LMFDB - Embedded newform 230.5.f.b.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,Mod(47,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	230.f (of order $4$, 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:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.3
Character	$\chi$	$=$	230.47
Dual form			230.5.f.b.93.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 2.00000i) q^{2} +(-9.95475 + 9.95475i) q^{3} +8.00000i q^{4} +(24.5881 + 4.51957i) q^{5} -39.8190 q^{6} +(-57.5399 - 57.5399i) q^{7} +(-16.0000 + 16.0000i) q^{8} -117.194i q^{9} +O(q^{10})$	\(q+(2.00000 + 2.00000i) q^{2} +(-9.95475 + 9.95475i) q^{3} +8.00000i q^{4} +(24.5881 + 4.51957i) q^{5} -39.8190 q^{6} +(-57.5399 - 57.5399i) q^{7} +(-16.0000 + 16.0000i) q^{8} -117.194i q^{9} +(40.1370 + 58.2153i) q^{10} +214.043 q^{11} +(-79.6380 - 79.6380i) q^{12} +(138.593 - 138.593i) q^{13} -230.160i q^{14} +(-289.759 + 199.777i) q^{15} -64.0000 q^{16} +(-226.471 - 226.471i) q^{17} +(234.388 - 234.388i) q^{18} -426.409i q^{19} +(-36.1566 + 196.705i) q^{20} +1145.59 q^{21} +(428.085 + 428.085i) q^{22} +(77.9968 - 77.9968i) q^{23} -318.552i q^{24} +(584.147 + 222.255i) q^{25} +554.372 q^{26} +(360.303 + 360.303i) q^{27} +(460.320 - 460.320i) q^{28} +669.108i q^{29} +(-979.073 - 179.965i) q^{30} -1037.73 q^{31} +(-128.000 - 128.000i) q^{32} +(-2130.74 + 2130.74i) q^{33} -905.883i q^{34} +(-1154.74 - 1674.85i) q^{35} +937.553 q^{36} +(431.277 + 431.277i) q^{37} +(852.818 - 852.818i) q^{38} +2759.32i q^{39} +(-465.722 + 321.096i) q^{40} +2571.74 q^{41} +(2291.18 + 2291.18i) q^{42} +(-431.207 + 431.207i) q^{43} +1712.34i q^{44} +(529.667 - 2881.58i) q^{45} +311.987 q^{46} +(-916.680 - 916.680i) q^{47} +(637.104 - 637.104i) q^{48} +4220.69i q^{49} +(723.784 + 1612.80i) q^{50} +4508.92 q^{51} +(1108.74 + 1108.74i) q^{52} +(2793.19 - 2793.19i) q^{53} +1441.21i q^{54} +(5262.90 + 967.380i) q^{55} +1841.28 q^{56} +(4244.80 + 4244.80i) q^{57} +(-1338.22 + 1338.22i) q^{58} -4821.51i q^{59} +(-1598.22 - 2318.07i) q^{60} -1707.70 q^{61} +(-2075.46 - 2075.46i) q^{62} +(-6743.34 + 6743.34i) q^{63} -512.000i q^{64} +(4034.11 - 2781.35i) q^{65} -8522.96 q^{66} +(450.780 + 450.780i) q^{67} +(1811.77 - 1811.77i) q^{68} +1552.88i q^{69} +(1040.22 - 5659.19i) q^{70} +2774.41 q^{71} +(1875.11 + 1875.11i) q^{72} +(4928.95 - 4928.95i) q^{73} +1725.11i q^{74} +(-8027.53 + 3602.54i) q^{75} +3411.27 q^{76} +(-12316.0 - 12316.0i) q^{77} +(-5518.63 + 5518.63i) q^{78} +7580.89i q^{79} +(-1573.64 - 289.252i) q^{80} +2319.26 q^{81} +(5143.47 + 5143.47i) q^{82} +(-1646.21 + 1646.21i) q^{83} +9164.73i q^{84} +(-4544.93 - 6592.03i) q^{85} -1724.83 q^{86} +(-6660.81 - 6660.81i) q^{87} +(-3424.68 + 3424.68i) q^{88} -3151.55i q^{89} +(6822.49 - 4703.82i) q^{90} -15949.3 q^{91} +(623.974 + 623.974i) q^{92} +(10330.3 - 10330.3i) q^{93} -3666.72i q^{94} +(1927.19 - 10484.6i) q^{95} +2548.42 q^{96} +(-5514.87 - 5514.87i) q^{97} +(-8441.38 + 8441.38i) q^{98} -25084.5i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8}+O(q^{10}) $ 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8	$ 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8} - 136 q^{10} - 632 q^{11} + 500 q^{13} + 12 q^{15} - 2816 q^{16} + 120 q^{17} + 2648 q^{18} - 736 q^{20} - 856 q^{21} - 1264 q^{22} + 2052 q^{25} + 2000 q^{26} + 588 q^{27} + 640 q^{28} - 1704 q^{30} + 3220 q^{31} - 5632 q^{32} - 2884 q^{33} + 720 q^{35} + 10592 q^{36} + 1856 q^{37} - 1696 q^{38} - 1856 q^{40} - 5156 q^{41} - 1712 q^{42} + 960 q^{43} + 460 q^{45} - 1224 q^{47} + 4456 q^{50} + 3640 q^{51} + 4000 q^{52} + 13556 q^{53} + 12980 q^{55} + 2560 q^{56} - 3072 q^{57} - 3112 q^{58} - 6912 q^{60} - 4864 q^{61} + 6440 q^{62} - 13484 q^{63} - 4100 q^{65} - 11536 q^{66} - 1888 q^{67} - 960 q^{68} + 8824 q^{70} - 1060 q^{71} + 21184 q^{72} + 16616 q^{73} - 11044 q^{75} - 6784 q^{76} + 8892 q^{77} - 23152 q^{78} - 1536 q^{80} - 4044 q^{81} - 10312 q^{82} - 27024 q^{83} - 11068 q^{85} + 3840 q^{86} - 8392 q^{87} + 10112 q^{88} - 7184 q^{90} - 54024 q^{91} + 22528 q^{93} - 25968 q^{95} - 3252 q^{97} - 27984 q^{98}+O(q^{100}) $ 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8 - 136 * q^10 - 632 * q^11 + 500 * q^13 + 12 * q^15 - 2816 * q^16 + 120 * q^17 + 2648 * q^18 - 736 * q^20 - 856 * q^21 - 1264 * q^22 + 2052 * q^25 + 2000 * q^26 + 588 * q^27 + 640 * q^28 - 1704 * q^30 + 3220 * q^31 - 5632 * q^32 - 2884 * q^33 + 720 * q^35 + 10592 * q^36 + 1856 * q^37 - 1696 * q^38 - 1856 * q^40 - 5156 * q^41 - 1712 * q^42 + 960 * q^43 + 460 * q^45 - 1224 * q^47 + 4456 * q^50 + 3640 * q^51 + 4000 * q^52 + 13556 * q^53 + 12980 * q^55 + 2560 * q^56 - 3072 * q^57 - 3112 * q^58 - 6912 * q^60 - 4864 * q^61 + 6440 * q^62 - 13484 * q^63 - 4100 * q^65 - 11536 * q^66 - 1888 * q^67 - 960 * q^68 + 8824 * q^70 - 1060 * q^71 + 21184 * q^72 + 16616 * q^73 - 11044 * q^75 - 6784 * q^76 + 8892 * q^77 - 23152 * q^78 - 1536 * q^80 - 4044 * q^81 - 10312 * q^82 - 27024 * q^83 - 11068 * q^85 + 3840 * q^86 - 8392 * q^87 + 10112 * q^88 - 7184 * q^90 - 54024 * q^91 + 22528 * q^93 - 25968 * q^95 - 3252 * q^97 - 27984 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$2$	2.00000	+	2.00000i	0.500000	+	0.500000i
$3$	−9.95475	+	9.95475i	−1.10608	+	1.10608i	−0.112423	+	0.993660i	$0.535861\pi$
$3$	−9.95475	+	9.95475i	−1.10608	+	1.10608i	−0.993660	+	0.112423i	$0.964139\pi$
$4$			8.00000i			0.500000i
$5$	24.5881	+	4.51957i	0.983523	+	0.180783i
$5$	24.5881	+	4.51957i	0.983523	+	0.180783i
$6$	−39.8190			−1.10608
$7$	−57.5399	−	57.5399i	−1.17428	−	1.17428i	−0.981178	−	0.193107i	$-0.938144\pi$
$7$	−57.5399	−	57.5399i	−1.17428	−	1.17428i	−0.193107	−	0.981178i	$-0.561856\pi$
$8$	−16.0000	+	16.0000i	−0.250000	+	0.250000i
$9$		−	117.194i		−	1.44684i
$10$	40.1370	+	58.2153i	0.401370	+	0.582153i
$11$	214.043			1.76895			0.884474	−	0.466590i	$-0.154518\pi$
$11$	214.043			1.76895			0.884474	+	0.466590i	$0.154518\pi$
$12$	−79.6380	−	79.6380i	−0.553042	−	0.553042i
$13$	138.593	−	138.593i	0.820077	−	0.820077i	−0.166042	−	0.986119i	$-0.553099\pi$
$13$	138.593	−	138.593i	0.820077	−	0.820077i	0.986119	+	0.166042i	$0.0530987\pi$
$14$		−	230.160i		−	1.17428i
$15$	−289.759	+	199.777i	−1.28782	+	0.887898i
$16$	−64.0000			−0.250000
$17$	−226.471	−	226.471i	−0.783636	−	0.783636i	0.196807	−	0.980442i	$-0.436943\pi$
$17$	−226.471	−	226.471i	−0.783636	−	0.783636i	−0.980442	+	0.196807i	$0.936943\pi$
$18$	234.388	−	234.388i	0.723420	−	0.723420i
$19$		−	426.409i		−	1.18119i	−0.806969	−	0.590594i	$-0.798893\pi$
$19$		−	426.409i		−	1.18119i	0.806969	−	0.590594i	$-0.201107\pi$
$20$	−36.1566	+	196.705i	−0.0903914	+	0.491762i
$21$	1145.59			2.59771
$22$	428.085	+	428.085i	0.884474	+	0.884474i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$24$		−	318.552i		−	0.553042i
$25$	584.147	+	222.255i	0.934635	+	0.355608i
$26$	554.372			0.820077
$27$	360.303	+	360.303i	0.494243	+	0.494243i
$28$	460.320	−	460.320i	0.587142	−	0.587142i
$29$			669.108i			0.795610i	0.917470	+	0.397805i	$0.130228\pi$
$29$			669.108i			0.795610i	−0.917470	+	0.397805i	$0.869772\pi$
$30$	−979.073	−	179.965i	−1.08786	−	0.199961i
$31$	−1037.73			−1.07984			−0.539921	−	0.841716i	$-0.681546\pi$
$31$	−1037.73			−1.07984			−0.539921	+	0.841716i	$0.681546\pi$
$32$	−128.000	−	128.000i	−0.125000	−	0.125000i
$33$	−2130.74	+	2130.74i	−1.95660	+	1.95660i
$34$		−	905.883i		−	0.783636i
$35$	−1154.74	−	1674.85i	−0.942646	−	1.36723i
$36$	937.553			0.723420
$37$	431.277	+	431.277i	0.315031	+	0.315031i	0.846855	−	0.531824i	$-0.178493\pi$
$37$	431.277	+	431.277i	0.315031	+	0.315031i	−0.531824	+	0.846855i	$0.678493\pi$
$38$	852.818	−	852.818i	0.590594	−	0.590594i
$39$			2759.32i			1.81415i
$40$	−465.722	+	321.096i	−0.291076	+	0.200685i
$41$	2571.74			1.52989			0.764943	−	0.644098i	$-0.222767\pi$
$41$	2571.74			1.52989			0.764943	+	0.644098i	$0.222767\pi$
$42$	2291.18	+	2291.18i	1.29886	+	1.29886i
$43$	−431.207	+	431.207i	−0.233211	+	0.233211i	−0.814032	−	0.580820i	$-0.802732\pi$
$43$	−431.207	+	431.207i	−0.233211	+	0.233211i	0.580820	+	0.814032i	$0.302732\pi$
$44$			1712.34i			0.884474i
$45$	529.667	−	2881.58i	0.261564	−	1.42300i
$46$	311.987			0.147442
$47$	−916.680	−	916.680i	−0.414975	−	0.414975i	0.468492	−	0.883468i	$-0.344797\pi$
$47$	−916.680	−	916.680i	−0.414975	−	0.414975i	−0.883468	+	0.468492i	$0.844797\pi$
$48$	637.104	−	637.104i	0.276521	−	0.276521i
$49$			4220.69i			1.75789i
$50$	723.784	+	1612.80i	0.289514	+	0.645122i
$51$	4508.92			1.73353
$52$	1108.74	+	1108.74i	0.410038	+	0.410038i
