LMFDB - Embedded newform 21.7.d.a.13.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,7,Mod(13,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("21.13");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	21.d (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.83113575602$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 212x^{6} - 1123x^{5} + 44168x^{4} - 138697x^{3} + 660109x^{2} + 680340x + 1040400 $ x^8 - x^7 + 212x^6 - 1123x^5 + 44168x^4 - 138697x^3 + 660109x^2 + 680340x + 1040400
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5}\cdot 3^{7}\cdot 7^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			13.6
Root			$2.28617 - 3.95977i$ of defining polynomial
Character	$\chi$	$=$	21.13
Dual form			21.7.d.a.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5.57235 q^{2} +15.5885i q^{3} -32.9490 q^{4} +205.672i q^{5} +86.8643i q^{6} +(342.970 - 4.53729i) q^{7} -540.233 q^{8} -243.000 q^{9} +O(q^{10})$	\(q+5.57235 q^{2} +15.5885i q^{3} -32.9490 q^{4} +205.672i q^{5} +86.8643i q^{6} +(342.970 - 4.53729i) q^{7} -540.233 q^{8} -243.000 q^{9} +1146.08i q^{10} +1024.73 q^{11} -513.624i q^{12} +281.691i q^{13} +(1911.15 - 25.2834i) q^{14} -3206.11 q^{15} -901.632 q^{16} +1177.35i q^{17} -1354.08 q^{18} -10294.8i q^{19} -6776.68i q^{20} +(70.7294 + 5346.37i) q^{21} +5710.14 q^{22} +18169.9 q^{23} -8421.40i q^{24} -26676.0 q^{25} +1569.68i q^{26} -3788.00i q^{27} +(-11300.5 + 149.499i) q^{28} +14651.3 q^{29} -17865.5 q^{30} +52698.9i q^{31} +29550.7 q^{32} +15973.9i q^{33} +6560.59i q^{34} +(933.194 + 70539.3i) q^{35} +8006.60 q^{36} -7820.49 q^{37} -57366.3i q^{38} -4391.13 q^{39} -111111. i q^{40} +35240.5i q^{41} +(394.129 + 29791.8i) q^{42} -45671.7 q^{43} -33763.7 q^{44} -49978.3i q^{45} +101249. q^{46} -158028. i q^{47} -14055.1i q^{48} +(117608. - 3112.31i) q^{49} -148648. q^{50} -18353.1 q^{51} -9281.42i q^{52} -4012.38 q^{53} -21108.0i q^{54} +210758. i q^{55} +(-185284. + 2451.20i) q^{56} +160480. q^{57} +81642.0 q^{58} +16961.9i q^{59} +105638. q^{60} -198032. i q^{61} +293657. i q^{62} +(-83341.7 + 1102.56i) q^{63} +222371. q^{64} -57935.9 q^{65} +89012.3i q^{66} -525053. q^{67} -38792.4i q^{68} +283240. i q^{69} +(5200.08 + 393069. i) q^{70} +28289.2 q^{71} +131277. q^{72} -584202. i q^{73} -43578.4 q^{74} -415837. i q^{75} +339204. i q^{76} +(351451. - 4649.49i) q^{77} -24468.9 q^{78} +339282. q^{79} -185440. i q^{80} +59049.0 q^{81} +196372. i q^{82} +134189. i q^{83} +(-2330.46 - 176157. i) q^{84} -242148. q^{85} -254499. q^{86} +228391. i q^{87} -553592. q^{88} -903779. i q^{89} -278496. i q^{90} +(1278.11 + 96611.5i) q^{91} -598678. q^{92} -821495. q^{93} -880586. i q^{94} +2.11735e6 q^{95} +460650. i q^{96} -1.07750e6i q^{97} +(655351. - 17342.9i) q^{98} -249009. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 10 q^{2} + 346 q^{4} + 28 q^{7} - 1462 q^{8} - 1944 q^{9}+O(q^{10}) $ 8 * q + 10 * q^2 + 346 * q^4 + 28 * q^7 - 1462 * q^8 - 1944 * q^9	$ 8 q + 10 q^{2} + 346 q^{4} + 28 q^{7} - 1462 q^{8} - 1944 q^{9} - 6848 q^{11} + 12082 q^{14} - 4536 q^{15} + 28466 q^{16} - 2430 q^{18} + 6804 q^{21} - 7764 q^{22} - 24320 q^{23} - 77056 q^{25} - 30142 q^{28} + 60496 q^{29} + 89424 q^{30} + 5082 q^{32} + 103656 q^{35} - 84078 q^{36} - 39112 q^{37} + 108864 q^{39} - 267624 q^{42} - 29272 q^{43} - 577884 q^{44} + 564972 q^{46} - 94864 q^{49} + 240154 q^{50} + 103032 q^{51} + 232288 q^{53} + 225722 q^{56} + 180792 q^{57} + 987684 q^{58} - 375192 q^{60} - 6804 q^{63} - 690734 q^{64} - 836304 q^{65} - 2163848 q^{67} - 366744 q^{70} - 506288 q^{71} + 355266 q^{72} + 512324 q^{74} + 1536304 q^{77} + 1272024 q^{78} - 93272 q^{79} + 472392 q^{81} - 653184 q^{84} + 3740760 q^{85} + 3846452 q^{86} - 2077548 q^{88} + 1890336 q^{91} - 9701580 q^{92} - 2153952 q^{93} + 4154832 q^{95} - 507542 q^{98} + 1664064 q^{99}+O(q^{100}) $ 8 * q + 10 * q^2 + 346 * q^4 + 28 * q^7 - 1462 * q^8 - 1944 * q^9 - 6848 * q^11 + 12082 * q^14 - 4536 * q^15 + 28466 * q^16 - 2430 * q^18 + 6804 * q^21 - 7764 * q^22 - 24320 * q^23 - 77056 * q^25 - 30142 * q^28 + 60496 * q^29 + 89424 * q^30 + 5082 * q^32 + 103656 * q^35 - 84078 * q^36 - 39112 * q^37 + 108864 * q^39 - 267624 * q^42 - 29272 * q^43 - 577884 * q^44 + 564972 * q^46 - 94864 * q^49 + 240154 * q^50 + 103032 * q^51 + 232288 * q^53 + 225722 * q^56 + 180792 * q^57 + 987684 * q^58 - 375192 * q^60 - 6804 * q^63 - 690734 * q^64 - 836304 * q^65 - 2163848 * q^67 - 366744 * q^70 - 506288 * q^71 + 355266 * q^72 + 512324 * q^74 + 1536304 * q^77 + 1272024 * q^78 - 93272 * q^79 + 472392 * q^81 - 653184 * q^84 + 3740760 * q^85 + 3846452 * q^86 - 2077548 * q^88 + 1890336 * q^91 - 9701580 * q^92 - 2153952 * q^93 + 4154832 * q^95 - 507542 * q^98 + 1664064 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$8$	$10$
$\chi(n)$	$1$	$-1$

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 $

$2$	5.57235			0.696543			0.348272	−	0.937394i	$-0.386769\pi$
$2$	5.57235			0.696543			0.348272	+	0.937394i	$0.386769\pi$
$3$			15.5885i			0.577350i
$3$			15.5885i			0.577350i
$4$	−32.9490			−0.514828
$5$			205.672i			1.64538i	0.568493	+	0.822688i	$0.307526\pi$
$5$			205.672i			1.64538i	−0.568493	+	0.822688i	$0.692474\pi$
$6$			86.8643i			0.402149i
$7$	342.970	−	4.53729i	0.999913	−	0.0132283i
$7$	342.970	−	4.53729i	0.999913	−	0.0132283i
$8$	−540.233			−1.05514
$9$	−243.000			−0.333333
$10$			1146.08i			1.14608i
$11$	1024.73			0.769893			0.384947	−	0.922939i	$-0.374220\pi$
$11$	1024.73			0.769893			0.384947	+	0.922939i	$0.374220\pi$
$12$		−	513.624i		−	0.297236i
$13$			281.691i			0.128216i	0.997943	+	0.0641081i	$0.0204202\pi$
$13$			281.691i			0.128216i	−0.997943	+	0.0641081i	$0.979580\pi$
$14$	1911.15	−	25.2834i	0.696482	−	0.00921405i
$15$	−3206.11			−0.949958
$16$	−901.632			−0.220125
$17$			1177.35i			0.239639i	0.992796	+	0.119820i	$0.0382317\pi$
$17$			1177.35i			0.239639i	−0.992796	+	0.119820i	$0.961768\pi$
$18$	−1354.08			−0.232181
$19$		−	10294.8i		−	1.50092i	−0.660915	−	0.750460i	$-0.729832\pi$
$19$		−	10294.8i		−	1.50092i	0.660915	−	0.750460i	$-0.270168\pi$
$20$		−	6776.68i		−	0.847085i
$21$	70.7294	+	5346.37i	0.00763734	+	0.577300i
$22$	5710.14			0.536264
$23$	18169.9			1.49337			0.746686	−	0.665176i	$-0.231644\pi$
$23$	18169.9			1.49337			0.746686	+	0.665176i	$0.231644\pi$
$24$		−	8421.40i		−	0.609187i
$25$	−26676.0			−1.70726
$26$			1569.68i			0.0893081i
$27$		−	3788.00i		−	0.192450i
$28$	−11300.5	+	149.499i	−0.514783	+	0.00681027i
$29$	14651.3			0.600733			0.300367	−	0.953824i	$-0.402891\pi$
$29$	14651.3			0.600733			0.300367	+	0.953824i	$0.402891\pi$
$30$	−17865.5			−0.661687
$31$			52698.9i			1.76895i	0.466584	+	0.884477i	$0.345485\pi$
$31$			52698.9i			1.76895i	−0.466584	+	0.884477i	$0.654515\pi$
$32$	29550.7			0.901816
$33$			15973.9i			0.444498i
$34$			6560.59i			0.166919i
$35$	933.194	+	70539.3i	0.0217655	+	1.64523i
$36$	8006.60			0.171609
$37$	−7820.49			−0.154393			−0.0771967	−	0.997016i	$-0.524597\pi$
$37$	−7820.49			−0.154393			−0.0771967	+	0.997016i	$0.524597\pi$
$38$		−	57366.3i		−	1.04546i
$39$	−4391.13			−0.0740256
$40$		−	111111.i		−	1.73611i
$41$			35240.5i			0.511317i	0.966767	+	0.255659i	$0.0822923\pi$
$41$			35240.5i			0.511317i	−0.966767	+	0.255659i	$0.917708\pi$
$42$	394.129	+	29791.8i	0.00531974	+	0.402114i
$43$	−45671.7			−0.574436			−0.287218	−	0.957865i	$-0.592730\pi$
$43$	−45671.7			−0.574436			−0.287218	+	0.957865i	$0.592730\pi$
$44$	−33763.7			−0.396362
$45$		−	49978.3i		−	0.548459i
$46$	101249.			1.04020
