.427298i	0.0820049	+	0.996632i	$0.473868\pi$
$228$	2.75428e7	−	1.63919e7i	2.32383	−	1.38300i
$229$	9.98184e6	−	1.72891e7i	0.831197	−	1.43968i	−0.0658921	−	0.997827i	$-0.520989\pi$
$229$	9.98184e6	−	1.72891e7i	0.831197	−	1.43968i	0.897089	−	0.441849i	$-0.145677\pi$
$230$		−	8.01988e6i		−	0.659150i
$231$	−5.23402e6	+	5.87689e6i	−0.424619	+	0.476773i
$232$	3.55862e7			2.84982
$233$	1.95352e6	+	1.12787e6i	0.154437	+	0.0891642i	0.575227	−	0.817994i	$-0.304914\pi$
$233$	1.95352e6	+	1.12787e6i	0.154437	+	0.0891642i	−0.420790	+	0.907158i	$0.638247\pi$
$234$	−1.08075e7	+	6.62733e6i	−0.843489	+	0.517239i
$235$	5.34622e6	+	9.25993e6i	0.411949	+	0.713516i
$236$	−2.50951e7	−	1.44887e7i	−1.90921	−	1.10228i
$237$	133078.	+	1.00507e7i	0.00999683	+	0.755011i
$238$	−1.39991e7	−	3.08999e6i	−1.03841	−	0.229206i
$239$		−	2.03216e7i		−	1.48855i	−0.667871	−	0.744277i	$-0.732794\pi$
$239$		−	2.03216e7i		−	1.48855i	0.667871	−	0.744277i	$-0.267206\pi$
$240$	−1.64389e7	+	2.93642e7i	−1.18916	+	2.12414i
$241$	−4.15089e6	−	7.18955e6i	−0.296544	−	0.513630i	0.678799	−	0.734325i	$-0.262501\pi$
$241$	−4.15089e6	−	7.18955e6i	−0.296544	−	0.513630i	−0.975343	+	0.220694i	$0.929168\pi$
$242$	1.38169e7	−	7.97717e6i	0.974907	−	0.562863i
$243$	−1.28739e7	−	6.33671e6i	−0.897204	−	0.441616i
$244$	8.20863e6			0.565069
$245$	6.41916e6	+	9.13162e6i	0.436495	+	0.620940i
$246$	320679.	+	2.42193e7i	0.0215410	+	1.62688i
$247$	4.06281e6	−	7.03699e6i	0.269610	−	0.466978i
$248$	−1.15674e7	+	6.67844e6i	−0.758369	+	0.437845i
$249$	3.35961e6	+	5.64507e6i	0.217616	+	0.365655i
$250$	−1.60452e7	+	2.77911e7i	−1.02689	+	1.77863i
$251$		−	9.61053e6i		−	0.607751i	−0.952712	−	0.303876i	$-0.901719\pi$
$251$		−	9.61053e6i		−	0.607751i	0.952712	−	0.303876i	$-0.0982808\pi$
$252$	4.10294e7	+	7.92331e6i	2.56386	+	0.495113i
$253$	−4.72493e6			−0.291766
$254$	−3.05523e7	−	1.76394e7i	−1.86442	−	1.07642i
$255$	6.05200e6	−	3.60179e6i	0.364988	−	0.217219i
$256$	−7.64798e6	−	1.32467e7i	−0.455855	−	0.789564i
$257$	2.16590e7	+	1.25048e7i	1.27597	+	0.736680i	0.976104	−	0.217302i	$-0.0697258\pi$
$257$	2.16590e7	+	1.25048e7i	1.27597	+	0.736680i	0.299863	+	0.953982i	$0.403059\pi$
$258$	1.55006e7	−	205237.i	0.902585	−	0.0119508i
$259$	−1.66325e7	+	1.81848e7i	−0.957322	+	1.04667i
$260$			1.81375e7i			1.03195i
$261$	1.45454e7	+	7.89184e6i	0.818094	+	0.443871i
$262$	−2.47640e7	−	4.28925e7i	−1.37694	−	2.38494i
$263$	9.79370e6	−	5.65439e6i	0.538368	−	0.310827i	−0.206049	−	0.978542i	$-0.566061\pi$
$263$	9.79370e6	−	5.65439e6i	0.538368	−	0.310827i	0.744417	+	0.667715i	$0.232727\pi$
$264$	3.13849e7	+	1.75702e7i	1.70572	+	0.954914i
$265$	−1.91936e7			−1.03138
$266$	−3.53155e7	+	1.11707e7i	−1.87638	+	0.593522i
$267$	−2.77466e7	+	367382.i	−1.45772	+	0.0193012i
$268$	2.61753e7	−	4.53369e7i	1.35984	−	2.35531i
$269$	−5.37820e6	+	3.10511e6i	−0.276300	+	0.159522i	−0.631747	−	0.775175i	$-0.717662\pi$
$269$	−5.37820e6	+	3.10511e6i	−0.276300	+	0.159522i	0.355447	+	0.934696i	$0.384329\pi$
$270$	−2.40034e7	+	1.51601e7i	−1.21950	+	0.770214i
$271$	3.35826e6	−	5.81667e6i	0.168735	−	0.292258i	−0.769240	−	0.638960i	$-0.779365\pi$
$271$	3.35826e6	−	5.81667e6i	0.168735	−	0.292258i	0.937975	+	0.346702i	$0.112698\pi$
$272$			3.61173e7i			1.79477i
$273$	1.00574e7	−	3.32840e6i	0.494309	−	0.163586i
$274$	−5.34046e6			−0.259613
$275$	4.87441e6	+	2.81424e6i	0.234382	+	0.135320i
$276$	1.28310e7	+	2.15596e7i	0.610287	+	1.02545i
$277$	7.91270e6	+	1.37052e7i	0.372293	+	0.644831i	0.989918	−	0.141642i	$-0.0452382\pi$
$277$	7.91270e6	+	1.37052e7i	0.372293	+	0.644831i	−0.617625	+	0.786473i	$0.711905\pi$
$278$	4.27691e6	+	2.46928e6i	0.199066	+	0.114931i
$279$	−6.20906e6	+	164453.i	−0.285900	+	0.00757232i
$280$	3.44311e7	−	3.76446e7i	1.56847	−	1.71486i
$281$		−	3.10647e7i		−	1.40007i	−0.714110	−	0.700033i	$-0.753168\pi$
$281$		−	3.10647e7i		−	1.40007i	0.714110	−	0.700033i	$-0.246832\pi$
$282$	−4.03646e7	−	2.25973e7i	−1.79992	−	1.00765i
$283$	7.49497e6	+	1.29817e7i	0.330682	+	0.572758i	0.982646	−	0.185492i	$-0.0593879\pi$
$283$	7.49497e6	+	1.29817e7i	0.330682	+	0.572758i	−0.651964	+	0.758250i	$0.726055\pi$
$284$	−1.45754e7	+	8.41510e6i	−0.636304	+	0.367370i
$285$	8.88868e6	−	1.58775e7i	0.383975	−	0.685877i
$286$	1.47780e7			0.631710
$287$	4.36254e6	−	1.97644e7i	0.184541	−	0.836060i
$288$	−1.91829e6	−	7.24269e7i	−0.0803041	−	3.03195i
$289$	−8.28952e6	+	1.43579e7i	−0.343428	+	0.594835i
$290$	2.83552e7	−	1.63709e7i	1.16262	−	0.671241i
$291$	−3.82335e7	+	2.27543e7i	−1.55155	+	0.923389i
$292$	−2.37039e7	+	4.10563e7i	−0.952074	+	1.64904i
$293$			9.12000e6i			0.362570i	0.983431	+	0.181285i	$0.0580257\pi$
$293$			9.12000e6i			0.362570i	−0.983431	+	0.181285i	$0.941974\pi$
$294$	−4.40697e7	−	1.97463e7i	−1.73420	−	0.777042i
$295$	−1.64509e7			−0.640803
$296$	9.75444e7	+	5.63173e7i	3.76121	+	2.17153i
$297$	8.93163e6	+	1.41417e7i	0.340927	+	0.539798i
$298$	7.40921e6	+	1.28331e7i	0.279977	+	0.484935i
$299$	5.50833e6	+	3.18024e6i	0.206066	+	0.118972i
$300$	−395684.	−	2.98840e7i	−0.0146550	−	1.10682i
$301$	−1.26494e7	−	2.79206e6i	−0.463841	−	0.102382i
$302$			3.24134e7i			1.17680i
$303$	279188.	−	498701.i	0.0100362	−	0.0179272i
$304$	4.66581e7	+	8.08142e7i	1.66076	+	2.87652i
$305$	4.03584e6	−	2.33009e6i	0.142244	−	0.0821247i
$306$	−1.45307e7	+	2.67814e7i	−0.507133	+	0.934692i
$307$	5.27834e7			1.82424			0.912121	−	0.409920i	$-0.134444\pi$
$307$	5.27834e7			1.82424			0.912121	+	0.409920i	$0.134444\pi$
$308$	−3.59433e7	−	3.28751e7i	−1.23017	−	1.12516i
$309$	595481.	+	4.49737e7i	0.0201833	+	1.52434i
$310$	−6.14462e6	+	1.06428e7i	−0.206258	+	0.357249i
$311$	−1.95682e7	+	1.12977e7i	−0.650532	+	0.375585i	−0.788660	−	0.614829i	$-0.789225\pi$
$311$	−1.95682e7	+	1.12977e7i	−0.650532	+	0.375585i	0.138128	+	0.990414i	$0.455892\pi$
$312$	−2.47624e7	−	4.16077e7i	−0.815323	−	1.36997i
$313$	2.08240e7	−	3.60682e7i	0.679096	−	1.17623i	−0.296157	−	0.955139i	$-0.595705\pi$
$313$	2.08240e7	−	3.60682e7i	0.679096	−	1.17623i	0.975253	−	0.221090i	$-0.0709615\pi$
$314$		−	5.60950e7i		−	1.81191i
$315$	2.24215e7	−	7.75101e6i	0.717355	−	0.247986i
$316$	−6.22153e7			−1.97168
$317$	−1.33924e7	−	7.73209e6i	−0.420417	−	0.242728i	0.274839	−	0.961490i	$-0.411375\pi$
$317$	−1.33924e7	−	7.73209e6i	−0.420417	−	0.242728i	−0.695256	+	0.718763i	$0.744709\pi$
$318$	7.13577e7	−	4.24678e7i	2.21901	−	1.32062i
$319$	−9.64495e6	−	1.67055e7i	−0.297117	−	0.514622i
$320$	−5.50632e7	−	3.17908e7i	−1.68040	−	0.970177i
$321$	2.80927e7	−	371966.i	0.849334	−	0.0112457i
$322$	−8.74409e6	−	2.76438e7i	−0.261907	−	0.828000i
$323$		−	1.95289e7i		−	0.579524i
$324$	4.02731e7	−	7.91577e7i	1.18408	−	2.32733i
$325$	−3.78839e6	−	6.56169e6i	−0.110358	−	0.191146i
$326$	2.98714e6	−	1.72462e6i	0.0862188	−	0.0497785i
$327$	−3.77836e7	−	2.11524e7i	−1.08059	−	0.604945i
$328$	−9.25067e7			−2.62151
$329$	2.85241e7	+	2.60892e7i	0.800984	+	0.732609i
$330$	3.30904e7	−	438139.i	0.920790	−	0.0121919i
$331$	1.97312e7	−	3.41755e7i	0.544089	−	0.942390i	−0.454575	−	0.890709i	$-0.650209\pi$
$331$	1.97312e7	−	3.41755e7i	0.544089	−	0.942390i	0.998664	−	0.0516811i	$-0.0164579\pi$