$53$	2793.19	−	2793.19i	0.994372	−	0.994372i	−0.00561243	−	0.999984i	$-0.501787\pi$
$53$	2793.19	−	2793.19i	0.994372	−	0.994372i	0.999984	+	0.00561243i	$0.00178650\pi$
$54$			1441.21i			0.494243i
$55$	5262.90	+	967.380i	1.73980	+	0.319795i
$56$	1841.28			0.587142
$57$	4244.80	+	4244.80i	1.30649	+	1.30649i
$58$	−1338.22	+	1338.22i	−0.397805	+	0.397805i
$59$		−	4821.51i		−	1.38509i	−0.721373	−	0.692547i	$-0.756489\pi$
$59$		−	4821.51i		−	1.38509i	0.721373	−	0.692547i	$-0.243511\pi$
$60$	−1598.22	−	2318.07i	−0.443949	−	0.643910i
$61$	−1707.70			−0.458937			−0.229468	−	0.973316i	$-0.573699\pi$
$61$	−1707.70			−0.458937			−0.229468	+	0.973316i	$0.573699\pi$
$62$	−2075.46	−	2075.46i	−0.539921	−	0.539921i
$63$	−6743.34	+	6743.34i	−1.69900	+	1.69900i
$64$		−	512.000i		−	0.125000i
$65$	4034.11	−	2781.35i	0.954820	−	0.658309i
$66$	−8522.96			−1.95660
$67$	450.780	+	450.780i	0.100419	+	0.100419i	0.755531	−	0.655113i	$-0.227379\pi$
$67$	450.780	+	450.780i	0.100419	+	0.100419i	−0.655113	+	0.755531i	$0.727379\pi$
$68$	1811.77	−	1811.77i	0.391818	−	0.391818i
$69$			1552.88i			0.326166i
$70$	1040.22	−	5659.19i	0.212290	−	1.15494i
$71$	2774.41			0.550370			0.275185	−	0.961391i	$-0.411261\pi$
$71$	2774.41			0.550370			0.275185	+	0.961391i	$0.411261\pi$
$72$	1875.11	+	1875.11i	0.361710	+	0.361710i
$73$	4928.95	−	4928.95i	0.924929	−	0.924929i	−0.0724435	−	0.997373i	$-0.523080\pi$
$73$	4928.95	−	4928.95i	0.924929	−	0.924929i	0.997373	+	0.0724435i	$0.0230797\pi$
$74$			1725.11i			0.315031i
$75$	−8027.53	+	3602.54i	−1.42712	+	0.640452i
$76$	3411.27			0.590594
$77$	−12316.0	−	12316.0i	−2.07725	−	2.07725i
$78$	−5518.63	+	5518.63i	−0.907073	+	0.907073i
$79$			7580.89i			1.21469i	0.794438	+	0.607346i	$0.207766\pi$
$79$			7580.89i			1.21469i	−0.794438	+	0.607346i	$0.792234\pi$
$80$	−1573.64	−	289.252i	−0.245881	−	0.0451957i
$81$	2319.26			0.353493
$82$	5143.47	+	5143.47i	0.764943	+	0.764943i
$83$	−1646.21	+	1646.21i	−0.238962	+	0.238962i	−0.816420	−	0.577458i	$-0.804045\pi$
$83$	−1646.21	+	1646.21i	−0.238962	+	0.238962i	0.577458	+	0.816420i	$0.304045\pi$
$84$			9164.73i			1.29886i
$85$	−4544.93	−	6592.03i	−0.629056	−	0.912392i
$86$	−1724.83			−0.233211
$87$	−6660.81	−	6660.81i	−0.880011	−	0.880011i
$88$	−3424.68	+	3424.68i	−0.442237	+	0.442237i
$89$		−	3151.55i		−	0.397872i	−0.980012	−	0.198936i	$-0.936251\pi$
$89$		−	3151.55i		−	0.397872i	0.980012	−	0.198936i	$-0.0637486\pi$
$90$	6822.49	−	4703.82i	0.842283	−	0.580719i
$91$	−15949.3			−1.92601
$92$	623.974	+	623.974i	0.0737210	+	0.0737210i
$93$	10330.3	−	10330.3i	1.19440	−	1.19440i
$94$		−	3666.72i		−	0.414975i
$95$	1927.19	−	10484.6i	0.213539	−	1.16173i
$96$	2548.42			0.276521
$97$	−5514.87	−	5514.87i	−0.586128	−	0.586128i	0.350453	−	0.936580i	$-0.386028\pi$
$97$	−5514.87	−	5514.87i	−0.586128	−	0.586128i	−0.936580	+	0.350453i	$0.886028\pi$
$98$	−8441.38	+	8441.38i	−0.878944	+	0.878944i
$99$		−	25084.5i		−	2.55938i
$100$	−1778.04	+	4673.18i	−0.177804	+	0.467318i
$101$	7113.39			0.697323			0.348661	−	0.937249i	$-0.386636\pi$
$101$	7113.39			0.697323			0.348661	+	0.937249i	$0.386636\pi$
$102$	9017.84	+	9017.84i	0.866766	+	0.866766i
$103$	−6700.83	+	6700.83i	−0.631618	+	0.631618i	−0.948474	−	0.316856i	$-0.897373\pi$
$103$	−6700.83	+	6700.83i	−0.631618	+	0.631618i	0.316856	+	0.948474i	$0.397373\pi$
$104$			4434.97i			0.410038i
$105$	28167.9	+	5177.58i	2.55491	+	0.469622i
$106$	11172.8			0.994372
$107$	−13632.0	−	13632.0i	−1.19067	−	1.19067i	−0.976880	−	0.213790i	$-0.931419\pi$
$107$	−13632.0	−	13632.0i	−1.19067	−	1.19067i	−0.213790	−	0.976880i	$-0.568581\pi$
$108$	−2882.43	+	2882.43i	−0.247122	+	0.247122i
$109$			5335.81i			0.449104i	0.974462	+	0.224552i	$0.0720919\pi$
$109$			5335.81i			0.449104i	−0.974462	+	0.224552i	$0.927908\pi$
$110$	8591.03	+	12460.6i	0.710002	+	1.02980i
$111$	−8586.51			−0.696900
$112$	3682.56	+	3682.56i	0.293571	+	0.293571i
$113$	237.694	−	237.694i	0.0186149	−	0.0186149i	−0.697738	−	0.716353i	$-0.745810\pi$
$113$	237.694	−	237.694i	0.0186149	−	0.0186149i	0.716353	+	0.697738i	$0.245810\pi$
$114$			16979.2i			1.30649i
$115$	2270.30	−	1565.28i	0.171668	−	0.118358i
$116$	−5352.87			−0.397805
$117$	−16242.3	−	16242.3i	−1.18652	−	1.18652i
$118$	9643.02	−	9643.02i	0.692547	−	0.692547i
$119$			26062.2i			1.84042i
$120$	1439.72	−	7832.58i	0.0999804	−	0.543929i
$121$	31173.2			2.12917
$122$	−3415.41	−	3415.41i	−0.229468	−	0.229468i
$123$	−25601.0	+	25601.0i	−1.69218	+	1.69218i
$124$		−	8301.83i		−	0.539921i
$125$	13358.6	+	8104.92i	0.854947	+	0.518715i
$126$	−26973.4			−1.69900
$127$	−5523.97	−	5523.97i	−0.342487	−	0.342487i	0.514815	−	0.857301i	$-0.327861\pi$
$127$	−5523.97	−	5523.97i	−0.342487	−	0.342487i	−0.857301	+	0.514815i	$0.827861\pi$
$128$	1024.00	−	1024.00i	0.0625000	−	0.0625000i
$129$		−	8585.13i		−	0.515902i
$130$	13630.9	+	2505.52i	0.806564	+	0.148256i
$131$	28958.9			1.68748			0.843742	−	0.536749i	$-0.180348\pi$
$131$	28958.9			1.68748			0.843742	+	0.536749i	$0.180348\pi$
$132$	−17045.9	−	17045.9i	−0.978301	−	0.978301i
$133$	−24535.6	+	24535.6i	−1.38705	+	1.38705i
$134$			1803.12i			0.100419i
$135$	7230.75	+	10487.6i	0.396749	+	0.575450i
$136$	7247.06			0.391818
$137$	−13866.9	−	13866.9i	−0.738822	−	0.738822i	0.233528	−	0.972350i	$-0.424973\pi$
$137$	−13866.9	−	13866.9i	−0.738822	−	0.738822i	−0.972350	+	0.233528i	$0.924973\pi$
$138$	−3105.75	+	3105.75i	−0.163083	+	0.163083i
$139$		−	16170.6i		−	0.836945i	−0.908230	−	0.418472i	$-0.862566\pi$
$139$		−	16170.6i		−	0.836945i	0.908230	−	0.418472i	$-0.137434\pi$
$140$	13398.8	−	9237.93i	0.683613	−	0.471323i
$141$	18250.6			0.917994
$142$	5548.83	+	5548.83i	0.275185	+	0.275185i
$143$	29664.8	−	29664.8i	1.45067	−	1.45067i
$144$			7500.42i			0.361710i
$145$	−3024.08	+	16452.1i	−0.143833	+	0.782501i
$146$	19715.8			0.924929
$147$	−42015.9	−	42015.9i	−1.94437	−	1.94437i
$148$	−3450.21	+	3450.21i	−0.157515	+	0.157515i
$149$		−	11633.8i		−	0.524020i	−0.965065	−	0.262010i	$-0.915615\pi$
$149$		−	11633.8i		−	0.524020i	0.965065	−	0.262010i	$-0.0843854\pi$
$150$	−23260.1	−	8849.97i	−1.03378	−	0.393332i
$151$	−16842.1			−0.738654			−0.369327	−	0.929299i	$-0.620412\pi$
$151$	−16842.1			−0.738654			−0.369327	+	0.929299i	$0.620412\pi$
$152$	6822.55	+	6822.55i	0.295297	+	0.295297i
$153$	−26541.0	+	26541.0i	−1.13380	+	1.13380i
$154$		−	49264.0i		−	2.07725i
$155$	−25515.8	−	4690.09i	−1.06205	−	0.195217i
$156$	−22074.5			−0.907073
$157$	6925.16	+	6925.16i	0.280951	+	0.280951i	0.833488	−	0.552537i	$-0.186340\pi$
$157$	6925.16	+	6925.16i	0.280951	+	0.280951i	−0.552537	+	0.833488i	$0.686340\pi$
$158$	−15161.8	+	15161.8i	−0.607346	+	0.607346i
$159$			55611.0i			2.19972i
$160$	−2568.77	−	3725.78i	−0.100343	−	0.145538i
$161$	−8975.86			−0.346278
$162$	4638.53	+	4638.53i	0.176746	+	0.176746i
$163$	36271.0	−	36271.0i	1.36516	−	1.36516i	0.497969	−	0.867195i	$-0.334079\pi$
$163$	36271.0	−	36271.0i	1.36516	−	1.36516i	0.867195	−	0.497969i	$-0.165921\pi$
$164$			20573.9i			0.764943i
$165$	−62020.8	+	42760.8i	−2.27808	+	1.57064i
$166$	−6584.85			−0.238962
$167$	19504.1	+	19504.1i	0.699348	+	0.699348i	0.964270	−	0.264922i	$-0.0853462\pi$
$167$	19504.1	+	19504.1i	0.699348	+	0.699348i	−0.264922	+	0.964270i	$0.585346\pi$
$168$	−18329.5	+	18329.5i	−0.649428	+	0.649428i
$169$		−	9855.02i		−	0.345052i
$170$	4094.20	−	22273.9i	0.141668	−	0.770724i
$171$	−49972.6			−1.70899
$172$	−3449.66	−	3449.66i	−0.116606	−	0.116606i
$173$	20394.7	−	20394.7i	0.681436	−	0.681436i	−0.278888	−	0.960324i	$-0.589966\pi$
$173$	20394.7	−	20394.7i	0.681436	−	0.681436i	0.960324	+	0.278888i	$0.0899658\pi$
$174$		−	26643.2i		−	0.880011i
$175$	−20823.2	−	46400.3i	−0.679943	−	1.51511i
$176$	−13698.7			−0.442237
$177$	47996.9	+	47996.9i	1.53203	+	1.53203i
$178$	6303.09	−	6303.09i	0.198936	−	0.198936i
$179$			6658.61i			0.207815i	0.994587	+	0.103908i	$0.0331346\pi$
$179$			6658.61i			0.207815i	−0.994587	+	0.103908i	$0.966865\pi$
$180$	23052.6	+	4237.34i	0.711501	+	0.130782i
$181$	30786.8			0.939738			0.469869	−	0.882736i	$-0.344301\pi$
$181$	30786.8			0.939738			0.469869	+	0.882736i	$0.344301\pi$
$182$	−31898.5	−	31898.5i	−0.963003	−	0.963003i
$183$	16999.8	−	16999.8i	0.507622	−	0.507622i
$184$			2495.90i			0.0737210i
$185$	8655.08	+	12553.5i	0.252888	+	0.366792i
$186$	41321.3			1.19440
$187$	−48474.4	−	48474.4i	−1.38621	−	1.38621i
$188$	7333.44	−	7333.44i	0.207488	−	0.207488i
$189$		−	41463.7i		−	1.16076i
$190$	24823.5	−	17114.8i	0.687632	−	0.474094i
$191$	−38847.3			−1.06486			−0.532432	−	0.846472i	$-0.678722\pi$
$191$	−38847.3			−1.06486			−0.532432	+	0.846472i	$0.678722\pi$