$47$		−	158028.i		−	1.52209i	−0.648700	−	0.761044i	$-0.724687\pi$
$47$		−	158028.i		−	1.52209i	0.648700	−	0.761044i	$-0.275313\pi$
$48$		−	14055.1i		−	0.127089i
$49$	117608.	−	3112.31i	0.999650	−	0.0264542i
$50$	−148648.			−1.18918
$51$	−18353.1			−0.138356
$52$		−	9281.42i		−	0.0660092i
$53$	−4012.38			−0.0269510			−0.0134755	−	0.999909i	$-0.504290\pi$
$53$	−4012.38			−0.0269510			−0.0134755	+	0.999909i	$0.504290\pi$
$54$		−	21108.0i		−	0.134050i
$55$			210758.i			1.26676i
$56$	−185284.	+	2451.20i	−1.05505	+	0.0139577i
$57$	160480.			0.866557
$58$	81642.0			0.418437
$59$			16961.9i			0.0825882i	0.999147	+	0.0412941i	$0.0131481\pi$
$59$			16961.9i			0.0825882i	−0.999147	+	0.0412941i	$0.986852\pi$
$60$	105638.			0.489065
$61$		−	198032.i		−	0.872459i	−0.899835	−	0.436229i	$-0.856314\pi$
$61$		−	198032.i		−	0.872459i	0.899835	−	0.436229i	$-0.143686\pi$
$62$			293657.i			1.23215i
$63$	−83341.7	+	1102.56i	−0.333304	+	0.00440942i
$64$	222371.			0.848279
$65$	−57935.9			−0.210964
$66$			89012.3i			0.309612i
$67$	−525053.			−1.74574			−0.872869	−	0.487955i	$-0.837743\pi$
$67$	−525053.			−1.74574			−0.872869	+	0.487955i	$0.837743\pi$
$68$		−	38792.4i		−	0.123373i
$69$			283240.i			0.862199i
$70$	5200.08	+	393069.i	0.0151606	+	1.14597i
$71$	28289.2			0.0790398			0.0395199	−	0.999219i	$-0.487417\pi$
$71$	28289.2			0.0790398			0.0395199	+	0.999219i	$0.487417\pi$
$72$	131277.			0.351714
$73$		−	584202.i		−	1.50174i	−0.660451	−	0.750870i	$-0.729635\pi$
$73$		−	584202.i		−	1.50174i	0.660451	−	0.750870i	$-0.270365\pi$
$74$	−43578.4			−0.107542
$75$		−	415837.i		−	0.985688i
$76$			339204.i			0.772715i
$77$	351451.	−	4649.49i	0.769826	−	0.0101843i
$78$	−24468.9			−0.0515620
$79$	339282.			0.688144			0.344072	−	0.938943i	$-0.388194\pi$
$79$	339282.			0.688144			0.344072	+	0.938943i	$0.388194\pi$
$80$		−	185440.i		−	0.362188i
$81$	59049.0			0.111111
$82$			196372.i			0.356155i
$83$			134189.i			0.234684i	0.993092	+	0.117342i	$0.0374374\pi$
$83$			134189.i			0.234684i	−0.993092	+	0.117342i	$0.962563\pi$
$84$	−2330.46	−	176157.i	−0.00393191	−	0.297210i
$85$	−242148.			−0.394297
$86$	−254499.			−0.400120
$87$			228391.i			0.346833i
$88$	−553592.			−0.812347
$89$		−	903779.i		−	1.28201i	−0.767536	−	0.641006i	$-0.778517\pi$
$89$		−	903779.i		−	1.28201i	0.767536	−	0.641006i	$-0.221483\pi$
$90$		−	278496.i		−	0.382025i
$91$	1278.11	+	96611.5i	0.00169608	+	0.128205i
$92$	−598678.			−0.768830
$93$	−821495.			−1.02131
$94$		−	880586.i		−	1.06020i
$95$	2.11735e6			2.46958
$96$			460650.i			0.520664i
$97$		−	1.07750e6i		−	1.18060i	−0.807184	−	0.590300i	$-0.799009\pi$
$97$		−	1.07750e6i		−	1.18060i	0.807184	−	0.590300i	$-0.200991\pi$
$98$	655351.	−	17342.9i	0.696299	−	0.0184265i
$99$	−249009.			−0.256631
$100$	878945.			0.878945
$101$			1.13426e6i			1.10090i	0.834867	+	0.550451i	$0.185544\pi$
$101$			1.13426e6i			1.10090i	−0.834867	+	0.550451i	$0.814456\pi$
$102$	−102270.			−0.0963709
$103$			1.02013e6i			0.933566i	0.884372	+	0.466783i	$0.154587\pi$
$103$			1.02013e6i			0.933566i	−0.884372	+	0.466783i	$0.845413\pi$
$104$		−	152179.i		−	0.135286i
$105$	−1.09960e6	+	14547.1i	−0.949875	+	0.0125663i
$106$	−22358.4			−0.0187725
$107$	−679617.			−0.554770			−0.277385	−	0.960759i	$-0.589468\pi$
$107$	−679617.			−0.554770			−0.277385	+	0.960759i	$0.589468\pi$
$108$			124811.i			0.0990786i
$109$	−779446.			−0.601876			−0.300938	−	0.953644i	$-0.597300\pi$
$109$	−779446.			−0.601876			−0.300938	+	0.953644i	$0.597300\pi$
$110$			1.17442e6i			0.882356i
$111$		−	121909.i		−	0.0891390i
$112$	−309233.	+	4090.97i	−0.220106	+	0.00291187i
$113$	720425.			0.499291			0.249645	−	0.968337i	$-0.419686\pi$
$113$	720425.			0.499291			0.249645	+	0.968337i	$0.419686\pi$
$114$	894252.			0.603594
$115$			3.73703e6i			2.45716i
$116$	−482745.			−0.309274
$117$		−	68450.9i		−	0.0427387i
$118$			94517.4i			0.0575262i
$119$	5341.98	+	403795.i	0.00317001	+	0.239619i
$120$	1.73205e6			1.00234
$121$	−721493.			−0.407264
$122$		−	1.10350e6i		−	0.607705i
$123$	−549345.			−0.295209
$124$		−	1.73637e6i		−	0.910706i
$125$		−	2.27287e6i		−	1.16371i
$126$	−464409.	+	6143.86i	−0.232161	+	0.00307135i
$127$	1.57673e6			0.769745			0.384872	−	0.922970i	$-0.374245\pi$
$127$	1.57673e6			0.769745			0.384872	+	0.922970i	$0.374245\pi$
$128$	−652116.			−0.310953
$129$		−	711952.i		−	0.331651i
$130$	−322839.			−0.146945
$131$			2.22946e6i			0.991713i	0.868404	+	0.495857i	$0.165146\pi$
$131$			2.22946e6i			0.991713i	−0.868404	+	0.495857i	$0.834854\pi$
$132$		−	526324.i		−	0.228840i
$133$	−46710.6	−	3.53081e6i	−0.0198546	−	1.50079i
$134$	−2.92578e6			−1.21598
$135$	779084.			0.316653
$136$		−	636043.i		−	0.252854i
$137$	1.46462e6			0.569591			0.284795	−	0.958588i	$-0.408074\pi$
$137$	1.46462e6			0.569591			0.284795	+	0.958588i	$0.408074\pi$
$138$			1.57831e6i			0.600559i
$139$		−	3.01232e6i		−	1.12165i	−0.827935	−	0.560824i	$-0.810484\pi$
$139$		−	3.01232e6i		−	1.12165i	0.827935	−	0.560824i	$-0.189516\pi$
$140$	−30747.8	−	2.32420e6i	−0.0112055	−	0.847011i
$141$	2.46341e6			0.878778
$142$	157637.			0.0550547
$143$			288657.i			0.0987128i
$144$	219097.			0.0733750
$145$			3.01336e6i			0.988432i
$146$		−	3.25538e6i		−	1.04603i
$147$	48516.1	+	1.83332e6i	0.0152733	+	0.577148i
$148$	257677.			0.0794859
$149$	−1.21803e6			−0.368212			−0.184106	−	0.982906i	$-0.558939\pi$
$149$	−1.21803e6			−0.368212			−0.184106	+	0.982906i	$0.558939\pi$
$150$		−	2.31719e6i		−	0.686574i
$151$	−1.18147e6			−0.343157			−0.171579	−	0.985170i	$-0.554887\pi$
$151$	−1.18147e6			−0.343157			−0.171579	+	0.985170i	$0.554887\pi$
$152$			5.56160e6i			1.58369i
$153$		−	286096.i		−	0.0798798i
$154$	1.95841e6	−	25908.6i	0.536217	−	0.00709384i
$155$	−1.08387e7			−2.91059
$156$	144683.			0.0381104
$157$			2.61222e6i			0.675012i	0.941323	+	0.337506i	$0.109583\pi$
$157$			2.61222e6i			0.675012i	−0.941323	+	0.337506i	$0.890417\pi$
$158$	1.89059e6			0.479322
$159$		−	62546.8i		−	0.0155601i
$160$			6.07775e6i			1.48383i
$161$	6.23172e6	−	82442.0i	1.49324	−	0.0197547i
$162$	329041.			0.0773937
$163$	5.95632e6			1.37536			0.687679	−	0.726015i	$-0.258630\pi$
$163$	5.95632e6			1.37536			0.687679	+	0.726015i	$0.258630\pi$
$164$		−	1.16114e6i		−	0.263240i
$165$	−3.28539e6			−0.731366
$166$			747749.i			0.163468i
$167$			5.91267e6i			1.26950i	0.772716	+	0.634752i	$0.218898\pi$
$167$			5.91267e6i			1.26950i	−0.772716	+	0.634752i	$0.781102\pi$
$168$	−38210.4	−	2.88829e6i	−0.00805848	−	0.609134i
$169$	4.74746e6			0.983561
$170$	−1.34933e6			−0.274645
$171$			2.50164e6i			0.500307i
$172$	1.50484e6			0.295736
$173$		−	5.27217e6i		−	1.01824i	−0.860695	−	0.509121i	$-0.829971\pi$
$173$		−	5.27217e6i		−	1.01824i	0.860695	−	0.509121i	$-0.170029\pi$
$174$			1.27267e6i			0.241585i
$175$	−9.14905e6	+	121037.i	−1.70711	+	0.0225841i
$176$	−923928.			−0.169473
$177$	−264409.			−0.0476823
$178$		−	5.03617e6i		−	0.892977i
$179$	1.17827e6			0.205440			0.102720	−	0.994710i	$-0.467245\pi$
$179$	1.17827e6			0.205440			0.102720	+	0.994710i	$0.467245\pi$
$180$			1.64673e6i			0.282362i
$181$		−	6.79315e6i		−	1.14561i	−0.819693	−	0.572804i	$-0.805856\pi$
$181$		−	6.79315e6i		−	1.14561i	0.819693	−	0.572804i	$-0.194144\pi$
$182$	7122.09	+	538353.i	0.00118139	+	0.0893003i
$183$	3.08701e6			0.503714
$184$	−9.81597e6			−1.57572
$185$		−	1.60845e6i		−	0.254035i
$186$	−4.57765e6			−0.711384
$187$			1.20646e6i			0.184497i
$188$			5.20685e6i			0.783613i
$189$	−17187.2	−	1.29917e6i	−0.00254578	−	0.192433i
$190$	1.17986e7			1.72017
$191$	8.89739e6			1.27692			0.638458	−	0.769656i	$-0.279572\pi$