$332$	−3.52128e7	+	2.03301e7i	−0.962247	+	0.555553i
$333$	2.73806e7	+	4.46510e7i	0.741498	+	1.20920i
$334$	2.58579e7	−	4.47871e7i	0.693990	−	1.20203i
$335$		−	2.97203e7i		−	0.790531i
$336$	−2.46478e7	+	1.19139e8i	−0.649770	+	3.14077i
$337$	−8.73243e6			−0.228163			−0.114082	−	0.993471i	$-0.536393\pi$
$337$	−8.73243e6			−0.228163			−0.114082	+	0.993471i	$0.536393\pi$
$338$	4.63207e7	+	2.67433e7i	1.19957	+	0.692571i
$339$	−2.90498e7	−	4.88117e7i	−0.745666	−	1.25292i
$340$	2.17957e7	+	3.77512e7i	0.554541	+	0.960492i
$341$	6.27023e6	+	3.62012e6i	0.158132	+	0.0912977i
$342$	2.08434e6	+	7.86960e7i	0.0521063	+	1.96732i
$343$	3.20825e7	+	2.44771e7i	0.795034	+	0.606565i
$344$			5.92050e7i			1.45440i
$345$	1.24284e7	+	6.95777e6i	0.302661	+	0.169439i
$346$	3.31888e7	+	5.74847e7i	0.801242	+	1.38779i
$347$	8.33092e6	−	4.80986e6i	0.199390	−	0.115118i	−0.396981	−	0.917827i	$-0.629942\pi$
$347$	8.33092e6	−	4.80986e6i	0.199390	−	0.115118i	0.596371	+	0.802709i	$0.296609\pi$
$348$	−5.00348e7	+	8.93750e7i	−1.18723	+	2.12070i
$349$	−7.83949e7			−1.84422			−0.922108	−	0.386934i	$-0.873534\pi$
$349$	−7.83949e7			−1.84422			−0.922108	+	0.386934i	$0.873534\pi$
$350$	−7.44435e6	+	3.37264e7i	−0.173629	+	0.786623i
$351$	−894084.	−	2.24981e7i	−0.0206756	−	0.520264i
$352$	−4.22277e7	+	7.31404e7i	−0.968209	+	1.67699i
$353$	−5.43787e7	+	3.13956e7i	−1.23625	+	0.713747i	−0.968325	−	0.249694i	$-0.919670\pi$
$353$	−5.43787e7	+	3.13956e7i	−1.23625	+	0.713747i	−0.267921	+	0.963441i	$0.586337\pi$
$354$	6.11610e7	−	3.63994e7i	1.37868	−	0.820511i
$355$	−4.77740e6	+	8.27470e6i	−0.106784	+	0.184955i
$356$		−	1.71754e8i		−	3.80678i
$357$	1.69337e7	−	1.90136e7i	0.372175	−	0.417887i
$358$	8.53374e7			1.85990
$359$	−5.89489e7	−	3.40342e7i	−1.27407	−	0.735583i	−0.298316	−	0.954467i	$-0.596425\pi$
$359$	−5.89489e7	−	3.40342e7i	−1.27407	−	0.735583i	−0.975751	+	0.218884i	$0.929758\pi$
$360$	−5.66808e7	−	9.24325e7i	−1.21487	−	1.98115i
$361$	−1.70551e6	−	2.95403e6i	−0.0362520	−	0.0627904i
$362$	3.35105e7	+	1.93473e7i	0.706407	+	0.407844i
$363$	375143.	+	2.83326e7i	0.00784290	+	0.592335i
$364$	1.97754e7	+	6.25184e7i	0.410035	+	1.29630i
$365$			2.69142e7i			0.553481i
$366$	−9.84880e6	+	1.75925e7i	−0.200882	+	0.358826i
$367$	2.31586e7	+	4.01119e7i	0.468505	+	0.811475i	0.999352	−	0.0359928i	$-0.0114593\pi$
$367$	2.31586e7	+	4.01119e7i	0.468505	+	0.811475i	−0.530847	+	0.847468i	$0.678126\pi$
$368$	−6.32588e7	+	3.65225e7i	−1.26934	+	0.732853i
$369$	−3.78108e7	−	2.05149e7i	−0.752552	−	0.408310i
$370$	1.03631e8			2.04591
$371$	−6.61587e7	+	2.09268e7i	−1.29558	+	0.409809i
$372$	−508991.	−	3.84416e7i	−0.00988739	−	0.746745i
$373$	−2.15706e7	+	3.73614e7i	−0.415658	+	0.719941i	−0.995497	−	0.0947900i	$-0.969782\pi$
$373$	−2.15706e7	+	3.73614e7i	−0.415658	+	0.719941i	0.579839	+	0.814731i	$0.303115\pi$
$374$	3.07588e7	−	1.77586e7i	0.587968	−	0.339464i
$375$	−2.91475e7	−	4.89758e7i	−0.552723	−	0.928727i
$376$	8.83373e7	−	1.53005e8i	1.66181	−	2.87833i
$377$			2.59671e7i			0.484619i
$378$	−6.62085e7	+	7.84266e7i	−1.22585	+	1.45207i
$379$	−3.53345e7			−0.649055			−0.324527	−	0.945876i	$-0.605205\pi$
$379$	−3.53345e7			−0.649055			−0.324527	+	0.945876i	$0.605205\pi$
$380$	9.75377e7	+	5.63134e7i	1.77755	+	1.02627i
$381$	5.38418e7	−	3.20434e7i	0.973519	−	0.579381i
$382$	−4.16904e7	−	7.22098e7i	−0.747903	−	1.29541i
$383$	6.95848e7	+	4.01748e7i	1.23856	+	0.715085i	0.968801	−	0.247842i	$-0.0797213\pi$
$383$	6.95848e7	+	4.01748e7i	1.23856	+	0.715085i	0.269763	+	0.962927i	$0.413055\pi$
$384$	1.03330e8	−	1.36815e6i	1.82487	−	0.0241624i
$385$	−2.70037e7	−	5.96046e6i	−0.473196	−	0.104447i
$386$		−	8.05182e7i		−	1.40001i
$387$	−1.31297e7	+	2.41992e7i	−0.226528	+	0.417511i
$388$	−1.37694e8	−	2.38493e8i	−2.35733	−	4.08301i
$389$	2.83908e7	−	1.63914e7i	0.482313	−	0.278464i	−0.239067	−	0.971003i	$-0.576841\pi$
$389$	2.83908e7	−	1.63914e7i	0.482313	−	0.278464i	0.721380	+	0.692539i	$0.243508\pi$
$390$	−3.88718e7	−	2.17616e7i	−0.655300	−	0.366857i
$391$	1.52866e7			0.255730
$392$	7.76371e7	−	1.67298e8i	1.28888	−	2.77736i
$393$	8.79546e7	−	1.16458e6i	1.44904	−	0.0191863i
$394$	−5.15044e7	+	8.92082e7i	−0.842084	+	1.45853i
$395$	−3.05886e7	+	1.76604e7i	−0.496328	+	0.286555i
$396$	−8.82552e7	+	5.41193e7i	−1.42120	+	0.871498i
$397$	−5.28094e7	+	9.14686e7i	−0.843995	+	1.46184i	0.0424967	+	0.999097i	$0.486469\pi$
$397$	−5.28094e7	+	9.14686e7i	−0.843995	+	1.46184i	−0.886491	+	0.462745i	$0.846865\pi$
$398$			9.69330e7i			1.53753i
$399$	1.33273e7	−	6.44195e7i	0.209808	−	1.01414i
$400$	8.70133e7			1.35958
$401$	7.62022e7	+	4.39953e7i	1.18177	+	0.682297i	0.956424	−	0.291981i	$-0.0943143\pi$
$401$	7.62022e7	+	4.39953e7i	1.18177	+	0.682297i	0.225349	+	0.974278i	$0.427648\pi$
$402$	6.57593e7	+	1.10494e8i	1.01223	+	1.70082i
$403$	−4.87323e6	−	8.44069e6i	−0.0744564	−	0.128962i
$404$	3.06360e6	+	1.76877e6i	0.0464609	+	0.0268242i
$405$	−2.66903e6	−	5.03504e7i	−0.0401779	−	0.757945i
$406$	7.98887e7	−	8.73448e7i	1.19373	−	1.30514i
$407$		−	6.10548e7i		−	0.905600i
$408$	−1.01540e8	−	5.68450e7i	−1.49505	−	0.836974i
$409$	−1.01262e7	−	1.75391e7i	−0.148005	−	0.256352i	0.782485	−	0.622669i	$-0.213952\pi$
$409$	−1.01262e7	−	1.75391e7i	−0.148005	−	0.256352i	−0.930490	+	0.366317i	$0.880618\pi$
$410$	−7.37096e7	+	4.25562e7i	−1.06948	+	0.617464i
$411$	4.63320e6	−	8.27609e6i	0.0667353	−	0.119206i
$412$	−2.78392e8			−3.98076
$413$	−5.67049e7	+	1.79365e7i	−0.804953	+	0.254617i
$414$	−6.16008e7	+	1.63155e6i	−0.868131	+	0.0229933i
$415$	−1.15418e7	+	1.99909e7i	−0.161483	+	0.279698i
$416$	9.84581e7	−	5.68448e7i	1.36764	−	0.789607i
$417$	−7.53713e6	+	4.48565e6i	−0.103944	+	0.0618611i
$418$	4.58828e7	−	7.94713e7i	0.628233	−	1.08813i
$419$			1.20677e8i			1.64052i	0.571991	+	0.820260i	$0.306171\pi$
$419$			1.20677e8i			1.64052i	−0.571991	+	0.820260i	$0.693829\pi$
$420$	4.61339e7	+	1.39403e8i	0.622691	+	1.88159i
$421$	4.92455e7			0.659964			0.329982	−	0.943987i	$-0.392957\pi$
$421$	4.92455e7			0.659964			0.329982	+	0.943987i	$0.392957\pi$
$422$	−1.28951e8	−	7.44496e7i	−1.71588	−	0.990661i
$423$	7.00380e7	−	4.29482e7i	0.925363	−	0.567445i
$424$	1.58571e8	+	2.74653e8i	2.08030	+	3.60319i
$425$	−1.57702e7	−	9.10495e6i	−0.205433	−	0.118607i
$426$	−547289.	−	4.13340e7i	−0.00707926	−	0.534661i
$427$	1.13707e7	−	1.24319e7i	0.146050	−	0.159681i
$428$			1.73897e8i			2.21800i
$429$	−1.28209e7	+	2.29014e7i	−0.162385	+	0.290062i
$430$	2.72363e7	+	4.71747e7i	0.342565	+	0.593340i
$431$	2.48879e7	−	1.43690e7i	0.310854	−	0.179472i	−0.336454	−	0.941700i	$-0.609228\pi$
$431$	2.48879e7	−	1.43690e7i	0.310854	−	0.179472i	0.647309	+	0.762228i	$0.275894\pi$
$432$	2.28891e8	+	1.20294e8i	2.83907	+	1.49208i
$433$	5.19787e6			0.0640268			0.0320134	−	0.999487i	$-0.489808\pi$
$433$	5.19787e6			0.0640268			0.0320134	+	0.999487i	$0.489808\pi$
$434$	−9.57611e6	+	4.33843e7i	−0.117144	+	0.530717i
$435$	769874.	+	5.81447e7i	0.00935302	+	0.706387i
$436$	1.34009e8	−	2.32111e8i	1.61687	−	2.80050i
$437$	3.42046e7	−	1.97480e7i	0.409864	−	0.236635i
$438$	−5.95504e7	−	1.00061e8i	−0.708700	−	1.19081i