$192$	5096.83	+	5096.83i	0.138260	+	0.138260i
$193$	−44490.8	+	44490.8i	−1.19442	+	1.19442i	−0.218603	+	0.975814i	$0.570150\pi$
$193$	−44490.8	+	44490.8i	−1.19442	+	1.19442i	−0.975814	+	0.218603i	$0.929850\pi$
$194$		−	22059.5i		−	0.586128i
$195$	−12470.9	+	67846.3i	−0.327966	+	1.78425i
$196$	−33765.5			−0.878944
$197$	21880.6	+	21880.6i	0.563803	+	0.563803i	0.930386	−	0.366582i	$-0.119472\pi$
$197$	21880.6	+	21880.6i	0.563803	+	0.563803i	−0.366582	+	0.930386i	$0.619472\pi$
$198$	50169.1	−	50169.1i	1.27969	−	1.27969i
$199$		−	22477.3i		−	0.567593i	−0.958885	−	0.283797i	$-0.908406\pi$
$199$		−	22477.3i		−	0.567593i	0.958885	−	0.283797i	$-0.0915940\pi$
$200$	−12902.4	+	5790.27i	−0.322561	+	0.144757i
$201$	−8974.80			−0.222143
$202$	14226.8	+	14226.8i	0.348661	+	0.348661i
$203$	38500.5	−	38500.5i	0.934273	−	0.934273i
$204$			36071.4i			0.866766i
$205$	63234.1	+	11623.1i	1.50468	+	0.276577i
$206$	−26803.3			−0.631618
$207$	−9140.76	−	9140.76i	−0.213325	−	0.213325i
$208$	−8869.95	+	8869.95i	−0.205019	+	0.205019i
$209$		−	91269.7i		−	2.08946i
$210$	45980.6	+	66690.9i	1.04264	+	1.51227i
$211$	−15685.8			−0.352325			−0.176162	−	0.984361i	$-0.556368\pi$
$211$	−15685.8			−0.352325			−0.176162	+	0.984361i	$0.556368\pi$
$212$	22345.5	+	22345.5i	0.497186	+	0.497186i
$213$	−27618.6	+	27618.6i	−0.608755	+	0.608755i
$214$		−	54527.9i		−	1.19067i
$215$	−12551.4	+	8653.69i	−0.271529	+	0.187208i
$216$	−11529.7			−0.247122
$217$	59710.8	+	59710.8i	1.26804	+	1.26804i
$218$	−10671.6	+	10671.6i	−0.224552	+	0.224552i
$219$			98132.9i			2.04610i
$220$	−7739.04	+	42103.2i	−0.159898	+	0.869900i
$221$	−62774.5			−1.28528
$222$	−17173.0	−	17173.0i	−0.348450	−	0.348450i
$223$	11639.7	−	11639.7i	0.234062	−	0.234062i	−0.580324	−	0.814386i	$-0.697074\pi$
$223$	11639.7	−	11639.7i	0.234062	−	0.234062i	0.814386	+	0.580324i	$0.197074\pi$
$224$			14730.2i			0.293571i
$225$	26047.0	−	68458.6i	0.514508	−	1.35227i
$226$	950.774			0.0186149
$227$	31514.3	+	31514.3i	0.611583	+	0.611583i	0.943359	−	0.331775i	$-0.107648\pi$
$227$	31514.3	+	31514.3i	0.611583	+	0.611583i	−0.331775	+	0.943359i	$0.607648\pi$
$228$	−33958.4	+	33958.4i	−0.653247	+	0.653247i
$229$			19818.4i			0.377918i	0.981985	+	0.188959i	$0.0605113\pi$
$229$			19818.4i			0.377918i	−0.981985	+	0.188959i	$0.939489\pi$
$230$	7671.16	+	1410.05i	0.145013	+	0.0266550i
$231$	245205.			4.59522
$232$	−10705.7	−	10705.7i	−0.198903	−	0.198903i
$233$	−14641.2	+	14641.2i	−0.269690	+	0.269690i	−0.828975	−	0.559285i	$-0.811076\pi$
$233$	−14641.2	+	14641.2i	−0.269690	+	0.269690i	0.559285	+	0.828975i	$0.311076\pi$
$234$		−	64969.1i		−	1.18652i
$235$	−18396.4	−	26682.4i	−0.333117	−	0.483158i
$236$	38572.1			0.692547
$237$	−75465.8	−	75465.8i	−1.34355	−	1.34355i
$238$	−52124.5	+	52124.5i	−0.920211	+	0.920211i
$239$			71454.7i			1.25094i	0.780250	+	0.625468i	$0.215092\pi$
$239$			71454.7i			1.25094i	−0.780250	+	0.625468i	$0.784908\pi$
$240$	18544.6	−	12785.7i	0.321955	−	0.221974i
$241$	2829.84			0.0487222			0.0243611	−	0.999703i	$-0.492245\pi$
$241$	2829.84			0.0487222			0.0243611	+	0.999703i	$0.492245\pi$
$242$	62346.5	+	62346.5i	1.06459	+	1.06459i
$243$	−52272.3	+	52272.3i	−0.885235	+	0.885235i
$244$		−	13661.6i		−	0.229468i
$245$	−19075.7	+	103779.i	−0.317796	+	1.72892i
$246$	−102404.			−1.69218
$247$	−59097.3	−	59097.3i	−0.968665	−	0.968665i
$248$	16603.7	−	16603.7i	0.269961	−	0.269961i
$249$		−	32775.3i		−	0.528625i
$250$	10507.3	+	42926.9i	0.168116	+	0.686831i
$251$	−95166.1			−1.51055			−0.755274	−	0.655409i	$-0.772496\pi$
$251$	−95166.1			−1.51055			−0.755274	+	0.655409i	$0.772496\pi$
$252$	−53946.7	−	53946.7i	−0.849501	−	0.849501i
$253$	16694.6	−	16694.6i	0.260817	−	0.260817i
$254$		−	22095.9i		−	0.342487i
$255$	110866.	+	20378.4i	1.70497	+	0.313393i
$256$	4096.00			0.0625000
$257$	45035.7	+	45035.7i	0.681852	+	0.681852i	0.960417	−	0.278565i	$-0.0898588\pi$
$257$	45035.7	+	45035.7i	0.681852	+	0.681852i	−0.278565	+	0.960417i	$0.589859\pi$
$258$	17170.3	−	17170.3i	0.257951	−	0.257951i
$259$		−	49631.3i		−	0.739871i
$260$	22250.8	+	32272.9i	0.329154	+	0.477410i
$261$	78415.5			1.15112
$262$	57917.8	+	57917.8i	0.843742	+	0.843742i
$263$	−24261.4	+	24261.4i	−0.350756	+	0.350756i	−0.860391	−	0.509635i	$-0.829780\pi$
$263$	−24261.4	+	24261.4i	−0.350756	+	0.350756i	0.509635	+	0.860391i	$0.329780\pi$
$264$		−	68183.7i		−	0.978301i
$265$	81303.2	−	56055.2i	1.15775	−	0.798222i
$266$	−98142.2			−1.38705
$267$	31372.9	+	31372.9i	0.440080	+	0.440080i
$268$	−3606.24	+	3606.24i	−0.0502094	+	0.0502094i
$269$		−	77339.5i		−	1.06880i	−0.845231	−	0.534401i	$-0.820537\pi$
$269$		−	77339.5i		−	1.06880i	0.845231	−	0.534401i	$-0.179463\pi$
$270$	−6513.66	+	35436.7i	−0.0893507	+	0.486100i
$271$	94524.4			1.28708			0.643540	−	0.765413i	$-0.277465\pi$
$271$	94524.4			1.28708			0.643540	+	0.765413i	$0.277465\pi$
$272$	14494.1	+	14494.1i	0.195909	+	0.195909i
$273$	158771.	−	158771.i	2.13032	−	2.13032i
$274$		−	55467.8i		−	0.738822i
$275$	125032.	+	47572.0i	1.65332	+	0.629052i
$276$	−12423.0			−0.163083
$277$	103413.	+	103413.i	1.34777	+	1.34777i	0.888074	+	0.459700i	$0.152043\pi$
$277$	103413.	+	103413.i	1.34777	+	1.34777i	0.459700	+	0.888074i	$0.347957\pi$
$278$	32341.2	−	32341.2i	0.418472	−	0.418472i
$279$			121616.i			1.56236i
$280$	45273.5	+	8321.79i	0.577468	+	0.106145i
$281$	−101454.			−1.28486			−0.642429	−	0.766345i	$-0.722073\pi$
$281$	−101454.			−1.28486			−0.642429	+	0.766345i	$0.722073\pi$
$282$	36501.3	+	36501.3i	0.458997	+	0.458997i
$283$	−96681.6	+	96681.6i	−1.20718	+	1.20718i	−0.235239	+	0.971937i	$0.575587\pi$
$283$	−96681.6	+	96681.6i	−1.20718	+	1.20718i	−0.971937	+	0.235239i	$0.924413\pi$
$284$			22195.3i			0.275185i
$285$	85186.7	+	123556.i	1.04877	+	1.52116i
$286$	118659.			1.45067
$287$	−147978.	−	147978.i	−1.79652	−	1.79652i
$288$	−15000.8	+	15000.8i	−0.180855	+	0.180855i
$289$			19057.0i			0.228170i
$290$	−38952.3	+	26856.0i	−0.463167	+	0.319334i
$291$	109798.			1.29661
$292$	39431.6	+	39431.6i	0.462464	+	0.462464i
$293$	−44895.6	+	44895.6i	−0.522960	+	0.522960i	−0.918464	−	0.395504i	$-0.870570\pi$
$293$	−44895.6	+	44895.6i	−0.522960	+	0.522960i	0.395504	+	0.918464i	$0.370570\pi$
$294$		−	168064.i		−	1.94437i
$295$	21791.1	−	118552.i	0.250401	−	1.36227i
$296$	−13800.9			−0.157515
$297$	77120.2	+	77120.2i	0.874290	+	0.874290i
$298$	23267.6	−	23267.6i	0.262010	−	0.262010i
$299$		−	21619.6i		−	0.241827i
$300$	−28820.3	−	64220.2i	−0.320226	−	0.713558i
$301$	49623.3			0.547713
$302$	−33684.1	−	33684.1i	−0.369327	−	0.369327i
$303$	−70812.0	+	70812.0i	−0.771297	+	0.771297i
$304$			27290.2i			0.295297i
$305$	−41989.2	−	7718.09i	−0.451375	−	0.0829679i
$306$	−106164.			−1.13380
$307$	−33655.2	−	33655.2i	−0.357088	−	0.357088i	0.505651	−	0.862738i	$-0.331253\pi$
$307$	−33655.2	−	33655.2i	−0.357088	−	0.357088i	−0.862738	+	0.505651i	$0.831253\pi$
$308$	98528.0	−	98528.0i	1.03862	−	1.03862i
$309$		−	133410.i		−	1.39724i
$310$	−41651.3	−	60411.7i	−0.433417	−	0.628633i
$311$	74750.7			0.772848			0.386424	−	0.922321i	$-0.373710\pi$
$311$	74750.7			0.772848			0.386424	+	0.922321i	$0.373710\pi$
$312$	−44149.1	−	44149.1i	−0.453537	−	0.453537i
$313$	−23129.4	+	23129.4i	−0.236089	+	0.236089i	−0.815228	−	0.579140i	$-0.803389\pi$
$313$	−23129.4	+	23129.4i	−0.236089	+	0.236089i	0.579140	+	0.815228i	$0.303389\pi$
$314$			27700.6i			0.280951i
$315$	−196283.	+	135329.i	−1.97816	+	1.36386i
$316$	−60647.1			−0.607346
$317$	−97994.5	−	97994.5i	−0.975177	−	0.975177i	0.0245227	−	0.999699i	$-0.492193\pi$
$317$	−97994.5	−	97994.5i	−0.975177	−	0.975177i	−0.999699	+	0.0245227i	$0.992193\pi$
$318$	−111222.	+	111222.i	−1.09986	+	1.09986i
$319$			143218.i			1.40739i
$320$	2314.02	−	12589.1i	0.0225978	−	0.122940i
$321$	271406.			2.63396
$322$	−17951.7	−	17951.7i	−0.173139	−	0.173139i
$323$	−96569.2	+	96569.2i	−0.925622	+	0.925622i
$324$			18554.1i			0.176746i
$325$	111762.	−	50155.7i	1.05810	−	0.474847i
$326$	145084.			1.36516
$327$	−53116.6	−	53116.6i	−0.496747	−	0.496747i
$328$	−41147.8	+	41147.8i	−0.382471	+	0.382471i
$329$			105491.i			0.974598i
$330$	−209563.	−	38520.1i	−1.92436	−	0.353720i
$331$	−37165.5			−0.339222			−0.169611	−	0.985511i	$-0.554251\pi$
$331$	−37165.5			−0.339222			−0.169611	+	0.985511i	$0.554251\pi$
$332$	−13169.7	−	13169.7i	−0.119481	−	0.119481i
$333$	50543.1	−	50543.1i	0.455799	−	0.455799i
$334$			78016.5i			0.699348i
$335$	9046.47	+	13121.1i	0.0806102	+	0.116918i
$336$	−73317.9			−0.649428
$337$	−80014.1	−	80014.1i	−0.704542	−	0.704542i	0.260840	−	0.965382i	$-0.416000\pi$
$337$	−80014.1	−	80014.1i	−0.704542	−	0.704542i	−0.965382	+	0.260840i	$0.916000\pi$