$191$	8.89739e6			1.27692			0.638458	+	0.769656i	$0.279572\pi$
$192$			3.46642e6i			0.489754i
$193$	−4.07635e6			−0.567021			−0.283510	−	0.958969i	$-0.591499\pi$
$193$	−4.07635e6			−0.567021			−0.283510	+	0.958969i	$0.591499\pi$
$194$		−	6.00422e6i		−	0.822339i
$195$		−	903132.i		−	0.121800i
$196$	−3.87506e6	+	102547.i	−0.514647	+	0.0136194i
$197$	−1.55937e6			−0.203963			−0.101981	−	0.994786i	$-0.532518\pi$
$197$	−1.55937e6			−0.203963			−0.101981	+	0.994786i	$0.532518\pi$
$198$	−1.38756e6			−0.178755
$199$		−	6.34593e6i		−	0.805260i	−0.915363	−	0.402630i	$-0.868096\pi$
$199$		−	6.34593e6i		−	0.805260i	0.915363	−	0.402630i	$-0.131904\pi$
$200$	1.44112e7			1.80140
$201$		−	8.18477e6i		−	1.00790i
$202$			6.32049e6i			0.766826i
$203$	5.02495e6	−	66477.1i	0.600681	−	0.00794665i
$204$	604714.			0.0712294
$205$	−7.24798e6			−0.841309
$206$			5.68453e6i			0.650269i
$207$	−4.41528e6			−0.497791
$208$		−	253982.i		−	0.0282236i
$209$		−	1.05494e7i		−	1.15555i
$210$	−6.12735e6	+	81061.2i	−0.661629	+	0.00875296i
$211$	−7.50986e6			−0.799437			−0.399719	−	0.916638i	$-0.630892\pi$
$211$	−7.50986e6			−0.799437			−0.399719	+	0.916638i	$0.630892\pi$
$212$	132204.			0.0138751
$213$			440985.i			0.0456337i
$214$	−3.78706e6			−0.386421
$215$		−	9.39339e6i		−	0.945164i
$216$			2.04640e6i			0.203062i
$217$	239110.	+	1.80741e7i	0.0234002	+	1.76880i
$218$	−4.34334e6			−0.419232
$219$	9.10681e6			0.867029
$220$		−	6.94425e6i		−	0.652165i
$221$	−331648.			−0.0307257
$222$		−	679321.i		−	0.0620892i
$223$		−	995503.i		−	0.0897693i	−0.998992	−	0.0448847i	$-0.985708\pi$
$223$		−	995503.i		−	0.0897693i	0.998992	−	0.0448847i	$-0.0142920\pi$
$224$	1.01350e7	−	134080.i	0.901737	−	0.0119295i
$225$	6.48226e6			0.569087
$226$	4.01446e6			0.347778
$227$			1.40753e7i			1.20332i	0.798753	+	0.601659i	$0.205493\pi$
$227$			1.40753e7i			1.20332i	−0.798753	+	0.601659i	$0.794507\pi$
$228$	−5.28766e6			−0.446127
$229$		−	1.09905e7i		−	0.915193i	−0.889160	−	0.457597i	$-0.848710\pi$
$229$		−	1.09905e7i		−	0.915193i	0.889160	−	0.457597i	$-0.151290\pi$
$230$			2.08240e7i			1.71152i
$231$	72478.4	+	5.47858e6i	0.00587994	+	0.444459i
$232$	−7.91511e6			−0.633859
$233$	−1.68832e7			−1.33471			−0.667354	−	0.744741i	$-0.732573\pi$
$233$	−1.68832e7			−1.33471			−0.667354	+	0.744741i	$0.732573\pi$
$234$		−	381432.i		−	0.0297694i
$235$	3.25019e7			2.50441
$236$		−	558876.i		−	0.0425187i
$237$			5.28888e6i			0.397300i
$238$	29767.3	+	2.25009e6i	0.00220805	+	0.166905i
$239$	−2.04863e7			−1.50062			−0.750308	−	0.661089i	$-0.770095\pi$
$239$	−2.04863e7			−1.50062			−0.750308	+	0.661089i	$0.770095\pi$
$240$	2.89073e6			0.209110
$241$			8.60956e6i			0.615077i	0.951536	+	0.307539i	$0.0995053\pi$
$241$			8.60956e6i			0.615077i	−0.951536	+	0.307539i	$0.900495\pi$
$242$	−4.02041e6			−0.283677
$243$			920483.i			0.0641500i
$244$			6.52494e6i			0.449166i
$245$	640115.	+	2.41886e7i	0.0435271	+	1.64480i
$246$	−3.06114e6			−0.205626
$247$	2.89996e6			0.192442
$248$		−	2.84697e7i		−	1.86650i
$249$	−2.09180e6			−0.135495
$250$		−	1.26652e7i		−	0.810574i
$251$		−	2.02637e7i		−	1.28143i	−0.767777	−	0.640717i	$-0.778637\pi$
$251$		−	2.02637e7i		−	1.28143i	0.767777	−	0.640717i	$-0.221363\pi$
$252$	2.74602e6	−	36328.3i	0.171594	−	0.00227009i
$253$	1.86192e7			1.14974
$254$	8.78610e6			0.536161
$255$		−	3.77471e6i		−	0.227647i
$256$	−1.78656e7			−1.06487
$257$			9.35156e6i			0.550915i	0.961313	+	0.275458i	$0.0888293\pi$
$257$			9.35156e6i			0.550915i	−0.961313	+	0.275458i	$0.911171\pi$
$258$		−	3.96724e6i		−	0.231009i
$259$	−2.68219e6	+	35483.8i	−0.154380	+	0.00204235i
$260$	1.90893e6			0.108610
$261$	−3.56026e6			−0.200244
$262$			1.24233e7i			0.690771i
$263$	−2.07021e7			−1.13801			−0.569007	−	0.822332i	$-0.692672\pi$
$263$	−2.07021e7			−1.13801			−0.569007	+	0.822332i	$0.692672\pi$
$264$		−	8.62965e6i		−	0.469009i
$265$		−	825233.i		−	0.0443444i
$266$	−260288.	−	1.96749e7i	−0.0138296	−	1.04536i
$267$	1.40885e7			0.740170
$268$	1.73000e7			0.898754
$269$		−	4.94276e6i		−	0.253929i	−0.991907	−	0.126965i	$-0.959477\pi$
$269$		−	4.94276e6i		−	0.253929i	0.991907	−	0.126965i	$-0.0405235\pi$
$270$	4.34133e6			0.220562
$271$		−	1.37411e7i		−	0.690421i	−0.938525	−	0.345211i	$-0.887808\pi$
$271$		−	1.37411e7i		−	0.690421i	0.938525	−	0.345211i	$-0.112192\pi$
$272$		−	1.06154e6i		−	0.0527507i
$273$	−1.50602e6	+	19923.8i	−0.0740192	+	0.000979230i
$274$	8.16136e6			0.396745
$275$	−2.73356e7			−1.31441
$276$		−	9.33247e6i		−	0.443884i
$277$	−2.32333e7			−1.09313			−0.546564	−	0.837417i	$-0.684065\pi$
$277$	−2.32333e7			−1.09313			−0.546564	+	0.837417i	$0.684065\pi$
$278$		−	1.67857e7i		−	0.781277i
$279$		−	1.28058e7i		−	0.589651i
$280$	−504142.	−	3.81077e7i	−0.0229657	−	1.73595i
$281$	1.33482e7			0.601593			0.300797	−	0.953688i	$-0.402747\pi$
$281$	1.33482e7			0.601593			0.300797	+	0.953688i	$0.402747\pi$
$282$	1.37270e7			0.612107
$283$			1.05219e7i			0.464230i	0.972688	+	0.232115i	$0.0745646\pi$
$283$			1.05219e7i			0.464230i	−0.972688	+	0.232115i	$0.925435\pi$
$284$	−932101.			−0.0406919
$285$			3.30063e7i			1.42581i
$286$			1.60849e6i			0.0687577i
$287$	159896.	+	1.20864e7i	0.00676384	+	0.511273i
$288$	−7.18082e6			−0.300605
$289$	2.27514e7			0.942573
$290$			1.67915e7i			0.688485i
$291$	1.67966e7			0.681620
$292$			1.92489e7i			0.773137i
$293$			3.12100e7i			1.24077i	0.784298	+	0.620385i	$0.213023\pi$
$293$			3.12100e7i			1.24077i	−0.784298	+	0.620385i	$0.786977\pi$
$294$	270349.	+	1.02159e7i	0.0106385	+	0.402009i
$295$	−3.48858e6			−0.135889
$296$	4.22489e6			0.162907
$297$		−	3.88166e6i		−	0.148166i
$298$	−6.78727e6			−0.256476
$299$			5.11829e6i			0.191475i
$300$			1.37014e7i			0.507459i
$301$	−1.56640e7	+	207226.i	−0.574386	+	0.00759879i
$302$	−6.58358e6			−0.239024
$303$	−1.76814e7			−0.635606
$304$			9.28214e6i			0.330390i
$305$	4.07295e7			1.43552
$306$		−	1.59422e6i		−	0.0556398i
$307$			1.71404e7i			0.592387i	0.955128	+	0.296193i	$0.0957173\pi$
$307$			1.71404e7i			0.592387i	−0.955128	+	0.296193i	$0.904283\pi$
$308$	−1.15799e7	+	153196.i	−0.396328	+	0.00524318i
$309$	−1.59023e7			−0.538994
$310$	−6.03969e7			−2.02735
$311$		−	1.84244e7i		−	0.612510i	−0.951949	−	0.306255i	$-0.900924\pi$
$311$		−	1.84244e7i		−	0.612510i	0.951949	−	0.306255i	$-0.0990761\pi$
$312$	2.37223e6			0.0781076
$313$			1.49867e7i			0.488734i	0.969683	+	0.244367i	$0.0785801\pi$
$313$			1.49867e7i			0.488734i	−0.969683	+	0.244367i	$0.921420\pi$
$314$			1.45562e7i			0.470175i
$315$	−226766.	−	1.71411e7i	−0.00725515	−	0.548411i
$316$	−1.11790e7			−0.354275
$317$	2.87070e7			0.901177			0.450589	−	0.892732i	$-0.351214\pi$
$317$	2.87070e7			0.901177			0.450589	+	0.892732i	$0.351214\pi$
$318$		−	348532.i		−	0.0108383i
$319$	1.50136e7			0.462501
$320$			4.57355e7i			1.39574i
$321$		−	1.05942e7i		−	0.320296i
$322$	3.47253e7	−	459395.i	1.04011	−	0.0137600i
$323$	1.21206e7			0.359680
$324$	−1.94560e6			−0.0572031
$325$		−	7.51437e6i		−	0.218898i
$326$	3.31907e7			0.957996
$327$		−	1.21504e7i		−	0.347493i
$328$		−	1.90381e7i		−	0.539513i
$329$	−717018.	−	5.41988e7i	−0.0201346	−	1.52196i
$330$	−1.83073e7			−0.509428
$331$	6.37392e6			0.175761			0.0878806	−	0.996131i	$-0.471991\pi$
$331$	6.37392e6			0.175761			0.0878806	+	0.996131i	$0.471991\pi$
$332$		−	4.42140e6i		−	0.120822i
$333$	1.90038e6			0.0514644
$334$			3.29474e7i			0.884264i
$335$		−	1.07989e8i		−	2.87239i
$336$	−63771.9	−	4.82046e6i	−0.00168117	−	0.127078i
$337$	−4.99962e7			−1.30631			−0.653157	−	0.757222i	$-0.726556\pi$