$439$	−4.48312e7	+	7.76498e7i	−0.529891	+	0.917798i	0.469501	+	0.882932i	$0.344434\pi$
$439$	−4.48312e7	+	7.76498e7i	−0.529891	+	0.917798i	−0.999392	+	0.0348659i	$0.988900\pi$
$440$			1.26390e8i			1.48373i
$441$	6.88342e7	−	5.11633e7i	0.802580	−	0.596545i
$442$	−4.78115e7			−0.553688
$443$	1.24331e6	+	717824.i	0.0143010	+	0.00825670i	0.507133	−	0.861868i	$-0.330705\pi$
$443$	1.24331e6	+	717824.i	0.0143010	+	0.00825670i	−0.492832	+	0.870124i	$0.664038\pi$
$444$	−2.78590e8	+	1.65800e8i	−3.18285	+	1.89425i
$445$	−4.87540e7	−	8.44444e7i	−0.553261	−	0.958277i
$446$	−1.64211e8	−	9.48072e7i	−1.85096	−	1.06865i
$447$	−2.63154e7	+	348433.i	−0.294637	+	0.00390119i
$448$	−2.24460e8	−	4.95444e7i	−2.49634	−	0.551011i
$449$		−	6.57827e7i		−	0.726729i	−0.931647	−	0.363365i	$-0.881628\pi$
$449$		−	6.57827e7i		−	0.726729i	0.931647	−	0.363365i	$-0.118372\pi$
$450$	6.45213e7	+	3.50072e7i	0.708053	+	0.384166i
$451$	2.50721e7	+	4.34262e7i	0.273314	+	0.473393i
$452$	3.04478e8	−	1.75790e8i	3.29716	−	1.90362i
$453$	−5.02309e7	−	2.81208e7i	−0.540352	−	0.302505i
$454$	1.51969e8			1.62401
$455$	2.74691e7	+	2.51243e7i	0.291615	+	0.266722i
$456$	−3.00635e8	+	3.98061e6i	−3.17063	+	0.0419812i
$457$	7.46008e7	−	1.29212e8i	0.781619	−	1.35380i	−0.149380	−	0.988780i	$-0.547728\pi$
$457$	7.46008e7	−	1.29212e8i	0.781619	−	1.35380i	0.930998	−	0.365023i	$-0.118939\pi$
$458$	−2.62838e8	+	1.51750e8i	−2.73585	+	1.57954i
$459$	−2.88966e7	−	4.57527e7i	−0.298819	−	0.473128i
$460$	−4.40804e7	+	7.63494e7i	−0.452868	+	0.784390i
$461$		−	1.28434e8i		−	1.31093i	−0.755227	−	0.655463i	$-0.772473\pi$
$461$		−	1.28434e8i		−	1.31093i	0.755227	−	0.655463i	$-0.227527\pi$
$462$	1.13582e8	−	3.75888e7i	1.15182	−	0.381182i
$463$	1.63804e8			1.65037			0.825186	−	0.564861i	$-0.191070\pi$
$463$	1.63804e8			1.65037			0.825186	+	0.564861i	$0.191070\pi$
$464$	−2.58259e8	−	1.49106e8i	−2.58524	−	1.49259i
$465$	−1.11622e7	−	1.87556e7i	−0.111018	−	0.186540i
$466$	−1.71465e7	−	2.96986e7i	−0.169441	−	0.293480i
$467$	6.28394e7	+	3.62803e7i	0.616994	+	0.356222i	0.775698	−	0.631104i	$-0.217398\pi$
$467$	6.28394e7	+	3.62803e7i	0.616994	+	0.356222i	−0.158703	+	0.987326i	$0.550731\pi$
$468$	1.39314e8	−	3.68987e6i	1.35912	−	0.0359976i
$469$	−3.24041e7	−	1.02443e8i	−0.314110	−	0.993036i
$470$		−	1.62553e8i		−	1.56567i
$471$	8.69302e7	+	4.86661e7i	0.831971	+	0.465762i
$472$	1.35912e8	+	2.35406e8i	1.29250	+	2.23868i
$473$	2.77931e7	−	1.60464e7i	0.262636	−	0.151633i
$474$	7.46466e7	−	1.33338e8i	0.700930	−	1.25204i
$475$	−4.70489e7			−0.439004
$476$	1.16288e8	+	1.06361e8i	1.07824	+	0.986194i
$477$	3.90472e6	+	1.47426e8i	0.0359778	+	1.35838i
$478$	−1.54471e8	+	2.67551e8i	−1.41437	+	2.44976i
$479$	1.28392e8	−	7.41274e7i	1.16824	−	0.674485i	0.214977	−	0.976619i	$-0.431032\pi$
$479$	1.28392e8	−	7.41274e7i	1.16824	−	0.674485i	0.953265	+	0.302134i	$0.0976990\pi$
$480$	2.18779e8	−	1.30204e8i	1.97825	−	1.17734i
$481$	−4.10945e7	+	7.11778e7i	−0.369274	+	0.639601i
$482$			1.26208e8i			1.12706i
$483$	5.04256e7	+	1.04322e7i	0.447517	+	0.0925833i
$484$	−1.75382e8			−1.54686
$485$	−1.35397e8	−	7.81714e7i	−1.18682	−	0.685208i
$486$	1.21328e8	+	1.81286e8i	1.05695	+	1.57927i
$487$	−2.70494e7	−	4.68510e7i	−0.234191	−	0.405632i	0.724846	−	0.688911i	$-0.241911\pi$
$487$	−2.70494e7	−	4.68510e7i	−0.234191	−	0.405632i	−0.959037	+	0.283279i	$0.908578\pi$
$488$	−6.66854e7	−	3.85008e7i	−0.573814	−	0.331292i
$489$	81103.9	+	6.12537e6i	0.000693610	+	0.0523849i
$490$	−1.51014e7	−	1.69019e8i	−0.128360	−	1.43664i
$491$			2.04007e8i			1.72346i	0.507366	+	0.861730i	$0.330619\pi$
$491$			2.04007e8i			1.72346i	−0.507366	+	0.861730i	$0.669381\pi$
$492$	1.30066e8	−	2.32331e8i	1.09211	−	1.95080i
$493$	3.12044e7	+	5.40477e7i	0.260421	+	0.451062i
$494$	−1.06980e8	+	6.17652e7i	−0.887409	+	0.512346i
$495$	−2.80291e7	+	5.16602e7i	−0.231097	+	0.425932i
$496$	1.11930e8			0.917282
$497$	−7.44535e6	+	3.37310e7i	−0.0606479	+	0.274764i
$498$	−1.32220e6	−	9.98593e7i	−0.0107056	−	0.808538i
$499$	1.41399e7	−	2.44911e7i	0.113801	−	0.197109i	−0.803499	−	0.595306i	$-0.797031\pi$
$499$	1.41399e7	−	2.44911e7i	0.113801	−	0.197109i	0.917300	+	0.398197i	$0.130364\pi$
$500$	3.05502e8	−	1.76381e8i	2.44401	−	1.41105i
$501$	4.69730e7	+	7.89276e7i	0.373538	+	0.627647i
$502$	−7.30524e7	+	1.26530e8i	−0.577462	+	1.00019i
$503$		−	2.25847e8i		−	1.77464i	−0.461150	−	0.887322i	$-0.652563\pi$
$503$		−	2.25847e8i		−	1.77464i	0.461150	−	0.887322i	$-0.347437\pi$
$504$	−2.96153e8	−	2.56807e8i	−2.31326	−	2.00593i
$505$	2.00832e6			0.0155941
$506$	6.22076e7	+	3.59156e7i	0.480167	+	0.277224i
$507$	−8.16302e7	+	4.85814e7i	−0.626364	+	0.372775i
$508$	1.93906e8	+	3.35855e8i	1.47911	+	2.56189i
$509$	4.94331e7	+	2.85402e7i	0.374856	+	0.216423i	0.675578	−	0.737289i	$-0.263894\pi$
$509$	4.94331e7	+	2.85402e7i	0.374856	+	0.216423i	−0.300722	+	0.953712i	$0.597228\pi$
$510$	−1.07058e8	+	1.41752e6i	−0.807064	+	0.0106861i
$511$	2.93446e7	+	9.27709e7i	0.219920	+	0.695263i
$512$		−	1.24130e7i		−	0.0924837i
$513$	−1.23763e8	−	6.50439e7i	−0.916726	−	0.481786i
$514$	−1.90106e8	−	3.29273e8i	−1.39993	−	2.42475i
$515$	−1.36874e8	+	7.90241e7i	−1.00207	+	0.578546i
$516$	−1.48694e8	−	8.32432e7i	−1.08229	−	0.605898i
$517$	−9.57684e7			−0.693028
$518$	3.57209e8	−	1.12990e8i	2.57000	−	0.812923i
$519$	−1.17877e8	+	1.56077e6i	−0.843195	+	0.0111645i
$520$	8.50702e7	−	1.47346e8i	0.605017	−	1.04792i
$521$	−3.68679e7	+	2.12857e7i	−0.260696	+	0.150513i	−0.624652	−	0.780903i	$-0.714759\pi$
$521$	−3.68679e7	+	2.12857e7i	−0.260696	+	0.150513i	0.363956	+	0.931416i	$0.381426\pi$
$522$	−1.31513e8	−	2.14466e8i	−0.924610	−	1.50781i
$523$	2.81822e7	−	4.88130e7i	0.197001	−	0.341217i	−0.750553	−	0.660810i	$-0.770213\pi$
$523$	2.81822e7	−	4.88130e7i	0.197001	−	0.341217i	0.947555	+	0.319593i	$0.103546\pi$
$524$			5.44450e8i			3.78411i
$525$	−4.58072e7	−	4.07964e7i	−0.316560	−	0.281932i
$526$	−1.71923e8			−1.18134
$527$	−2.02862e7	−	1.17122e7i	−0.138602	−	0.0800216i
$528$	−1.54150e8	−	2.59014e8i	−1.04723	−	1.75963i
$529$	−5.85598e7	−	1.01429e8i	−0.395579	−	0.685162i
$530$	2.52700e8	+	1.45896e8i	1.69737	+	0.979978i
$531$	3.34676e6	+	1.26360e8i	0.0223532	+	0.843966i
$532$	3.97603e8	+	8.77618e7i	2.64067	+	0.582869i
$533$		−	6.75018e7i		−	0.445793i
$534$	3.68099e8	+	2.06073e8i	2.41736	+	1.35331i
$535$	4.93622e7	+	8.54979e7i	0.322354	+	0.558334i
$536$	−4.25286e8	+	2.45539e8i	−2.76177	+	1.59451i
$537$	−7.40358e7	+	1.32247e8i	−0.478101	+	0.854010i
$538$	9.44113e7			0.606285
$539$	−9.95781e7	+	8.89701e6i	−0.635913	+	0.0568169i
$540$	3.11839e8	−	1.23926e7i	1.98038	−	0.0787014i
$541$	−5.57242e7	+	9.65171e7i	−0.351926	+	0.609555i	−0.986587	−	0.163237i	$-0.947807\pi$
$541$	−5.57242e7	+	9.65171e7i	−0.351926	+	0.609555i	0.634660	+	0.772791i	$0.281140\pi$
$542$	−8.84284e7	+	5.10542e7i	−0.555385	+	0.320652i
$543$	−5.90550e7	+	3.51460e7i	−0.368856	+	0.219521i
$544$	1.36620e8	−	2.36632e8i	0.848626	−	1.46986i
$545$		−	1.52159e8i		−	0.939955i
$546$	−1.57714e8	−	3.26283e7i	−0.968931	−	0.200455i
$547$	1.01171e8			0.618148			0.309074	−	0.951038i	$-0.399981\pi$