$338$	19710.0	−	19710.0i	0.172526	−	0.172526i
$339$			4732.36i			0.0411793i
$340$	52736.2	−	36359.4i	0.456196	−	0.314528i
$341$	−222118.			−1.91018
$342$	−99945.3	−	99945.3i	−0.854496	−	0.854496i
$343$	104705.	−	104705.i	0.889977	−	0.889977i
$344$		−	13798.6i		−	0.116606i
$345$	−7018.34	+	38182.3i	−0.0589652	+	0.320792i
$346$	81578.8			0.681436
$347$	99381.2	+	99381.2i	0.825363	+	0.825363i	0.986871	−	0.161508i	$-0.0516357\pi$
$347$	99381.2	+	99381.2i	0.825363	+	0.825363i	−0.161508	+	0.986871i	$0.551636\pi$
$348$	53286.4	−	53286.4i	0.440006	−	0.440006i
$349$		−	164525.i		−	1.35077i	−0.737466	−	0.675385i	$-0.763978\pi$
$349$		−	164525.i		−	1.35077i	0.737466	−	0.675385i	$-0.236022\pi$
$350$	51154.2	−	134447.i	0.417585	−	1.09753i
$351$	99871.0			0.810635
$352$	−27397.5	−	27397.5i	−0.221118	−	0.221118i
$353$	−133606.	+	133606.i	−1.07220	+	1.07220i	−0.0750176	+	0.997182i	$0.523901\pi$
$353$	−133606.	+	133606.i	−1.07220	+	1.07220i	−0.997182	+	0.0750176i	$0.976099\pi$
$354$			191988.i			1.53203i
$355$	68217.5	+	12539.2i	0.541301	+	0.0994974i
$356$	25212.4			0.198936
$357$	−259443.	−	259443.i	−2.03566	−	2.03566i
$358$	−13317.2	+	13317.2i	−0.103908	+	0.103908i
$359$		−	5929.48i		−	0.0460074i	−0.999735	−	0.0230037i	$-0.992677\pi$
$359$		−	5929.48i		−	0.0460074i	0.999735	−	0.0230037i	$-0.00732296\pi$
$360$	37630.6	+	54579.9i	0.290359	+	0.421141i
$361$	−51503.7			−0.395207
$362$	61573.5	+	61573.5i	0.469869	+	0.469869i
$363$	−310322.	+	310322.i	−2.35504	+	2.35504i
$364$		−	127594.i		−	0.963003i
$365$	143470.	−	98916.6i	1.07690	−	0.742478i
$366$	67999.1			0.507622
$367$	−16902.8	−	16902.8i	−0.125495	−	0.125495i	0.641570	−	0.767065i	$-0.278284\pi$
$367$	−16902.8	−	16902.8i	−0.125495	−	0.125495i	−0.767065	+	0.641570i	$0.778284\pi$
$368$	−4991.79	+	4991.79i	−0.0368605	+	0.0368605i
$369$		−	301392.i		−	2.21350i
$370$	−7796.74	+	42417.1i	−0.0569521	+	0.309840i
$371$	−321440.			−2.33535
$372$	82642.6	+	82642.6i	0.597198	+	0.597198i
$373$	−33187.6	+	33187.6i	−0.238538	+	0.238538i	−0.816245	−	0.577706i	$-0.803948\pi$
$373$	−33187.6	+	33187.6i	−0.238538	+	0.238538i	0.577706	+	0.816245i	$0.303948\pi$
$374$		−	193898.i		−	1.38621i
$375$	−213663.	+	52298.6i	−1.51938	+	0.371901i
$376$	29333.8			0.207488
$377$	92733.7	+	92733.7i	0.652461	+	0.652461i
$378$	82927.3	−	82927.3i	0.580382	−	0.580382i
$379$			66334.9i			0.461810i	0.972976	+	0.230905i	$0.0741687\pi$
$379$			66334.9i			0.461810i	−0.972976	+	0.230905i	$0.925831\pi$
$380$	83876.6	+	15417.5i	0.580863	+	0.106769i
$381$	109979.			0.757637
$382$	−77694.7	−	77694.7i	−0.532432	−	0.532432i
$383$	142823.	−	142823.i	0.973646	−	0.973646i	−0.0260159	−	0.999662i	$-0.508282\pi$
$383$	142823.	−	142823.i	0.973646	−	0.973646i	0.999662	+	0.0260159i	$0.00828204\pi$
$384$			20387.3i			0.138260i
$385$	−247164.	−	358490.i	−1.66749	−	2.41855i
$386$	−177963.			−1.19442
$387$	50535.0	+	50535.0i	0.337419	+	0.337419i
$388$	44119.0	−	44119.0i	0.293064	−	0.293064i
$389$		−	205349.i		−	1.35704i	−0.734581	−	0.678521i	$-0.762621\pi$
$389$		−	205349.i		−	1.35704i	0.734581	−	0.678521i	$-0.237379\pi$
$390$	−160634.	+	110751.i	−1.05611	+	0.728144i
$391$	−35328.0			−0.231082
$392$	−67531.0	−	67531.0i	−0.439472	−	0.439472i
$393$	−288279.	+	288279.i	−1.86650	+	1.86650i
$394$			87522.6i			0.563803i
$395$	−34262.3	+	186399.i	−0.219595	+	1.19468i
$396$	200676.			1.27969
$397$	141271.	+	141271.i	0.896336	+	0.896336i	0.995110	−	0.0987742i	$-0.0314922\pi$
$397$	141271.	+	141271.i	0.896336	+	0.896336i	−0.0987742	+	0.995110i	$0.531492\pi$
$398$	44954.5	−	44954.5i	0.283797	−	0.283797i
$399$		−	488491.i		−	3.06839i
$400$	−37385.4	−	14224.3i	−0.233659	−	0.0889020i
$401$	−75557.7			−0.469884			−0.234942	−	0.972009i	$-0.575490\pi$
$401$	−75557.7			−0.469884			−0.234942	+	0.972009i	$0.575490\pi$
$402$	−17949.6	−	17949.6i	−0.111071	−	0.111071i
$403$	−143822.	+	143822.i	−0.885554	+	0.885554i
$404$			56907.1i			0.348661i
$405$	57026.3	+	10482.1i	0.347668	+	0.0639054i
$406$	154002.			0.934273
$407$	92311.6	+	92311.6i	0.557272	+	0.557272i
$408$	−72142.7	+	72142.7i	−0.433383	+	0.433383i
$409$		−	57009.5i		−	0.340801i	−0.985375	−	0.170400i	$-0.945494\pi$
$409$		−	57009.5i		−	0.340801i	0.985375	−	0.170400i	$-0.0545061\pi$
$410$	103222.	+	149714.i	0.614050	+	0.890627i
$411$	276084.			1.63440
$412$	−53606.6	−	53606.6i	−0.315809	−	0.315809i
$413$	−277429.	+	277429.i	−1.62649	+	1.62649i
$414$		−	36563.1i		−	0.213325i
$415$	−47917.4	+	33037.0i	−0.278225	+	0.191825i
$416$	−35479.8			−0.205019
$417$	160974.	+	160974.i	0.925731	+	0.925731i
$418$	182539.	−	182539.i	1.04473	−	1.04473i
$419$			198757.i			1.13212i	0.824363	+	0.566061i	$0.191533\pi$
$419$			198757.i			1.13212i	−0.824363	+	0.566061i	$0.808467\pi$
$420$	−41420.6	+	225343.i	−0.234811	+	1.27746i
$421$	−215358.			−1.21506			−0.607529	−	0.794297i	$-0.707839\pi$
$421$	−215358.			−1.21506			−0.607529	+	0.794297i	$0.707839\pi$
$422$	−31371.7	−	31371.7i	−0.176162	−	0.176162i
$423$	−107429.	+	107429.i	−0.600403	+	0.600403i
$424$			89382.1i			0.497186i
$425$	−81957.9	−	182626.i	−0.453746	−	1.01108i
$426$	−110474.			−0.608755
$427$	98261.2	+	98261.2i	0.538923	+	0.538923i
$428$	109056.	−	109056.i	0.595335	−	0.595335i
$429$			590611.i			3.20913i
$430$	−42410.2	−	7795.49i	−0.229369	−	0.0421606i
$431$	−61164.7			−0.329266			−0.164633	−	0.986355i	$-0.552644\pi$
$431$	−61164.7			−0.329266			−0.164633	+	0.986355i	$0.552644\pi$
$432$	−23059.4	−	23059.4i	−0.123561	−	0.123561i
$433$	−206063.	+	206063.i	−1.09906	+	1.09906i	−0.104544	+	0.994520i	$0.533338\pi$
$433$	−206063.	+	206063.i	−1.09906	+	1.09906i	−0.994520	+	0.104544i	$0.966662\pi$
$434$			238843.i			1.26804i
$435$	−133672.	−	193880.i	−0.706421	−	1.02460i
$436$	−42686.5			−0.224552
$437$	−33258.5	−	33258.5i	−0.174157	−	0.174157i
$438$	−196266.	+	196266.i	−1.02305	+	1.02305i
$439$		−	2988.00i		−	0.0155043i	−0.999970	−	0.00775215i	$-0.997532\pi$
$439$		−	2988.00i		−	0.0155043i	0.999970	−	0.00775215i	$-0.00246761\pi$
$440$	−99684.4	+	68728.2i	−0.514899	+	0.355001i
$441$	494640.			2.54338
$442$	−125549.	−	125549.i	−0.642641	−	0.642641i
$443$	183770.	−	183770.i	0.936413	−	0.936413i	−0.0616832	−	0.998096i	$-0.519647\pi$
$443$	183770.	−	183770.i	0.936413	−	0.936413i	0.998096	+	0.0616832i	$0.0196468\pi$
$444$		−	68692.0i		−	0.348450i
$445$	14243.6	−	77490.4i	0.0719285	−	0.391316i
$446$	46558.7			0.234062
$447$	115811.	+	115811.i	0.579610	+	0.579610i
$448$	−29460.5	+	29460.5i	−0.146786	+	0.146786i
$449$		−	49347.4i		−	0.244777i	−0.992482	−	0.122389i	$-0.960945\pi$
$449$		−	49347.4i		−	0.244777i	0.992482	−	0.122389i	$-0.0390555\pi$
$450$	189011.	−	84823.2i	0.933388	−	0.418880i
$451$	550461.			2.70629
$452$	1901.55	+	1901.55i	0.00930745	+	0.00930745i
$453$	167659.	−	167659.i	0.817013	−	0.817013i
$454$			126057.i			0.611583i
$455$	−392162.	−	72083.8i	−1.89427	−	0.348189i
$456$	−135833.			−0.653247
$457$	−56155.9	−	56155.9i	−0.268883	−	0.268883i	0.559767	−	0.828650i	$-0.310891\pi$
$457$	−56155.9	−	56155.9i	−0.268883	−	0.268883i	−0.828650	+	0.559767i	$0.810891\pi$
$458$	−39636.8	+	39636.8i	−0.188959	+	0.188959i
$459$		−	163196.i		−	0.774613i
$460$	12522.2	+	18162.4i	0.0591788	+	0.0858338i
$461$	308530.			1.45176			0.725882	−	0.687819i	$-0.241432\pi$
$461$	308530.			1.45176			0.725882	+	0.687819i	$0.241432\pi$
$462$	490411.	+	490411.i	2.29761	+	2.29761i
$463$	167742.	−	167742.i	0.782492	−	0.782492i	−0.197759	−	0.980251i	$-0.563366\pi$
$463$	167742.	−	167742.i	0.782492	−	0.782492i	0.980251	+	0.197759i	$0.0633662\pi$
$464$		−	42822.9i		−	0.198903i
$465$	300692.	−	207314.i	1.39064	−	0.958790i
$466$	−58564.8			−0.269690
$467$	135622.	+	135622.i	0.621864	+	0.621864i	0.946008	−	0.324144i	$-0.105076\pi$
$467$	135622.	+	135622.i	0.621864	+	0.621864i	−0.324144	+	0.946008i	$0.605076\pi$
$468$	129938.	−	129938.i	0.593260	−	0.593260i
$469$		−	51875.7i		−	0.235840i
$470$	16572.0	−	90157.6i	0.0750203	−	0.408138i
$471$	−137876.			−0.621510
$472$	77144.2	+	77144.2i	0.346273	+	0.346273i
$473$	−92296.8	+	92296.8i	−0.412538	+	0.412538i
$474$		−	301863.i		−	1.34355i
$475$	94771.6	−	249086.i	0.420040	−	1.10398i
$476$	−208498.			−0.920211
$477$	−327345.	−	327345.i	−1.43870	−	1.43870i
$478$	−142909.	+	142909.i	−0.625468	+	0.625468i
$479$		−	306495.i		−	1.33583i	−0.744236	−	0.667917i	$-0.767186\pi$
$479$		−	306495.i		−	1.33583i	0.744236	−	0.667917i	$-0.232814\pi$
$480$	62660.6	+	11517.7i	0.271965	+	0.0499902i
$481$	119544.			0.516698
$482$	5659.67	+	5659.67i	0.0243611	+	0.0243611i
$483$	89352.5	−	89352.5i	0.383012	−	0.383012i
