LMFDB - Embedded newform 198.6.e.b.67.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [198,6,Mod(67,198)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(198, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("198.67");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 198 = 2 \cdot 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	198.e (of order $3$, 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:	$31.7559963230$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.11
Character	$\chi$	$=$	198.67
Dual form			198.6.e.b.133.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 + 3.46410i) q^{2} +(14.1729 + 6.49073i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(23.5822 - 40.8457i) q^{5} +(5.86120 + 62.0777i) q^{6} +(78.0548 + 135.195i) q^{7} -64.0000 q^{8} +(158.741 + 183.985i) q^{9} +O(q^{10})$	\(q+(2.00000 + 3.46410i) q^{2} +(14.1729 + 6.49073i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(23.5822 - 40.8457i) q^{5} +(5.86120 + 62.0777i) q^{6} +(78.0548 + 135.195i) q^{7} -64.0000 q^{8} +(158.741 + 183.985i) q^{9} +188.658 q^{10} +(-60.5000 - 104.789i) q^{11} +(-203.321 + 144.459i) q^{12} +(-289.998 + 502.292i) q^{13} +(-312.219 + 540.780i) q^{14} +(599.346 - 425.834i) q^{15} +(-128.000 - 221.703i) q^{16} +1715.83 q^{17} +(-319.860 + 917.864i) q^{18} -2116.13 q^{19} +(377.316 + 653.530i) q^{20} +(228.748 + 2422.73i) q^{21} +(242.000 - 419.156i) q^{22} +(1743.64 - 3020.08i) q^{23} +(-907.064 - 415.407i) q^{24} +(450.255 + 779.865i) q^{25} -2319.99 q^{26} +(1055.62 + 3637.94i) q^{27} -2497.75 q^{28} +(3911.98 + 6775.76i) q^{29} +(2673.83 + 1224.53i) q^{30} +(-3215.29 + 5569.04i) q^{31} +(512.000 - 886.810i) q^{32} +(-177.301 - 1877.85i) q^{33} +(3431.66 + 5943.81i) q^{34} +7362.83 q^{35} +(-3819.29 + 727.701i) q^{36} +6047.12 q^{37} +(-4232.25 - 7330.48i) q^{38} +(-7370.35 + 5236.62i) q^{39} +(-1509.26 + 2614.12i) q^{40} +(-2515.49 + 4356.96i) q^{41} +(-7935.10 + 5637.87i) q^{42} +(1180.92 + 2045.42i) q^{43} +1936.00 q^{44} +(11258.4 - 2145.10i) q^{45} +13949.1 q^{46} +(-10110.4 - 17511.7i) q^{47} +(-375.117 - 3972.98i) q^{48} +(-3781.61 + 6549.93i) q^{49} +(-1801.02 + 3119.46i) q^{50} +(24318.3 + 11137.0i) q^{51} +(-4639.97 - 8036.67i) q^{52} -28773.1 q^{53} +(-10490.9 + 10932.6i) q^{54} -5706.90 q^{55} +(-4995.51 - 8652.47i) q^{56} +(-29991.6 - 13735.2i) q^{57} +(-15647.9 + 27103.0i) q^{58} +(-8658.67 + 14997.3i) q^{59} +(1105.76 + 11711.5i) q^{60} +(-15147.3 - 26235.9i) q^{61} -25722.3 q^{62} +(-12483.3 + 35821.8i) q^{63} +4096.00 q^{64} +(13677.6 + 23690.3i) q^{65} +(6150.47 - 4369.89i) q^{66} +(25181.9 - 43616.4i) q^{67} +(-13726.6 + 23775.2i) q^{68} +(44315.0 - 31485.7i) q^{69} +(14725.7 + 25505.6i) q^{70} +66728.4 q^{71} +(-10159.4 - 11775.0i) q^{72} -31117.1 q^{73} +(12094.2 + 20947.8i) q^{74} +(1319.52 + 13975.4i) q^{75} +(16929.0 - 29321.9i) q^{76} +(9444.63 - 16358.6i) q^{77} +(-32880.9 - 15058.4i) q^{78} +(27614.2 + 47829.1i) q^{79} -12074.1 q^{80} +(-8651.69 + 58411.8i) q^{81} -20123.9 q^{82} +(1280.27 + 2217.50i) q^{83} +(-35400.4 - 16212.2i) q^{84} +(40463.1 - 70084.2i) q^{85} +(-4723.69 + 8181.67i) q^{86} +(11464.5 + 121424. i) q^{87} +(3872.00 + 6706.50i) q^{88} -120300. q^{89} +(29947.7 + 34710.2i) q^{90} -90543.0 q^{91} +(27898.3 + 48321.3i) q^{92} +(-81717.0 + 58059.8i) q^{93} +(40441.5 - 70046.8i) q^{94} +(-49903.0 + 86434.6i) q^{95} +(13012.6 - 9245.39i) q^{96} +(50433.0 + 87352.6i) q^{97} -30252.8 q^{98} +(9675.76 - 27765.4i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9}+O(q^{10}) $ 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9	\( 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9} - 56 q^{10} - 1452 q^{11} + 336 q^{12} - 688 q^{13} - 96 q^{14} - 1500 q^{15} - 3072 q^{16} + 3512 q^{17} + 1164 q^{18} - 3836 q^{19} - 112 q^{20} + 1842 q^{21} + 5808 q^{22} - 680 q^{23} - 1344 q^{24} - 7759 q^{25} - 5504 q^{26} + 3024 q^{27} - 768 q^{28} - 3210 q^{29} - 4596 q^{30} + 857 q^{31} + 12288 q^{32} - 5082 q^{33} + 7024 q^{34} + 29824 q^{35} + 13344 q^{36} + 7166 q^{37} - 7672 q^{38} - 23076 q^{39} + 448 q^{40} - 27726 q^{41} - 10680 q^{42} - 15092 q^{43} + 46464 q^{44} + 38667 q^{45} - 5440 q^{46} - 28938 q^{47} - 10752 q^{48} + 17322 q^{49} + 31036 q^{50} + 37032 q^{51} - 11008 q^{52} - 12652 q^{53} + 59832 q^{54} + 1694 q^{55} - 1536 q^{56} - 168660 q^{57} + 12840 q^{58} - 33123 q^{59} + 5616 q^{60} + 36262 q^{61} + 6856 q^{62} + 47496 q^{63} + 98304 q^{64} - 31470 q^{65} - 10164 q^{66} + 35563 q^{67} - 28096 q^{68} + 123459 q^{69} + 59648 q^{70} + 295146 q^{71} + 34752 q^{72} + 12056 q^{73} + 14332 q^{74} - 244221 q^{75} + 30688 q^{76} + 2904 q^{77} - 64200 q^{78} + 128058 q^{79} + 3584 q^{80} + 90621 q^{81} - 221808 q^{82} - 209888 q^{83} - 72192 q^{84} + 228182 q^{85} + 60368 q^{86} - 89802 q^{87} + 92928 q^{88} - 46724 q^{89} + 96972 q^{90} - 305924 q^{91} - 10880 q^{92} - 187767 q^{93} + 115752 q^{94} - 118660 q^{95} - 21504 q^{96} + 240799 q^{97} + 138576 q^{98} - 35211 q^{99}+O(q^{100}) \) 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9 - 56 * q^10 - 1452 * q^11 + 336 * q^12 - 688 * q^13 - 96 * q^14 - 1500 * q^15 - 3072 * q^16 + 3512 * q^17 + 1164 * q^18 - 3836 * q^19 - 112 * q^20 + 1842 * q^21 + 5808 * q^22 - 680 * q^23 - 1344 * q^24 - 7759 * q^25 - 5504 * q^26 + 3024 * q^27 - 768 * q^28 - 3210 * q^29 - 4596 * q^30 + 857 * q^31 + 12288 * q^32 - 5082 * q^33 + 7024 * q^34 + 29824 * q^35 + 13344 * q^36 + 7166 * q^37 - 7672 * q^38 - 23076 * q^39 + 448 * q^40 - 27726 * q^41 - 10680 * q^42 - 15092 * q^43 + 46464 * q^44 + 38667 * q^45 - 5440 * q^46 - 28938 * q^47 - 10752 * q^48 + 17322 * q^49 + 31036 * q^50 + 37032 * q^51 - 11008 * q^52 - 12652 * q^53 + 59832 * q^54 + 1694 * q^55 - 1536 * q^56 - 168660 * q^57 + 12840 * q^58 - 33123 * q^59 + 5616 * q^60 + 36262 * q^61 + 6856 * q^62 + 47496 * q^63 + 98304 * q^64 - 31470 * q^65 - 10164 * q^66 + 35563 * q^67 - 28096 * q^68 + 123459 * q^69 + 59648 * q^70 + 295146 * q^71 + 34752 * q^72 + 12056 * q^73 + 14332 * q^74 - 244221 * q^75 + 30688 * q^76 + 2904 * q^77 - 64200 * q^78 + 128058 * q^79 + 3584 * q^80 + 90621 * q^81 - 221808 * q^82 - 209888 * q^83 - 72192 * q^84 + 228182 * q^85 + 60368 * q^86 - 89802 * q^87 + 92928 * q^88 - 46724 * q^89 + 96972 * q^90 - 305924 * q^91 - 10880 * q^92 - 187767 * q^93 + 115752 * q^94 - 118660 * q^95 - 21504 * q^96 + 240799 * q^97 + 138576 * q^98 - 35211 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/198\mathbb{Z}\right)^\times$.