$547$	1.01171e8			0.618148			0.309074	+	0.951038i	$0.399981\pi$
$548$	5.08413e7	+	2.93532e7i	0.308941	+	0.178367i
$549$	−1.87185e7	−	3.05253e7i	−0.113124	−	0.184477i
$550$	−4.27837e7	−	7.41036e7i	−0.257152	−	0.445401i
$551$	1.39643e8	+	8.06228e7i	0.834764	+	0.481951i
$552$	−3.11589e6	−	2.35328e8i	−0.0185253	−	1.39912i
$553$	−8.61812e7	+	9.42246e7i	−0.509609	+	0.557171i
$554$		−	2.40587e8i		−	1.41496i
$555$	−8.99071e7	+	1.60597e8i	−0.525915	+	0.939418i
$556$	−2.71442e7	−	4.70151e7i	−0.157926	−	0.273535i
$557$	7.01201e7	−	4.04839e7i	0.405767	−	0.234270i	−0.283202	−	0.959060i	$-0.591397\pi$
$557$	7.01201e7	−	4.04839e7i	0.405767	−	0.234270i	0.688969	+	0.724790i	$0.258063\pi$
$558$	8.29975e7	+	4.50317e7i	0.477708	+	0.259189i
$559$	−4.32017e7			−0.247323
$560$	−4.07606e8	+	1.28931e8i	−2.32101	+	0.734165i
$561$	835133.	+	6.30734e7i	0.00473006	+	0.357238i
$562$	−2.36132e8	+	4.08993e8i	−1.33029	+	2.30413i
$563$	8.14216e7	−	4.70088e7i	0.456262	−	0.263423i	−0.254209	−	0.967149i	$-0.581815\pi$
$563$	8.14216e7	−	4.70088e7i	0.456262	−	0.263423i	0.710471	+	0.703726i	$0.248482\pi$
$564$	2.60068e8	+	4.36987e8i	1.44961	+	2.43574i
$565$	9.97993e7	−	1.72857e8i	0.553327	−	0.958391i
$566$		−	2.27886e8i		−	1.25681i
$567$	−6.40970e7	−	1.70643e8i	−0.351632	−	0.936138i
$568$	1.57877e8			0.861536
$569$	−1.28522e8	−	7.42023e7i	−0.697656	−	0.402792i	0.108818	−	0.994062i	$-0.465293\pi$
$569$	−1.28522e8	−	7.42023e7i	−0.697656	−	0.402792i	−0.806474	+	0.591270i	$0.798627\pi$
$570$	−2.37716e8	+	1.41474e8i	−1.28361	+	0.763929i
$571$	827390.	+	1.43308e6i	0.00444428	+	0.00769773i	0.868239	−	0.496146i	$-0.165252\pi$
$571$	827390.	+	1.43308e6i	0.00444428	+	0.00769773i	−0.863795	+	0.503844i	$0.831919\pi$
$572$	−1.40687e8	−	8.12256e7i	−0.751737	−	0.434015i
$573$	1.48072e8	−	1.96057e6i	0.787064	−	0.0104212i
$574$	−2.07671e8	+	2.27053e8i	−1.09810	+	1.20058i
$575$		−	3.68284e7i		−	0.193722i
$576$	−2.32983e8	+	4.29408e8i	−1.21915	+	2.24700i
$577$	2.51308e7	+	4.35278e7i	0.130821	+	0.226589i	0.923993	−	0.382408i	$-0.124905\pi$
$577$	2.51308e7	+	4.35278e7i	0.130821	+	0.226589i	−0.793172	+	0.608998i	$0.791572\pi$
$578$	2.18277e8	−	1.26022e8i	1.13038	−	0.652625i
$579$	1.24779e8	+	6.98549e7i	0.642843	+	0.359883i
$580$	−3.59923e8			−1.84470
$581$	−1.79873e7	+	8.14910e7i	−0.0917144	+	0.415510i
$582$	6.76338e8	−	8.95515e6i	3.43080	−	0.0454260i
$583$	8.59552e7	−	1.48879e8i	0.433777	−	0.751323i
$584$	3.85132e8	−	2.22356e8i	1.93362	−	1.11638i
$585$	6.74476e7	−	4.13598e7i	0.336899	−	0.206591i
$586$	6.93238e7	−	1.20072e8i	0.344500	−	0.596692i
$587$			2.79611e8i			1.38242i	0.722654	+	0.691210i	$0.242922\pi$
$587$			2.79611e8i			1.38242i	−0.722654	+	0.691210i	$0.757078\pi$
$588$	3.11011e8	+	4.30210e8i	1.52983	+	2.11616i
$589$	−6.05217e7			−0.296186
$590$	2.16590e8	+	1.25048e8i	1.05459	+	0.608866i
$591$	−9.35621e7	−	1.57210e8i	−0.453249	−	0.761584i
$592$	−4.71937e8	−	8.17419e8i	−2.27467	−	3.93985i
$593$	−3.01296e8	−	1.73953e8i	−1.44487	−	0.834198i	−0.446703	−	0.894682i	$-0.647402\pi$
$593$	−3.01296e8	−	1.73953e8i	−1.44487	−	0.834198i	−0.998169	+	0.0604846i	$0.980735\pi$
$594$	−1.00972e7	−	2.54079e8i	−0.0481773	−	1.21230i
$595$	8.73654e7	+	1.92840e7i	0.414752	+	0.0915472i
$596$		−	1.62895e8i		−	0.769432i
$597$	−1.50217e8	−	8.40957e7i	−0.705984	−	0.395231i
$598$	−4.83478e7	−	8.37409e7i	−0.226086	−	0.391592i
$599$	3.86903e7	−	2.23379e7i	0.180020	−	0.103935i	−0.407282	−	0.913303i	$-0.633523\pi$
$599$	3.86903e7	−	2.23379e7i	0.180020	−	0.103935i	0.587302	+	0.809368i	$0.300190\pi$
$600$	−1.36950e8	+	2.44628e8i	−0.634029	+	1.13254i
$601$	6.06419e7			0.279350			0.139675	−	0.990197i	$-0.455394\pi$
$601$	6.06419e7			0.279350			0.139675	+	0.990197i	$0.455394\pi$
$602$	1.45316e8	+	1.32911e8i	0.666076	+	0.609217i
$603$	−2.28282e8	+	6.04626e6i	−1.04117	+	0.0275762i
$604$	1.78157e8	−	3.08576e8i	0.808521	−	1.40040i
$605$	−8.62281e7	+	4.97838e7i	−0.389388	+	0.224813i
$606$	−7.46650e6	+	4.44362e6i	−0.0335505	+	0.0199673i
$607$	1.78273e8	−	3.08778e8i	0.797113	−	1.38064i	−0.124376	−	0.992235i	$-0.539693\pi$
$607$	1.78273e8	−	3.08778e8i	0.797113	−	1.38064i	0.921489	−	0.388405i	$-0.126974\pi$
$608$		−	7.05968e8i		−	3.14105i
$609$	6.60490e7	+	1.99580e8i	0.292425	+	0.883621i
$610$	−7.08468e7			−0.312127
$611$	1.11647e8	+	6.44594e7i	0.489467	+	0.282594i
$612$	2.85533e8	−	1.75093e8i	1.24567	−	0.763860i
$613$	8.81058e7	+	1.52604e8i	0.382493	+	0.662497i	0.991418	−	0.130731i	$-0.0417324\pi$
$613$	8.81058e7	+	1.52604e8i	0.382493	+	0.662497i	−0.608925	+	0.793228i	$0.708399\pi$
$614$	−6.94937e8	−	4.01222e8i	−3.00221	−	1.73332i
$615$	−2.00129e6	−	1.51148e8i	−0.00860370	−	0.649795i
$616$	1.37804e8	+	4.35656e8i	0.589547	+	1.86381i
$617$			3.09108e8i			1.31599i	0.753020	+	0.657997i	$0.228596\pi$
$617$			3.09108e8i			1.31599i	−0.753020	+	0.657997i	$0.771404\pi$
$618$	3.34018e8	−	5.96642e8i	1.41516	−	2.52783i
$619$	−8.14542e7	−	1.41083e8i	−0.343433	−	0.594843i	0.641635	−	0.767010i	$-0.278256\pi$
$619$	−8.14542e7	−	1.41083e8i	−0.343433	−	0.594843i	−0.985068	+	0.172167i	$0.944923\pi$
$620$	1.16994e8	−	6.75464e7i	0.490894	−	0.283418i
$621$	5.09143e7	−	9.68779e7i	0.212601	−	0.404529i
$622$	3.43508e8			1.42747
$623$	−2.60121e8	−	2.37916e8i	−1.07575	−	0.983919i
$624$	5.37190e6	+	4.05713e8i	0.0221093	+	1.66980i
$625$	4.83885e7	−	8.38114e7i	0.198199	−	0.343292i
$626$	−5.48331e8	+	3.16579e8i	−2.23522	+	1.29050i
$627$	8.33500e7	+	1.40051e8i	0.338145	+	0.568177i
$628$	−3.08320e8	+	5.34026e8i	−1.24487	+	2.15617i
$629$			1.97531e8i			0.793750i
$630$	−3.54116e8	−	6.83842e7i	−1.41620	−	0.273486i
$631$	−1.60048e7			−0.0637033			−0.0318516	−	0.999493i	$-0.510140\pi$
$631$	−1.60048e7			−0.0637033			−0.0318516	+	0.999493i	$0.510140\pi$
$632$	5.05426e8	+	2.91808e8i	2.00219	+	1.15597i
$633$	2.27247e8	−	1.35244e8i	0.895958	−	0.533221i
$634$	1.17548e8	+	2.03599e8i	0.461261	+	0.798927i
$635$	1.90671e8	+	1.10084e8i	0.744667	+	0.429934i
$636$	−9.12746e8	+	1.20854e7i	−3.54796	+	0.0469773i
$637$	1.22077e8	+	5.66515e7i	0.472296	+	0.219176i
$638$			2.93256e8i			1.12924i
$639$	6.45299e7	+	3.50118e7i	0.247320	+	0.134188i
$640$	1.81562e8	+	3.14475e8i	0.692606	+	1.19963i
$641$	2.84297e8	−	1.64139e8i	1.07944	−	0.623214i	0.148694	−	0.988883i	$-0.452493\pi$
$641$	2.84297e8	−	1.64139e8i	1.07944	−	0.623214i	0.930745	+	0.365669i	$0.119160\pi$
$642$	−3.72691e8	−	2.08644e8i	−1.40846	−	0.788497i
$643$	8.93787e7			0.336203			0.168101	−	0.985770i	$-0.446236\pi$
$643$	8.93787e7			0.336203			0.168101	+	0.985770i	$0.446236\pi$
$644$	−6.86972e7	+	3.11231e8i	−0.257206	+	1.16526i
$645$	−9.67357e7	+	1.28084e6i	−0.360502	+	0.00477328i
$646$	−1.48445e8	+	2.57115e8i	−0.550641	+	0.953738i
$647$	4.17800e8	−	2.41217e8i	1.54261	−	0.890625i	0.543934	−	0.839128i	$-0.316934\pi$
$647$	4.17800e8	−	2.41217e8i	1.54261	−	0.890625i	0.998673	−	0.0514968i	$-0.0163992\pi$
$648$	−6.98444e8	+	4.54170e8i	−2.56688	+	1.66914i
$649$	7.36726e7	−	1.27605e8i	0.269508	−	0.466802i
$650$			1.15187e8i			0.419433i
$651$	−5.89245e7	−	5.24788e7i	−0.213576	−	0.190213i
$652$	−3.79168e7			−0.136801