$484$			249386.i			1.06459i
$485$	−110675.	−	160525.i	−0.470508	−	0.682432i
$486$	−209089.			−0.885235
$487$	−318523.	−	318523.i	−1.34302	−	1.34302i	−0.893038	−	0.449981i	$-0.851431\pi$
$487$	−318523.	−	318523.i	−1.34302	−	1.34302i	−0.449981	−	0.893038i	$-0.648569\pi$
$488$	27323.3	−	27323.3i	0.114734	−	0.114734i
$489$			722138.i			3.01997i
$490$	−245709.	+	169406.i	−1.02336	+	0.705564i
$491$	198197.			0.822118			0.411059	−	0.911609i	$-0.365159\pi$
$491$	198197.			0.822118			0.411059	+	0.911609i	$0.365159\pi$
$492$	−204808.	−	204808.i	−0.846090	−	0.846090i
$493$	151533.	−	151533.i	0.623469	−	0.623469i
$494$		−	236389.i		−	0.968665i
$495$	113371.	−	616780.i	0.462693	−	2.51721i
$496$	66414.6			0.269961
$497$	−159640.	−	159640.i	−0.646291	−	0.646291i
$498$	65550.5	−	65550.5i	0.264312	−	0.264312i
$499$		−	222466.i		−	0.893436i	−0.894675	−	0.446718i	$-0.852593\pi$
$499$		−	222466.i		−	0.893436i	0.894675	−	0.446718i	$-0.147407\pi$
$500$	−64839.3	+	106868.i	−0.259357	+	0.427474i
$501$	−388317.			−1.54707
$502$	−190332.	−	190332.i	−0.755274	−	0.755274i
$503$	−85616.5	+	85616.5i	−0.338393	+	0.338393i	−0.855762	−	0.517369i	$-0.826911\pi$
$503$	−85616.5	+	85616.5i	−0.338393	+	0.338393i	0.517369	+	0.855762i	$0.326911\pi$
$504$		−	215787.i		−	0.849501i
$505$	174905.	+	32149.5i	0.685833	+	0.126064i
$506$	66778.5			0.260817
$507$	98104.2	+	98104.2i	0.381656	+	0.381656i
$508$	44191.7	−	44191.7i	0.171243	−	0.171243i
$509$		−	237404.i		−	0.916330i	−0.888867	−	0.458165i	$-0.848507\pi$
$509$		−	237404.i		−	0.916330i	0.888867	−	0.458165i	$-0.151493\pi$
$510$	180975.	+	262488.i	0.695788	+	1.00918i
$511$	−567223.			−2.17226
$512$	8192.00	+	8192.00i	0.0312500	+	0.0312500i
$513$	153637.	−	153637.i	0.583794	−	0.583794i
$514$			180143.i			0.681852i
$515$	−195045.	+	134476.i	−0.735396	+	0.507025i
$516$	68681.0			0.257951
$517$	−196209.	−	196209.i	−0.734069	−	0.734069i
$518$	99262.6	−	99262.6i	0.369936	−	0.369936i
$519$			406048.i			1.50745i
$520$	−20044.2	+	109047.i	−0.0741279	+	0.403282i
$521$	−121899.			−0.449082			−0.224541	−	0.974465i	$-0.572088\pi$
$521$	−121899.			−0.449082			−0.224541	+	0.974465i	$0.572088\pi$
$522$	156831.	+	156831.i	0.575561	+	0.575561i
$523$	212234.	−	212234.i	0.775912	−	0.775912i	−0.203221	−	0.979133i	$-0.565141\pi$
$523$	212234.	−	212234.i	0.775912	−	0.775912i	0.979133	+	0.203221i	$0.0651410\pi$
$524$			231671.i			0.843742i
$525$	669194.	+	254614.i	2.42791	+	0.923768i
$526$	−97045.7			−0.350756
$527$	235015.	+	235015.i	0.846203	+	0.846203i
$528$	136367.	−	136367.i	0.489151	−	0.489151i
$529$		−	12167.0i		−	0.0434783i
$530$	274717.	+	50496.1i	0.977988	+	0.179765i
$531$	−565052.			−2.00401
$532$	−196284.	−	196284.i	−0.693526	−	0.693526i
$533$	356425.	−	356425.i	1.25462	−	1.25462i
$534$			125491.i			0.440080i
$535$	−273573.	−	396795.i	−0.955798	−	1.38630i
$536$	−14424.9			−0.0502094
$537$	−66284.8	−	66284.8i	−0.229861	−	0.229861i
$538$	154679.	−	154679.i	0.534401	−	0.534401i
$539$			903408.i			3.10961i
$540$	−83900.6	+	57846.0i	−0.287725	+	0.198374i
$541$	105565.			0.360683			0.180342	−	0.983604i	$-0.442280\pi$
$541$	105565.			0.360683			0.180342	+	0.983604i	$0.442280\pi$
$542$	189049.	+	189049.i	0.643540	+	0.643540i
$543$	−306474.	+	306474.i	−1.03943	+	1.03943i
$544$			57976.5i			0.195909i
$545$	−24115.6	+	131197.i	−0.0811903	+	0.441704i
$546$	635084.			2.13032
$547$	−183750.	−	183750.i	−0.614119	−	0.614119i	0.329898	−	0.944017i	$-0.392986\pi$
$547$	−183750.	−	183750.i	−0.614119	−	0.614119i	−0.944017	+	0.329898i	$0.892986\pi$
$548$	110936.	−	110936.i	0.369411	−	0.369411i
$549$			200133.i			0.664009i
$550$	154921.	+	345209.i	0.512134	+	1.14119i
$551$	285314.			0.939766
$552$	−24846.0	−	24846.0i	−0.0815415	−	0.0815415i
$553$	436204.	−	436204.i	1.42639	−	1.42639i
$554$			413653.i			1.34777i
$555$	−211126.	−	38807.3i	−0.685417	−	0.125988i
$556$	129365.			0.418472
$557$	218612.	+	218612.i	0.704635	+	0.704635i	0.965402	−	0.260767i	$-0.0839753\pi$
$557$	218612.	+	218612.i	0.704635	+	0.704635i	−0.260767	+	0.965402i	$0.583975\pi$
$558$	−243231.	+	243231.i	−0.781180	+	0.781180i
$559$			119525.i			0.382502i
$560$	73903.4	+	107191.i	0.235661	+	0.341807i
$561$	965101.			3.06653
$562$	−202907.	−	202907.i	−0.642429	−	0.642429i
$563$	−116096.	+	116096.i	−0.366270	+	0.366270i	−0.866115	−	0.499845i	$-0.833390\pi$
$563$	−116096.	+	116096.i	−0.366270	+	0.366270i	0.499845	+	0.866115i	$0.333390\pi$
$564$			146005.i			0.458997i
$565$	6918.70	−	4770.16i	0.0216734	−	0.0149429i
$566$	−386726.			−1.20718
$567$	−133450.	−	133450.i	−0.415101	−	0.415101i
$568$	−44390.6	+	44390.6i	−0.137592	+	0.137592i
$569$			353626.i			1.09224i	0.837706	+	0.546122i	$0.183897\pi$
$569$			353626.i			1.09224i	−0.837706	+	0.546122i	$0.816103\pi$
$570$	−76738.6	+	417485.i	−0.236191	+	1.28497i
$571$	−108852.			−0.333859			−0.166930	−	0.985969i	$-0.553385\pi$
$571$	−108852.			−0.333859			−0.166930	+	0.985969i	$0.553385\pi$
$572$	237318.	+	237318.i	0.725336	+	0.725336i
$573$	386716.	−	386716.i	1.17783	−	1.17783i
$574$		−	591911.i		−	1.79652i
$575$	62896.8	−	28226.4i	0.190236	−	0.0853729i
$576$	−60003.4			−0.180855
$577$	−427295.	−	427295.i	−1.28344	−	1.28344i	−0.938696	−	0.344747i	$-0.887965\pi$
$577$	−427295.	−	427295.i	−1.28344	−	1.28344i	−0.344747	−	0.938696i	$-0.612035\pi$
$578$	−38114.0	+	38114.0i	−0.114085	+	0.114085i
$579$		−	885790.i		−	2.64225i
$580$	−131617.	−	24192.7i	−0.391251	−	0.0719163i
$581$	189446.			0.561220
$582$	219597.	+	219597.i	0.648306	+	0.648306i
$583$	597862.	−	597862.i	1.75899	−	1.75899i
$584$			157726.i			0.462464i
$585$	−325958.	−	472774.i	−0.952468	−	1.38147i
$586$	−179582.			−0.522960
$587$	−156745.	−	156745.i	−0.454902	−	0.454902i	0.442076	−	0.896978i	$-0.354242\pi$
$587$	−156745.	−	156745.i	−0.454902	−	0.454902i	−0.896978	+	0.442076i	$0.854242\pi$
$588$	336127.	−	336127.i	0.972186	−	0.972186i
$589$			442497.i			1.27550i
$590$	280686.	−	193521.i	0.806336	−	0.555935i
$591$	−435633.			−1.24723
$592$	−27601.7	−	27601.7i	−0.0787576	−	0.0787576i
$593$	−417659.	+	417659.i	−1.18771	+	1.18771i	−0.210017	+	0.977698i	$0.567352\pi$
$593$	−417659.	+	417659.i	−1.18771	+	1.18771i	−0.977698	+	0.210017i	$0.932648\pi$
$594$			308481.i			0.874290i
$595$	−117790.	+	640820.i	−0.332717	+	1.81010i
$596$	93070.2			0.262010
$597$	223755.	+	223755.i	0.627805	+	0.627805i
$598$	43239.2	−	43239.2i	0.120914	−	0.120914i
$599$			160209.i			0.446513i	0.974760	+	0.223256i	$0.0716687\pi$
$599$			160209.i			0.446513i	−0.974760	+	0.223256i	$0.928331\pi$
$600$	70799.8	−	186081.i	0.196666	−	0.516892i
$601$	−264784.			−0.733066			−0.366533	−	0.930405i	$-0.619455\pi$
$601$	−264784.			−0.733066			−0.366533	+	0.930405i	$0.619455\pi$
$602$	99246.6	+	99246.6i	0.273856	+	0.273856i
$603$	52828.7	−	52828.7i	0.145290	−	0.145290i
$604$		−	134736.i		−	0.369327i
$605$	766490.	+	140890.i	2.09409	+	0.384918i
$606$	−283248.			−0.771297
$607$	252728.	+	252728.i	0.685925	+	0.685925i	0.961329	−	0.275404i	$-0.0888116\pi$
$607$	252728.	+	252728.i	0.685925	+	0.685925i	−0.275404	+	0.961329i	$0.588812\pi$
$608$	−54580.4	+	54580.4i	−0.147649	+	0.147649i
$609$			766525.i			2.06677i
$610$	−68542.1	−	99414.5i	−0.184204	−	0.267171i
$611$	−254091.			−0.680623
$612$	−212328.	−	212328.i	−0.566898	−	0.566898i
$613$	352783.	−	352783.i	0.938829	−	0.938829i	−0.0594046	−	0.998234i	$-0.518920\pi$
$613$	352783.	−	352783.i	0.938829	−	0.938829i	0.998234	+	0.0594046i	$0.0189202\pi$
$614$		−	134621.i		−	0.357088i
$615$	−745185.	+	513774.i	−1.97022	+	1.35838i
$616$	394112.			1.03862
$617$	301197.	+	301197.i	0.791190	+	0.791190i	0.981688	−	0.190497i	$-0.0610101\pi$
$617$	301197.	+	301197.i	0.791190	+	0.791190i	−0.190497	+	0.981688i	$0.561010\pi$
$618$	266820.	−	266820.i	0.698622	−	0.698622i
$619$			402993.i			1.05176i	0.850559	+	0.525880i	$0.176264\pi$
$619$			402993.i			1.05176i	−0.850559	+	0.525880i	$0.823736\pi$
$620$	37520.7	−	204126.i	0.0976085	−	0.531025i
$621$	56205.0			0.145744
$622$	149501.	+	149501.i	0.386424	+	0.386424i
$623$	−181340.	+	181340.i	−0.467215	+	0.467215i
$624$		−	176596.i		−	0.453537i
$625$	291830.	+	259659.i	0.747086	+	0.664728i
$626$	−92517.6			−0.236089
$627$	908567.	+	908567.i	2.31112	+	2.31112i
$628$	−55401.3	+	55401.3i	−0.140475	+	0.140475i
$629$		−	195343.i		−	0.493738i
$630$	−663223.	−	121908.i	−1.67101	−	0.307150i
$631$	86760.4			0.217903			0.108951	−	0.994047i	$-0.465251\pi$
$631$	86760.4			0.217903			0.108951	+	0.994047i	$0.465251\pi$
$632$	−121294.	−	121294.i	−0.303673	−	0.303673i
$633$	156149.	−	156149.i	0.389700	−	0.389700i
$634$		−	391978.i		−	0.975177i