$n$	$145$	$155$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$2$	2.00000	+	3.46410i	0.353553	+	0.612372i
$3$	14.1729	+	6.49073i	0.909190	+	0.416381i
$3$	14.1729	+	6.49073i	0.909190	+	0.416381i
$4$	−8.00000	+	13.8564i	−0.250000	+	0.433013i
$5$	23.5822	−	40.8457i	0.421852	−	0.730669i	−0.574269	−	0.818667i	$-0.694713\pi$
$5$	23.5822	−	40.8457i	0.421852	−	0.730669i	0.996121	+	0.0879977i	$0.0280468\pi$
$6$	5.86120	+	62.0777i	0.0664674	+	0.703976i
$7$	78.0548	+	135.195i	0.602080	+	1.04283i	0.992506	+	0.122199i	$0.0389947\pi$
$7$	78.0548	+	135.195i	0.602080	+	1.04283i	−0.390425	+	0.920635i	$0.627672\pi$
$8$	−64.0000			−0.353553
$9$	158.741	+	183.985i	0.653255	+	0.757138i
$10$	188.658			0.596589
$11$	−60.5000	−	104.789i	−0.150756	−	0.261116i
$11$	−60.5000	−	104.789i	−0.150756	−	0.261116i
$12$	−203.321	+	144.459i	−0.407596	+	0.289596i
$13$	−289.998	+	502.292i	−0.475923	+	0.824323i	−0.999620	−	0.0275817i	$-0.991219\pi$
$13$	−289.998	+	502.292i	−0.475923	+	0.824323i	0.523696	+	0.851905i	$0.324553\pi$
$14$	−312.219	+	540.780i	−0.425735	+	0.737395i
$15$	599.346	−	425.834i	0.687780	−	0.488666i
$16$	−128.000	−	221.703i	−0.125000	−	0.216506i
$17$	1715.83			1.43997			0.719983	−	0.693992i	$-0.244150\pi$
$17$	1715.83			1.43997			0.719983	+	0.693992i	$0.244150\pi$
$18$	−319.860	+	917.864i	−0.232690	+	0.667724i
$19$	−2116.13			−1.34480			−0.672400	−	0.740188i	$-0.734737\pi$
$19$	−2116.13			−1.34480			−0.672400	+	0.740188i	$0.734737\pi$
$20$	377.316	+	653.530i	0.210926	+	0.365335i
$21$	228.748	+	2422.73i	0.113190	+	1.19883i
$22$	242.000	−	419.156i	0.106600	−	0.184637i
$23$	1743.64	−	3020.08i	0.687287	−	1.19042i	−0.285425	−	0.958401i	$-0.592135\pi$
$23$	1743.64	−	3020.08i	0.687287	−	1.19042i	0.972712	−	0.232015i	$-0.0745318\pi$
$24$	−907.064	−	415.407i	−0.321447	−	0.147213i
$25$	450.255	+	779.865i	0.144082	+	0.249557i
$26$	−2319.99			−0.673057
$27$	1055.62	+	3637.94i	0.278675	+	0.960385i
$28$	−2497.75			−0.602080
$29$	3911.98	+	6775.76i	0.863778	+	1.49611i	0.868255	+	0.496117i	$0.165241\pi$
$29$	3911.98	+	6775.76i	0.863778	+	1.49611i	−0.00447743	+	0.999990i	$0.501425\pi$
$30$	2673.83	+	1224.53i	0.542413	+	0.248408i
$31$	−3215.29	+	5569.04i	−0.600919	+	1.04082i	0.391764	+	0.920066i	$0.371865\pi$
$31$	−3215.29	+	5569.04i	−0.600919	+	1.04082i	−0.992682	+	0.120756i	$0.961468\pi$
$32$	512.000	−	886.810i	0.0883883	−	0.153093i
$33$	−177.301	−	1877.85i	−0.0283418	−	0.300176i
$34$	3431.66	+	5943.81i	0.509105	+	0.881795i
$35$	7362.83			1.01596
$36$	−3819.29	+	727.701i	−0.491164	+	0.0935829i
$37$	6047.12			0.726180			0.363090	−	0.931754i	$-0.381722\pi$
$37$	6047.12			0.726180			0.363090	+	0.931754i	$0.381722\pi$
$38$	−4232.25	−	7330.48i	−0.475459	−	0.823519i
$39$	−7370.35	+	5236.62i	−0.775937	+	0.551302i
$40$	−1509.26	+	2614.12i	−0.149147	+	0.258331i
$41$	−2515.49	+	4356.96i	−0.233703	+	0.404785i	−0.958895	−	0.283762i	$-0.908418\pi$
$41$	−2515.49	+	4356.96i	−0.233703	+	0.404785i	0.725192	+	0.688546i	$0.241751\pi$
$42$	−7935.10	+	5637.87i	−0.694111	+	0.493165i
$43$	1180.92	+	2045.42i	0.0973980	+	0.168698i	0.910607	−	0.413274i	$-0.135615\pi$
$43$	1180.92	+	2045.42i	0.0973980	+	0.168698i	−0.813209	+	0.581972i	$0.802281\pi$
$44$	1936.00			0.150756
$45$	11258.4	−	2145.10i	0.828794	−	0.157913i
$46$	13949.1			0.971970
$47$	−10110.4	−	17511.7i	−0.667610	−	1.15634i	−0.978570	−	0.205912i	$-0.933984\pi$
$47$	−10110.4	−	17511.7i	−0.667610	−	1.15634i	0.310960	−	0.950423i	$-0.399349\pi$
$48$	−375.117	−	3972.98i	−0.0234998	−	0.248893i
$49$	−3781.61	+	6549.93i	−0.225002	+	0.389715i
$50$	−1801.02	+	3119.46i	−0.101881	+	0.176463i
$51$	24318.3	+	11137.0i	1.30920	+	0.599574i
$52$	−4639.97	−	8036.67i	−0.237962	−	0.412162i
$53$	−28773.1			−1.40701			−0.703506	−	0.710689i	$-0.748383\pi$
$53$	−28773.1			−1.40701			−0.703506	+	0.710689i	$0.748383\pi$
$54$	−10490.9	+	10932.6i	−0.489587	+	0.510200i
$55$	−5706.90			−0.254386
$56$	−4995.51	−	8652.47i	−0.212868	−	0.368698i
$57$	−29991.6	−	13735.2i	−1.22268	−	0.559949i
$58$	−15647.9	+	27103.0i	−0.610783	+	1.05791i
$59$	−8658.67	+	14997.3i	−0.323833	+	0.560895i	−0.981275	−	0.192610i	$-0.938305\pi$
$59$	−8658.67	+	14997.3i	−0.323833	+	0.560895i	0.657442	+	0.753505i	$0.271638\pi$
$60$	1105.76	+	11711.5i	0.0396537	+	0.419984i
$61$	−15147.3	−	26235.9i	−0.521208	−	0.902758i	−0.999696	−	0.0246641i	$-0.992148\pi$
$61$	−15147.3	−	26235.9i	−0.521208	−	0.902758i	0.478488	−	0.878094i	$-0.341185\pi$
$62$	−25722.3			−0.849827
$63$	−12483.3	+	35821.8i	−0.396258	+	1.13709i
$64$	4096.00			0.125000
$65$	13677.6	+	23690.3i	0.401538	+	0.695485i
$66$	6150.47	−	4369.89i	0.173799	−	0.123484i
$67$	25181.9	−	43616.4i	0.685334	−	1.18703i	−0.287998	−	0.957631i	$-0.592990\pi$
$67$	25181.9	−	43616.4i	0.685334	−	1.18703i	0.973332	−	0.229402i	$-0.0736770\pi$
$68$	−13726.6	+	23775.2i	−0.359991	+	0.623523i
$69$	44315.0	−	31485.7i	1.12054	−	0.796142i
$70$	14725.7	+	25505.6i	0.359195	+	0.622143i
$71$	66728.4			1.57096			0.785479	−	0.618888i	$-0.212417\pi$
$71$	66728.4			1.57096			0.785479	+	0.618888i	$0.212417\pi$
$72$	−10159.4	−	11775.0i	−0.230960	−	0.267689i
$73$	−31117.1			−0.683428			−0.341714	−	0.939804i	$-0.611007\pi$
$73$	−31117.1			−0.683428			−0.341714	+	0.939804i	$0.611007\pi$
$74$	12094.2	+	20947.8i	0.256743	+	0.444692i
$75$	1319.52	+	13975.4i	0.0270871	+	0.286887i
$76$	16929.0	−	29321.9i	0.336200	−	0.582316i
$77$	9444.63	−	16358.6i	0.181534	−	0.314426i
$78$	−32880.9	−	15058.4i	−0.611937	−	0.280248i
$79$	27614.2	+	47829.1i	0.497811	+	0.862233i	0.999997	−	0.00252614i	$-0.000804097\pi$
$79$	27614.2	+	47829.1i	0.497811	+	0.862233i	−0.502186	+	0.864760i	$0.667471\pi$
$80$	−12074.1			−0.210926
$81$	−8651.69	+	58411.8i	−0.146517	+	0.989208i
$82$	−20123.9			−0.330505
$83$	1280.27	+	2217.50i	0.0203990	+	0.0353320i	0.876045	−	0.482230i	$-0.160173\pi$
$83$	1280.27	+	2217.50i	0.0203990	+	0.0353320i	−0.855646	+	0.517562i	$0.826840\pi$
$84$	−35400.4	−	16212.2i	−0.547406	−	0.250695i
$85$	40463.1	−	70084.2i	0.607452	−	1.05214i
$86$	−4723.69	+	8181.67i	−0.0688708	+	0.119288i
$87$	11464.5	+	121424.i	0.162389	+	1.71991i
$88$	3872.00	+	6706.50i	0.0533002	+	0.0923186i
$89$	−120300.			−1.60986			−0.804932	−	0.593367i	$-0.797798\pi$
$89$	−120300.			−1.60986			−0.804932	+	0.593367i	$0.797798\pi$
$90$	29947.7	+	34710.2i	0.389724	+	0.451700i
$91$	−90543.0			−1.14618
$92$	27898.3	+	48321.3i	0.343643	+	0.595208i
$93$	−81717.0	+	58059.8i	−0.979727	+	0.696094i
$94$	40441.5	−	70046.8i	0.472072	−	0.817652i
$95$	−49903.0	+	86434.6i	−0.567307	+	0.982604i
$96$	13012.6	−	9245.39i	0.144107	−	0.102388i
$97$	50433.0	+	87352.6i	0.544234	+	0.942641i	0.998655	+	0.0518537i	$0.0165129\pi$
$97$	50433.0	+	87352.6i	0.544234	+	0.942641i	−0.454421	+	0.890787i	$0.650154\pi$
$98$	−30252.8			−0.318201
$99$	9675.76	−	27765.4i	0.0992195	−	0.284718i
$100$	−14408.2			−0.144082
$101$	−3401.89	−	5892.25i	−0.0331831	−	0.0574749i	0.848957	−	0.528462i	$-0.177231\pi$