$653$	1.40623e8	+	8.11888e7i	0.505030	+	0.291579i	0.730788	−	0.682604i	$-0.239153\pi$
$653$	1.40623e8	+	8.11888e7i	0.505030	+	0.291579i	−0.225758	+	0.974183i	$0.572486\pi$
$654$	3.36667e8	+	5.65693e8i	1.20356	+	2.02231i
$655$	1.54547e8	+	2.67683e8i	0.549966	+	0.952569i
$656$	6.71346e8	+	3.87602e8i	2.37813	+	1.37301i
$657$	2.06728e8	−	5.47539e6i	0.728960	−	0.0193072i
$658$	−1.77232e8	−	5.60305e8i	−0.622105	−	1.96674i
$659$			3.80251e7i			0.132866i	0.997791	+	0.0664330i	$0.0211619\pi$
$659$			3.80251e7i			0.132866i	−0.997791	+	0.0664330i	$0.978838\pi$
$660$	−3.17430e8	−	1.77707e8i	−1.10412	−	0.618119i
$661$	4.26336e7	+	7.38435e7i	0.147621	+	0.255687i	0.930348	−	0.366679i	$-0.119505\pi$
$661$	4.26336e7	+	7.38435e7i	0.147621	+	0.255687i	−0.782727	+	0.622365i	$0.786172\pi$
$662$	−5.19555e8	+	2.99965e8i	−1.79084	+	1.03394i
$663$	4.14796e7	−	7.40932e7i	0.142329	−	0.254236i
$664$	3.81417e8			1.30285
$665$	2.20396e8	−	6.97142e7i	0.749444	−	0.237059i
$666$	−2.10827e7	−	7.95994e8i	−0.0713679	−	2.69456i
$667$	−6.31090e7	+	1.09308e8i	−0.212674	+	0.368362i
$668$	−4.92335e8	+	2.84250e8i	−1.65170	+	0.953610i
$669$	2.89386e8	−	1.72225e8i	0.966494	−	0.575199i
$670$	−2.25913e8	+	3.91292e8i	−0.751132	+	1.30100i
$671$			4.17396e7i			0.138160i
$672$	6.12150e8	−	6.87337e8i	2.01720	−	2.26497i
$673$	−4.10685e8			−1.34730			−0.673649	−	0.739052i	$-0.735274\pi$
$673$	−4.10685e8			−1.34730			−0.673649	+	0.739052i	$0.735274\pi$
$674$	1.14970e8	+	6.63777e7i	0.375494	+	0.216792i
$675$	−1.10227e8	+	6.96173e7i	−0.358407	+	0.226363i
$676$	−2.93983e8	−	5.09193e8i	−0.951659	−	1.64832i
$677$	−1.21840e8	−	7.03444e7i	−0.392667	−	0.226706i	0.290648	−	0.956830i	$-0.406129\pi$
$677$	−1.21840e8	−	7.03444e7i	−0.392667	−	0.226706i	−0.683315	+	0.730124i	$0.739462\pi$
$678$	1.14328e7	+	8.63463e8i	0.0366829	+	2.77048i
$679$	−5.51931e8	−	1.21826e8i	−1.76309	−	0.389164i
$680$		−	4.08912e8i		−	1.30048i
$681$	−1.31843e8	+	2.35506e8i	−0.417462	+	0.745694i
$682$	−5.50352e7	−	9.53237e7i	−0.173495	−	0.300502i
$683$	−4.97482e8	+	2.87222e8i	−1.56140	+	0.901478i	−0.564290	+	0.825577i	$0.690850\pi$
$683$	−4.97482e8	+	2.87222e8i	−1.56140	+	0.901478i	−0.997115	+	0.0759006i	$0.975817\pi$
$684$	4.12701e8	−	7.60644e8i	1.28964	−	2.37691i
$685$	3.33287e7			0.103692
$686$	−2.36335e8	−	5.66129e8i	−0.732075	−	1.75365i
$687$	−7.13634e6	−	5.38972e8i	−0.0220093	−	1.66225i
$688$	2.48068e8	−	4.29667e8i	0.761738	−	1.31937i
$689$	−2.00413e8	+	1.15709e8i	−0.612730	+	0.353760i
$690$	−1.10742e8	−	1.86076e8i	−0.337104	−	0.566427i
$691$	−2.89223e7	+	5.00949e7i	−0.0876595	+	0.151831i	−0.906521	−	0.422160i	$-0.861272\pi$
$691$	−2.89223e7	+	5.00949e7i	−0.0876595	+	0.151831i	0.818862	+	0.573991i	$0.194605\pi$
$692$		−	7.29675e8i		−	2.20197i
$693$	−4.02888e7	+	2.08628e8i	−0.121055	+	0.626864i
$694$	−1.46245e8			−0.437523
$695$	−2.66913e7	−	1.54102e7i	−0.0795089	−	0.0459045i
$696$	8.25668e8	−	4.91389e8i	2.44894	−	1.45746i
$697$	−8.11162e7	−	1.40497e8i	−0.239557	−	0.414925i
$698$	1.03213e9	+	5.95903e8i	3.03508	+	1.75230i
$699$	6.08995e7	−	806349.i	0.178313	−	0.00236098i
$700$	2.56244e8	−	2.80159e8i	0.747067	−	0.816791i
$701$			4.13267e8i			1.19971i	0.800108	+	0.599855i	$0.204775\pi$
$701$			4.13267e8i			1.19971i	−0.800108	+	0.599855i	$0.795225\pi$
$702$	−1.59243e8	+	3.03002e8i	−0.460308	+	0.875858i
$703$	2.55181e8	+	4.41986e8i	0.734483	+	1.27216i
$704$	4.93181e8	−	2.84738e8i	1.41348	−	0.816071i
$705$	2.51907e8	+	1.41025e8i	0.718908	+	0.402466i
$706$	9.54588e8			2.71270
$707$	6.92251e6	−	2.18968e6i	0.0195887	−	0.00619615i
$708$	−7.82319e8	+	1.03584e7i	−2.20437	+	0.0291873i
$709$	2.03929e8	−	3.53215e8i	0.572189	−	0.991060i	−0.424152	−	0.905591i	$-0.639428\pi$
$709$	2.03929e8	−	3.53215e8i	0.572189	−	0.991060i	0.996341	−	0.0854692i	$-0.0272389\pi$
$710$	1.25797e8	−	7.26288e7i	0.351475	−	0.202924i
$711$	1.41872e8	+	2.31359e8i	0.394720	+	0.643691i
$712$	−8.05578e8	+	1.39530e9i	−2.23186	+	3.86570i
$713$		−	4.73745e7i		−	0.130700i
$714$	−3.67474e8	+	1.21611e8i	−1.00956	+	0.334103i
$715$	−9.22264e7			−0.252312
$716$	−8.12414e8	−	4.69048e8i	−2.21329	−	1.27784i
$717$	−2.80609e8	−	4.71500e8i	−0.761280	−	1.27916i
$718$	5.17407e8	+	8.96176e8i	1.39785	+	2.42114i
$719$	−1.40812e8	−	8.12980e7i	−0.378838	−	0.218722i	0.298475	−	0.954418i	$-0.403522\pi$
$719$	−1.40812e8	−	8.12980e7i	−0.378838	−	0.218722i	−0.677313	+	0.735695i	$0.736856\pi$
$720$	2.40572e7	+	9.08300e8i	0.0644536	+	2.43350i
$721$	−3.85632e8	+	4.21623e8i	−1.02889	+	1.12491i
$722$			5.18563e7i			0.137781i
$723$	−1.95585e8	−	1.09494e8i	−0.517511	−	0.289718i
$724$	−2.12680e8	−	3.68373e8i	−0.560418	−	0.970672i
$725$	1.30211e8	−	7.51773e7i	0.341691	−	0.197275i
$726$	2.10426e8	−	3.75874e8i	0.549906	−	0.982274i
$727$	−6.16984e8			−1.60572			−0.802861	−	0.596166i	$-0.796690\pi$
$727$	−6.16984e8			−1.60572			−0.802861	+	0.596166i	$0.796690\pi$
$728$	1.32578e8	−	6.00641e8i	0.343619	−	1.55676i
$729$	−3.86199e8	+	3.07440e7i	−0.996846	+	0.0793557i
$730$	2.04583e8	−	3.54348e8i	0.525896	−	0.910879i
$731$	−8.99194e7	+	5.19150e7i	−0.230198	+	0.132905i
$732$	1.90456e8	−	1.13348e8i	0.485580	−	0.288989i
$733$	2.32660e7	−	4.02978e7i	0.0590757	−	0.102322i	−0.834975	−	0.550288i	$-0.814518\pi$
$733$	2.32660e7	−	4.02978e7i	0.0590757	−	0.102322i	0.894051	+	0.447966i	$0.147851\pi$
$734$		−	7.04142e8i		−	1.78062i
$735$	2.75030e8	+	1.23233e8i	0.692656	+	0.310359i
$736$	5.52609e8			1.38607
$737$	2.30531e8	+	1.33097e8i	0.575873	+	0.332481i
$738$	3.41870e8	+	5.57506e8i	0.850535	+	1.38701i
$739$	2.69977e8	+	4.67613e8i	0.668949	+	1.15865i	0.978198	+	0.207672i	$0.0665887\pi$
$739$	2.69977e8	+	4.67613e8i	0.668949	+	1.15865i	−0.309250	+	0.950981i	$0.600078\pi$
$740$	−9.86574e8	−	5.69599e8i	−2.43464	−	1.40564i
$741$	−2.90463e6	−	2.19373e8i	−0.00713899	−	0.539172i
$742$	1.03010e9	+	2.27372e8i	2.52156	+	0.556578i
$743$		−	3.31530e8i		−	0.808269i	−0.914700	−	0.404135i	$-0.867573\pi$
$743$		−	3.31530e8i		−	0.808269i	0.914700	−	0.404135i	$-0.132427\pi$
$744$	−1.76167e8	+	3.14680e8i	−0.427766	+	0.764099i
$745$	−4.62393e7	−	8.00888e7i	−0.111826	−	0.193688i
$746$	5.67990e8	−	3.27929e8i	1.36812	−	0.789885i
$747$	1.55899e8	+	8.45855e7i	0.374007	+	0.202924i
$748$	−3.90432e8			−0.932912
$749$	2.63366e8	+	2.40884e8i	0.626778	+	0.573274i
$750$	1.14712e7	+	8.66366e8i	0.0271911	+	2.05361i
$751$	1.26938e8	−	2.19864e8i	0.299690	−	0.519079i	−0.676375	−	0.736558i	$-0.736450\pi$
$751$	1.26938e8	−	2.19864e8i	0.299690	−	0.519079i	0.976065	+	0.217479i	$0.0697833\pi$
$752$	−1.28218e9	+	7.40264e8i	−3.01505	+	1.74074i
$753$	−1.32706e8	−	2.22982e8i	−0.310817	−	0.522259i
$754$	1.97384e8	−	3.41879e8i	0.460466	−	0.797550i
$755$		−	2.02285e8i		−	0.470028i
$756$	1.06137e9	−	3.82715e8i	2.45641	−	0.885748i
$757$	3.97326e8			0.915925			0.457962	−	0.888972i	$-0.348579\pi$
$757$	3.97326e8			0.915925			0.457962	+	0.888972i	$0.348579\pi$
$758$	4.65208e8	+	2.68588e8i	1.06817	+	0.616707i
$759$	−1.09627e8	+	6.52437e7i	−0.250723	+	0.149215i
$760$	−5.28252e8	−	9.14960e8i	−1.20337	−	2.08430i
$761$	−2.56758e8	−	1.48239e8i	−0.582600	−	0.336364i	0.179566	−	0.983746i	$-0.442531\pi$