$337$	−4.99962e7			−1.30631			−0.653157	+	0.757222i	$0.726556\pi$
$338$	2.64545e7			0.685092
$339$			1.12303e7i			0.288266i
$340$	7.97851e6			0.202995
$341$			5.40021e7i			1.36191i
$342$			1.39400e7i			0.348485i
$343$	4.03218e7	−	1.60105e6i	0.999213	−	0.0396755i
$344$	2.46734e7			0.606112
$345$	−5.82546e7			−1.41864
$346$		−	2.93784e7i		−	0.709250i
$347$	−5.54761e7			−1.32775			−0.663876	−	0.747842i	$-0.731090\pi$
$347$	−5.54761e7			−1.32775			−0.663876	+	0.747842i	$0.731090\pi$
$348$		−	7.52524e6i		−	0.178559i
$349$		−	5.76564e7i		−	1.35635i	−0.734901	−	0.678174i	$-0.762771\pi$
$349$		−	5.76564e7i		−	1.35635i	0.734901	−	0.678174i	$-0.237229\pi$
$350$	−5.09817e7	+	674458.i	−1.18908	+	0.0157308i
$351$	1.06704e6			0.0246752
$352$	3.02814e7			0.694302
$353$			4.59116e7i			1.04375i	0.853021	+	0.521877i	$0.174768\pi$
$353$			4.59116e7i			1.04375i	−0.853021	+	0.521877i	$0.825232\pi$
$354$	−1.47338e6			−0.0332128
$355$			5.81830e6i			0.130050i
$356$			2.97786e7i			0.660015i
$357$	−6.29455e6	+	83273.2i	−0.138344	+	0.00183021i
$358$	6.56572e6			0.143098
$359$	7.69147e6			0.166236			0.0831182	−	0.996540i	$-0.473512\pi$
$359$	7.69147e6			0.166236			0.0831182	+	0.996540i	$0.473512\pi$
$360$			2.69999e7i			0.578702i
$361$	−5.89374e7			−1.25276
$362$		−	3.78538e7i		−	0.797965i
$363$		−	1.12470e7i		−	0.235134i
$364$	−42112.5	−	3.18325e6i	−0.000873187	−	0.0660034i
$365$	1.20154e8			2.47092
$366$	1.72019e7			0.350859
$367$		−	6.06593e7i		−	1.22715i	−0.789635	−	0.613577i	$-0.789730\pi$
$367$		−	6.06593e7i		−	1.22715i	0.789635	−	0.613577i	$-0.210270\pi$
$368$	−1.63825e7			−0.328729
$369$		−	8.56344e6i		−	0.170439i
$370$		−	8.96286e6i		−	0.176946i
$371$	−1.37612e6	+	18205.3i	−0.0269486	+	0.000356514i
$372$	2.70674e7			0.525797
$373$	2.87490e7			0.553982			0.276991	−	0.960873i	$-0.410663\pi$
$373$	2.87490e7			0.553982			0.276991	+	0.960873i	$0.410663\pi$
$374$			6.72283e6i			0.128510i
$375$	3.54306e7			0.671868
$376$			8.53719e7i			1.60602i
$377$			4.12713e6i			0.0770237i
$378$	−95773.2	−	7.23942e6i	−0.00177325	−	0.134038i
$379$	−4.26080e7			−0.782661			−0.391330	−	0.920250i	$-0.627985\pi$
$379$	−4.26080e7			−0.782661			−0.391330	+	0.920250i	$0.627985\pi$
$380$	−6.97647e7			−1.27141
$381$			2.45788e7i			0.444412i
$382$	4.95793e7			0.889428
$383$		−	1.92986e7i		−	0.343502i	−0.985140	−	0.171751i	$-0.945057\pi$
$383$		−	1.92986e7i		−	0.343502i	0.985140	−	0.171751i	$-0.0549425\pi$
$384$		−	1.01655e7i		−	0.179529i
$385$	956270.	+	7.22836e7i	0.0167571	+	1.26665i
$386$	−2.27148e7			−0.394955
$387$	1.10982e7			0.191479
$388$			3.55026e7i			0.607806i
$389$	−7.73123e7			−1.31341			−0.656704	−	0.754148i	$-0.728050\pi$
$389$	−7.73123e7			−1.31341			−0.656704	+	0.754148i	$0.728050\pi$
$390$		−	5.03256e6i		−	0.0848389i
$391$			2.13923e7i			0.357871i
$392$	−6.35356e7	+	1.68137e6i	−1.05477	+	0.0279130i
$393$	−3.47539e7			−0.572566
$394$	−8.68935e6			−0.142069
$395$			6.97807e7i			1.13225i
$396$	8.20459e6			0.132121
$397$		−	3.56825e7i		−	0.570275i	−0.958487	−	0.285137i	$-0.907961\pi$
$397$		−	3.56825e7i		−	0.570275i	0.958487	−	0.285137i	$-0.0920392\pi$
$398$		−	3.53617e7i		−	0.560898i
$399$	5.50399e7	−	728146.i	0.866481	−	0.0114630i
$400$	2.40519e7			0.375811
$401$	1.15741e8			1.79495			0.897476	−	0.441062i	$-0.145398\pi$
$401$	1.15741e8			1.79495			0.897476	+	0.441062i	$0.145398\pi$
$402$		−	4.56084e7i		−	0.702047i
$403$	−1.48448e7			−0.226809
$404$		−	3.73727e7i		−	0.566775i
$405$			1.21447e7i			0.182820i
$406$	2.80008e7	−	370434.i	0.418400	−	0.00553519i
$407$	−8.01387e6			−0.118866
$408$	9.91493e6			0.145985
$409$			7.94139e7i			1.16072i	0.814361	+	0.580359i	$0.197088\pi$
$409$			7.94139e7i			1.16072i	−0.814361	+	0.580359i	$0.802912\pi$
$410$	−4.03883e7			−0.586008
$411$			2.28311e7i			0.328853i
$412$		−	3.36123e7i		−	0.480625i
$413$	76961.0	+	5.81741e6i	0.00109250	+	0.0825809i
$414$	−2.46035e7			−0.346733
$415$	−2.75990e7			−0.386143
$416$			8.32417e6i			0.115627i
$417$	4.69574e7			0.647584
$418$		−	5.87848e7i		−	0.804890i
$419$			1.24462e8i			1.69198i	0.533198	+	0.845991i	$0.320990\pi$
$419$			1.24462e8i			1.69198i	−0.533198	+	0.845991i	$0.679010\pi$
$420$	3.62306e7	−	479310.i	0.489022	−	0.00646947i
$421$	−6.52445e7			−0.874374			−0.437187	−	0.899371i	$-0.644025\pi$
$421$	−6.52445e7			−0.874374			−0.437187	+	0.899371i	$0.644025\pi$
$422$	−4.18475e7			−0.556843
$423$			3.84008e7i			0.507363i
$424$	2.16762e6			0.0284371
$425$		−	3.14069e7i		−	0.409127i
$426$			2.45732e6i			0.0317858i
$427$	−898527.	−	6.79189e7i	−0.0115411	−	0.872383i
$428$	2.23927e7			0.285611
$429$	−4.49971e6			−0.0569918
$430$		−	5.23432e7i		−	0.658347i
$431$	5.68606e6			0.0710199			0.0355099	−	0.999369i	$-0.488694\pi$
$431$	5.68606e6			0.0710199			0.0355099	+	0.999369i	$0.488694\pi$
$432$			3.41538e6i			0.0423631i
$433$			8.64649e6i			0.106506i	0.998581	+	0.0532532i	$0.0169591\pi$
$433$			8.64649e6i			0.106506i	−0.998581	+	0.0532532i	$0.983041\pi$
$434$	1.33241e6	+	1.00715e8i	0.0162992	+	1.23205i
$435$	−4.69736e7			−0.570671
$436$	2.56820e7			0.309862
$437$		−	1.87055e8i		−	2.24143i
$438$	5.07463e7			0.603923
$439$		−	6.79349e7i		−	0.802971i	−0.915865	−	0.401485i	$-0.868494\pi$
$439$		−	6.79349e7i		−	0.802971i	0.915865	−	0.401485i	$-0.131506\pi$
$440$		−	1.13858e8i		−	1.33662i
$441$	−2.85787e7	+	756291.i	−0.333217	+	0.00881807i
$442$	−1.84806e6			−0.0214017
$443$	−1.22356e8			−1.40739			−0.703694	−	0.710503i	$-0.748468\pi$
$443$	−1.22356e8			−1.40739			−0.703694	+	0.710503i	$0.748468\pi$
$444$			4.01679e6i			0.0458912i
$445$	1.85882e8			2.10939
$446$		−	5.54729e6i		−	0.0625282i
$447$		−	1.89872e7i		−	0.212587i
$448$	7.62667e7	−	1.00896e6i	0.848205	−	0.0112213i
$449$	−6.40665e6			−0.0707770			−0.0353885	−	0.999374i	$-0.511267\pi$
$449$	−6.40665e6			−0.0707770			−0.0353885	+	0.999374i	$0.511267\pi$
$450$	3.61214e7			0.396394
$451$			3.61119e7i			0.393660i
$452$	−2.37373e7			−0.257049
$453$		−	1.84173e7i		−	0.198122i
$454$			7.84325e7i			0.838163i
$455$	−1.98703e7	+	262872.i	−0.210945	+	0.00279068i
$456$	−8.66968e7			−0.914341
$457$	−2.23679e7			−0.234356			−0.117178	−	0.993111i	$-0.537385\pi$
$457$	−2.23679e7			−0.234356			−0.117178	+	0.993111i	$0.537385\pi$
$458$		−	6.12431e7i		−	0.637472i
$459$	4.45979e6			0.0461186
$460$		−	1.23131e8i		−	1.26501i
$461$			1.17283e8i			1.19711i	0.801082	+	0.598554i	$0.204258\pi$
$461$			1.17283e8i			1.19711i	−0.801082	+	0.598554i	$0.795742\pi$
$462$	403875.	+	3.05285e7i	0.00409563	+	0.309585i
$463$	9.23784e7			0.930738			0.465369	−	0.885117i	$-0.345922\pi$
$463$	9.23784e7			0.930738			0.465369	+	0.885117i	$0.345922\pi$
$464$	−1.32101e7			−0.132236
$465$		−	1.68958e8i		−	1.68043i
$466$	−9.40788e7			−0.929681
$467$		−	4.24329e7i		−	0.416632i	−0.978062	−	0.208316i	$-0.933202\pi$
$467$		−	4.24329e7i		−	0.416632i	0.978062	−	0.208316i	$-0.0667982\pi$
$468$			2.25539e6i			0.0220031i
$469$	−1.80077e8	+	2.38232e6i	−1.74558	+	0.0230931i
$470$	1.81112e8			1.74443
$471$	−4.07206e7			−0.389718
$472$		−	9.16337e6i		−	0.0871423i
$473$	−4.68011e7			−0.442255
$474$			2.94714e7i			0.276737i
$475$			2.74624e8i			2.56246i
$476$	−176013.	−	1.33046e7i	−0.00163201	−	0.123362i
$477$	975008.			0.00898365
$478$	−1.14157e8			−1.04524
$479$			5.08998e7i			0.463137i	0.972819	+	0.231568i	$0.0743857\pi$
$479$			5.08998e7i			0.463137i	−0.972819	+	0.231568i	$0.925614\pi$
$480$	−9.47428e7			−0.856688
$481$		−	2.20296e6i		−	0.0197957i
$482$			4.79754e7i			0.428428i
$483$	1.28514e6	+	9.71429e7i	0.0114054	+	0.862124i
$484$	2.37725e7			0.209671
$485$	2.21612e8			1.94253