$101$	−3401.89	−	5892.25i	−0.0331831	−	0.0574749i	−0.882140	+	0.470987i	$0.843898\pi$
$102$	10056.8	+	106515.i	0.0957108	+	1.01370i
$103$	101808.	−	176337.i	0.945559	−	1.63776i	0.190931	−	0.981604i	$-0.438849\pi$
$103$	101808.	−	176337.i	0.945559	−	1.63776i	0.754628	−	0.656153i	$-0.227817\pi$
$104$	18559.9	−	32146.7i	0.168264	−	0.291442i
$105$	104352.	+	47790.1i	0.923697	+	0.423024i
$106$	−57546.3	−	99673.1i	−0.497454	−	0.861615i
$107$	86748.3			0.732490			0.366245	−	0.930519i	$-0.380643\pi$
$107$	86748.3			0.732490			0.366245	+	0.930519i	$0.380643\pi$
$108$	−58853.7	−	14476.4i	−0.485528	−	0.119427i
$109$	−74518.7			−0.600758			−0.300379	−	0.953820i	$-0.597113\pi$
$109$	−74518.7			−0.600758			−0.300379	+	0.953820i	$0.597113\pi$
$110$	−11413.8	−	19769.3i	−0.0899392	−	0.155779i
$111$	85705.0	+	39250.2i	0.660236	+	0.302367i
$112$	19982.0	−	34609.9i	0.150520	−	0.260709i
$113$	63569.6	−	110106.i	0.468332	−	0.811174i	−0.531013	−	0.847363i	$-0.678189\pi$
$113$	63569.6	−	110106.i	0.468332	−	0.811174i	0.999345	+	0.0361894i	$0.0115220\pi$
$114$	−12403.1	−	131364.i	−0.0893854	−	0.946707i
$115$	−82238.0	−	142440.i	−0.579867	−	1.00436i
$116$	−125184.			−0.863778
$117$	−138449.	+	26379.0i	−0.935026	+	0.178153i
$118$	−69269.4			−0.457969
$119$	133929.	+	231972.i	0.866975	+	1.50164i
$120$	−38358.2	+	27253.4i	−0.243167	+	0.172770i
$121$	−7320.50	+	12679.5i	−0.0454545	+	0.0787296i
$122$	60589.2	−	104944.i	0.368549	−	0.638346i
$123$	−63931.6	+	45423.3i	−0.381025	+	0.270717i
$124$	−51444.6	−	89104.7i	−0.300459	−	0.520411i
$125$	189861.			1.08683
$126$	−149057.	+	28400.3i	−0.836424	+	0.159366i
$127$	226288.			1.24495			0.622474	−	0.782640i	$-0.286128\pi$
$127$	226288.			1.24495			0.622474	+	0.782640i	$0.286128\pi$
$128$	8192.00	+	14189.0i	0.0441942	+	0.0765466i
$129$	3460.81	+	36654.5i	0.0183106	+	0.193933i
$130$	−54710.5	+	94761.3i	−0.283931	+	0.491782i
$131$	119388.	−	206787.i	0.607833	−	1.05280i	−0.383764	−	0.923431i	$-0.625372\pi$
$131$	119388.	−	206787.i	0.607833	−	1.05280i	0.991597	−	0.129366i	$-0.0412943\pi$
$132$	27438.7	+	12566.1i	0.137066	+	0.0627717i
$133$	−165174.	−	286090.i	−0.809678	−	1.40240i
$134$	201456.			0.969208
$135$	173488.	+	42673.2i	0.819284	+	0.201521i
$136$	−109813.			−0.509105
$137$	−176605.	−	305889.i	−0.803899	−	1.39239i	−0.917032	−	0.398814i	$-0.869422\pi$
$137$	−176605.	−	305889.i	−0.803899	−	1.39239i	0.113133	−	0.993580i	$-0.463911\pi$
$138$	197700.	+	90540.1i	0.883706	+	0.404710i
$139$	133598.	−	231399.i	0.586493	−	1.01584i	−0.408194	−	0.912895i	$-0.633841\pi$
$139$	133598.	−	231399.i	0.586493	−	1.01584i	0.994687	−	0.102941i	$-0.0328252\pi$
$140$	−58902.6	+	102022.i	−0.253989	+	0.439922i
$141$	−29629.5	−	313815.i	−0.125510	−	1.32931i
$142$	133457.	+	231154.i	0.555418	+	0.962012i
$143$	70179.6			0.286993
$144$	20471.0	−	58743.3i	0.0822685	−	0.236076i
$145$	369014.			1.45755
$146$	−62234.3	−	107793.i	−0.241628	−	0.418512i
$147$	−96110.1	+	68286.0i	−0.366839	+	0.260638i
$148$	−48376.9	+	83791.3i	−0.181545	+	0.314445i
$149$	−5047.90	+	8743.23i	−0.0186271	+	0.0322631i	−0.875189	−	0.483782i	$-0.839263\pi$
$149$	−5047.90	+	8743.23i	−0.0186271	+	0.0322631i	0.856562	+	0.516045i	$0.172596\pi$
$150$	−45773.2	+	32521.8i	−0.166105	+	0.118017i
$151$	74262.7	+	128627.i	0.265051	+	0.459081i	0.967577	−	0.252577i	$-0.0812780\pi$
$151$	74262.7	+	128627.i	0.265051	+	0.459081i	−0.702526	+	0.711658i	$0.747945\pi$
$152$	135432.			0.475459
$153$	272372.	+	315686.i	0.940664	+	1.09025i
$154$	75557.1			0.256728
$155$	151647.	+	262661.i	0.506997	+	0.878145i
$156$	−13597.9	−	144020.i	−0.0447364	−	0.473816i
$157$	285642.	−	494747.i	0.924854	−	1.60189i	0.133059	−	0.991108i	$-0.457520\pi$
$157$	285642.	−	494747.i	0.924854	−	1.60189i	0.791795	−	0.610787i	$-0.209147\pi$
$158$	−110457.	+	191317.i	−0.352005	+	0.609691i
$159$	−407798.	−	186759.i	−1.27924	−	0.585852i
$160$	−24148.2	−	41825.9i	−0.0745736	−	0.129165i
$161$	544399.			1.65521
$162$	−219648.	+	86853.2i	−0.657565	+	0.260015i
$163$	−82937.4			−0.244501			−0.122251	−	0.992499i	$-0.539011\pi$
$163$	−82937.4			−0.244501			−0.122251	+	0.992499i	$0.539011\pi$
$164$	−40247.9	−	69711.4i	−0.116851	−	0.202392i
$165$	−80883.2	−	37042.0i	−0.231286	−	0.105922i
$166$	−5121.10	+	8870.00i	−0.0144242	+	0.0249835i
$167$	62610.3	−	108444.i	0.173722	−	0.300895i	−0.765996	−	0.642845i	$-0.777754\pi$
$167$	62610.3	−	108444.i	0.173722	−	0.300895i	0.939718	+	0.341950i	$0.111087\pi$
$168$	−14639.8	−	155055.i	−0.0400187	−	0.423850i
$169$	17448.5	+	30221.7i	0.0469939	+	0.0813959i
$170$	323705.			0.859067
$171$	−335916.	−	389335.i	−0.878497	−	1.01820i
$172$	−37789.5			−0.0973980
$173$	−40285.9	−	69777.2i	−0.102338	−	0.177255i	0.810309	−	0.586002i	$-0.199299\pi$
$173$	−40285.9	−	69777.2i	−0.102338	−	0.177255i	−0.912648	+	0.408747i	$0.865966\pi$
$174$	−397695.	+	282561.i	−0.995810	+	0.707521i
$175$	−70289.2	+	121744.i	−0.173498	+	0.300507i
$176$	−15488.0	+	26826.0i	−0.0376889	+	0.0652791i
$177$	−220061.	+	156353.i	−0.527972	+	0.375123i
$178$	−240599.	−	416730.i	−0.569173	−	0.985836i
$179$	359026.			0.837516			0.418758	−	0.908098i	$-0.362466\pi$
$179$	359026.			0.837516			0.418758	+	0.908098i	$0.362466\pi$
$180$	−60344.1	+	173162.i	−0.138820	+	0.398357i
$181$	−64942.6			−0.147344			−0.0736722	−	0.997283i	$-0.523472\pi$
$181$	−64942.6			−0.147344			−0.0736722	+	0.997283i	$0.523472\pi$
$182$	−181086.	−	313650.i	−0.405235	−	0.701887i
$183$	−44390.7	−	470155.i	−0.0979861	−	1.03780i
$184$	−111593.	+	193285.i	−0.242993	+	0.420875i
$185$	142605.	−	246998.i	0.306340	−	0.530597i
$186$	−364559.	−	166957.i	−0.772655	−	0.353851i
$187$	−103808.	−	179800.i	−0.217083	−	0.375999i
$188$	323532.			0.667610
$189$	−409434.	+	426673.i	−0.833738	+	0.868841i
$190$	−399224.			−0.802293
$191$	75565.6	+	130883.i	0.149879	+	0.259598i	0.931183	−	0.364553i	$-0.118778\pi$
$191$	75565.6	+	130883.i	0.149879	+	0.259598i	−0.781304	+	0.624151i	$0.785445\pi$
$192$	58052.1	+	26586.0i	0.113649	+	0.0520476i
$193$	269807.	−	467319.i	0.521386	−	0.903067i	−0.478305	−	0.878194i	$-0.658749\pi$
$193$	269807.	−	467319.i	0.521386	−	0.903067i	0.999691	−	0.0248728i	$-0.00791807\pi$
$194$	−201732.	+	349410.i	−0.384832	+	0.666548i
$195$	40083.7	+	424538.i	0.0754885	+	0.799521i
$196$	−60505.7	−	104799.i	−0.112501	−	0.194857i
$197$	−477727.			−0.877029			−0.438515	−	0.898724i	$-0.644495\pi$
$197$	−477727.			−0.877029			−0.438515	+	0.898724i	$0.644495\pi$
$198$	115534.	−	22012.9i	0.209433	−	0.0399039i
$199$	−1.01763e6			−1.82162			−0.910809	−	0.412827i	$-0.864541\pi$
$199$	−1.01763e6			−1.82162			−0.910809	+	0.412827i	$0.864541\pi$
$200$	−28816.3	−	49911.4i	−0.0509406	−	0.0882316i
$201$	640003.	−	454721.i	1.11736	−	0.793879i
$202$	13607.6	−	23569.0i	0.0234640	−	0.0406409i
$203$	−610698.	+	1.05776e6i	−1.04013	+	1.80155i
$204$	−348865.	+	247868.i	−0.586924	+	0.417008i
$205$	118642.	+	205494.i	0.197176	+	0.341519i
$206$	814464.			1.33722
$207$	832435.	−	158606.i	1.35028	−	0.257273i