$761$	−2.56758e8	−	1.48239e8i	−0.582600	−	0.336364i	−0.762166	+	0.647382i	$0.775864\pi$
$762$	−9.52443e8	+	1.26110e7i	−2.15265	+	0.0285025i
$763$	−1.65899e8	−	5.24477e8i	−0.373482	−	1.18074i
$764$			9.16585e8i			2.05538i
$765$	9.06830e7	−	1.67137e8i	0.202554	−	0.373326i
$766$	−6.10761e8	−	1.05787e9i	−1.35889	−	2.35367i
$767$	−1.71775e8	+	9.91744e7i	−0.380692	+	0.219793i
$768$	−3.60363e8	−	2.01742e8i	−0.795530	−	0.445362i
$769$	5.82855e8			1.28168			0.640842	−	0.767673i	$-0.278585\pi$
$769$	5.82855e8			1.28168			0.640842	+	0.767673i	$0.278585\pi$
$770$	3.10219e8	+	2.83737e8i	0.679510	+	0.621505i
$771$	6.75202e8	−	8.94012e6i	1.47323	−	0.0195065i
$772$	−4.42559e8	+	7.66535e8i	−0.961877	+	1.66602i
$773$	−5.75386e7	+	3.32199e7i	−0.124572	+	0.0719217i	−0.560991	−	0.827822i	$-0.689580\pi$
$773$	−5.75386e7	+	3.32199e7i	−0.124572	+	0.0719217i	0.436419	+	0.899744i	$0.356247\pi$
$774$	3.56808e8	−	2.18800e8i	0.769506	−	0.471872i
$775$	−2.82169e7	+	4.88732e7i	−0.0606184	+	0.104994i
$776$			2.58330e9i			5.52828i
$777$	−1.34803e8	+	6.51590e8i	−0.287366	+	1.38903i
$778$	−4.98385e8			−1.05834
$779$	−3.63003e8	−	2.09580e8i	−0.767887	−	0.443340i
$780$	2.50450e8	+	4.20825e8i	0.527761	+	0.886784i
$781$	−4.27894e7	−	7.41135e7i	−0.0898222	−	0.155577i
$782$	−2.01261e8	−	1.16198e8i	−0.420862	−	0.242985i
$783$	4.46454e8	−	1.77423e7i	0.930018	−	0.0369594i
$784$	−1.26441e9	+	8.88828e8i	−2.62385	+	1.84446i
$785$			3.50077e8i			0.723694i
$786$	−1.16685e9	−	6.53236e8i	−2.40296	−	1.34525i
$787$	−1.17888e8	−	2.04187e8i	−0.241849	−	0.418894i	0.719392	−	0.694604i	$-0.244420\pi$
$787$	−1.17888e8	−	2.04187e8i	−0.241849	−	0.418894i	−0.961241	+	0.275710i	$0.911087\pi$
$788$	9.80645e8	−	5.66176e8i	2.00416	−	1.15710i
$789$	1.49154e8	−	2.66428e8i	0.303672	−	0.542436i
$790$	5.36966e8			1.08909
$791$	1.55533e8	−	7.04636e8i	0.314262	−	1.42375i
$792$	9.70804e8	−	2.57127e7i	1.95414	−	0.0517573i
$793$	2.80939e7	−	4.86601e7i	0.0563369	−	0.0975783i
$794$	1.39056e9	−	8.02839e8i	2.77797	−	1.60386i
$795$	−4.45328e8	+	2.65033e8i	−0.886296	+	0.527471i
$796$	5.32781e8	−	9.22804e8i	1.05635	−	1.82966i
$797$		−	4.53453e8i		−	0.895689i	−0.894111	−	0.447844i	$-0.852192\pi$
$797$		−	4.53453e8i		−	0.895689i	0.894111	−	0.447844i	$-0.147808\pi$
$798$	−6.65136e8	+	7.46832e8i	−1.30889	+	1.46965i
$799$	3.09841e8			0.607433
$800$	−5.70091e8	−	3.29142e8i	−1.11346	−	0.642856i
$801$	−6.38700e8	+	3.91659e8i	−1.24279	+	0.762098i
$802$	−6.68843e8	−	1.15847e9i	−1.29659	−	2.24575i
$803$	−2.08765e8	−	1.20530e8i	−0.403191	−	0.232782i
$804$	−1.87135e7	−	1.41334e9i	−0.0360071	−	2.71943i
$805$	5.45700e7	+	1.72519e8i	0.104608	+	0.330712i
$806$			1.48171e8i			0.282982i
$807$	−8.19080e7	+	1.46309e8i	−0.155850	+	0.278387i
$808$	−1.65921e7	−	2.87383e7i	−0.0314533	−	0.0544787i
$809$	−2.02451e8	+	1.16885e8i	−0.382361	+	0.220756i	−0.678845	−	0.734282i	$-0.737519\pi$
$809$	−2.02451e8	+	1.16885e8i	−0.382361	+	0.220756i	0.296484	+	0.955038i	$0.404186\pi$
$810$	−3.47588e8	+	6.83192e8i	−0.654048	+	1.28555i
$811$	−4.40365e8			−0.825563			−0.412782	−	0.910830i	$-0.635443\pi$
$811$	−4.40365e8			−0.825563			−0.412782	+	0.910830i	$0.635443\pi$
$812$	−1.24062e9	+	3.92425e8i	−2.31724	+	0.732973i
$813$	−2.40093e6	−	1.81330e8i	−0.00446794	−	0.337441i
$814$	−4.64095e8	+	8.03836e8i	−0.860466	+	1.49037i
$815$	−1.86421e7	+	1.07630e7i	−0.0344367	+	0.0198820i
$816$	4.98722e8	+	8.37990e8i	0.917884	+	1.54230i
$817$	−1.34133e8	+	2.32325e8i	−0.245962	+	0.426019i
$818$			3.07888e8i			0.562514i
$819$	1.87391e8	−	2.16102e8i	0.341113	−	0.393375i
$820$	9.35622e8			1.69691
$821$	4.75091e8	+	2.74294e8i	0.858515	+	0.495664i	0.863515	−	0.504324i	$-0.168258\pi$
$821$	4.75091e8	+	2.74294e8i	0.858515	+	0.495664i	−0.00499994	+	0.999988i	$0.501592\pi$
$822$	−1.23909e8	+	7.37432e7i	−0.223094	+	0.132772i
$823$	−2.03027e8	−	3.51652e8i	−0.364211	−	0.630832i	0.624438	−	0.781074i	$-0.285328\pi$
$823$	−2.03027e8	−	3.51652e8i	−0.364211	−	0.630832i	−0.988649	+	0.150242i	$0.951995\pi$
$824$	2.26161e9	+	1.30574e9i	4.04237	+	2.33386i
$825$	1.51956e8	−	2.01199e6i	0.270617	−	0.00358314i
$826$	8.82907e8	+	1.94882e8i	1.56666	+	0.345805i
$827$		−	3.18160e8i		−	0.562508i	−0.959633	−	0.281254i	$-0.909250\pi$
$827$		−	3.18160e8i		−	0.562508i	0.959633	−	0.281254i	$-0.0907503\pi$
$828$	5.95408e8	+	3.23049e8i	1.04888	+	0.569086i
$829$	5.14283e8	+	8.90765e8i	0.902691	+	1.56351i	0.823988	+	0.566608i	$0.191745\pi$
$829$	5.14283e8	+	8.90765e8i	0.902691	+	1.56351i	0.0787030	+	0.996898i	$0.474922\pi$
$830$	3.03914e8	−	1.75465e8i	0.531516	−	0.306871i
$831$	3.72836e8	+	2.08725e8i	0.649704	+	0.363724i
$832$	−7.66602e8			−1.33107
$833$	3.22166e8	−	2.87846e7i	0.557372	−	0.0497996i
$834$	1.33329e8	−	1.76537e6i	0.229841	−	0.00304324i
$835$	−1.61374e8	+	2.79507e8i	−0.277187	+	0.480102i
$836$	−8.73610e8	+	5.04379e8i	−1.49520	+	0.863253i
$837$	−1.41791e8	+	8.95528e7i	−0.241809	+	0.152722i
$838$	9.17299e8	−	1.58881e9i	1.55876	−	2.69985i
$839$			6.14712e8i			1.04084i	0.853909	+	0.520422i	$0.174225\pi$
$839$			6.14712e8i			1.04084i	−0.853909	+	0.520422i	$0.825775\pi$
$840$	2.79056e8	−	1.34886e9i	0.470819	−	2.27578i
$841$	7.95286e7			0.133701
$842$	−6.48357e8	−	3.74329e8i	−1.08612	−	0.627072i
$843$	−4.28954e8	−	7.20761e8i	−0.716025	−	1.20312i
$844$	8.18408e8	+	1.41752e9i	1.36126	+	2.35778i
$845$	−2.89078e8	−	1.66899e8i	−0.479120	−	0.276620i
$846$	−1.24857e9	+	3.30695e7i	−2.06206	+	0.0546156i
$847$	−2.42941e8	+	2.65615e8i	−0.399808	+	0.437122i
$848$		−	2.65764e9i		−	4.35822i
$849$	3.53153e8	+	1.97706e8i	0.577086	+	0.323070i
$850$	1.38419e8	+	2.39748e8i	0.225392	+	0.390390i
$851$	−3.45972e8	+	1.99747e8i	−0.561375	+	0.324110i
$852$	−2.21977e8	+	3.96509e8i	−0.358914	+	0.641112i
$853$	−6.37747e8			−1.02755			−0.513773	−	0.857926i	$-0.671753\pi$
$853$	−6.37747e8			−1.02755			−0.513773	+	0.857926i	$0.671753\pi$
$854$	−2.44203e8	+	7.72445e7i	−0.392082	+	0.124021i
$855$	−1.30079e7	−	4.91125e8i	−0.0208118	−	0.785768i
$856$	8.15628e8	−	1.41271e9i	1.30038	−	2.25233i
$857$	6.99750e8	−	4.04001e8i	1.11173	−	0.641860i	0.172456	−	0.985017i	$-0.444830\pi$
$857$	6.99750e8	−	4.04001e8i	1.11173	−	0.641860i	0.939278	+	0.343158i	$0.111497\pi$
$858$	3.42878e8	−	2.04061e8i	0.542847	−	0.323070i
$859$	−3.04611e8	+	5.27601e8i	−0.480580	+	0.832389i	−0.999752	−	0.0222808i	$-0.992907\pi$
$859$	−3.04611e8	+	5.27601e8i	−0.480580	+	0.832389i	0.519172	+	0.854670i	$0.326241\pi$
$860$		−	5.98806e8i		−	0.941435i
$861$	−1.71695e8	−	5.18811e8i	−0.268997	−	0.812830i
$862$	−4.36893e8			−0.682109
$863$	2.75235e6	+	1.58907e6i	0.00428225	+	0.00247236i	0.502140	−	0.864787i	$-0.332546\pi$
$863$	2.75235e6	+	1.58907e6i	0.00428225	+	0.00247236i	−0.497857	+	0.867259i	$0.665880\pi$
$864$	−1.04461e9	−	1.65395e9i	−1.61962	−	2.56438i
$865$	−2.07125e8	−	3.58750e8i	−0.320024	−	0.554299i
$866$	−6.84343e7	−	3.95105e7i	−0.105371	−	0.0608358i
$867$	5.92645e6	+	4.47595e8i	0.00909363	+	0.686796i
$868$	3.29622e8	−	3.60385e8i	0.504030	−	0.551071i
$869$		−	3.16355e8i		−	0.482076i
$870$	4.31839e8	−	7.71375e8i	0.655789	−	1.17141i
$871$	−1.79169e8	−	3.10330e8i	−0.271149	−	0.469644i