$486$			5.12925e6i			0.0446833i
$487$	1.12456e8			0.973635			0.486818	−	0.873504i	$-0.338158\pi$
$487$	1.12456e8			0.973635			0.486818	+	0.873504i	$0.338158\pi$
$488$			1.06983e8i			0.920569i
$489$			9.28499e7i			0.794063i
$490$	3.56694e6	+	1.34787e8i	0.0303185	+	1.14567i
$491$	1.78723e8			1.50986			0.754928	−	0.655807i	$-0.227672\pi$
$491$	1.78723e8			1.50986			0.754928	+	0.655807i	$0.227672\pi$
$492$	1.81003e7			0.151982
$493$			1.72497e7i			0.143959i
$494$	1.61596e7			0.134044
$495$		−	5.12142e7i		−	0.422255i
$496$		−	4.75150e7i		−	0.389391i
$497$	9.70236e6	−	128356.i	0.0790329	−	0.00104556i
$498$	−1.16563e7			−0.0943780
$499$	5.15442e6			0.0414837			0.0207419	−	0.999785i	$-0.493397\pi$
$499$	5.15442e6			0.0414837			0.0207419	+	0.999785i	$0.493397\pi$
$500$			7.48888e7i			0.599110i
$501$	−9.21693e7			−0.732948
$502$		−	1.12916e8i		−	0.892575i
$503$			9.20266e7i			0.723119i	0.932349	+	0.361559i	$0.117755\pi$
$503$			9.20266e7i			0.723119i	−0.932349	+	0.361559i	$0.882245\pi$
$504$	4.50240e7	−	595641.i	0.351684	−	0.00465257i
$505$	−2.33286e8			−1.81140
$506$	1.03752e8			0.800842
$507$			7.40056e7i			0.567859i
$508$	−5.19517e7			−0.396286
$509$		−	6.15378e7i		−	0.466647i	−0.972399	−	0.233324i	$-0.925040\pi$
$509$		−	6.15378e7i		−	0.466647i	0.972399	−	0.233324i	$-0.0749602\pi$
$510$		−	2.10340e7i		−	0.158566i
$511$	−2.65070e6	−	2.00364e8i	−0.0198654	−	1.50161i
$512$	−5.78177e7			−0.430776
$513$	−3.89967e7			−0.288852
$514$			5.21101e7i			0.383736i
$515$	−2.09813e8			−1.53607
$516$			2.34581e7i			0.170743i
$517$		−	1.61936e8i		−	1.17185i
$518$	−1.49461e7	+	197728.i	−0.107532	+	0.00142259i
$519$	8.21850e7			0.587882
$520$	3.12989e7			0.222597
$521$		−	1.07337e8i		−	0.758989i	−0.925194	−	0.379494i	$-0.876098\pi$
$521$		−	1.07337e8i		−	0.758989i	0.925194	−	0.379494i	$-0.123902\pi$
$522$	−1.98390e7			−0.139479
$523$			1.11340e8i			0.778297i	0.921175	+	0.389149i	$0.127231\pi$
$523$			1.11340e8i			0.778297i	−0.921175	+	0.389149i	$0.872769\pi$
$524$		−	7.34585e7i		−	0.510561i
$525$	−1.88677e6	−	1.42620e8i	−0.0130389	−	0.985601i
$526$	−1.15359e8			−0.792676
$527$	−6.20450e7			−0.423911
$528$		−	1.44026e7i		−	0.0978452i
$529$	1.82108e8			1.23016
$530$		−	4.59849e6i		−	0.0308878i
$531$		−	4.12174e6i		−	0.0275294i
$532$	1.53907e6	+	1.16337e8i	0.0102217	+	0.772648i
$533$	−9.92693e6			−0.0655591
$534$	7.85061e7			0.515561
$535$		−	1.39778e8i		−	0.912804i
$536$	2.83651e8			1.84200
$537$			1.83674e7i			0.118611i
$538$		−	2.75428e7i		−	0.176873i
$539$	1.20516e8	−	3.18927e6i	0.769624	−	0.0203669i
$540$	−2.56700e7			−0.163022
$541$	−1.42994e8			−0.903080			−0.451540	−	0.892251i	$-0.649125\pi$
$541$	−1.42994e8			−0.903080			−0.451540	+	0.892251i	$0.649125\pi$
$542$		−	7.65702e7i		−	0.480908i
$543$	1.05895e8			0.661417
$544$			3.47915e7i			0.216111i
$545$		−	1.60310e8i		−	0.990312i
$546$	−8.39209e6	+	111022.i	−0.0515575	+	0.000682076i
$547$	1.09975e8			0.671940			0.335970	−	0.941873i	$-0.390936\pi$
$547$	1.09975e8			0.671940			0.335970	+	0.941873i	$0.390936\pi$
$548$	−4.82577e7			−0.293241
$549$			4.81217e7i			0.290820i
$550$	−1.52323e8			−0.915543
$551$		−	1.50832e8i		−	0.901653i
$552$		−	1.53016e8i		−	0.909743i
$553$	1.16363e8	−	1.53942e6i	0.688083	−	0.00910294i
$554$	−1.29464e8			−0.761412
$555$	2.50733e7			0.146667
$556$			9.92528e7i			0.577456i
$557$	−1.43076e8			−0.827943			−0.413971	−	0.910290i	$-0.635859\pi$
$557$	−1.43076e8			−0.827943			−0.413971	+	0.910290i	$0.635859\pi$
$558$		−	7.13585e7i		−	0.410718i
$559$		−	1.28653e7i		−	0.0736520i
$560$	−841397.	−	6.36005e7i	−0.00479112	−	0.362157i
$561$	−1.88069e7			−0.106519
$562$	7.43807e7			0.419036
$563$			2.52572e8i			1.41534i	0.706543	+	0.707670i	$0.250253\pi$
$563$			2.52572e8i			1.41534i	−0.706543	+	0.707670i	$0.749747\pi$
$564$	−8.11668e7			−0.452419
$565$			1.48171e8i			0.821521i
$566$			5.86315e7i			0.323356i
$567$	2.02520e7	−	267923.i	0.111101	−	0.00146981i
$568$	−1.52828e7			−0.0833983
$569$	−2.19967e7			−0.119405			−0.0597023	−	0.998216i	$-0.519015\pi$
$569$	−2.19967e7			−0.119405			−0.0597023	+	0.998216i	$0.519015\pi$
$570$			1.83923e8i			0.993140i
$571$	1.22188e8			0.656328			0.328164	−	0.944621i	$-0.393570\pi$
$571$	1.22188e8			0.656328			0.328164	+	0.944621i	$0.393570\pi$
$572$		−	9.51093e6i		−	0.0508200i
$573$			1.38697e8i			0.737228i
$574$	890998.	+	6.73498e7i	0.00471130	+	0.356123i
$575$	−4.84699e8			−2.54958
$576$	−5.40362e7			−0.282760
$577$		−	2.81945e8i		−	1.46770i	−0.679313	−	0.733849i	$-0.737722\pi$
$577$		−	2.81945e8i		−	1.46770i	0.679313	−	0.733849i	$-0.262278\pi$
$578$	1.26779e8			0.656543
$579$		−	6.35439e7i		−	0.327370i
$580$		−	9.92870e7i		−	0.508872i
$581$	608856.	+	4.60229e7i	0.00310446	+	0.234663i
$582$	9.35965e7			0.474778
$583$	−4.11160e6			−0.0207494
$584$			3.15605e8i			1.58455i
$585$	1.40784e7			0.0703212
$586$			1.73913e8i			0.864249i
$587$			3.01594e7i			0.149110i	0.997217	+	0.0745552i	$0.0237537\pi$
$587$			3.01594e7i			0.149110i	−0.997217	+	0.0745552i	$0.976246\pi$
$588$	−1.59856e6	−	6.04061e7i	−0.00786314	−	0.297132i
$589$	5.42526e8			2.65506
$590$	−1.94396e7			−0.0946523
$591$		−	2.43082e7i		−	0.117758i
$592$	7.05120e6			0.0339858
$593$			2.00723e8i			0.962574i	0.876563	+	0.481287i	$0.159831\pi$
$593$			2.00723e8i			0.962574i	−0.876563	+	0.481287i	$0.840169\pi$
$594$		−	2.16300e7i		−	0.103204i
$595$	−8.30494e7	+	1.09869e6i	−0.394262	+	0.00521586i
$596$	4.01327e7			0.189566
$597$	9.89233e7			0.464917
$598$			2.85209e7i			0.133370i
$599$	−3.25533e8			−1.51466			−0.757328	−	0.653035i	$-0.773496\pi$
$599$	−3.25533e8			−1.51466			−0.757328	+	0.653035i	$0.773496\pi$
$600$			2.24649e8i			1.04004i
$601$		−	3.30353e8i		−	1.52179i	−0.648875	−	0.760895i	$-0.724760\pi$
$601$		−	3.30353e8i		−	1.52179i	0.648875	−	0.760895i	$-0.275240\pi$
$602$	−8.72854e7	+	1.15473e6i	−0.400085	+	0.00529289i
$603$	1.27588e8			0.581912
$604$	3.89283e7			0.176667
$605$		−	1.48391e8i		−	0.670103i
$606$	−9.85267e7			−0.442727
$607$			3.92510e8i			1.75503i	0.479548	+	0.877516i	$0.340801\pi$
$607$			3.92510e8i			1.75503i	−0.479548	+	0.877516i	$0.659199\pi$
$608$		−	3.04219e8i		−	1.35355i
$609$	1.03628e6	+	7.83312e7i	0.00458800	+	0.346803i
$610$	2.26959e8			0.999904
$611$	4.45150e7			0.195156
$612$			9.42656e6i			0.0411243i
$613$	−3.18938e8			−1.38460			−0.692302	−	0.721608i	$-0.743403\pi$
$613$	−3.18938e8			−1.38460			−0.692302	+	0.721608i	$0.743403\pi$
$614$			9.55121e7i			0.412623i
$615$		−	1.12985e8i		−	0.485730i
$616$	−1.89865e8	+	2.51181e6i	−0.812276	+	0.0107459i
$617$	−1.82463e8			−0.776819			−0.388410	−	0.921487i	$-0.626975\pi$
$617$	−1.82463e8			−0.776819			−0.388410	+	0.921487i	$0.626975\pi$
$618$	−8.86130e7			−0.375433
$619$			2.32150e8i			0.978808i	0.872057	+	0.489404i	$0.162786\pi$
$619$			2.32150e8i			0.978808i	−0.872057	+	0.489404i	$0.837214\pi$
$620$	3.57124e8			1.49845
$621$		−	6.88274e7i		−	0.287400i
$622$		−	1.02667e8i		−	0.426640i
$623$	−4.10071e6	−	3.09969e8i	−0.0169588	−	1.28190i
$624$	3.95918e6			0.0162949
$625$	5.06541e7			0.207479
$626$			8.35110e7i			0.340424i
$627$	1.64449e8			0.667157
$628$		−	8.60701e7i		−	0.347515i
$629$		−	9.20744e6i		−	0.0369987i
$630$	−1.26362e6	−	9.55159e7i	−0.00505353	−	0.381992i
$631$	−4.73100e7			−0.188306			−0.0941532	−	0.995558i	$-0.530014\pi$
$631$	−4.73100e7			−0.188306			−0.0941532	+	0.995558i	$0.530014\pi$
$632$	−1.83291e8			−0.726090
$633$		−	1.17067e8i		−	0.461555i
$634$	1.59965e8			0.627709
$635$			3.24290e8i			1.26652i
$636$			2.06085e6i			0.00801079i
$637$	876709.	+	3.31291e7i	0.00339186	+	0.128171i