$208$	148479.			0.237962
$209$	128026.	+	221747.i	0.202736	+	0.351149i
$210$	43155.1	+	457068.i	0.0675279	+	0.715208i
$211$	−3383.61	+	5860.58i	−0.00523208	+	0.00906222i	−0.868630	−	0.495462i	$-0.834999\pi$
$211$	−3383.61	+	5860.58i	−0.00523208	+	0.00906222i	0.863398	+	0.504524i	$0.168332\pi$
$212$	230185.	−	398692.i	0.351753	−	0.609254i
$213$	945733.	+	433116.i	1.42830	+	0.654116i
$214$	173497.	+	300505.i	0.258974	+	0.448556i
$215$	111395.			0.164350
$216$	−67559.7	−	232828.i	−0.0985265	−	0.339548i
$217$	−1.00387e6			−1.44721
$218$	−149037.	−	258140.i	−0.212400	−	0.367887i
$219$	−441020.	−	201973.i	−0.621366	−	0.284566i
$220$	45655.2	−	79077.2i	0.0635966	−	0.110153i
$221$	−497588.	+	861847.i	−0.685313	+	1.18700i
$222$	35443.4	+	375391.i	0.0482673	+	0.511213i
$223$	−199630.	−	345769.i	−0.268821	−	0.465611i	0.699737	−	0.714401i	$-0.253301\pi$
$223$	−199630.	−	345769.i	−0.268821	−	0.465611i	−0.968558	+	0.248789i	$0.919967\pi$
$224$	159856.			0.212868
$225$	−72009.3	+	206636.i	−0.0948270	+	0.272114i
$226$	508557.			0.662321
$227$	90440.9	+	156648.i	0.116493	+	0.201772i	0.918376	−	0.395710i	$-0.129501\pi$
$227$	90440.9	+	156648.i	0.116493	+	0.201772i	−0.801883	+	0.597482i	$0.796168\pi$
$228$	430254.	−	305694.i	0.548135	−	0.389449i
$229$	6569.72	−	11379.1i	0.00827862	−	0.0143390i	−0.861856	−	0.507152i	$-0.830698\pi$
$229$	6569.72	−	11379.1i	0.00827862	−	0.0143390i	0.870135	+	0.492813i	$0.164031\pi$
$230$	328952.	−	569762.i	0.410028	−	0.710189i
$231$	240037.	−	170546.i	0.295970	−	0.210286i
$232$	−250367.	−	433648.i	−0.305392	−	0.528954i
$233$	901778.			1.08820			0.544101	−	0.839020i	$-0.316871\pi$
$233$	901778.			1.08820			0.544101	+	0.839020i	$0.316871\pi$
$234$	−368277.	−	426842.i	−0.439678	−	0.509597i
$235$	−953702.			−1.12653
$236$	−138539.	−	239956.i	−0.161917	−	0.280448i
$237$	80926.1	+	857113.i	0.0935875	+	0.991213i
$238$	−535715.	+	927886.i	−0.613044	+	1.06182i
$239$	714241.	−	1.23710e6i	0.808816	−	1.40091i	−0.104868	−	0.994486i	$-0.533442\pi$
$239$	714241.	−	1.23710e6i	0.808816	−	1.40091i	0.913684	−	0.406425i	$-0.133225\pi$
$240$	−171125.	−	78369.8i	−0.191772	−	0.0878255i
$241$	−624452.	−	1.08158e6i	−0.692559	−	1.19955i	−0.970997	−	0.239093i	$-0.923150\pi$
$241$	−624452.	−	1.08158e6i	−0.692559	−	1.19955i	0.278438	−	0.960454i	$-0.410183\pi$
$242$	−58564.0			−0.0642824
$243$	−501754.	+	771707.i	−0.545099	+	0.838372i
$244$	484714.			0.521208
$245$	178358.	+	308924.i	0.189835	+	0.328804i
$246$	−285214.	−	130619.i	−0.300492	−	0.137616i
$247$	613673.	−	1.06291e6i	0.640022	−	1.10855i
$248$	205778.	−	356419.i	0.212457	−	0.367986i
$249$	3751.98	+	39738.3i	0.00383497	+	0.0406173i
$250$	379722.	+	657698.i	0.384252	+	0.665544i
$251$	969704.			0.971527			0.485763	−	0.874090i	$-0.338542\pi$
$251$	969704.			0.971527			0.485763	+	0.874090i	$0.338542\pi$
$252$	−396496.	−	459548.i	−0.393312	−	0.455858i
$253$	−421962.			−0.414450
$254$	452575.	+	783883.i	0.440156	+	0.762372i
$255$	1.02838e6	−	730660.i	0.990380	−	0.703663i
$256$	−32768.0	+	56755.8i	−0.0312500	+	0.0541266i
$257$	−799073.	+	1.38404e6i	−0.754664	+	1.30712i	0.190877	+	0.981614i	$0.438867\pi$
$257$	−799073.	+	1.38404e6i	−0.754664	+	1.30712i	−0.945541	+	0.325503i	$0.894466\pi$
$258$	−120053.	+	85297.6i	−0.112286	+	0.0797788i
$259$	472007.	+	817539.i	0.437219	+	0.757285i
$260$	−437684.			−0.401538
$261$	−625643.	+	1.79533e6i	−0.568493	+	1.63134i
$262$	955108.			0.859606
$263$	619940.	+	1.07377e6i	0.552662	+	0.957239i	0.998081	+	0.0619171i	$0.0197215\pi$
$263$	619940.	+	1.07377e6i	0.552662	+	0.957239i	−0.445419	+	0.895322i	$0.646945\pi$
$264$	11347.3	+	120183.i	0.0100203	+	0.106128i
$265$	−678536.	+	1.17526e6i	−0.593551	+	1.02806i
$266$	660696.	−	1.14436e6i	0.572529	−	0.991649i
$267$	−1.70499e6	−	780832.i	−1.46367	−	0.670316i
$268$	402911.	+	697862.i	0.342667	+	0.593517i
$269$	−258951.			−0.218191			−0.109096	−	0.994031i	$-0.534795\pi$
$269$	−258951.			−0.218191			−0.109096	+	0.994031i	$0.534795\pi$
$270$	199151.	+	686326.i	0.166254	+	0.572955i
$271$	−1.08905e6			−0.900796			−0.450398	−	0.892828i	$-0.648718\pi$
$271$	−1.08905e6			−0.900796			−0.450398	+	0.892828i	$0.648718\pi$
$272$	−219626.	−	380404.i	−0.179996	−	0.311762i
$273$	−1.28326e6	−	587690.i	−1.04209	−	0.477246i
$274$	706420.	−	1.22355e6i	0.568442	−	0.984571i
$275$	54480.9	−	94363.7i	0.0434423	−	0.0752442i
$276$	81758.8	+	865931.i	0.0646043	+	0.684244i
$277$	−798315.	−	1.38272e6i	−0.625137	−	1.08277i	−0.988514	−	0.151126i	$-0.951710\pi$
$277$	−798315.	−	1.38272e6i	−0.625137	−	1.08277i	0.363378	−	0.931642i	$-0.381623\pi$
$278$	1.06878e6			0.829427
$279$	−1.53502e6	+	292471.i	−1.18060	+	0.224943i
$280$	−471221.			−0.359195
$281$	−17517.7	−	30341.6i	−0.0132346	−	0.0229231i	0.859332	−	0.511418i	$-0.170880\pi$
$281$	−17517.7	−	30341.6i	−0.0132346	−	0.0229231i	−0.872567	+	0.488495i	$0.837546\pi$
$282$	1.02783e6	−	730270.i	0.769658	−	0.546840i
$283$	−113449.	+	196499.i	−0.0842041	+	0.145846i	−0.905052	−	0.425301i	$-0.860168\pi$
$283$	−113449.	+	196499.i	−0.0842041	+	0.145846i	0.820848	+	0.571147i	$0.193501\pi$
$284$	−533827.	+	924616.i	−0.392740	+	0.680245i
$285$	−1.26829e6	+	901120.i	−0.924927	+	0.657159i
$286$	140359.	+	243109.i	0.101467	+	0.175746i
$287$	−785385.			−0.562831
$288$	244435.	−	46572.8i	0.173653	−	0.0330866i
$289$	1.52422e6			1.07350
$290$	738027.	+	1.27830e6i	0.515320	+	0.892561i
$291$	147799.	+	1.56538e6i	0.102315	+	1.08365i
$292$	248937.	−	431172.i	0.170857	−	0.295933i
$293$	−1.11158e6	+	1.92531e6i	−0.756433	+	1.31018i	0.188225	+	0.982126i	$0.439726\pi$
$293$	−1.11158e6	+	1.92531e6i	−0.756433	+	1.31018i	−0.944659	+	0.328055i	$0.893607\pi$
$294$	−428770.	−	196363.i	−0.289305	−	0.132493i
$295$	408382.	+	707338.i	0.273219	+	0.473230i
$296$	−387016.			−0.256743
$297$	317351.	−	330713.i	0.208761	−	0.217550i
$298$	−40383.2			−0.0263427
$299$	1.01131e6	+	1.75163e6i	0.654192	+	1.13309i
$300$	−204205.	−	93519.5i	−0.130998	−	0.0599928i
$301$	−184353.	+	319309.i	−0.117283	+	0.203140i
$302$	−297051.	+	514507.i	−0.187419	+	0.324619i
$303$	−9969.60	−	105591.i	−0.00623837	−	0.0660724i
$304$	270864.	+	469151.i	0.168100	+	0.291158i
$305$	−1.42883e6			−0.879490
$306$	−548825.	+	1.57490e6i	−0.335066	+	0.961499i
$307$	690572.			0.418180			0.209090	−	0.977896i	$-0.432950\pi$
$307$	690572.			0.418180			0.209090	+	0.977896i	$0.432950\pi$
$308$	151114.	+	261737.i	0.0907671	+	0.157213i
$309$	2.58746e6	−	1.83839e6i	1.54162	−	1.09532i
$310$	−606590.	+	1.05064e6i	−0.358501	+	0.620943i
$311$	−1.16872e6	+	2.02428e6i	−0.685186	+	1.18678i	0.288193	+	0.957572i	$0.406946\pi$
$311$	−1.16872e6	+	2.02428e6i	−0.685186	+	1.18678i	−0.973378	+	0.229204i	$0.926388\pi$
$312$	471702.	−	335144.i	0.274335	−	0.194915i
$313$	−76992.2	−	133354.i	−0.0444207	−	0.0769390i	0.842960	−	0.537976i	$-0.180811\pi$
$313$	−76992.2	−	133354.i	−0.0444207	−	0.0769390i	−0.887381	+	0.461037i	$0.847478\pi$
$314$	2.28514e6			1.30794