$872$	−2.17733e9	+	1.25708e9i	−3.28379	+	1.89589i
$873$	−5.72890e8	+	1.05589e9i	−0.861050	+	1.58699i
$874$	−6.00442e8			−0.899367
$875$	1.56055e8	−	7.07005e8i	0.232946	−	1.05535i
$876$	1.69467e7	+	1.27990e9i	0.0252099	+	1.90398i
$877$	−1.74062e8	+	3.01484e8i	−0.258050	+	0.446956i	−0.965720	−	0.259588i	$-0.916413\pi$
$877$	−1.74062e8	+	3.01484e8i	−0.258050	+	0.446956i	0.707669	+	0.706544i	$0.249747\pi$
$878$	1.18048e9	−	6.81549e8i	1.74411	−	1.00696i
$879$	1.25933e8	+	2.11601e8i	0.185426	+	0.311567i
$880$	5.29573e8	−	9.17248e8i	0.777102	−	1.34598i
$881$			5.32307e8i			0.778456i	0.921141	+	0.389228i	$0.127258\pi$
$881$			5.32307e8i			0.778456i	−0.921141	+	0.389228i	$0.872742\pi$
$882$	−1.29517e9	+	1.50379e8i	−1.88764	+	0.219170i
$883$	−1.18318e8			−0.171857			−0.0859285	−	0.996301i	$-0.527386\pi$
$883$	−1.18318e8			−0.171857			−0.0859285	+	0.996301i	$0.527386\pi$
$884$	4.55166e8	+	2.62790e8i	0.658890	+	0.380411i
$885$	−3.81693e8	+	2.27161e8i	−0.550661	+	0.327721i
$886$	−1.09128e7	−	1.89015e7i	−0.0156904	−	0.0271766i
$887$	−2.78219e8	−	1.60630e8i	−0.398672	−	0.230173i	0.287239	−	0.957859i	$-0.407263\pi$
$887$	−2.78219e8	−	1.60630e8i	−0.398672	−	0.230173i	−0.685911	+	0.727686i	$0.740596\pi$
$888$	3.04087e9	−	4.02630e7i	4.34269	−	0.0575000i
$889$	7.77249e8	+	1.71560e8i	1.10625	+	0.244181i
$890$			1.48237e9i			2.10275i
$891$	4.02505e8	+	2.04782e8i	0.569033	+	0.289507i
$892$	1.04219e9	+	1.80513e9i	1.46843	+	2.54340i
$893$	6.93283e8	−	4.00267e8i	0.973546	−	0.562077i
$894$	3.49113e8	+	1.95444e8i	0.488599	+	0.273533i
$895$	−5.32573e8			−0.742865
$896$	9.68703e8	+	8.86011e8i	1.34669	+	1.23173i
$897$	1.71718e8	−	2.27366e6i	0.237924	−	0.00315027i
$898$	−5.00034e8	+	8.66084e8i	−0.690510	+	1.19600i
$899$	1.67498e8	−	9.67049e7i	0.230531	−	0.133097i
$900$	−4.21831e8	−	6.87903e8i	−0.578643	−	0.943625i
$901$	−2.78092e8	+	4.81669e8i	−0.380201	+	0.658528i
$902$		−	7.62322e8i		−	1.03877i
$903$	−3.32043e8	+	1.09886e8i	−0.450953	+	0.149238i
$904$	−3.29803e9			−4.46426
$905$	−2.09132e8	−	1.20742e8i	−0.282146	−	0.162897i
$906$	4.47577e8	+	7.52053e8i	0.601843	+	1.01126i
$907$	−5.35830e8	−	9.28084e8i	−0.718133	−	1.24384i	−0.961739	−	0.273969i	$-0.911664\pi$
$907$	−5.35830e8	−	9.28084e8i	−0.718133	−	1.24384i	0.243606	−	0.969874i	$-0.421670\pi$
$908$	−1.44675e9	−	8.35281e8i	−1.93257	−	1.11577i
$909$	−408570.	−	1.54259e7i	−0.000543970	−	0.0205381i
$910$	−1.70677e8	−	5.39582e8i	−0.226491	−	0.716034i
$911$			7.75322e7i			0.102548i	0.998685	+	0.0512740i	$0.0163282\pi$
$911$			7.75322e7i			0.102548i	−0.998685	+	0.0512740i	$0.983672\pi$
$912$	2.19847e9	+	1.23077e9i	2.89825	+	1.62253i
$913$	−1.03375e8	−	1.79052e8i	−0.135833	−	0.235270i
$914$	−1.96436e9	+	1.13412e9i	−2.57266	+	1.48533i
$915$	6.14643e7	−	1.09791e8i	0.0802342	−	0.143319i
$916$	3.33630e9			4.34089
$917$	8.24564e8	+	7.54177e8i	1.06934	+	0.978059i
$918$	3.26677e7	+	8.22024e8i	0.0422270	+	1.06257i
$919$	1.42180e8	−	2.46264e8i	0.183186	−	0.317288i	−0.759777	−	0.650183i	$-0.774692\pi$
$919$	1.42180e8	−	2.46264e8i	0.183186	−	0.317288i	0.942964	+	0.332895i	$0.108025\pi$
$920$	7.16201e8	−	4.13499e8i	0.919754	−	0.531020i
$921$	1.22468e9	−	7.28854e8i	1.56763	−	0.932958i
$922$	−9.76267e8	+	1.69094e9i	−1.24559	+	2.15743i
$923$			1.15202e8i			0.146506i
$924$	−1.28791e9	−	2.66445e8i	−1.63256	−	0.337747i
$925$	4.75890e8			0.601286
$926$	−2.15662e9	−	1.24512e9i	−2.71606	−	1.56812i
$927$	6.34831e8	+	1.03525e9i	0.796927	+	1.29959i
$928$	1.12803e9	+	1.95381e9i	1.41149	+	2.44478i
$929$	−9.64770e8	−	5.57010e8i	−1.20331	−	0.694730i	−0.242018	−	0.970272i	$-0.577809\pi$
$929$	−9.64770e8	−	5.57010e8i	−1.20331	−	0.694730i	−0.961289	+	0.275542i	$0.911143\pi$
$930$	4.39299e6	+	3.31781e8i	0.00546149	+	0.412479i
$931$	6.83677e8	−	4.80597e8i	0.847232	−	0.595569i
$932$			3.76975e8i			0.465656i
$933$	−2.98016e8	+	5.32333e8i	−0.366939	+	0.655448i
$934$	−5.51555e8	−	9.55321e8i	−0.676937	−	1.17249i
$935$	−1.91959e8	+	1.10828e8i	−0.234841	+	0.135585i
$936$	−1.14907e9	−	6.23449e8i	−1.40126	−	0.760280i
$937$	1.58842e8			0.193085			0.0965423	−	0.995329i	$-0.469222\pi$
$937$	1.58842e8			0.193085			0.0965423	+	0.995329i	$0.469222\pi$
$938$	−3.52075e8	+	1.59506e9i	−0.426605	+	1.93272i
$939$	−1.48878e7	−	1.12440e9i	−0.0179818	−	1.35807i
$940$	−8.93453e8	+	1.54751e9i	−1.07569	+	1.86315i
$941$	−7.97898e8	+	4.60667e8i	−0.957587	+	0.552863i	−0.895430	−	0.445203i	$-0.853132\pi$
$941$	−7.97898e8	+	4.60667e8i	−0.957587	+	0.552863i	−0.0621578	+	0.998066i	$0.519798\pi$
$942$	−7.74582e8	−	1.30151e9i	−0.926648	−	1.55702i
$943$	1.64052e8	−	2.84147e8i	0.195635	−	0.338850i
$944$		−	2.27788e9i		−	2.70779i
$945$	4.13194e8	−	4.89444e8i	0.489619	−	0.579972i
$946$	−4.87892e8			−0.576302
$947$	1.08603e9	+	6.27019e8i	1.27877	+	0.738296i	0.976621	−	0.214966i	$-0.0689641\pi$
$947$	1.08603e9	+	6.27019e8i	1.27877	+	0.738296i	0.302145	+	0.953262i	$0.402297\pi$
$948$	−1.44351e9	+	8.59093e8i	−1.69432	+	1.00836i
$949$	1.62252e8	+	2.81029e8i	0.189842	+	0.328816i
$950$	6.19437e8	+	3.57632e8i	0.722481	+	0.417125i
$951$	−4.17496e8	+	5.52792e6i	−0.485413	+	0.00642718i
$952$	−4.45837e8	−	1.40948e9i	−0.516732	−	1.63361i
$953$			3.07127e8i			0.354845i	0.984135	+	0.177423i	$0.0567759\pi$
$953$			3.07127e8i			0.354845i	−0.984135	+	0.177423i	$0.943224\pi$
$954$	1.06922e9	−	1.97067e9i	1.23147	−	2.26970i
$955$	2.60181e8	+	4.50646e8i	0.298720	+	0.517399i
$956$	2.94113e9	−	1.69806e9i	3.36620	−	1.94348i
$957$	−4.54458e8	−	2.54419e8i	−0.518511	−	0.290278i
$958$	−2.25386e9			−2.56348
$959$	1.14881e8	−	3.63384e7i	0.130254	−	0.0412012i
$960$	−1.71655e9	+	2.27282e7i	−1.94018	+	0.0256893i
$961$	4.07455e8	−	7.05732e8i	0.459102	−	0.795188i
$962$	1.08209e9	−	6.24743e8i	1.21545	−	0.701739i
$963$	6.46668e8	−	3.96545e8i	0.724107	−	0.444032i
$964$	6.93690e8	−	1.20151e9i	0.774345	−	1.34120i
$965$			5.02497e8i			0.559180i
$966$	−5.84596e8	−	5.20647e8i	−0.648522	−	0.577580i
$967$	6.94764e8			0.768348			0.384174	−	0.923261i	$-0.374486\pi$
$967$	6.94764e8			0.768348			0.384174	+	0.923261i	$0.374486\pi$
$968$	1.42477e9	+	8.22594e8i	1.57080	+	0.906900i
$969$	−2.69663e8	−	4.53109e8i	−0.296381	−	0.498002i
$970$	1.18841e9	+	2.05838e9i	1.30212	+	2.25533i
$971$	1.27672e9	+	7.37116e8i	1.39457	+	0.805153i	0.993816	−	0.111035i	$-0.0354166\pi$
$971$	1.27672e9	+	7.37116e8i	1.39457	+	0.805153i	0.400749	+	0.916188i	$0.368750\pi$
$972$	−1.58628e8	−	2.39272e9i	−0.172735	−	2.60551i
$973$	−1.08804e8	−	2.40161e7i	−0.118116	−	0.0260714i
$974$			8.22442e8i			0.890079i
$975$	−1.78504e8	−	9.99321e7i	−0.192591	−	0.107818i
$976$	3.22636e8	+	5.58822e8i	0.347027	+	0.601069i
$977$	3.99820e8	−	2.30836e8i	0.428727	−	0.247526i	−0.270077	−	0.962839i	$-0.587049\pi$
$977$	3.99820e8	−	2.30836e8i	0.428727	−	0.247526i	0.698804	+	0.715313i	$0.253716\pi$
$978$	4.54929e7	−	8.12621e7i	0.0486326	−	0.0868703i
$979$	8.73345e8			0.930760
$980$	−7.85229e8	+	1.69207e9i	−0.834292	+	1.79779i
$981$	−1.16873e9	+	3.09550e7i	−1.23796	+	0.0327886i
$982$	1.55072e9	−	2.68593e9i	1.63757	−	2.83635i
$983$	−6.33676e8	+	3.65853e8i	−0.667124	+	0.385164i	−0.794986	−	0.606628i	$-0.792522\pi$