$638$	8.36609e7			0.322152
$639$	−6.87428e6			−0.0263466
$640$		−	1.34122e8i		−	0.511635i
$641$	4.20577e8			1.59688			0.798438	−	0.602077i	$-0.205660\pi$
$641$	4.20577e8			1.59688			0.798438	+	0.602077i	$0.205660\pi$
$642$		−	5.90344e7i		−	0.223100i
$643$			2.95514e8i			1.11159i	0.831319	+	0.555796i	$0.187586\pi$
$643$			2.95514e8i			1.11159i	−0.831319	+	0.555796i	$0.812414\pi$
$644$	−2.05329e8	+	2.71638e6i	−0.768762	+	0.0101703i
$645$	1.46428e8			0.545691
$646$	6.75401e7			0.250533
$647$		−	2.50702e8i		−	0.925645i	−0.886451	−	0.462822i	$-0.846837\pi$
$647$		−	2.50702e8i		−	0.925645i	0.886451	−	0.462822i	$-0.153163\pi$
$648$	−3.19002e7			−0.117238
$649$			1.73813e7i			0.0635841i
$650$		−	4.18727e7i		−	0.152472i
$651$	−2.81748e8	+	3.72736e6i	−1.02122	+	0.0135101i
$652$	−1.96255e8			−0.708072
$653$	−1.58732e8			−0.570065			−0.285033	−	0.958518i	$-0.592004\pi$
$653$	−1.58732e8			−0.570065			−0.285033	+	0.958518i	$0.592004\pi$
$654$		−	6.77060e7i		−	0.242044i
$655$	−4.58538e8			−1.63174
$656$		−	3.17740e7i		−	0.112554i
$657$			1.41961e8i			0.500580i
$658$	−3.99547e6	−	3.02014e8i	−0.0140246	−	1.06011i
$659$	−1.89027e8			−0.660491			−0.330245	−	0.943895i	$-0.607132\pi$
$659$	−1.89027e8			−0.660491			−0.330245	+	0.943895i	$0.607132\pi$
$660$	1.08250e8			0.376528
$661$			6.40868e7i			0.221904i	0.993826	+	0.110952i	$0.0353899\pi$
$661$			6.40868e7i			0.221904i	−0.993826	+	0.110952i	$0.964610\pi$
$662$	3.55177e7			0.122425
$663$		−	5.16989e6i		−	0.0177395i
$664$		−	7.24935e7i		−	0.247625i
$665$	7.26189e8	−	9.60706e6i	2.46936	−	0.0326682i
$666$	1.05896e7			0.0358472
$667$	2.66212e8			0.897119
$668$		−	1.94816e8i		−	0.653575i
$669$	1.55184e7			0.0518283
$670$		−	6.01750e8i		−	2.00075i
$671$		−	2.02929e8i		−	0.671700i
$672$	2.09010e6	+	1.57989e8i	0.00688748	+	0.520618i
$673$	−2.20177e8			−0.722314			−0.361157	−	0.932505i	$-0.617618\pi$
$673$	−2.20177e8			−0.722314			−0.361157	+	0.932505i	$0.617618\pi$
$674$	−2.78596e8			−0.909904
$675$			1.01048e8i			0.328563i
$676$	−1.56424e8			−0.506364
$677$			3.41426e8i			1.10035i	0.835050	+	0.550175i	$0.185439\pi$
$677$			3.41426e8i			1.10035i	−0.835050	+	0.550175i	$0.814561\pi$
$678$			6.25792e7i			0.200790i
$679$	−4.88894e6	−	3.69551e8i	−0.0156173	−	1.18050i
$680$	1.30816e8			0.416040
$681$	−2.19412e8			−0.694736
$682$			3.00918e8i			0.948626i
$683$	4.44791e8			1.39603			0.698014	−	0.716084i	$-0.254067\pi$
$683$	4.44791e8			1.39603			0.698014	+	0.716084i	$0.254067\pi$
$684$		−	8.24265e7i		−	0.257572i
$685$			3.01231e8i			0.937191i
$686$	2.24687e8	−	8.92160e6i	0.695995	−	0.0276357i
$687$	1.71326e8			0.528387
$688$	4.11791e7			0.126448
$689$		−	1.13025e6i		−	0.00345555i
$690$	−3.24615e8			−0.988145
$691$		−	2.82738e8i		−	0.856938i	−0.903557	−	0.428469i	$-0.859053\pi$
$691$		−	2.82738e8i		−	0.856938i	0.903557	−	0.428469i	$-0.140947\pi$
$692$			1.73713e8i			0.524219i
$693$	−8.54026e7	+	1.12983e6i	−0.256609	+	0.00339478i
$694$	−3.09132e8			−0.924837
$695$	6.19550e8			1.84553
$696$		−	1.23384e8i		−	0.365959i
$697$	−4.14904e7			−0.122532
$698$		−	3.21282e8i		−	0.944756i
$699$		−	2.63182e8i		−	0.770594i
$700$	3.01452e8	−	3.98803e6i	0.878868	−	0.0116269i
$701$	−3.07225e8			−0.891872			−0.445936	−	0.895065i	$-0.647129\pi$
$701$	−3.07225e8			−0.891872			−0.445936	+	0.895065i	$0.647129\pi$
$702$	5.94594e6			0.0171873
$703$			8.05105e7i			0.231732i
$704$	2.27870e8			0.653084
$705$			5.06654e8i			1.44592i
$706$			2.55835e8i			0.727020i
$707$	5.14647e6	+	3.89017e8i	0.0145630	+	1.10081i
$708$	8.71202e6			0.0245482
$709$	−5.44457e8			−1.52765			−0.763827	−	0.645421i	$-0.776682\pi$
$709$	−5.44457e8			−1.52765			−0.763827	+	0.645421i	$0.776682\pi$
$710$			3.24216e7i			0.0905856i
$711$	−8.24454e7			−0.229381
$712$			4.88252e8i			1.35271i
$713$			9.57532e8i			2.64171i
$714$	−3.50754e7	+	464027.i	−0.0963624	+	0.00127482i
$715$	−5.93686e7			−0.162420
$716$	−3.88227e7			−0.105766
$717$		−	3.19350e8i		−	0.866381i
$718$	4.28595e7			0.115791
$719$		−	4.85390e8i		−	1.30588i	−0.757408	−	0.652942i	$-0.773535\pi$
$719$		−	4.85390e8i		−	1.30588i	0.757408	−	0.652942i	$-0.226465\pi$
$720$			4.50620e7i			0.120729i
$721$	4.62864e6	+	3.49875e8i	0.0123494	+	0.933484i
$722$	−3.28419e8			−0.872604
$723$	−1.34210e8			−0.355115
$724$			2.23827e8i			0.589790i
$725$	−3.90837e8			−1.02561
$726$		−	6.26720e7i		−	0.163781i
$727$			1.31144e8i			0.341307i	0.985331	+	0.170653i	$0.0545878\pi$
$727$			1.31144e8i			0.341307i	−0.985331	+	0.170653i	$0.945412\pi$
$728$	−690479.	−	5.21927e7i	−0.00178960	−	0.135275i
$729$	−1.43489e7			−0.0370370
$730$	6.69539e8			1.72111
$731$		−	5.37715e7i		−	0.137658i
$732$	−1.01714e8			−0.259326
$733$			2.76794e7i			0.0702821i	0.999382	+	0.0351410i	$0.0111880\pi$
$733$			2.76794e7i			0.0702821i	−0.999382	+	0.0351410i	$0.988812\pi$
$734$		−	3.38015e8i		−	0.854766i
$735$	−3.77063e8	+	9.97840e6i	−0.949626	+	0.0251304i
$736$	5.36933e8			1.34675
$737$	−5.38037e8			−1.34403
$738$		−	4.77185e7i		−	0.118718i
$739$	1.98664e8			0.492250			0.246125	−	0.969238i	$-0.420843\pi$
$739$	1.98664e8			0.492250			0.246125	+	0.969238i	$0.420843\pi$
$740$			5.29969e7i			0.130784i
$741$			4.52058e7i			0.111107i
$742$	−7.66824e6	+	101446.i	−0.0187709	+	0.000248327i
$743$	5.97876e8			1.45762			0.728810	−	0.684716i	$-0.240074\pi$
$743$	5.97876e8			1.45762			0.728810	+	0.684716i	$0.240074\pi$
$744$	4.43799e8			1.07762
$745$		−	2.50514e8i		−	0.605847i
$746$	1.60199e8			0.385872
$747$		−	3.26080e7i		−	0.0782280i
$748$		−	3.97517e7i		−	0.0949841i
$749$	−2.33088e8	+	3.08362e6i	−0.554721	+	0.00733863i
$750$	1.97431e8			0.467985
$751$	1.69782e8			0.400841			0.200421	−	0.979710i	$-0.435769\pi$
$751$	1.69782e8			0.400841			0.200421	+	0.979710i	$0.435769\pi$
$752$			1.42483e8i			0.335050i
$753$	3.15879e8			0.739837
$754$			2.29978e7i			0.0536503i
$755$		−	2.42996e8i		−	0.564622i
$756$	566302.	+	4.28063e7i	0.00131064	+	0.0990699i
$757$	7.63371e8			1.75974			0.879869	−	0.475216i	$-0.157630\pi$
$757$	7.63371e8			1.75974			0.879869	+	0.475216i	$0.157630\pi$
$758$	−2.37426e8			−0.545157
$759$			2.90244e8i			0.663802i
$760$	−1.14387e9			−2.60576
$761$		−	3.06542e8i		−	0.695562i	−0.937576	−	0.347781i	$-0.886935\pi$
$761$		−	3.06542e8i		−	0.695562i	0.937576	−	0.347781i	$-0.113065\pi$
$762$			1.36962e8i			0.309552i
$763$	−2.67327e8	+	3.53658e6i	−0.601823	+	0.00796177i
$764$	−2.93160e8			−0.657392
$765$	5.88419e7			0.131432
$766$		−	1.07539e8i		−	0.239264i
$767$	−4.77801e6			−0.0105891
$768$		−	2.78497e8i		−	0.614804i
$769$		−	6.33269e8i		−	1.39254i	−0.717778	−	0.696272i	$-0.754841\pi$
$769$		−	6.33269e8i		−	1.39254i	0.717778	−	0.696272i	$-0.245159\pi$
$770$	5.32867e6	+	4.02789e8i	0.0116720	+	0.882279i
$771$	−1.45776e8			−0.318071
$772$	1.34311e8			0.291918
$773$		−	6.62322e8i		−	1.43394i	−0.697105	−	0.716969i	$-0.745529\pi$
$773$		−	6.62322e8i		−	1.43394i	0.697105	−	0.716969i	$-0.254471\pi$
$774$	6.18432e7			0.133373
$775$		−	1.40579e9i		−	3.02007i
$776$			5.82102e8i			1.24570i
$777$	−553138.	−	4.18112e7i	−0.00117915	−	0.0891312i
$778$	−4.30811e8			−0.914845
$779$	3.62794e8			0.767447
$780$			2.97572e7i			0.0627060i
$781$	2.89888e7			0.0608522
$782$			1.19205e8i			0.249273i
$783$		−	5.54990e7i		−	0.115611i
$784$	−1.06039e8	+	2.80616e6i	−0.220048	+	0.00582323i
$785$	−5.37261e8			−1.11065
$786$	−1.93661e8			−0.398817
$787$		−	3.68530e8i		−	0.756047i	−0.925796	−	0.378023i	$-0.876604\pi$
$787$		−	3.68530e8i		−	0.756047i	0.925796	−	0.378023i	$-0.123396\pi$
$788$	5.13796e7			0.105006
$789$		−	3.22714e8i		−	0.657033i