$315$	1.16878e6	+	1.35465e6i	0.663678	+	0.769219i
$316$	−883653.			−0.497811
$317$	−1.06926e6	−	1.85202e6i	−0.597636	−	1.03514i	−0.993169	−	0.116684i	$-0.962773\pi$
$317$	−1.06926e6	−	1.85202e6i	−0.597636	−	1.03514i	0.395533	−	0.918452i	$-0.370560\pi$
$318$	−168645.	−	1.78617e6i	−0.0935204	−	0.990502i
$319$	473350.	−	819866.i	0.260439	−	0.451093i
$320$	96592.9	−	167304.i	0.0527315	−	0.0913337i
$321$	1.22947e6	+	563060.i	0.665972	+	0.304994i
$322$	1.08880e6	+	1.88585e6i	0.585204	+	1.01360i
$323$	−3.63092e6			−1.93647
$324$	−740163.	−	587175.i	−0.391710	−	0.310746i
$325$	−522293.			−0.274287
$326$	−165875.	−	287303.i	−0.0864443	−	0.149726i
$327$	−1.05614e6	−	483681.i	−0.546203	−	0.250144i
$328$	160992.	−	278846.i	0.0826263	−	0.143113i
$329$	1.57833e6	−	2.73374e6i	0.803910	−	1.39241i
$330$	−33449.3	−	354272.i	−0.0169084	−	0.179082i
$331$	−267103.	−	462636.i	−0.134001	−	0.232097i	0.791214	−	0.611539i	$-0.209449\pi$
$331$	−267103.	−	462636.i	−0.134001	−	0.232097i	−0.925215	+	0.379442i	$0.876116\pi$
$332$	−40968.8			−0.0203990
$333$	959925.	+	1.11258e6i	0.474380	+	0.549818i
$334$	500883.			0.245680
$335$	−1.18769e6	−	2.05715e6i	−0.578219	−	1.00150i
$336$	507846.	−	360824.i	0.245405	−	0.174360i
$337$	−1.33902e6	+	2.31924e6i	−0.642260	+	1.11243i	0.342667	+	0.939457i	$0.388670\pi$
$337$	−1.33902e6	+	2.31924e6i	−0.642260	+	1.11243i	−0.984927	+	0.172970i	$0.944664\pi$
$338$	−69794.1	+	120887.i	−0.0332297	+	0.0575556i
$339$	1.61563e6	−	1.14790e6i	0.763560	−	0.542508i
$340$	647410.	+	1.12135e6i	0.303726	+	0.526069i
$341$	778100.			0.362368
$342$	676864.	−	1.94232e6i	0.312922	−	0.897955i
$343$	1.44304e6			0.662284
$344$	−75579.0	−	130907.i	−0.0344354	−	0.0596438i
$345$	−241007.	−	2.55258e6i	−0.109014	−	1.15460i
$346$	161144.	−	279109.i	0.0723640	−	0.125338i
$347$	1.55946e6	−	2.70107e6i	0.695266	−	1.20424i	−0.274825	−	0.961494i	$-0.588620\pi$
$347$	1.55946e6	−	2.70107e6i	0.695266	−	1.20424i	0.970091	−	0.242742i	$-0.0780467\pi$
$348$	−1.77421e6	−	812532.i	−0.785339	−	0.359660i
$349$	−423763.	−	733979.i	−0.186234	−	0.322567i	0.757758	−	0.652536i	$-0.226295\pi$
$349$	−423763.	−	733979.i	−0.186234	−	0.322567i	−0.943992	+	0.329969i	$0.892962\pi$
$350$	−562313.			−0.245363
$351$	−2.13343e6	−	524766.i	−0.924296	−	0.227351i
$352$	−123904.			−0.0533002
$353$	12150.7	+	21045.6i	0.00518995	+	0.00898926i	0.868609	−	0.495499i	$-0.165015\pi$
$353$	12150.7	+	21045.6i	0.00518995	+	0.00898926i	−0.863419	+	0.504488i	$0.831681\pi$
$354$	−981746.	−	449609.i	−0.416381	−	0.190689i
$355$	1.57361e6	−	2.72556e6i	0.662712	−	1.14785i
$356$	962397.	−	1.66692e6i	0.402466	−	0.697092i
$357$	392492.	+	4.15700e6i	0.162990	+	1.72627i
$358$	718052.	+	1.24370e6i	0.296107	+	0.512872i
$359$	1.81357e6			0.742676			0.371338	−	0.928498i	$-0.378899\pi$
$359$	1.81357e6			0.742676			0.371338	+	0.928498i	$0.378899\pi$
$360$	−720540.	+	137287.i	−0.293023	+	0.0558305i
$361$	2.00190e6			0.808488
$362$	−129885.	−	224968.i	−0.0520941	−	0.0902296i
$363$	−186052.	+	132189.i	−0.0741083	+	0.0526538i
$364$	724344.	−	1.25460e6i	0.286544	−	0.496309i
$365$	−733812.	+	1.27100e6i	−0.288305	+	0.499360i
$366$	1.53988e6	−	1.09408e6i	0.600877	−	0.426922i
$367$	179990.	+	311753.i	0.0697564	+	0.120822i	0.898794	−	0.438371i	$-0.144444\pi$
$367$	179990.	+	311753.i	0.0697564	+	0.120822i	−0.829038	+	0.559193i	$0.811111\pi$
$368$	−892745.			−0.343643
$369$	−1.20093e6	+	228816.i	−0.459145	+	0.0874823i
$370$	1.14084e6			0.433231
$371$	−2.24588e6	−	3.88998e6i	−0.847134	−	1.46728i
$372$	−150764.	−	1.59678e6i	−0.0564858	−	0.598258i
$373$	−698844.	+	1.21043e6i	−0.260081	+	0.450473i	−0.966263	−	0.257557i	$-0.917083\pi$
$373$	−698844.	+	1.21043e6i	−0.260081	+	0.450473i	0.706182	+	0.708030i	$0.250416\pi$
$374$	415231.	−	719201.i	0.153501	−	0.265871i
$375$	2.69088e6	+	1.23234e6i	0.988134	+	0.452534i
$376$	647065.	+	1.12075e6i	0.236036	+	0.408826i
$377$	−4.53787e6			−1.64437
$378$	−2.29691e6	−	564976.i	−0.826825	−	0.203376i
$379$	2.39373e6			0.856006			0.428003	−	0.903777i	$-0.359217\pi$
$379$	2.39373e6			0.856006			0.428003	+	0.903777i	$0.359217\pi$
$380$	−798449.	−	1.38295e6i	−0.283653	−	0.491302i
$381$	3.20715e6	+	1.46877e6i	1.13190	+	0.518372i
$382$	−302262.	+	523534.i	−0.105980	+	0.183563i
$383$	−1.13417e6	+	1.96445e6i	−0.395078	+	0.684295i	−0.993111	−	0.117176i	$-0.962616\pi$
$383$	−1.13417e6	+	1.96445e6i	−0.395078	+	0.684295i	0.598033	+	0.801471i	$0.295949\pi$
$384$	24007.5	+	254270.i	0.00830843	+	0.0879970i
$385$	−445451.	−	771544.i	−0.153161	−	0.265283i
$386$	2.15845e6			0.737351
$387$	−188865.	+	541963.i	−0.0641023	+	0.183947i
$388$	−1.61386e6			−0.544234
$389$	−611369.	−	1.05892e6i	−0.204847	−	0.354805i	0.745237	−	0.666800i	$-0.232336\pi$
$389$	−611369.	−	1.05892e6i	−0.204847	−	0.354805i	−0.950084	+	0.311994i	$0.899003\pi$
$390$	−1.39048e6	+	987930.i	−0.462916	+	0.328901i
$391$	2.99180e6	−	5.18194e6i	0.989669	−	1.71416i
$392$	242023.	−	419196.i	0.0795502	−	0.137785i
$393$	3.03428e6	−	2.15585e6i	0.991000	−	0.704104i
$394$	−955454.	−	1.65489e6i	−0.310077	−	0.537069i
$395$	2.60482e6			0.840010
$396$	307322.	+	356194.i	0.0984818	+	0.114143i
$397$	−5.55541e6			−1.76905			−0.884524	−	0.466495i	$-0.845517\pi$
$397$	−5.55541e6			−1.76905			−0.884524	+	0.466495i	$0.845517\pi$
$398$	−2.03526e6	−	3.52518e6i	−0.644039	−	1.11551i
$399$	−484059.	−	5.12681e6i	−0.152218	−	1.61219i
$400$	115265.	−	199645.i	0.0360204	−	0.0623892i
$401$	−1.04125e6	+	1.80350e6i	−0.323366	+	0.560086i	−0.981180	−	0.193094i	$-0.938148\pi$
$401$	−1.04125e6	+	1.80350e6i	−0.323366	+	0.560086i	0.657815	+	0.753180i	$0.271481\pi$
$402$	2.85520e6	+	1.30759e6i	0.881195	+	0.403560i
$403$	−1.86486e6	−	3.23002e6i	−0.571982	−	0.990703i
$404$	108861.			0.0331831
$405$	2.18184e6	+	1.73086e6i	0.660975	+	0.524355i
$406$	−4.88559e6			−1.47096
$407$	−365851.	−	633672.i	−0.109476	−	0.189617i
$408$	−1.55637e6	−	712768.i	−0.462873	−	0.211981i
$409$	−1.22114e6	+	2.11507e6i	−0.360957	+	0.625197i	−0.988119	−	0.153693i	$-0.950883\pi$
$409$	−1.22114e6	+	2.11507e6i	−0.360957	+	0.625197i	0.627161	+	0.778889i	$0.284217\pi$
$410$	−474568.	+	821976.i	−0.139424	+	0.241490i
$411$	−517559.	−	5.48162e6i	−0.151132	−	1.60068i
$412$	1.62893e6	+	2.82138e6i	0.472779	+	0.818878i
$413$	−2.70340e6			−0.779894
$414$	2.21430e6	+	2.56643e6i	0.634944	+	0.735916i
$415$	120767.			0.0344214
$416$	296958.	+	514347.i	0.0841322	+	0.145721i
$417$	3.39541e6	−	2.41243e6i	0.956208	−	0.679384i
$418$	−512103.	+	886988.i	−0.143356	+	0.248300i
$419$	2.25745e6	−	3.91001e6i	0.628177	−	1.08803i	−0.359740	−	0.933053i	$-0.617135\pi$
$419$	2.25745e6	−	3.91001e6i	0.628177	−	1.08803i	0.987917	−	0.154982i	$-0.0495321\pi$
$420$	−1.49702e6	+	1.06363e6i	−0.414099	+	0.294217i
$421$	−1.06829e6	−	1.85033e6i	−0.293754	−	0.508796i	0.680941	−	0.732339i	$-0.261571\pi$
$421$	−1.06829e6	−	1.85033e6i	−0.293754	−	0.508796i	−0.974694	+	0.223543i	$0.928238\pi$
$422$	−27068.9			−0.00739927