$983$	−6.33676e8	+	3.65853e8i	−0.667124	+	0.385164i	0.127862	+	0.991792i	$0.459188\pi$
$984$	−2.14633e9	+	1.27737e9i	−2.25274	+	1.34070i
$985$	3.21428e8	−	5.56729e8i	0.336337	−	0.582553i
$986$		−	9.48776e8i		−	0.989767i
$987$	1.02206e9	+	2.11447e8i	1.06298	+	0.219912i
$988$	1.35794e9			1.40802
$989$	−1.81856e8	−	1.04995e8i	−0.187992	−	0.108537i
$990$	7.61711e8	−	4.67091e8i	0.785027	−	0.481389i
$991$	−5.23864e8	−	9.07360e8i	−0.538267	−	0.932306i	−0.998998	−	0.0447659i	$-0.985746\pi$
$991$	−5.23864e8	−	9.07360e8i	−0.538267	−	0.932306i	0.460730	−	0.887540i	$-0.347588\pi$
$992$	−7.33341e8	−	4.23395e8i	−0.751227	−	0.433721i
$993$	−1.41065e7	−	1.06539e9i	−0.0144069	−	1.08808i
$994$	3.54423e8	−	3.87502e8i	0.360880	−	0.394561i
$995$		−	6.04938e8i		−	0.614104i
$996$	−5.36278e8	+	9.57930e8i	−0.542765	+	0.969517i
$997$	1.20716e8	+	2.09086e8i	0.121809	+	0.210980i	0.920481	−	0.390787i	$-0.127797\pi$
$997$	1.20716e8	+	2.09086e8i	0.121809	+	0.210980i	−0.798672	+	0.601767i	$0.794464\pi$
$998$	−3.72328e8	+	2.14963e8i	−0.374571	+	0.216258i
$999$	1.25184e9	+	6.57906e8i	1.25560	+	0.659884i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.h.a.2.1	✓	28
3.2	odd	2	inner	21.7.h.a.2.14	yes	28
7.2	even	3		147.7.b.e.50.14		14
7.4	even	3	inner	21.7.h.a.11.14	yes	28
7.5	odd	6		147.7.b.d.50.14		14
21.2	odd	6		147.7.b.e.50.1		14
21.5	even	6		147.7.b.d.50.1		14
21.11	odd	6	inner	21.7.h.a.11.1	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.h.a.2.1	✓	28	1.1	even	1	trivial
21.7.h.a.2.14	yes	28	3.2	odd	2	inner
21.7.h.a.11.1	yes	28	21.11	odd	6	inner
21.7.h.a.11.14	yes	28	7.4	even	3	inner
147.7.b.d.50.1		14	21.5	even	6
147.7.b.d.50.14		14	7.5	odd	6
147.7.b.e.50.1		14	21.2	odd	6
147.7.b.e.50.14		14	7.2	even	3

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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-13.1658 - 7.60129i) q^{2} +(23.2019 - 13.8084i) q^{3} +(83.5593 + 144.729i) q^{4} +(82.1651 + 47.4381i) q^{5} +(-410.434 + 5.43441i) q^{6} +(334.938 + 73.9300i) q^{7} -1567.67i q^{8} +(347.657 - 640.762i) q^{9} +O(q^{10})\)	\(q+(-13.1658 - 7.60129i) q^{2} +(23.2019 - 13.8084i) q^{3} +(83.5593 + 144.729i) q^{4} +(82.1651 + 47.4381i) q^{5} +(-410.434 + 5.43441i) q^{6} +(334.938 + 73.9300i) q^{7} -1567.67i q^{8} +(347.657 - 640.762i) q^{9} +(-721.181 - 1249.12i) q^{10} +(-735.924 + 424.886i) q^{11} +(3937.21 + 2204.17i) q^{12} +1143.92 q^{13} +(-3847.77 - 3519.31i) q^{14} +(2561.43 - 33.9150i) q^{15} +(-6568.51 + 11377.0i) q^{16} +(2380.94 - 1374.64i) q^{17} +(-9447.80 + 5793.52i) q^{18} +(3551.65 - 6151.64i) q^{19} +15855.6i q^{20} +(8792.05 - 2909.64i) q^{21} +12918.7 q^{22} +(4815.31 + 2780.12i) q^{23} +(-21647.0 - 36372.9i) q^{24} +(-3311.76 - 5736.14i) q^{25} +(-15060.7 - 8695.28i) q^{26} +(-781.596 - 19667.5i) q^{27} +(17287.4 + 54652.7i) q^{28} +22700.1i q^{29} +(-33981.1 - 19023.7i) q^{30} +(-4260.11 - 7378.73i) q^{31} +(86070.7 - 49692.9i) q^{32} +(-11207.8 + 20020.1i) q^{33} -41796.1 q^{34} +(24013.1 + 21963.3i) q^{35} +(121787. - 3225.64i) q^{36} +(-35924.2 + 62222.6i) q^{37} +(-93520.8 + 53994.3i) q^{38} +(26541.2 - 15795.7i) q^{39} +(74367.1 - 128808. i) q^{40} -59009.1i q^{41} +(-137872. - 28523.2i) q^{42} -37766.3 q^{43} +(-122987. - 71006.3i) q^{44} +(58961.8 - 36156.1i) q^{45} +(-42265.0 - 73205.1i) q^{46} +(97600.2 + 56349.5i) q^{47} +(4696.04 + 354668. i) q^{48} +(106718. + 49523.9i) q^{49} +100695. i q^{50} +(36260.9 - 64771.2i) q^{51} +(95585.3 + 165559. i) q^{52} +(-175198. + 101151. i) q^{53} +(-139208. + 264880. i) q^{54} -80623.0 q^{55} +(115898. - 525071. i) q^{56} +(-2539.19 - 191772. i) q^{57} +(172550. - 298866. i) q^{58} +(-150163. + 86696.9i) q^{59} +(218940. + 367879. i) q^{60} +(24559.3 - 42538.0i) q^{61} +129529. i q^{62} +(163815. - 188913. i) q^{63} -670153. q^{64} +(93990.5 + 54265.4i) q^{65} +(299739. - 178387. i) q^{66} +(-156627. - 271286. i) q^{67} +(397900. + 229728. i) q^{68} +(150113. - 1987.60i) q^{69} +(-149203. - 471695. i) q^{70} +100708. i q^{71} +(-1.00450e6 - 545010. i) q^{72} +(141839. + 245672. i) q^{73} +(945944. - 546141. i) q^{74} +(-156046. - 87359.2i) q^{75} +1.18709e6 q^{76} +(-277901. + 87903.5i) q^{77} +(-469504. + 6216.54i) q^{78} +(-186141. + 322406. i) q^{79} +(-1.07941e6 + 623195. i) q^{80} +(-289711. - 445530. i) q^{81} +(-448545. + 776903. i) q^{82} +243302. i q^{83} +(1.15577e6 + 1.02934e6i) q^{84} +260841. q^{85} +(497224. + 287073. i) q^{86} +(313452. + 526686. i) q^{87} +(666080. + 1.15368e6i) q^{88} +(-890049. - 513870. i) q^{89} +(-1.05111e6 + 27839.7i) q^{90} +(383143. + 84570.1i) q^{91} +929219. i q^{92} +(-200731. - 112375. i) q^{93} +(-856658. - 1.48377e6i) q^{94} +(583644. - 336967. i) q^{95} +(1.31082e6 - 2.34147e6i) q^{96} -1.64786e6 q^{97} +(-1.02858e6 - 1.46322e6i) q^{98} +(16401.9 + 619266. i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9}+O(q^{10}) \) 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9	\( 28 q - q^{3} + 382 q^{4} - 356 q^{6} + 1120 q^{7} + 1031 q^{9} - 930 q^{10} - 404 q^{12} + 3632 q^{13} + 5450 q^{15} - 13706 q^{16} + 1612 q^{18} + 6830 q^{19} - 11333 q^{21} - 27348 q^{22} - 54498 q^{24} - 7640 q^{25} + 13268 q^{27} + 88522 q^{28} + 32380 q^{30} + 69410 q^{31} - 85459 q^{33} - 31344 q^{34} + 399028 q^{36} - 71830 q^{37} + 104570 q^{39} + 230250 q^{40} - 467782 q^{42} - 498904 q^{43} - 85375 q^{45} - 342660 q^{46} - 324728 q^{48} + 395668 q^{49} + 42177 q^{51} + 218000 q^{52} - 402122 q^{54} + 231660 q^{55} + 786782 q^{57} + 459522 q^{58} + 1021150 q^{60} + 153158 q^{61} + 179011 q^{63} - 1399412 q^{64} + 80896 q^{66} - 977098 q^{67} - 1520742 q^{69} - 139650 q^{70} - 1001352 q^{72} - 488350 q^{73} + 1434610 q^{75} + 6196280 q^{76} + 245176 q^{78} + 380762 q^{79} + 893531 q^{81} - 3665004 q^{82} + 1231496 q^{84} - 912540 q^{85} + 1452416 q^{87} - 1522482 q^{88} - 11713820 q^{90} - 1529416 q^{91} - 1690071 q^{93} - 3034044 q^{94} + 7549346 q^{96} + 7212176 q^{97} + 435866 q^{99}+O(q^{100}) \) 28 * q - q^3 + 382 * q^4 - 356 * q^6 + 1120 * q^7 + 1031 * q^9 - 930 * q^10 - 404 * q^12 + 3632 * q^13 + 5450 * q^15 - 13706 * q^16 + 1612 * q^18 + 6830 * q^19 - 11333 * q^21 - 27348 * q^22 - 54498 * q^24 - 7640 * q^25 + 13268 * q^27 + 88522 * q^28 + 32380 * q^30 + 69410 * q^31 - 85459 * q^33 - 31344 * q^34 + 399028 * q^36 - 71830 * q^37 + 104570 * q^39 + 230250 * q^40 - 467782 * q^42 - 498904 * q^43 - 85375 * q^45 - 342660 * q^46 - 324728 * q^48 + 395668 * q^49 + 42177 * q^51 + 218000 * q^52 - 402122 * q^54 + 231660 * q^55 + 786782 * q^57 + 459522 * q^58 + 1021150 * q^60 + 153158 * q^61 + 179011 * q^63 - 1399412 * q^64 + 80896 * q^66 - 977098 * q^67 - 1520742 * q^69 - 139650 * q^70 - 1001352 * q^72 - 488350 * q^73 + 1434610 * q^75 + 6196280 * q^76 + 245176 * q^78 + 380762 * q^79 + 893531 * q^81 - 3665004 * q^82 + 1231496 * q^84 - 912540 * q^85 + 1452416 * q^87 - 1522482 * q^88 - 11713820 * q^90 - 1529416 * q^91 - 1690071 * q^93 - 3034044 * q^94 + 7549346 * q^96 + 7212176 * q^97 + 435866 * q^99

Introduction

L-functions

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