$635$	−110858.	−	160790.i	−0.274928	−	0.398759i
$636$	−444888.			−1.09986
$637$	584958.	+	584958.i	1.44160	+	1.44160i
$638$	−286435.	+	286435.i	−0.703696	+	0.703696i
$639$		−	325145.i		−	0.796297i
$640$	29806.2	−	20550.2i	0.0727691	−	0.0501713i
$641$	−307105.			−0.747431			−0.373716	−	0.927543i	$-0.621916\pi$
$641$	−307105.			−0.747431			−0.373716	+	0.927543i	$0.621916\pi$
$642$	542812.	+	542812.i	1.31698	+	1.31698i
$643$	−174957.	+	174957.i	−0.423165	+	0.423165i	−0.886292	−	0.463127i	$-0.846727\pi$
$643$	−174957.	+	174957.i	−0.423165	+	0.423165i	0.463127	+	0.886292i	$0.346727\pi$
$644$		−	71806.9i		−	0.173139i
$645$	38801.1	−	211092.i	0.0932662	−	0.507402i
$646$	−386277.			−0.925622
$647$	446385.	+	446385.i	1.06635	+	1.06635i	0.997636	+	0.0687167i	$0.0218905\pi$
$647$	446385.	+	446385.i	1.06635	+	1.06635i	0.0687167	+	0.997636i	$0.478110\pi$
$648$	−37108.2	+	37108.2i	−0.0883731	+	0.0883731i
$649$		−	1.03201e6i		−	2.45016i
$650$	323835.	+	123212.i	0.766473	+	0.291626i
$651$	−1.18881e6			−2.80512
$652$	290168.	+	290168.i	0.682582	+	0.682582i
$653$	−46347.4	+	46347.4i	−0.108692	+	0.108692i	−0.759361	−	0.650669i	$-0.774489\pi$
$653$	−46347.4	+	46347.4i	−0.108692	+	0.108692i	0.650669	+	0.759361i	$0.274489\pi$
$654$		−	212467.i		−	0.496747i
$655$	712044.	+	130882.i	1.65968	+	0.305068i
$656$	−164591.			−0.382471
$657$	−577643.	−	577643.i	−1.33822	−	1.33822i
$658$	−210983.	+	210983.i	−0.487299	+	0.487299i
$659$			573662.i			1.32095i	0.750850	+	0.660473i	$0.229644\pi$
$659$			573662.i			1.32095i	−0.750850	+	0.660473i	$0.770356\pi$
$660$	−342086.	−	496167.i	−0.785322	−	1.13904i
$661$	162865.			0.372755			0.186378	−	0.982478i	$-0.440325\pi$
$661$	162865.			0.372755			0.186378	+	0.982478i	$0.440325\pi$
$662$	−74331.0	−	74331.0i	−0.169611	−	0.169611i
$663$	624904.	−	624904.i	1.42163	−	1.42163i
$664$		−	52678.8i		−	0.119481i
$665$	−714172.	+	492392.i	−1.61495	+	1.11344i
$666$	202172.			0.455799
$667$	52188.3	+	52188.3i	0.117306	+	0.117306i
$668$	−156033.	+	156033.i	−0.349674	+	0.349674i
$669$			231740.i			0.517784i
$670$	−8149.32	+	44335.2i	−0.0181540	+	0.0987641i
$671$	−365521.			−0.811835
$672$	−146636.	−	146636.i	−0.324714	−	0.324714i
$673$	−386501.	+	386501.i	−0.853336	+	0.853336i	−0.990542	−	0.137206i	$-0.956188\pi$
$673$	−386501.	+	386501.i	−0.853336	+	0.853336i	0.137206	+	0.990542i	$0.456188\pi$
$674$		−	320056.i		−	0.704542i
$675$	130391.	+	290549.i	0.286180	+	0.637694i
$676$	78840.1			0.172526
$677$	−363.595	−	363.595i	−0.000793306	−	0.000793306i	0.706710	−	0.707503i	$-0.250179\pi$
$677$	−363.595	−	363.595i	−0.000793306	−	0.000793306i	−0.707503	+	0.706710i	$0.750179\pi$
$678$	−9464.72	+	9464.72i	−0.0205896	+	0.0205896i
$679$			634651.i			1.37656i
$680$	178191.	+	32753.6i	0.385362	+	0.0708339i
$681$	−627434.			−1.35292
$682$	−444236.	−	444236.i	−0.955092	−	0.955092i
$683$	−309069.	+	309069.i	−0.662543	+	0.662543i	−0.955979	−	0.293436i	$-0.905201\pi$
$683$	−309069.	+	309069.i	−0.662543	+	0.662543i	0.293436	+	0.955979i	$0.405201\pi$
$684$		−	399781.i		−	0.854496i
$685$	−278289.	−	403634.i	−0.593082	−	0.860215i
$686$	418820.			0.889977
$687$	−197287.	−	197287.i	−0.418008	−	0.418008i
$688$	27597.3	−	27597.3i	0.0583028	−	0.0583028i
$689$		−	774233.i		−	1.63092i
$690$	−90401.2	+	62327.9i	−0.189879	+	0.130913i
$691$	−434793.			−0.910598			−0.455299	−	0.890339i	$-0.650468\pi$
$691$	−434793.			−0.910598			−0.455299	+	0.890339i	$0.650468\pi$
$692$	163158.	+	163158.i	0.340718	+	0.340718i
$693$	−1.44336e6	+	1.44336e6i	−3.00545	+	3.00545i
$694$			397525.i			0.825363i
$695$	73084.2	−	397604.i	0.151305	−	0.823154i
$696$	213146.			0.440006
$697$	−582423.	−	582423.i	−1.19887	−	1.19887i
$698$	329050.	−	329050.i	0.675385	−	0.675385i
$699$		−	291499.i		−	0.596599i
$700$	371203.	−	166586.i	0.757556	−	0.339971i
$701$	−722572.			−1.47043			−0.735217	−	0.677832i	$-0.762920\pi$
$701$	−722572.			−1.47043			−0.735217	+	0.677832i	$0.762920\pi$
$702$	199742.	+	199742.i	0.405317	+	0.405317i
$703$	183900.	−	183900.i	0.372111	−	0.372111i
$704$		−	109590.i		−	0.221118i
$705$	448748.	+	82485.0i	0.902868	+	0.165958i
$706$	−534423.			−1.07220
$707$	−409304.	−	409304.i	−0.818855	−	0.818855i
$708$	−383975.	+	383975.i	−0.766014	+	0.766014i
$709$			111126.i			0.221066i	0.993872	+	0.110533i	$0.0352558\pi$
$709$			111126.i			0.221066i	−0.993872	+	0.110533i	$0.964744\pi$
$710$	111357.	+	161513.i	0.220902	+	0.320399i
$711$	888435.			1.75746
$712$	50424.7	+	50424.7i	0.0994681	+	0.0994681i
$713$	−80939.5	+	80939.5i	−0.159214	+	0.159214i
$714$		−	1.03777e6i		−	2.03566i
$715$	863472.	−	595328.i	1.68903	−	1.16451i
$716$	−53268.9			−0.103908
$717$	−711313.	−	711313.i	−1.38364	−	1.38364i
$718$	11859.0	−	11859.0i	0.0230037	−	0.0230037i
$719$		−	218419.i		−	0.422506i	−0.977431	−	0.211253i	$-0.932246\pi$
$719$		−	218419.i		−	0.422506i	0.977431	−	0.211253i	$-0.0677545\pi$
$720$	−33898.7	+	184421.i	−0.0653910	+	0.355750i
$721$	771131.			1.48340
$722$	−103007.	−	103007.i	−0.197603	−	0.197603i
$723$	−28170.3	+	28170.3i	−0.0538908	+	0.0538908i
$724$			246294.i			0.469869i
$725$	−148713.	+	390858.i	−0.282925	+	0.743605i
$726$	−1.24129e6			−2.35504
$727$	336785.	+	336785.i	0.637211	+	0.637211i	0.949867	−	0.312655i	$-0.101219\pi$
$727$	336785.	+	336785.i	0.637211	+	0.637211i	−0.312655	+	0.949867i	$0.601219\pi$
$728$	255188.	−	255188.i	0.481502	−	0.481502i
$729$		−	852854.i		−	1.60480i
$730$	484773.	+	89106.9i	0.909689	+	0.167211i
$731$	195312.			0.365505
$732$	135998.	+	135998.i	0.253811	+	0.253811i
$733$	−58617.7	+	58617.7i	−0.109099	+	0.109099i	−0.759549	−	0.650450i	$-0.774580\pi$
$733$	−58617.7	+	58617.7i	−0.109099	+	0.109099i	0.650450	+	0.759549i	$0.274580\pi$
$734$		−	67611.3i		−	0.125495i
$735$	−843197.	−	1.22298e6i	−1.56083	−	2.26384i
$736$	−19967.2			−0.0368605
$737$	96486.0	+	96486.0i	0.177635	+	0.177635i
$738$	602785.	−	602785.i	1.10675	−	1.10675i
$739$		−	382560.i		−	0.700504i	−0.936656	−	0.350252i	$-0.886096\pi$
$739$		−	382560.i		−	0.700504i	0.936656	−	0.350252i	$-0.113904\pi$
$740$	−100428.	+	69240.7i	−0.183396	+	0.126444i
$741$	1.17660e6			2.14285
$742$	−642880.	−	642880.i	−1.16768	−	1.16768i
$743$	121447.	−	121447.i	0.219993	−	0.219993i	−0.588503	−	0.808495i	$-0.700282\pi$
$743$	121447.	−	121447.i	0.219993	−	0.219993i	0.808495	+	0.588503i	$0.200282\pi$
$744$			330571.i			0.597198i
$745$	52579.7	−	286052.i	0.0947339	−	0.515386i
$746$	−132750.			−0.238538
$747$	192926.	+	192926.i	0.345741	+	0.345741i
$748$	387795.	−	387795.i	0.693105	−	0.693105i
$749$			1.56877e6i			2.79637i
$750$	−531924.	−	322730.i	−0.945643	−	0.573742i
$751$	628356.			1.11410			0.557052	−	0.830478i	$-0.311932\pi$
$751$	628356.			1.11410			0.557052	+	0.830478i	$0.311932\pi$
$752$	58667.5	+	58667.5i	0.103744	+	0.103744i
$753$	947355.	−	947355.i	1.67079	−	1.67079i
$754$			370935.i			0.652461i
$755$	−414114.	−	76118.9i	−0.726484	−	0.133536i
$756$	331709.			0.580382
$757$	689201.	+	689201.i	1.20269	+	1.20269i	0.973345	+	0.229345i	$0.0736585\pi$
$757$	689201.	+	689201.i	1.20269	+	1.20269i	0.229345	+	0.973345i	$0.426341\pi$
$758$	−132670.	+	132670.i	−0.230905	+	0.230905i
$759$			332382.i			0.576971i
$760$	136918.	+	198588.i	0.237047	+	0.343816i
$761$	−128943.			−0.222652			−0.111326	−	0.993784i	$-0.535510\pi$
$761$	−128943.			−0.222652			−0.111326	+	0.993784i	$0.535510\pi$
$762$	219959.	+	219959.i	0.378819	+	0.378819i
$763$	307022.	−	307022.i	0.527376	−	0.527376i
$764$		−	310779.i		−	0.532432i
$765$	−772547.	+	532639.i	−1.32009	+	0.910144i
$766$	571292.			0.973646
$767$	−668227.	−	668227.i	−1.13588	−	1.13588i
$768$	−40774.7	+	40774.7i	−0.0691302	+	0.0691302i
$769$		−	290033.i		−	0.490450i	−0.969466	−	0.245225i	$-0.921138\pi$
$769$		−	290033.i		−	0.490450i	0.969466	−	0.245225i	$-0.0788618\pi$
$770$	222652.	−	1.21131e6i	0.375531	−	2.04302i
$771$	−896638.			−1.50837
$772$	−355927.	−	355927.i	−0.597209	−	0.597209i
$773$	577364.	−	577364.i	0.966253	−	0.966253i	−0.0331957	−	0.999449i	$-0.510568\pi$
$773$	577364.	−	577364.i	0.966253	−	0.966253i	0.999449	+	0.0331957i	$0.0105684\pi$
$774$			202140.i			0.337419i
$775$	−606186.	−	230640.i	−1.00926	−	0.384001i
$776$	176476.			0.293064
$777$	494067.	+	494067.i	0.818359	+	0.818359i
$778$	410698.	−	410698.i	0.678521	−	0.678521i
$779$		−	1.09661e6i		−	1.80708i
$780$	−542770.	−	99767.4i	−0.892127	−	0.163983i
$781$	593843.			0.973575
$782$	−70656.0	−	70656.0i	−0.115541	−	0.115541i
$783$	−241082.	+	241082.i	−0.393225	+	0.393225i
$784$		−	270124.i		−	0.439472i
$785$	138978.	+	201575.i	0.225531	+	0.327113i
$786$	−1.15312e6			−1.86650