$423$	1.61695e6	−	4.63998e6i	0.439386	−	1.26085i
$424$	1.84148e6			0.497454
$425$	772562.	+	1.33812e6i	0.207473	+	0.359353i
$426$	391109.	+	4.14235e6i	0.104418	+	1.10592i
$427$	2.36464e6	−	4.09568e6i	0.627618	−	1.08707i
$428$	−693986.	+	1.20202e6i	−0.183122	+	0.317177i
$429$	994646.	+	455517.i	0.260931	+	0.119498i
$430$	222790.	+	385884.i	0.0581066	+	0.100644i
$431$	−3.19783e6			−0.829205			−0.414603	−	0.910003i	$-0.636079\pi$
$431$	−3.19783e6			−0.829205			−0.414603	+	0.910003i	$0.636079\pi$
$432$	671420.	−	699689.i	0.173095	−	0.180383i
$433$	844610.			0.216489			0.108245	−	0.994124i	$-0.465477\pi$
$433$	844610.			0.216489			0.108245	+	0.994124i	$0.465477\pi$
$434$	−2.00775e6	−	3.47752e6i	−0.511664	−	0.886229i
$435$	5.22998e6	+	2.39517e6i	1.32519	+	0.606894i
$436$	596150.	−	1.03256e6i	0.150189	−	0.260136i
$437$	−3.68977e6	+	6.39087e6i	−0.924263	+	1.60087i
$438$	−182384.	−	1.93168e6i	−0.0454257	−	0.481117i
$439$	830808.	+	1.43900e6i	0.205750	+	0.356369i	0.950371	−	0.311118i	$-0.100703\pi$
$439$	830808.	+	1.43900e6i	0.205750	+	0.356369i	−0.744622	+	0.667487i	$0.767370\pi$
$440$	365242.			0.0899392
$441$	−1.80538e6	+	343985.i	−0.442051	+	0.0842253i
$442$	−3.98070e6			−0.969179
$443$	−3.82338e6	−	6.62228e6i	−0.925631	−	1.60324i	−0.790543	−	0.612406i	$-0.790202\pi$
$443$	−3.82338e6	−	6.62228e6i	−0.925631	−	1.60324i	−0.135088	−	0.990834i	$-0.543132\pi$
$444$	−1.22951e6	+	873562.i	−0.295988	+	0.210299i
$445$	−2.83694e6	+	4.91372e6i	−0.679124	+	1.17628i
$446$	798519.	−	1.38307e6i	0.190085	−	0.329237i
$447$	−128293.	+	91152.1i	−0.0303693	+	0.0215773i
$448$	319712.	+	553758.i	0.0752601	+	0.130354i
$449$	−1.20840e6			−0.282876			−0.141438	−	0.989947i	$-0.545173\pi$
$449$	−1.20840e6			−0.282876			−0.141438	+	0.989947i	$0.545173\pi$
$450$	−859828.	+	163826.i	−0.200161	+	0.0381373i
$451$	608749.			0.140928
$452$	1.01711e6	+	1.76169e6i	0.234166	+	0.405587i
$453$	217635.	+	2.30503e6i	0.0498290	+	0.527754i
$454$	−361764.	+	626593.i	−0.0823731	+	0.142674i
$455$	−2.13521e6	+	3.69829e6i	−0.483517	+	0.837476i
$456$	1.91946e6	+	879053.i	0.432282	+	0.197972i
$457$	3.50541e6	+	6.07154e6i	0.785142	+	1.35991i	0.928914	+	0.370294i	$0.120743\pi$
$457$	3.50541e6	+	6.07154e6i	0.785142	+	1.35991i	−0.143773	+	0.989611i	$0.545923\pi$
$458$	52557.7			0.0117077
$459$	1.81126e6	+	6.24208e6i	0.401282	+	1.38292i
$460$	2.63162e6			0.579867
$461$	−2.12561e6	−	3.68166e6i	−0.465834	−	0.806848i	0.533405	−	0.845860i	$-0.320912\pi$
$461$	−2.12561e6	−	3.68166e6i	−0.465834	−	0.806848i	−0.999239	+	0.0390121i	$0.987579\pi$
$462$	1.07086e6	+	490420.i	0.233415	+	0.106897i
$463$	2.54841e6	−	4.41398e6i	0.552481	−	0.956924i	−0.445614	−	0.895225i	$-0.647015\pi$
$463$	2.54841e6	−	4.41398e6i	0.552481	−	0.956924i	0.998095	−	0.0616993i	$-0.0196520\pi$
$464$	1.00147e6	−	1.73459e6i	0.215945	−	0.374027i
$465$	444418.	+	4.70697e6i	0.0953146	+	1.00951i
$466$	1.80356e6	+	3.12385e6i	0.384738	+	0.666385i
$467$	100963.			0.0214225			0.0107112	−	0.999943i	$-0.496590\pi$
$467$	100963.			0.0214225			0.0107112	+	0.999943i	$0.496590\pi$
$468$	742070.	−	2.12943e6i	0.156614	−	0.449416i
$469$	7.86229e6			1.65050
$470$	−1.90740e6	−	3.30372e6i	−0.398289	−	0.689857i
$471$	7.25964e6	−	5.15796e6i	1.50787	−	1.07134i
$472$	554155.	−	959824.i	0.114492	−	0.198306i
$473$	142892.	−	247495.i	0.0293666	−	0.0508644i
$474$	−2.80727e6	+	1.99456e6i	−0.573903	+	0.407757i
$475$	−952797.	−	1.65029e6i	−0.193761	−	0.335604i
$476$	−4.28572e6			−0.866975
$477$	−4.56747e6	−	5.29382e6i	−0.919137	−	1.06530i
$478$	5.71393e6			1.14384
$479$	1.30852e6	+	2.26642e6i	0.260580	+	0.451338i	0.966396	−	0.257057i	$-0.0827528\pi$
$479$	1.30852e6	+	2.26642e6i	0.260580	+	0.451338i	−0.705816	+	0.708395i	$0.749419\pi$
$480$	−70768.8	−	749534.i	−0.0140197	−	0.148487i
$481$	−1.75365e6	+	3.03742e6i	−0.345606	+	0.598607i
$482$	2.49781e6	−	4.32633e6i	0.489713	−	0.848208i
$483$	7.71570e6	+	3.53355e6i	1.50490	+	0.689196i
$484$	−117128.	−	202872.i	−0.0227273	−	0.0393648i
$485$	4.75730e6			0.918345
$486$	−3.67678e6	−	194714.i	−0.706117	−	0.0373944i
$487$	−2.88561e6			−0.551335			−0.275668	−	0.961253i	$-0.588899\pi$
$487$	−2.88561e6			−0.551335			−0.275668	+	0.961253i	$0.588899\pi$
$488$	969427.	+	1.67910e6i	0.184275	+	0.319173i
$489$	−1.17546e6	−	538324.i	−0.222298	−	0.101806i
$490$	−713430.	+	1.23570e6i	−0.134234	+	0.232499i
$491$	−5.27240e6	+	9.13207e6i	−0.986972	+	1.70949i	−0.354149	+	0.935189i	$0.615229\pi$
$491$	−5.27240e6	+	9.13207e6i	−0.986972	+	1.70949i	−0.632823	+	0.774296i	$0.718104\pi$
$492$	−117951.	−	1.24925e6i	−0.0219678	−	0.232668i
$493$	6.71230e6	+	1.16260e7i	1.24381	+	2.15434i
$494$	4.90939e6			0.905128
$495$	−905919.	−	1.04998e6i	−0.166179	−	0.192606i
$496$	1.64623e6			0.300459
$497$	5.20847e6	+	9.02134e6i	0.945843	+	1.63825i
$498$	−130153.	+	92473.8i	−0.0235170	+	0.0167088i
$499$	−4.93015e6	+	8.53926e6i	−0.886357	+	1.53521i	−0.0422055	+	0.999109i	$0.513438\pi$
$499$	−4.93015e6	+	8.53926e6i	−0.886357	+	1.53521i	−0.844151	+	0.536106i	$0.819895\pi$
$500$	−1.51889e6	+	2.63079e6i	−0.271707	+	0.470611i
$501$	1.59125e6	−	1.13058e6i	0.283233	−	0.201237i
$502$	1.93941e6	+	3.35915e6i	0.343487	+	0.594936i
$503$	3.88975e6			0.685492			0.342746	−	0.939428i	$-0.388643\pi$
$503$	3.88975e6			0.685492			0.342746	+	0.939428i	$0.388643\pi$
$504$	798931.	−	2.29260e6i	0.140098	−	0.402024i
$505$	−320897.			−0.0559935
$506$	−843923.	−	1.46172e6i	−0.146530	−	0.253797i
$507$	51134.7	+	541582.i	0.00883478	+	0.0935717i
$508$	−1.81030e6	+	3.13553e6i	−0.311237	+	0.539079i
$509$	−4.39569e6	+	7.61356e6i	−0.752026	+	1.30255i	0.194813	+	0.980840i	$0.437590\pi$
$509$	−4.39569e6	+	7.61356e6i	−0.752026	+	1.30255i	−0.946839	+	0.321707i	$0.895743\pi$
$510$	4.58783e6	+	2.10108e6i	0.781056	+	0.357699i
$511$	−2.42884e6	−	4.20688e6i	−0.411479	−	0.712702i
$512$	−262144.			−0.0441942
$513$	−2.23383e6	−	7.69833e6i	−0.374762	−	1.29153i
$514$	−6.39259e6			−1.06726
$515$	−4.80172e6	−	8.31682e6i	−0.797772	−	1.38178i
$516$	−535586.	−	245281.i	−0.0885533	−	0.0405546i
$517$	−1.22336e6	+	2.11892e6i	−0.201292	+	0.348648i
$518$	−1.88803e6	+	3.27016e6i	−0.309160	+	0.535481i
$519$	−118062.	−	1.25043e6i	−0.0192394	−	0.203770i
$520$	−875368.	−	1.51618e6i	−0.141965	−	0.245891i
$521$	2.52390e6			0.407359			0.203680	−	0.979038i	$-0.434710\pi$
$521$	2.52390e6			0.407359			0.203680	+	0.979038i	$0.434710\pi$
$522$	−7.47051e6	+	1.42338e6i	−1.19998	+	0.228635i
$523$	616502.			0.0985554			0.0492777	−	0.998785i	$-0.484308\pi$
$523$	616502.			0.0985554			0.0492777	+	0.998785i	$0.484308\pi$
$524$	1.91022e6	+	3.30859e6i	0.303916	+	0.526399i
$525$	−1.78641e6	+	1.26924e6i	−0.282867	+	0.200977i
$526$	−2.47976e6	+	4.29507e6i	−0.390791	+	0.676871i
$527$	−5.51689e6	+	9.55553e6i	−0.865302	+	1.49875i
$528$	−393630.	+	279673.i	−0.0614474	+	0.0436582i
$529$	−2.86241e6	−	4.95784e6i	−0.444726	−	0.770289i
$530$	−5.42828e6			−0.839408
$531$	−4.13375e6	+	787615.i	−0.636221	+	0.121221i