$790$			3.88842e8i			0.788664i
$791$	2.47084e8	−	3.26878e6i	0.499247	−	0.00660475i
$792$	1.34523e8			0.270782
$793$	5.57837e7			0.111863
$794$		−	1.98835e8i		−	0.397221i
$795$	1.28641e7			0.0256023
$796$			2.09092e8i			0.414570i
$797$		−	7.10614e8i		−	1.40365i	−0.712349	−	0.701825i	$-0.752369\pi$
$797$		−	7.10614e8i		−	1.40365i	0.712349	−	0.701825i	$-0.247631\pi$
$798$	3.06701e8	−	4.05748e6i	0.603542	−	0.00798450i
$799$	1.86054e8			0.364753
$800$	−7.88294e8			−1.53964
$801$			2.19618e8i			0.427338i
$802$	6.44947e8			1.25026
$803$		−	5.98648e8i		−	1.15618i
$804$			2.69680e8i			0.518896i
$805$	1.69560e7	+	1.28169e9i	0.0325039	+	2.45694i
$806$	−8.27204e7			−0.157982
$807$	7.70500e7			0.146606
$808$		−	6.12765e8i		−	1.16161i
$809$	2.52109e8			0.476148			0.238074	−	0.971247i	$-0.423484\pi$
$809$	2.52109e8			0.476148			0.238074	+	0.971247i	$0.423484\pi$
$810$			6.76746e7i			0.127342i
$811$			3.03162e8i			0.568344i	0.958773	+	0.284172i	$0.0917187\pi$
$811$			3.03162e8i			0.568344i	−0.958773	+	0.284172i	$0.908281\pi$
$812$	−1.65567e8	+	2.19035e6i	−0.309247	+	0.00409116i
$813$	2.14203e8			0.398615
$814$	−4.46561e7			−0.0827956
$815$			1.22505e9i			2.26298i
$816$	1.65477e7			0.0304556
$817$			4.70182e8i			0.862184i
$818$			4.42522e8i			0.808490i
$819$	−310582.	−	2.34766e7i	−0.000565359	−	0.0427350i
$820$	2.38814e8			0.433129
$821$	5.08243e8			0.918421			0.459211	−	0.888327i	$-0.348132\pi$
$821$	5.08243e8			0.918421			0.459211	+	0.888327i	$0.348132\pi$
$822$			1.27223e8i			0.229061i
$823$	2.14089e8			0.384056			0.192028	−	0.981389i	$-0.438494\pi$
$823$	2.14089e8			0.384056			0.192028	+	0.981389i	$0.438494\pi$
$824$		−	5.51109e8i		−	0.985045i
$825$		−	4.26120e8i		−	0.758874i
$826$	428853.	+	3.24166e7i	0.000760972	+	0.0575212i
$827$	−6.98578e8			−1.23509			−0.617545	−	0.786536i	$-0.711873\pi$
$827$	−6.98578e8			−1.23509			−0.617545	+	0.786536i	$0.711873\pi$
$828$	1.45479e8			0.256277
$829$			4.44146e8i			0.779584i	0.920903	+	0.389792i	$0.127453\pi$
$829$			4.44146e8i			0.779584i	−0.920903	+	0.389792i	$0.872547\pi$
$830$	−1.53791e8			−0.268966
$831$		−	3.62171e8i		−	0.631118i
$832$			6.26400e7i			0.108763i
$833$	3.66427e6	+	1.38465e8i	0.00633947	+	0.239556i
$834$	2.61663e8			0.451070
$835$	−1.21607e9			−2.08881
$836$			3.47591e8i			0.594908i
$837$	1.99623e8			0.340435
$838$			6.93547e8i			1.17854i
$839$		−	3.92031e8i		−	0.663796i	−0.943315	−	0.331898i	$-0.892311\pi$
$839$		−	3.92031e8i		−	0.663796i	0.943315	−	0.331898i	$-0.107689\pi$
$840$	5.94040e8	−	7.85880e6i	1.00225	−	0.0132592i
$841$	−3.80163e8			−0.639120
$842$	−3.63565e8			−0.609039
$843$			2.08078e8i			0.347330i
$844$	2.47442e8			0.411572
$845$			9.76419e8i			1.61833i
$846$			2.13982e8i			0.353400i
$847$	−2.47451e8	+	3.27363e6i	−0.407229	+	0.00538740i
$848$	3.61769e6			0.00593258
$849$	−1.64020e8			−0.268023
$850$		−	1.75010e8i		−	0.284975i
$851$	−1.42097e8			−0.230567
$852$		−	1.45300e7i		−	0.0234935i
$853$		−	3.13906e7i		−	0.0505770i	−0.999680	−	0.0252885i	$-0.991950\pi$
$853$		−	3.13906e7i		−	0.0505770i	0.999680	−	0.0252885i	$-0.00805043\pi$
$854$	−5.00690e6	−	3.78468e8i	−0.00803888	−	0.607652i
$855$	−5.14517e8			−0.823193
$856$	3.67151e8			0.585361
$857$			2.46373e8i			0.391427i	0.980661	+	0.195714i	$0.0627023\pi$
$857$			2.46373e8i			0.391427i	−0.980661	+	0.195714i	$0.937298\pi$
$858$	−2.50739e7			−0.0396973
$859$		−	1.69546e8i		−	0.267490i	−0.991016	−	0.133745i	$-0.957300\pi$
$859$		−	1.69546e8i		−	0.267490i	0.991016	−	0.133745i	$-0.0427002\pi$
$860$			3.09503e8i			0.486596i
$861$	−1.88409e8	+	2.49254e6i	−0.295183	+	0.00390510i
$862$	3.16847e7			0.0494684
$863$	5.35397e8			0.832997			0.416499	−	0.909136i	$-0.363257\pi$
$863$	5.35397e8			0.832997			0.416499	+	0.909136i	$0.363257\pi$
$864$		−	1.11938e8i		−	0.173555i
$865$	1.08434e9			1.67539
$866$			4.81812e7i			0.0741863i
$867$			3.54660e8i			0.544195i
$868$	−7.87844e6	−	5.95524e8i	−0.0120471	−	0.910627i
$869$	3.47671e8			0.529797
$870$	−2.61753e8			−0.397497
$871$		−	1.47903e8i		−	0.223832i
$872$	4.21083e8			0.635065
$873$			2.61833e8i			0.393534i
$874$		−	1.04234e9i		−	1.56126i
$875$	−1.03127e7	−	7.79527e8i	−0.0153939	−	1.16361i
$876$	−3.00060e8			−0.446371
$877$	1.84921e8			0.274150			0.137075	−	0.990561i	$-0.456230\pi$
$877$	1.84921e8			0.274150			0.137075	+	0.990561i	$0.456230\pi$
$878$		−	3.78557e8i		−	0.559304i
$879$	−4.86516e8			−0.716358
$880$		−	1.90026e8i		−	0.278846i
$881$		−	1.93933e8i		−	0.283612i	−0.989894	−	0.141806i	$-0.954709\pi$
$881$		−	1.93933e8i		−	0.283612i	0.989894	−	0.141806i	$-0.0452909\pi$
$882$	−1.59250e8	+	4.21432e6i	−0.232100	+	0.00614216i
$883$	−2.55437e8			−0.371023			−0.185512	−	0.982642i	$-0.559394\pi$
$883$	−2.55437e8			−0.371023			−0.185512	+	0.982642i	$0.559394\pi$
$884$	1.09275e7			0.0158184
$885$		−	5.43816e7i		−	0.0784553i
$886$	−6.81810e8			−0.980307
$887$		−	9.55493e7i		−	0.136917i	−0.997654	−	0.0684584i	$-0.978192\pi$
$887$		−	9.55493e7i		−	0.136917i	0.997654	−	0.0684584i	$-0.0218080\pi$
$888$			6.58594e7i			0.0940544i
$889$	5.40772e8	−	7.15410e6i	0.769678	−	0.0101824i
$890$	1.03580e9			1.46928
$891$	6.05092e7			0.0855437
$892$			3.28008e7i			0.0462157i
$893$	−1.62687e9			−2.28453
$894$		−	1.05803e8i		−	0.148076i
$895$			2.42337e8i			0.338026i
$896$	−2.23656e8	+	2.95884e6i	−0.310926	+	0.00411337i
$897$	−7.97862e7			−0.110548
$898$	−3.57001e7			−0.0492993
$899$			7.72107e8i			1.06267i
$900$	−2.13584e8			−0.292982
$901$		−	4.72397e6i		−	0.00645851i
$902$			2.01228e8i			0.274201i
$903$	−3.23033e6	−	2.44178e8i	−0.00438716	−	0.331622i
$904$	−3.89198e8			−0.526823
$905$	1.39716e9			1.88495
$906$		−	1.02628e8i		−	0.138000i
$907$	−3.77348e8			−0.505731			−0.252866	−	0.967501i	$-0.581373\pi$
$907$	−3.77348e8			−0.505731			−0.252866	+	0.967501i	$0.581373\pi$
$908$		−	4.63767e8i		−	0.619501i
$909$		−	2.75625e8i		−	0.366967i
$910$	−1.10724e8	+	1.46481e6i	−0.146932	+	0.00194383i
$911$	1.11171e9			1.47040			0.735202	−	0.677848i	$-0.237087\pi$
$911$	1.11171e9			1.47040			0.735202	+	0.677848i	$0.237087\pi$
$912$	−1.44694e8			−0.190751
$913$			1.37508e8i			0.180682i
$914$	−1.24642e8			−0.163239
$915$			6.34911e8i			0.828799i
$916$			3.62127e8i			0.471167i
$917$	1.01157e7	+	7.64638e8i	0.0131186	+	0.991626i
$918$	2.48515e7			0.0321236
$919$	2.08706e8			0.268898			0.134449	−	0.990920i	$-0.457073\pi$
$919$	2.08706e8			0.268898			0.134449	+	0.990920i	$0.457073\pi$
$920$		−	2.01887e9i		−	2.59265i
$921$	−2.67192e8			−0.342015
$922$			6.53543e8i			0.833838i
$923$			7.96882e6i			0.0101342i
$924$	−2.38809e6	−	1.80513e8i	−0.00302715	−	0.228820i
$925$	2.08619e8			0.263590
$926$	5.14764e8			0.648299
$927$		−	2.47892e8i		−	0.311189i
$928$	4.32956e8			0.541751
$929$			3.29239e8i			0.410642i	0.978695	+	0.205321i	$0.0658239\pi$
$929$			3.29239e8i			0.410642i	−0.978695	+	0.205321i	$0.934176\pi$
$930$		−	9.41495e8i		−	1.17049i
$931$	−3.20407e7	−	1.21075e9i	−0.0397057	−	1.50040i
$932$	5.56283e8			0.687144
$933$	2.87209e8			0.353633
$934$		−	2.36451e8i		−	0.290202i
$935$	−2.48135e8			−0.303567
$936$			3.69794e7i			0.0450955i
$937$		−	1.02957e8i		−	0.125151i	−0.998040	−	0.0625756i	$-0.980069\pi$
$937$		−	1.02957e8i		−	0.125151i	0.998040	−	0.0625756i	$-0.0199315\pi$
$938$	−1.00345e9	+	1.32751e7i	−1.21588	+	0.0160853i
$939$	−2.33619e8			−0.282171
$940$	−1.07090e9			−1.28934
$941$		−	8.83375e8i		−	1.06017i	−0.847944	−	0.530086i	$-0.822160\pi$
$941$		−	8.83375e8i		−	1.06017i	0.847944	−	0.530086i	$-0.177840\pi$
$942$	−2.26909e8			−0.271456
$943$			6.40315e8i			0.763587i