$787$	341182.	+	341182.i	0.550854	+	0.550854i	0.926687	−	0.375833i	$-0.122643\pi$
$787$	341182.	+	341182.i	0.550854	+	0.550854i	−0.375833	+	0.926687i	$0.622643\pi$
$788$	−175045.	+	175045.i	−0.281902	+	0.281902i
$789$		−	483033.i		−	0.775930i
$790$	−441324.	+	304274.i	−0.707136	+	0.487541i
$791$	−27353.8			−0.0437184
$792$	401352.	+	401352.i	0.639846	+	0.639846i
$793$	−236676.	+	236676.i	−0.376363	+	0.376363i
$794$			565082.i			0.896336i
$795$	−251338.	+	1.36737e6i	−0.397671	+	2.16347i
$796$	179818.			0.283797
$797$	−280772.	−	280772.i	−0.442015	−	0.442015i	0.450674	−	0.892689i	$-0.351184\pi$
$797$	−280772.	−	280772.i	−0.442015	−	0.442015i	−0.892689	+	0.450674i	$0.851184\pi$
$798$	976981.	−	976981.i	1.53419	−	1.53419i
$799$			415202.i			0.650379i
$800$	−46322.2	−	103219.i	−0.0723784	−	0.161280i
$801$	−369343.			−0.575658
$802$	−151115.	−	151115.i	−0.234942	−	0.234942i
$803$	1.05500e6	−	1.05500e6i	1.63615	−	1.63615i
$804$		−	71798.4i		−	0.111071i
$805$	−220699.	−	40567.0i	−0.340572	−	0.0626010i
$806$	−575288.			−0.885554
$807$	769896.	+	769896.i	1.18218	+	1.18218i
$808$	−113814.	+	113814.i	−0.174331	+	0.174331i
$809$			1.21869e6i			1.86208i	0.364923	+	0.931038i	$0.381095\pi$
$809$			1.21869e6i			1.86208i	−0.364923	+	0.931038i	$0.618905\pi$
$810$	93088.3	+	135017.i	0.141881	+	0.205787i
$811$	−905569.			−1.37683			−0.688414	−	0.725318i	$-0.741693\pi$
$811$	−905569.			−1.37683			−0.688414	+	0.725318i	$0.741693\pi$
$812$	308004.	+	308004.i	0.467136	+	0.467136i
$813$	−940967.	+	940967.i	−1.42362	+	1.42362i
$814$			369246.i			0.557272i
$815$	1.05576e6	−	727906.i	1.58947	−	1.09587i
$816$	−288571.			−0.433383
$817$	183871.	+	183871.i	0.275466	+	0.275466i
$818$	114019.	−	114019.i	0.170400	−	0.170400i
$819$			1.86916e6i			2.78663i
$820$	−92985.2	+	505873.i	−0.138288	+	0.752339i
$821$	248926.			0.369304			0.184652	−	0.982804i	$-0.440884\pi$
$821$	248926.			0.369304			0.184652	+	0.982804i	$0.440884\pi$
$822$	552168.	+	552168.i	0.817199	+	0.817199i
$823$	158909.	−	158909.i	0.234612	−	0.234612i	−0.580003	−	0.814615i	$-0.696949\pi$
$823$	158909.	−	158909.i	0.234612	−	0.234612i	0.814615	+	0.580003i	$0.196949\pi$
$824$		−	214427.i		−	0.315809i
$825$	−1.71823e6	+	771098.i	−2.52449	+	1.13293i
$826$	−1.10972e6			−1.62649
$827$	542256.	+	542256.i	0.792854	+	0.792854i	0.981957	−	0.189103i	$-0.0605581\pi$
$827$	542256.	+	542256.i	0.792854	+	0.792854i	−0.189103	+	0.981957i	$0.560558\pi$
$828$	73126.1	−	73126.1i	0.106663	−	0.106663i
$829$			374527.i			0.544972i	0.962160	+	0.272486i	$0.0878459\pi$
$829$			374527.i			0.544972i	−0.962160	+	0.272486i	$0.912154\pi$
$830$	−161909.	−	29760.7i	−0.235025	−	0.0432003i
$831$	−2.05891e6			−2.98150
$832$	−70959.6	−	70959.6i	−0.102510	−	0.102510i
$833$	955863.	−	955863.i	1.37754	−	1.37754i
$834$			643897.i			0.925731i
$835$	391418.	+	567719.i	0.561395	+	0.814255i
$836$	730158.			1.04473
$837$	−373897.	−	373897.i	−0.533705	−	0.533705i
$838$	−397513.	+	397513.i	−0.566061	+	0.566061i
$839$			1.20568e6i			1.71280i	0.516314	+	0.856400i	$0.327304\pi$
$839$			1.20568e6i			1.71280i	−0.516314	+	0.856400i	$0.672696\pi$
$840$	−533528.	+	367845.i	−0.756133	+	0.521322i
$841$	259575.			0.367004
$842$	−430716.	−	430716.i	−0.607529	−	0.607529i
$843$	1.00995e6	−	1.00995e6i	1.42116	−	1.42116i
$844$		−	125487.i		−	0.176162i
$845$	44540.4	−	242316.i	0.0623794	−	0.339366i
$846$	−429718.			−0.600403
$847$	−1.79371e6	−	1.79371e6i	−2.50026	−	2.50026i
$848$	−178764.	+	178764.i	−0.248593	+	0.248593i
$849$		−	1.92488e6i		−	2.67048i
$850$	201337.	−	529169.i	0.278667	−	0.732414i
$851$	67276.4			0.0928974
$852$	−220949.	−	220949.i	−0.304377	−	0.304377i
$853$	357733.	−	357733.i	0.491655	−	0.491655i	−0.417172	−	0.908827i	$-0.636979\pi$
$853$	357733.	−	357733.i	0.491655	−	0.491655i	0.908827	+	0.417172i	$0.136979\pi$
$854$			393045.i			0.538923i
$855$	−1.22873e6	−	225855.i	−1.68083	−	0.308956i
$856$	436223.			0.595335
$857$	−594526.	−	594526.i	−0.809486	−	0.809486i	0.175070	−	0.984556i	$-0.443985\pi$
$857$	−594526.	−	594526.i	−0.809486	−	0.809486i	−0.984556	+	0.175070i	$0.943985\pi$
$858$	−1.18122e6	+	1.18122e6i	−1.60456	+	1.60456i
$859$			703123.i			0.952895i	0.879203	+	0.476447i	$0.158076\pi$
$859$			703123.i			0.952895i	−0.879203	+	0.476447i	$0.841924\pi$
$860$	−69229.5	−	100411.i	−0.0936040	−	0.135765i
$861$	2.94616e6			3.97420
$862$	−122329.	−	122329.i	−0.164633	−	0.164633i
$863$	659651.	−	659651.i	0.885712	−	0.885712i	−0.108396	−	0.994108i	$-0.534571\pi$
$863$	659651.	−	659651.i	0.885712	−	0.885712i	0.994108	+	0.108396i	$0.0345713\pi$
$864$		−	92237.6i		−	0.123561i
$865$	593641.	−	409291.i	0.793400	−	0.547016i
$866$	−824250.			−1.09906
$867$	−189707.	−	189707.i	−0.252375	−	0.252375i
$868$	−477687.	+	477687.i	−0.634021	+	0.634021i
$869$			1.62263e6i			2.14872i
$870$	120416.	−	655106.i	0.159091	−	0.865511i
$871$	124950.			0.164702
$872$	−85372.9	−	85372.9i	−0.112276	−	0.112276i
$873$	−646311.	+	646311.i	−0.848033	+	0.848033i
$874$		−	133034.i		−	0.174157i
$875$	−302294.	−	1.23501e6i	−0.394833	−	1.61307i
$876$	−785063.			−1.02305
$877$	553850.	+	553850.i	0.720100	+	0.720100i	0.968625	−	0.248525i	$-0.0799459\pi$
$877$	553850.	+	553850.i	0.720100	+	0.720100i	−0.248525	+	0.968625i	$0.579946\pi$
$878$	5976.01	−	5976.01i	0.00775215	−	0.00775215i
$879$		−	893849.i		−	1.15687i
$880$	−336825.	−	61912.3i	−0.434950	−	0.0799488i
$881$	775973.			0.999757			0.499879	−	0.866095i	$-0.333378\pi$
$881$	775973.			0.999757			0.499879	+	0.866095i	$0.333378\pi$
$882$	989280.	+	989280.i	1.27169	+	1.27169i
$883$	−966096.	+	966096.i	−1.23908	+	1.23908i	−0.278700	+	0.960378i	$0.589904\pi$
$883$	−966096.	+	966096.i	−1.23908	+	1.23908i	−0.960378	+	0.278700i	$0.910096\pi$
$884$		−	502196.i		−	0.642641i
$885$	963227.	+	1.39708e6i	1.22982	+	1.78375i
$886$	735080.			0.936413
$887$	305761.	+	305761.i	0.388629	+	0.388629i	0.874198	−	0.485569i	$-0.161388\pi$
$887$	305761.	+	305761.i	0.388629	+	0.388629i	−0.485569	+	0.874198i	$0.661388\pi$
$888$	137384.	−	137384.i	0.174225	−	0.174225i
$889$			635697.i			0.804354i
$890$	183468.	−	126494.i	0.231622	−	0.159694i
$891$	496421.			0.625310
$892$	93117.3	+	93117.3i	0.117031	+	0.117031i
$893$	−390881.	+	390881.i	−0.490164	+	0.490164i
$894$			463245.i			0.579610i
$895$	−30094.1	+	163722.i	−0.0375694	+	0.204391i
$896$	−117842.			−0.146786
$897$	215218.	+	215218.i	0.267481	+	0.267481i
$898$	98694.8	−	98694.8i	0.122389	−	0.122389i
$899$		−	694353.i		−	0.859134i
$900$	547669.	+	208376.i	0.676134	+	0.257254i
$901$	−1.26515e6			−1.55845
$902$	1.10092e6	+	1.10092e6i	1.35314	+	1.35314i
$903$	−493988.	+	493988.i	−0.605816	+	0.605816i
$904$			7606.19i			0.00930745i
$905$	756987.	+	139143.i	0.924254	+	0.169888i
$906$	670634.			0.817013
$907$	309134.	+	309134.i	0.375778	+	0.375778i	0.869577	−	0.493798i	$-0.164392\pi$
$907$	309134.	+	309134.i	0.375778	+	0.375778i	−0.493798	+	0.869577i	$0.664392\pi$
$908$	−252114.	+	252114.i	−0.305792	+	0.305792i
$909$		−	833647.i		−	1.00891i
$910$	−640156.	−	928491.i	−0.773042	−	1.12123i
$911$	1.01209e6			1.21950			0.609752	−	0.792592i	$-0.291269\pi$
$911$	1.01209e6			1.21950			0.609752	+	0.792592i	$0.291269\pi$
$912$	−271667.	−	271667.i	−0.326623	−	0.326623i
$913$	−352360.	+	352360.i	−0.422712	+	0.422712i
$914$		−	224623.i		−	0.268883i
$915$	494823.	−	341160.i	0.591028	−	0.407489i
$916$	−158547.			−0.188959
$917$	−1.66629e6	−	1.66629e6i	−1.98159	−	1.98159i
$918$	326393.	−	326393.i	0.387307	−	0.387307i
$919$			214226.i			0.253654i	0.991925	+	0.126827i	$0.0404793\pi$
$919$			214226.i			0.253654i	−0.991925	+	0.126827i	$0.959521\pi$
$920$	−11280.4	+	61369.3i	−0.0133275	+	0.0725063i
$921$	670058.			0.789938
$922$	617061.	+	617061.i	0.725882	+	0.725882i
$923$	384514.	−	384514.i	0.451345	−	0.451345i
$924$			1.96164e6i			2.29761i
$925$	156076.	+	347783.i	0.182411	+	0.406466i
$926$	670968.			0.782492
$927$	785298.	+	785298.i	0.913850	+	0.913850i
$928$	85645.9	−	85645.9i	0.0994513	−	0.0994513i
$929$			1.01084e6i			1.17125i	0.810582	+	0.585625i	$0.199151\pi$
$929$			1.01084e6i			1.17125i	−0.810582	+	0.585625i	$0.800849\pi$
$930$	1.01601e6	+	186755.i	1.17472	+	0.215926i
$931$	1.79974e6			2.07640
$932$	−117130.	−	117130.i	−0.134845	−	0.134845i
$933$	−744124.	+	744124.i	−0.854835	+	0.854835i
$934$			542487.i			0.621864i
$935$	−972808.	−	1.41098e6i	−1.11277	−	1.61397i
$936$	519753.			0.593260
$937$	−659193.	−	659193.i	−0.750816	−	0.750816i	0.223816	−	0.974631i	$-0.428149\pi$
$937$	−659193.	−	659193.i	−0.750816	−	0.750816i	−0.974631	+	0.223816i	$0.928149\pi$
$938$	103751.	−	103751.i	0.117920	−	0.117920i