$532$	5.28556e6			0.809678
$533$	−1.45898e6	−	2.52702e6i	−0.222449	−	0.385293i
$534$	−705101.	−	7.46793e6i	−0.107003	−	1.13331i
$535$	2.04572e6	−	3.54329e6i	0.309002	−	0.535208i
$536$	−1.61164e6	+	2.79145e6i	−0.242302	+	0.419680i
$537$	5.08843e6	+	2.33034e6i	0.761462	+	0.348725i
$538$	−517902.	−	897033.i	−0.0771422	−	0.133614i
$539$	915149.			0.135681
$540$	−1.97920e6	+	2.06253e6i	−0.292082	+	0.304380i
$541$	5.89331e6			0.865697			0.432848	−	0.901467i	$-0.357509\pi$
$541$	5.89331e6			0.865697			0.432848	+	0.901467i	$0.357509\pi$
$542$	−2.17811e6	−	3.77260e6i	−0.318480	−	0.551623i
$543$	−920424.	−	421525.i	−0.133964	−	0.0613513i
$544$	878505.	−	1.52162e6i	0.127276	−	0.220449i
$545$	−1.75732e6	+	3.04377e6i	−0.253431	+	0.438955i
$546$	−530691.	−	5.62071e6i	−0.0761834	−	0.806881i
$547$	2.44631e6	+	4.23712e6i	0.349577	+	0.605484i	0.986174	−	0.165712i	$-0.0529921\pi$
$547$	2.44631e6	+	4.23712e6i	0.349577	+	0.605484i	−0.636598	+	0.771196i	$0.719659\pi$
$548$	5.65136e6			0.803899
$549$	2.42251e6	−	6.95158e6i	0.343032	−	0.984357i
$550$	435847.			0.0614366
$551$	−8.27826e6	−	1.43384e7i	−1.16161	−	2.01197i
$552$	−2.83616e6	+	2.01508e6i	−0.396171	+	0.281479i
$553$	−4.31084e6	+	7.46659e6i	−0.599444	+	1.03827i
$554$	3.19326e6	−	5.53089e6i	0.442038	−	0.765633i
$555$	3.62432e6	−	2.57507e6i	0.499452	−	0.354860i
$556$	2.13757e6	+	3.70238e6i	0.293247	+	0.507918i
$557$	1.94520e6			0.265660			0.132830	−	0.991139i	$-0.457594\pi$
$557$	1.94520e6			0.265660			0.132830	+	0.991139i	$0.457594\pi$
$558$	−4.08318e6	−	4.73251e6i	−0.555153	−	0.643437i
$559$	−1.36986e6			−0.185416
$560$	−942442.	−	1.63236e6i	−0.126994	−	0.219961i
$561$	−304219.	−	3.22208e6i	−0.0408112	−	0.432244i
$562$	70070.9	−	121366.i	0.00935830	−	0.0162091i
$563$	1.85772e6	−	3.21766e6i	0.247006	−	0.427828i	−0.715687	−	0.698421i	$-0.753886\pi$
$563$	1.85772e6	−	3.21766e6i	0.247006	−	0.427828i	0.962694	+	0.270593i	$0.0872198\pi$
$564$	4.58538e6	+	2.09996e6i	0.606985	+	0.277980i
$565$	−2.99823e6	−	5.19308e6i	−0.395133	−	0.684391i
$566$	−907589.			−0.119083
$567$	−8.57228e6	+	3.38965e6i	−1.11979	+	0.442790i
$568$	−4.27062e6			−0.555418
$569$	2.90610e6	+	5.03351e6i	0.376296	+	0.651764i	0.990520	−	0.137368i	$-0.0438642\pi$
$569$	2.90610e6	+	5.03351e6i	0.376296	+	0.651764i	−0.614224	+	0.789132i	$0.710531\pi$
$570$	−5.65816e6	−	2.59126e6i	−0.729437	−	0.334059i
$571$	−886055.	+	1.53469e6i	−0.113729	+	0.196984i	−0.917271	−	0.398264i	$-0.869613\pi$
$571$	−886055.	+	1.53469e6i	−0.113729	+	0.196984i	0.803542	+	0.595248i	$0.202946\pi$
$572$	−561437.	+	972437.i	−0.0717481	+	0.124271i
$573$	221453.	+	2.34547e6i	0.0281770	+	0.298431i
$574$	−1.57077e6	−	2.72065e6i	−0.198991	−	0.344662i
$575$	3.14034e6			0.396102
$576$	650203.	+	753601.i	0.0816568	+	0.0946423i
$577$	−1.21608e7			−1.52063			−0.760314	−	0.649556i	$-0.774955\pi$
$577$	−1.21608e7			−1.52063			−0.760314	+	0.649556i	$0.774955\pi$
$578$	3.04843e6	+	5.28004e6i	0.379540	+	0.657382i
$579$	6.85717e6	−	4.87201e6i	0.850058	−	0.603965i
$580$	−2.95211e6	+	5.11320e6i	−0.364387	+	0.631136i
$581$	−199863.	+	346173.i	−0.0245636	+	0.0425454i
$582$	−5.12705e6	+	3.64276e6i	−0.627423	+	0.445782i
$583$	1.74078e6	+	3.01511e6i	0.212115	+	0.367394i
$584$	1.99150e6			0.241628
$585$	−2.18746e6	+	6.27710e6i	−0.264272	+	0.758349i
$586$	−8.89262e6			−1.06976
$587$	1.54212e6	+	2.67104e6i	0.184724	+	0.319952i	0.943484	−	0.331419i	$-0.107527\pi$
$587$	1.54212e6	+	2.67104e6i	0.184724	+	0.319952i	−0.758759	+	0.651371i	$0.774194\pi$
$588$	−177318.	−	1.87803e6i	−0.0211500	−	0.224006i
$589$	6.80396e6	−	1.17848e7i	0.808115	−	1.39970i
$590$	−1.63353e6	+	2.82935e6i	−0.193195	+	0.334624i
$591$	−6.77076e6	−	3.10080e6i	−0.797387	−	0.365178i
$592$	−774031.	−	1.34066e6i	−0.0907725	−	0.157223i
$593$	1.51564e7			1.76994			0.884971	−	0.465646i	$-0.154178\pi$
$593$	1.51564e7			1.76994			0.884971	+	0.465646i	$0.154178\pi$
$594$	1.78032e6	+	437911.i	0.207030	+	0.0509236i
$595$	1.26334e7			1.46294
$596$	−80766.5	−	139892.i	−0.00931355	−	0.0161315i
$597$	−1.44228e7	−	6.60517e6i	−1.65620	−	0.758487i
$598$	−4.04523e6	+	7.00654e6i	−0.462583	+	0.801218i
$599$	−3.45073e6	+	5.97684e6i	−0.392956	+	0.680620i	−0.992838	−	0.119468i	$-0.961881\pi$
$599$	−3.45073e6	+	5.97684e6i	−0.392956	+	0.680620i	0.599882	+	0.800089i	$0.295214\pi$
$600$	−84449.2	−	894427.i	−0.00957673	−	0.101430i
$601$	931395.	+	1.61322e6i	0.105184	+	0.182183i	0.913813	−	0.406135i	$-0.133124\pi$
$601$	931395.	+	1.61322e6i	0.105184	+	0.182183i	−0.808630	+	0.588318i	$0.799790\pi$
$602$	−1.47483e6			−0.165863
$603$	1.20221e7	−	2.29061e6i	1.34645	−	0.256542i
$604$	−2.37641e6			−0.265051
$605$	345268.	+	598021.i	0.0383502	+	0.0664245i
$606$	345839.	−	245718.i	0.0382553	−	0.0271803i
$607$	−808832.	+	1.40094e6i	−0.0891019	+	0.154329i	−0.907132	−	0.420847i	$-0.861733\pi$
$607$	−808832.	+	1.40094e6i	−0.0891019	+	0.154329i	0.818030	+	0.575176i	$0.195066\pi$
$608$	−1.08346e6	+	1.87660e6i	−0.118865	+	0.205880i
$609$	−1.55210e7	+	1.10276e7i	−1.69581	+	1.20487i
$610$	−2.85766e6	−	4.94961e6i	−0.310947	−	0.538575i
$611$	1.17280e7			1.27093
$612$	−6.55326e6	+	1.24861e6i	−0.707259	+	0.134756i
$613$	−7.08284e6			−0.761301			−0.380650	−	0.924719i	$-0.624300\pi$
$613$	−7.08284e6			−0.761301			−0.380650	+	0.924719i	$0.624300\pi$
$614$	1.38114e6	+	2.39221e6i	0.147849	+	0.256082i
$615$	347692.	+	3.68251e6i	0.0370687	+	0.392606i
$616$	−604456.	+	1.04695e6i	−0.0641820	+	0.111166i
$617$	7.02941e6	−	1.21753e7i	0.743372	−	1.28756i	−0.207580	−	0.978218i	$-0.566559\pi$
$617$	7.02941e6	−	1.21753e7i	0.743372	−	1.28756i	0.950952	−	0.309340i	$-0.100108\pi$
$618$	1.15433e7	+	5.28646e6i	1.21579	+	0.556793i
$619$	5.27085e6	+	9.12938e6i	0.552909	+	0.957667i	0.998063	+	0.0622128i	$0.0198158\pi$
$619$	5.27085e6	+	9.12938e6i	0.552909	+	0.957667i	−0.445154	+	0.895454i	$0.646851\pi$
$620$	−4.85272e6			−0.506997
$621$	1.28275e7	+	3.15521e6i	1.33479	+	0.328321i
$622$	−9.34974e6			−0.968999
$623$	−9.38996e6	−	1.62639e7i	−0.969268	−	1.67882i
$624$	2.10438e6	+	963738.i	0.216352	+	0.0990826i
$625$	3.07031e6	−	5.31792e6i	0.314399	−	0.544556i
$626$	307969.	−	533417.i	0.0314102	−	0.0544041i
$627$	375192.	+	3.97377e6i	0.0381141	+	0.403677i
$628$	4.57028e6	+	7.91595e6i	0.462427	+	0.800947i
$629$	1.03758e7			1.04567
$630$	−2.35507e6	+	6.75808e6i	−0.236403	+	0.678378i
$631$	−6.42506e6			−0.642398			−0.321199	−	0.947012i	$-0.604086\pi$
$631$	−6.42506e6			−0.642398			−0.321199	+	0.947012i	$0.604086\pi$
$632$	−1.76731e6	−	3.06107e6i	−0.176003	−	0.304846i
$633$	−85994.9	+	61099.2i	−0.00853029	+	0.00606075i
$634$	4.27706e6	−	7.40808e6i	0.422592	−	0.731952i
$635$	5.33637e6	−	9.24286e6i	0.525184	−	0.909646i
$636$	5.85019e6	−	4.15655e6i	0.573492	−	0.407465i
$637$	−2.19332e6	−	3.79894e6i	−0.214167	−	0.370949i
$638$	3.78680e6			0.368316
$639$	1.05925e7	+	1.22770e7i	1.02624	+	1.18943i
$640$	772743.			0.0745736
$641$	846384.	+	1.46598e6i	0.0813622	+	0.140923i	0.903835	−	0.427881i	$-0.140740\pi$