$944$		−	1.52934e7i		−	0.0181797i
$945$	2.67203e8	−	3.53493e6i	0.316625	−	0.00418876i
$946$	−2.60792e8			−0.308050
$947$	3.27614e8			0.385756			0.192878	−	0.981223i	$-0.438218\pi$
$947$	3.27614e8			0.385756			0.192878	+	0.981223i	$0.438218\pi$
$948$		−	1.74263e8i		−	0.204541i
$949$	1.64564e8			0.192547
$950$			1.53030e9i			1.78487i
$951$			4.47498e8i			0.520295i
$952$	−2.88591e6	−	2.18144e8i	−0.00334482	−	0.252832i
$953$	−6.09231e8			−0.703887			−0.351944	−	0.936021i	$-0.614479\pi$
$953$	−6.09231e8			−0.703887			−0.351944	+	0.936021i	$0.614479\pi$
$954$	5.43308e6			0.00625750
$955$			1.82994e9i			2.10101i
$956$	6.75002e8			0.772558
$957$			2.34039e8i			0.267025i
$958$			2.83631e8i			0.322595i
$959$	5.02320e8	−	6.64540e6i	0.569541	−	0.00753469i
$960$	−7.12946e8			−0.805830
$961$	−1.88967e9			−2.12920
$962$		−	1.22757e7i		−	0.0137886i
$963$	1.65147e8			0.184923
$964$		−	2.83676e8i		−	0.316659i
$965$		−	8.38390e8i		−	0.932962i
$966$	7.16126e6	+	5.41314e8i	0.00794435	+	0.600507i
$967$	−2.63834e8			−0.291777			−0.145889	−	0.989301i	$-0.546604\pi$
$967$	−2.63834e8			−0.291777			−0.145889	+	0.989301i	$0.546604\pi$
$968$	3.89775e8			0.429722
$969$			1.88941e8i			0.207661i
$970$	1.23490e9			1.35306
$971$			3.75022e8i			0.409637i	0.978800	+	0.204818i	$0.0656604\pi$
$971$			3.75022e8i			0.409637i	−0.978800	+	0.204818i	$0.934340\pi$
$972$		−	3.03290e7i		−	0.0330262i
$973$	−1.36678e7	−	1.03314e9i	−0.0148375	−	1.12155i
$974$	6.26645e8			0.678179
$975$	1.17137e8			0.126381
$976$			1.78552e8i			0.192050i
$977$	−1.19688e9			−1.28341			−0.641705	−	0.766951i	$-0.721773\pi$
$977$	−1.19688e9			−1.28341			−0.641705	+	0.766951i	$0.721773\pi$
$978$			5.17392e8i			0.553099i
$979$		−	9.26128e8i		−	0.987013i
$980$	−2.10911e7	−	7.96990e8i	−0.0224089	−	0.846788i
$981$	1.89405e8			0.200625
$982$	9.95906e8			1.05168
$983$			1.68493e9i			1.77387i	0.461894	+	0.886935i	$0.347170\pi$
$983$			1.68493e9i			1.77387i	−0.461894	+	0.886935i	$0.652830\pi$
$984$	2.96774e8			0.311488
$985$		−	3.20719e8i		−	0.335595i
$986$			9.61211e7i			0.100274i
$987$	8.44876e8	−	1.11772e7i	0.878701	−	0.0116247i
$988$	−9.55505e7			−0.0990746
$989$	−8.29849e8			−0.857848
$990$		−	2.85383e8i		−	0.294119i
$991$	6.07265e8			0.623960			0.311980	−	0.950089i	$-0.399008\pi$
$991$	6.07265e8			0.623960			0.311980	+	0.950089i	$0.399008\pi$
$992$			1.55729e9i			1.59527i
$993$			9.93596e7i			0.101476i
$994$	5.40649e7	−	715247.i	0.0550498	−	0.000728277i
$995$	1.30518e9			1.32496
$996$	6.89228e7			0.0697565
$997$		−	4.56005e8i		−	0.460134i	−0.973175	−	0.230067i	$-0.926106\pi$
$997$		−	4.56005e8i		−	0.460134i	0.973175	−	0.230067i	$-0.0738945\pi$
$998$	2.87222e7			0.0288952
$999$			2.96240e7i			0.0297130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.7.d.a.13.6	yes	8
3.2	odd	2		63.7.d.f.55.3		8
4.3	odd	2		336.7.f.a.97.4		8
7.2	even	3		147.7.f.b.31.2		8
7.3	odd	6		147.7.f.b.19.2		8
7.4	even	3		147.7.f.c.19.2		8
7.5	odd	6		147.7.f.c.31.2		8
7.6	odd	2	inner	21.7.d.a.13.5	✓	8
21.20	even	2		63.7.d.f.55.4		8
28.27	even	2		336.7.f.a.97.5		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.7.d.a.13.5	✓	8	7.6	odd	2	inner
21.7.d.a.13.6	yes	8	1.1	even	1	trivial
63.7.d.f.55.3		8	3.2	odd	2
63.7.d.f.55.4		8	21.20	even	2
147.7.f.b.19.2		8	7.3	odd	6
147.7.f.b.31.2		8	7.2	even	3
147.7.f.c.19.2		8	7.4	even	3
147.7.f.c.31.2		8	7.5	odd	6
336.7.f.a.97.4		8	4.3	odd	2
336.7.f.a.97.5		8	28.27	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	21.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+5.57235 q^{2} +15.5885i q^{3} -32.9490 q^{4} +205.672i q^{5} +86.8643i q^{6} +(342.970 - 4.53729i) q^{7} -540.233 q^{8} -243.000 q^{9} +O(q^{10})\)	\(q+5.57235 q^{2} +15.5885i q^{3} -32.9490 q^{4} +205.672i q^{5} +86.8643i q^{6} +(342.970 - 4.53729i) q^{7} -540.233 q^{8} -243.000 q^{9} +1146.08i q^{10} +1024.73 q^{11} -513.624i q^{12} +281.691i q^{13} +(1911.15 - 25.2834i) q^{14} -3206.11 q^{15} -901.632 q^{16} +1177.35i q^{17} -1354.08 q^{18} -10294.8i q^{19} -6776.68i q^{20} +(70.7294 + 5346.37i) q^{21} +5710.14 q^{22} +18169.9 q^{23} -8421.40i q^{24} -26676.0 q^{25} +1569.68i q^{26} -3788.00i q^{27} +(-11300.5 + 149.499i) q^{28} +14651.3 q^{29} -17865.5 q^{30} +52698.9i q^{31} +29550.7 q^{32} +15973.9i q^{33} +6560.59i q^{34} +(933.194 + 70539.3i) q^{35} +8006.60 q^{36} -7820.49 q^{37} -57366.3i q^{38} -4391.13 q^{39} -111111. i q^{40} +35240.5i q^{41} +(394.129 + 29791.8i) q^{42} -45671.7 q^{43} -33763.7 q^{44} -49978.3i q^{45} +101249. q^{46} -158028. i q^{47} -14055.1i q^{48} +(117608. - 3112.31i) q^{49} -148648. q^{50} -18353.1 q^{51} -9281.42i q^{52} -4012.38 q^{53} -21108.0i q^{54} +210758. i q^{55} +(-185284. + 2451.20i) q^{56} +160480. q^{57} +81642.0 q^{58} +16961.9i q^{59} +105638. q^{60} -198032. i q^{61} +293657. i q^{62} +(-83341.7 + 1102.56i) q^{63} +222371. q^{64} -57935.9 q^{65} +89012.3i q^{66} -525053. q^{67} -38792.4i q^{68} +283240. i q^{69} +(5200.08 + 393069. i) q^{70} +28289.2 q^{71} +131277. q^{72} -584202. i q^{73} -43578.4 q^{74} -415837. i q^{75} +339204. i q^{76} +(351451. - 4649.49i) q^{77} -24468.9 q^{78} +339282. q^{79} -185440. i q^{80} +59049.0 q^{81} +196372. i q^{82} +134189. i q^{83} +(-2330.46 - 176157. i) q^{84} -242148. q^{85} -254499. q^{86} +228391. i q^{87} -553592. q^{88} -903779. i q^{89} -278496. i q^{90} +(1278.11 + 96611.5i) q^{91} -598678. q^{92} -821495. q^{93} -880586. i q^{94} +2.11735e6 q^{95} +460650. i q^{96} -1.07750e6i q^{97} +(655351. - 17342.9i) q^{98} -249009. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 10 q^{2} + 346 q^{4} + 28 q^{7} - 1462 q^{8} - 1944 q^{9}+O(q^{10}) \) 8 * q + 10 * q^2 + 346 * q^4 + 28 * q^7 - 1462 * q^8 - 1944 * q^9	\( 8 q + 10 q^{2} + 346 q^{4} + 28 q^{7} - 1462 q^{8} - 1944 q^{9} - 6848 q^{11} + 12082 q^{14} - 4536 q^{15} + 28466 q^{16} - 2430 q^{18} + 6804 q^{21} - 7764 q^{22} - 24320 q^{23} - 77056 q^{25} - 30142 q^{28} + 60496 q^{29} + 89424 q^{30} + 5082 q^{32} + 103656 q^{35} - 84078 q^{36} - 39112 q^{37} + 108864 q^{39} - 267624 q^{42} - 29272 q^{43} - 577884 q^{44} + 564972 q^{46} - 94864 q^{49} + 240154 q^{50} + 103032 q^{51} + 232288 q^{53} + 225722 q^{56} + 180792 q^{57} + 987684 q^{58} - 375192 q^{60} - 6804 q^{63} - 690734 q^{64} - 836304 q^{65} - 2163848 q^{67} - 366744 q^{70} - 506288 q^{71} + 355266 q^{72} + 512324 q^{74} + 1536304 q^{77} + 1272024 q^{78} - 93272 q^{79} + 472392 q^{81} - 653184 q^{84} + 3740760 q^{85} + 3846452 q^{86} - 2077548 q^{88} + 1890336 q^{91} - 9701580 q^{92} - 2153952 q^{93} + 4154832 q^{95} - 507542 q^{98} + 1664064 q^{99}+O(q^{100}) \) 8 * q + 10 * q^2 + 346 * q^4 + 28 * q^7 - 1462 * q^8 - 1944 * q^9 - 6848 * q^11 + 12082 * q^14 - 4536 * q^15 + 28466 * q^16 - 2430 * q^18 + 6804 * q^21 - 7764 * q^22 - 24320 * q^23 - 77056 * q^25 - 30142 * q^28 + 60496 * q^29 + 89424 * q^30 + 5082 * q^32 + 103656 * q^35 - 84078 * q^36 - 39112 * q^37 + 108864 * q^39 - 267624 * q^42 - 29272 * q^43 - 577884 * q^44 + 564972 * q^46 - 94864 * q^49 + 240154 * q^50 + 103032 * q^51 + 232288 * q^53 + 225722 * q^56 + 180792 * q^57 + 987684 * q^58 - 375192 * q^60 - 6804 * q^63 - 690734 * q^64 - 836304 * q^65 - 2163848 * q^67 - 366744 * q^70 - 506288 * q^71 + 355266 * q^72 + 512324 * q^74 + 1536304 * q^77 + 1272024 * q^78 - 93272 * q^79 + 472392 * q^81 - 653184 * q^84 + 3740760 * q^85 + 3846452 * q^86 - 2077548 * q^88 + 1890336 * q^91 - 9701580 * q^92 - 2153952 * q^93 + 4154832 * q^95 - 507542 * q^98 + 1664064 * q^99

Introduction

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