$939$		−	460495.i		−	0.522268i
$940$	213459.	−	147171.i	0.241579	−	0.166559i
$941$	−522797.			−0.590411			−0.295205	−	0.955434i	$-0.595388\pi$
$941$	−522797.			−0.590411			−0.295205	+	0.955434i	$0.595388\pi$
$942$	−275753.	−	275753.i	−0.310755	−	0.310755i
$943$	200587.	−	200587.i	0.225569	−	0.225569i
$944$			308577.i			0.346273i
$945$	187398.	−	1.01951e6i	0.209846	−	1.14164i
$946$	−369187.			−0.412538
$947$	602872.	+	602872.i	0.672241	+	0.672241i	0.958232	−	0.285991i	$-0.0923228\pi$
$947$	602872.	+	602872.i	0.672241	+	0.672241i	−0.285991	+	0.958232i	$0.592323\pi$
$948$	603727.	−	603727.i	0.671775	−	0.671775i
$949$		−	1.36623e6i		−	1.51703i
$950$	687714.	−	308628.i	0.762010	−	0.341970i
$951$	1.95102e6			2.15725
$952$	−416996.	−	416996.i	−0.460106	−	0.460106i
$953$	−877660.	+	877660.i	−0.966364	+	0.966364i	−0.999452	−	0.0330886i	$-0.989466\pi$
$953$	−877660.	+	877660.i	−0.966364	+	0.966364i	0.0330886	+	0.999452i	$0.489466\pi$
$954$		−	1.30938e6i		−	1.43870i
$955$	−955181.	−	175573.i	−1.04732	−	0.192509i
$956$	−571637.			−0.625468
$957$	−1.42570e6	−	1.42570e6i	−1.55669	−	1.55669i
$958$	612990.	−	612990.i	0.667917	−	0.667917i
$959$			1.59581e6i			1.73517i
$960$	102286.	+	148357.i	0.110987	+	0.160977i
$961$	153360.			0.166060
$962$	239088.	+	239088.i	0.258349	+	0.258349i
$963$	−1.59759e6	+	1.59759e6i	−1.72271	+	1.72271i
$964$			22638.7i			0.0243611i
$965$	−1.29502e6	+	892865.i	−1.39067	+	0.958807i
$966$	357410.			0.383012
$967$	369776.	+	369776.i	0.395445	+	0.395445i	0.876623	−	0.481178i	$-0.159791\pi$
$967$	369776.	+	369776.i	0.395445	+	0.395445i	−0.481178	+	0.876623i	$0.659791\pi$
$968$	−498772.	+	498772.i	−0.532293	+	0.532293i
$969$		−	1.92264e6i		−	2.04763i
$970$	99699.4	−	542401.i	0.105962	−	0.576470i
$971$	1.56775e6			1.66280			0.831399	−	0.555677i	$-0.187541\pi$
$971$	1.56775e6			1.66280			0.831399	+	0.555677i	$0.187541\pi$
$972$	−418178.	−	418178.i	−0.442618	−	0.442618i
$973$	−930456.	+	930456.i	−0.982811	+	0.982811i
$974$		−	1.27409e6i		−	1.34302i
$975$	−613272.	+	1.61185e6i	−0.645125	+	1.69556i
$976$	109293.			0.114734
$977$	998393.	+	998393.i	1.04595	+	1.04595i	0.998892	+	0.0470619i	$0.0149858\pi$
$977$	998393.	+	998393.i	1.04595	+	1.04595i	0.0470619	+	0.998892i	$0.485014\pi$
$978$	−1.44428e6	+	1.44428e6i	−1.50999	+	1.50999i
$979$		−	674565.i		−	0.703815i
$980$	−830229.	−	152606.i	−0.864462	−	0.158898i
$981$	625325.			0.649783
$982$	396394.	+	396394.i	0.411059	+	0.411059i
$983$	189295.	−	189295.i	0.195899	−	0.195899i	−0.602340	−	0.798240i	$-0.705765\pi$
$983$	189295.	−	189295.i	0.195899	−	0.195899i	0.798240	+	0.602340i	$0.205765\pi$
$984$		−	819232.i		−	0.846090i
$985$	439112.	+	636894.i	0.452588	+	0.656440i
$986$	606134.			0.623469
$987$	−1.05014e6	−	1.05014e6i	−1.07799	−	1.07799i
$988$	472778.	−	472778.i	0.484333	−	0.484333i
$989$			67265.6i			0.0687702i
$990$	1.46030e6	−	1.00682e6i	1.48995	−	1.02726i
$991$	517798.			0.527246			0.263623	−	0.964626i	$-0.415083\pi$
$991$	517798.			0.527246			0.263623	+	0.964626i	$0.415083\pi$
$992$	132829.	+	132829.i	0.134980	+	0.134980i
$993$	369973.	−	369973.i	0.375208	−	0.375208i
$994$		−	638558.i		−	0.646291i
$995$	101588.	−	552672.i	0.102611	−	0.558241i
$996$	262202.			0.264312
$997$	−248946.	−	248946.i	−0.250446	−	0.250446i	0.570707	−	0.821154i	$-0.306669\pi$
$997$	−248946.	−	248946.i	−0.250446	−	0.250446i	−0.821154	+	0.570707i	$0.806669\pi$
$998$	444933.	−	444933.i	0.446718	−	0.446718i
$999$			310781.i			0.311403i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.b.47.3	✓	44
5.3	odd	4	inner	230.5.f.b.93.3	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.b.47.3	✓	44	1.1	even	1	trivial
230.5.f.b.93.3	yes	44	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 2.00000i) q^{2} +(-9.95475 + 9.95475i) q^{3} +8.00000i q^{4} +(24.5881 + 4.51957i) q^{5} -39.8190 q^{6} +(-57.5399 - 57.5399i) q^{7} +(-16.0000 + 16.0000i) q^{8} -117.194i q^{9} +O(q^{10})\)	\(q+(2.00000 + 2.00000i) q^{2} +(-9.95475 + 9.95475i) q^{3} +8.00000i q^{4} +(24.5881 + 4.51957i) q^{5} -39.8190 q^{6} +(-57.5399 - 57.5399i) q^{7} +(-16.0000 + 16.0000i) q^{8} -117.194i q^{9} +(40.1370 + 58.2153i) q^{10} +214.043 q^{11} +(-79.6380 - 79.6380i) q^{12} +(138.593 - 138.593i) q^{13} -230.160i q^{14} +(-289.759 + 199.777i) q^{15} -64.0000 q^{16} +(-226.471 - 226.471i) q^{17} +(234.388 - 234.388i) q^{18} -426.409i q^{19} +(-36.1566 + 196.705i) q^{20} +1145.59 q^{21} +(428.085 + 428.085i) q^{22} +(77.9968 - 77.9968i) q^{23} -318.552i q^{24} +(584.147 + 222.255i) q^{25} +554.372 q^{26} +(360.303 + 360.303i) q^{27} +(460.320 - 460.320i) q^{28} +669.108i q^{29} +(-979.073 - 179.965i) q^{30} -1037.73 q^{31} +(-128.000 - 128.000i) q^{32} +(-2130.74 + 2130.74i) q^{33} -905.883i q^{34} +(-1154.74 - 1674.85i) q^{35} +937.553 q^{36} +(431.277 + 431.277i) q^{37} +(852.818 - 852.818i) q^{38} +2759.32i q^{39} +(-465.722 + 321.096i) q^{40} +2571.74 q^{41} +(2291.18 + 2291.18i) q^{42} +(-431.207 + 431.207i) q^{43} +1712.34i q^{44} +(529.667 - 2881.58i) q^{45} +311.987 q^{46} +(-916.680 - 916.680i) q^{47} +(637.104 - 637.104i) q^{48} +4220.69i q^{49} +(723.784 + 1612.80i) q^{50} +4508.92 q^{51} +(1108.74 + 1108.74i) q^{52} +(2793.19 - 2793.19i) q^{53} +1441.21i q^{54} +(5262.90 + 967.380i) q^{55} +1841.28 q^{56} +(4244.80 + 4244.80i) q^{57} +(-1338.22 + 1338.22i) q^{58} -4821.51i q^{59} +(-1598.22 - 2318.07i) q^{60} -1707.70 q^{61} +(-2075.46 - 2075.46i) q^{62} +(-6743.34 + 6743.34i) q^{63} -512.000i q^{64} +(4034.11 - 2781.35i) q^{65} -8522.96 q^{66} +(450.780 + 450.780i) q^{67} +(1811.77 - 1811.77i) q^{68} +1552.88i q^{69} +(1040.22 - 5659.19i) q^{70} +2774.41 q^{71} +(1875.11 + 1875.11i) q^{72} +(4928.95 - 4928.95i) q^{73} +1725.11i q^{74} +(-8027.53 + 3602.54i) q^{75} +3411.27 q^{76} +(-12316.0 - 12316.0i) q^{77} +(-5518.63 + 5518.63i) q^{78} +7580.89i q^{79} +(-1573.64 - 289.252i) q^{80} +2319.26 q^{81} +(5143.47 + 5143.47i) q^{82} +(-1646.21 + 1646.21i) q^{83} +9164.73i q^{84} +(-4544.93 - 6592.03i) q^{85} -1724.83 q^{86} +(-6660.81 - 6660.81i) q^{87} +(-3424.68 + 3424.68i) q^{88} -3151.55i q^{89} +(6822.49 - 4703.82i) q^{90} -15949.3 q^{91} +(623.974 + 623.974i) q^{92} +(10330.3 - 10330.3i) q^{93} -3666.72i q^{94} +(1927.19 - 10484.6i) q^{95} +2548.42 q^{96} +(-5514.87 - 5514.87i) q^{97} +(-8441.38 + 8441.38i) q^{98} -25084.5i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8}+O(q^{10}) \) 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8	\( 44 q + 88 q^{2} + 24 q^{5} - 80 q^{7} - 704 q^{8} - 136 q^{10} - 632 q^{11} + 500 q^{13} + 12 q^{15} - 2816 q^{16} + 120 q^{17} + 2648 q^{18} - 736 q^{20} - 856 q^{21} - 1264 q^{22} + 2052 q^{25} + 2000 q^{26} + 588 q^{27} + 640 q^{28} - 1704 q^{30} + 3220 q^{31} - 5632 q^{32} - 2884 q^{33} + 720 q^{35} + 10592 q^{36} + 1856 q^{37} - 1696 q^{38} - 1856 q^{40} - 5156 q^{41} - 1712 q^{42} + 960 q^{43} + 460 q^{45} - 1224 q^{47} + 4456 q^{50} + 3640 q^{51} + 4000 q^{52} + 13556 q^{53} + 12980 q^{55} + 2560 q^{56} - 3072 q^{57} - 3112 q^{58} - 6912 q^{60} - 4864 q^{61} + 6440 q^{62} - 13484 q^{63} - 4100 q^{65} - 11536 q^{66} - 1888 q^{67} - 960 q^{68} + 8824 q^{70} - 1060 q^{71} + 21184 q^{72} + 16616 q^{73} - 11044 q^{75} - 6784 q^{76} + 8892 q^{77} - 23152 q^{78} - 1536 q^{80} - 4044 q^{81} - 10312 q^{82} - 27024 q^{83} - 11068 q^{85} + 3840 q^{86} - 8392 q^{87} + 10112 q^{88} - 7184 q^{90} - 54024 q^{91} + 22528 q^{93} - 25968 q^{95} - 3252 q^{97} - 27984 q^{98}+O(q^{100}) \) 44 * q + 88 * q^2 + 24 * q^5 - 80 * q^7 - 704 * q^8 - 136 * q^10 - 632 * q^11 + 500 * q^13 + 12 * q^15 - 2816 * q^16 + 120 * q^17 + 2648 * q^18 - 736 * q^20 - 856 * q^21 - 1264 * q^22 + 2052 * q^25 + 2000 * q^26 + 588 * q^27 + 640 * q^28 - 1704 * q^30 + 3220 * q^31 - 5632 * q^32 - 2884 * q^33 + 720 * q^35 + 10592 * q^36 + 1856 * q^37 - 1696 * q^38 - 1856 * q^40 - 5156 * q^41 - 1712 * q^42 + 960 * q^43 + 460 * q^45 - 1224 * q^47 + 4456 * q^50 + 3640 * q^51 + 4000 * q^52 + 13556 * q^53 + 12980 * q^55 + 2560 * q^56 - 3072 * q^57 - 3112 * q^58 - 6912 * q^60 - 4864 * q^61 + 6440 * q^62 - 13484 * q^63 - 4100 * q^65 - 11536 * q^66 - 1888 * q^67 - 960 * q^68 + 8824 * q^70 - 1060 * q^71 + 21184 * q^72 + 16616 * q^73 - 11044 * q^75 - 6784 * q^76 + 8892 * q^77 - 23152 * q^78 - 1536 * q^80 - 4044 * q^81 - 10312 * q^82 - 27024 * q^83 - 11068 * q^85 + 3840 * q^86 - 8392 * q^87 + 10112 * q^88 - 7184 * q^90 - 54024 * q^91 + 22528 * q^93 - 25968 * q^95 - 3252 * q^97 - 27984 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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