$641$	846384.	+	1.46598e6i	0.0813622	+	0.140923i	−0.822473	+	0.568804i	$0.807406\pi$
$642$	508449.	+	5.38514e6i	0.0486867	+	0.515655i
$643$	−3.36613e6	+	5.83031e6i	−0.321073	+	0.556115i	−0.980710	−	0.195470i	$-0.937377\pi$
$643$	−3.36613e6	+	5.83031e6i	−0.321073	+	0.556115i	0.659637	+	0.751585i	$0.270710\pi$
$644$	−4.35519e6	+	7.54341e6i	−0.413802	+	0.716726i
$645$	1.57879e6	+	723036.i	0.149426	+	0.0684322i
$646$	−7.26183e6	−	1.25779e7i	−0.684644	−	1.18584i
$647$	1.67254e7			1.57078			0.785389	−	0.619002i	$-0.212463\pi$
$647$	1.67254e7			1.57078			0.785389	+	0.619002i	$0.212463\pi$
$648$	553708.	−	3.73835e6i	0.0518016	−	0.349738i
$649$	2.09540e6			0.195279
$650$	−1.04459e6	−	1.80928e6i	−0.0969752	−	0.167966i
$651$	−1.42278e7	−	6.51588e6i	−1.31579	−	0.602588i
$652$	663499.	−	1.14921e6i	0.0611253	−	0.105872i
$653$	−3.34975e6	+	5.80194e6i	−0.307418	+	0.532464i	−0.977797	−	0.209555i	$-0.932798\pi$
$653$	−3.34975e6	+	5.80194e6i	−0.307418	+	0.532464i	0.670379	+	0.742019i	$0.266132\pi$
$654$	−436769.	−	4.62595e6i	−0.0399308	−	0.422919i
$655$	−5.63090e6	−	9.75300e6i	−0.512831	−	0.888250i
$656$	1.28793e6			0.116851
$657$	−4.93956e6	−	5.72508e6i	−0.446452	−	0.517449i
$658$	1.26266e7			1.13690
$659$	1.89976e6	+	3.29048e6i	0.170406	+	0.295152i	0.938562	−	0.345111i	$-0.112159\pi$
$659$	1.89976e6	+	3.29048e6i	0.170406	+	0.295152i	−0.768156	+	0.640263i	$0.778825\pi$
$660$	1.16033e6	−	824415.i	0.103687	−	0.0736692i
$661$	−5.18879e6	+	8.98725e6i	−0.461915	+	0.800061i	−0.999056	−	0.0434314i	$-0.986171\pi$
$661$	−5.18879e6	+	8.98725e6i	−0.461915	+	0.800061i	0.537141	+	0.843493i	$0.319504\pi$
$662$	1.06841e6	−	1.85054e6i	0.0947532	−	0.164117i
$663$	−1.26463e7	+	8.98515e6i	−1.11732	+	0.793855i
$664$	−81937.6	−	141920.i	−0.00721212	−	0.0124918i
$665$	−1.55807e7			−1.36626
$666$	−1.93423e6	+	5.55043e6i	−0.168975	+	0.484888i
$667$	2.72844e7			2.37465
$668$	1.00177e6	+	1.73511e6i	0.0868610	+	0.150448i
$669$	−585035.	−	6.19628e6i	−0.0505378	−	0.535261i
$670$	4.75077e6	−	8.22858e6i	0.408863	−	0.708171i
$671$	−1.83282e6	+	3.17454e6i	−0.157150	+	0.272192i
$672$	2.26562e6	+	1.03758e6i	0.193537	+	0.0886339i
$673$	−1.10255e7	−	1.90967e7i	−0.938342	−	1.62526i	−0.768563	−	0.639774i	$-0.779028\pi$
$673$	−1.10255e7	−	1.90967e7i	−0.938342	−	1.62526i	−0.169779	−	0.985482i	$-0.554305\pi$
$674$	−1.07121e7			−0.908293
$675$	−2.36180e6	+	2.46124e6i	−0.199519	+	0.207919i
$676$	−558353.			−0.0469939
$677$	4.13753e6	+	7.16640e6i	0.346952	+	0.600938i	0.985706	−	0.168472i	$-0.0538834\pi$
$677$	4.13753e6	+	7.16640e6i	0.346952	+	0.600938i	−0.638755	+	0.769410i	$0.720550\pi$
$678$	7.20771e6	+	3.30091e6i	0.602176	+	0.275777i
$679$	−7.87308e6	+	1.36366e7i	−0.655345	+	1.13509i
$680$	−2.58964e6	+	4.48539e6i	−0.214767	+	0.371987i
$681$	265046.	+	2.80718e6i	0.0219005	+	0.231955i
$682$	1.55620e6	+	2.69542e6i	0.128116	+	0.221904i
$683$	−1.02694e7			−0.842353			−0.421176	−	0.906979i	$-0.638383\pi$
$683$	−1.02694e7			−0.842353			−0.421176	+	0.906979i	$0.638383\pi$
$684$	8.08211e6	−	1.53991e6i	0.660518	−	0.125850i
$685$	−1.66590e7			−1.35651
$686$	2.88609e6	+	4.99885e6i	0.234153	+	0.405565i
$687$	166970.	−	118632.i	0.0134973	−	0.00958982i
$688$	302316.	−	523627.i	0.0243495	−	0.0421746i
$689$	8.34416e6	−	1.44525e7i	0.669630	−	1.15983i
$690$	8.36037e6	−	5.94002e6i	0.668502	−	0.474969i
$691$	7.00664e6	+	1.21359e7i	0.558232	+	0.966886i	0.997644	+	0.0686008i	$0.0218535\pi$
$691$	7.00664e6	+	1.21359e7i	0.558232	+	0.966886i	−0.439412	+	0.898286i	$0.644813\pi$
$692$	1.28915e6			0.102338
$693$	4.50898e6	−	859108.i	0.356652	−	0.0679540i
$694$	1.24757e7			0.983254
$695$	−6.30108e6	−	1.09138e7i	−0.494827	−	0.857065i
$696$	−733726.	−	7.77111e6i	−0.0574131	−	0.608079i
$697$	−4.31616e6	+	7.47581e6i	−0.336524	+	0.582876i
$698$	1.69505e6	−	2.93592e6i	0.131687	−	0.228089i
$699$	1.27808e7	+	5.85319e6i	0.989383	+	0.453106i
$700$	−1.12463e6	−	1.94791e6i	−0.0867488	−	0.150253i
$701$	−4.08006e6			−0.313597			−0.156799	−	0.987631i	$-0.550117\pi$
$701$	−4.08006e6			−0.313597			−0.156799	+	0.987631i	$0.550117\pi$
$702$	−2.44902e6	−	8.43996e6i	−0.187564	−	0.646394i
$703$	−1.27965e7			−0.976567
$704$	−247808.	−	429216.i	−0.0188445	−	0.0326396i
$705$	−1.35167e7	−	6.19022e6i	−1.02423	−	0.469066i
$706$	−48602.7	+	84182.3i	−0.00366985	+	0.00635637i
$707$	531068.	−	919838.i	0.0399578	−	0.0692090i
$708$	−406002.	−	4.30009e6i	−0.0304400	−	0.322399i
$709$	−1.14065e7	−	1.97566e7i	−0.852189	−	1.47603i	−0.879228	−	0.476400i	$-0.841941\pi$
$709$	−1.14065e7	−	1.97566e7i	−0.852189	−	1.47603i	0.0270394	−	0.999634i	$-0.491392\pi$
$710$	1.25888e7			0.937216
$711$	−4.41633e6	+	1.26730e7i	−0.327633	+	0.940169i
$712$	7.69917e6			0.569173
$713$	1.12126e7	+	1.94208e7i	0.826007	+	1.43069i
$714$	−1.36153e7	+	9.67363e6i	−0.999496	+	0.710140i
$715$	1.65499e6	−	2.86653e6i	0.121068	−	0.209697i
$716$	−2.87221e6	+	4.97481e6i	−0.209379	+	0.362655i
$717$	1.81525e7	−	1.28973e7i	1.31868	−	0.936919i
$718$	3.62715e6	+	6.28241e6i	0.262576	+	0.454794i
$719$	1.04115e7			0.751091			0.375546	−	0.926804i	$-0.377455\pi$
$719$	1.04115e7			0.751091			0.375546	+	0.926804i	$0.377455\pi$
$720$	−1.91665e6	−	2.22145e6i	−0.137788	−	0.159700i
$721$	3.17864e7			2.27721
$722$	4.00379e6	+	6.93477e6i	0.285844	+	0.495095i
$723$	−1.83002e6	−	1.93823e7i	−0.130200	−	1.37898i
$724$	519541.	−	899871.i	0.0368361	−	0.0638020i
$725$	−3.52278e6	+	6.10164e6i	−0.248909	+	0.431123i
$726$	−830020.	−	380123.i	−0.0584450	−	0.0267660i
$727$	−6.37443e6	−	1.10408e7i	−0.447307	−	0.774758i	0.550903	−	0.834569i	$-0.314283\pi$
$727$	−6.37443e6	−	1.10408e7i	−0.447307	−	0.774758i	−0.998210	+	0.0598113i	$0.980950\pi$
$728$	5.79475e6			0.405235
$729$	−1.21202e7	+	7.68055e6i	−0.844680	+	0.535271i
$730$	−5.87050e6			−0.407725
$731$	2.02626e6	+	3.50959e6i	0.140250	+	0.242920i
$732$	6.86979e6	+	3.14615e6i	0.473877	+	0.217021i
$733$	−6.43874e6	+	1.11522e7i	−0.442630	+	0.766658i	−0.997884	−	0.0650231i	$-0.979288\pi$
$733$	−6.43874e6	+	1.11522e7i	−0.442630	+	0.766658i	0.555254	+	0.831681i	$0.312621\pi$
$734$	−719962.	+	1.24701e6i	−0.0493253	+	0.0854339i
$735$	522695.	+	5.53602e6i	0.0356886	+	0.377989i
$736$	−1.78549e6	−	3.09256e6i	−0.121496	−	0.210438i
$737$	−6.09403e6			−0.413272
$738$	−3.19449e6	−	3.70250e6i	−0.215904	−	0.250238i
$739$	−734825.			−0.0494963			−0.0247482	−	0.999694i	$-0.507878\pi$
$739$	−734825.			−0.0494963			−0.0247482	+	0.999694i	$0.507878\pi$
$740$	2.28167e6	+	3.95197e6i	0.153170	+	0.265299i
$741$	1.55966e7	−	1.10813e7i	1.04348	−	0.741391i
$742$	8.98353e6	−	1.55599e7i	0.599014	−	1.03752i
$743$	8.28264e6	−	1.43459e7i	0.550423	−	0.953360i	−0.447821	−	0.894123i	$-0.647800\pi$
$743$	8.28264e6	−	1.43459e7i	0.550423	−	0.953360i	0.998244	−	0.0592372i	$-0.0188668\pi$
$744$	5.22989e6	−	3.71583e6i	0.346386	−	0.246106i
$745$	238082.	+	412370.i	0.0157158	+	0.0272205i
$746$	−5.59075e6			−0.367810
$747$	−204754.	+	587559.i	−0.0134255	+	0.0385256i
$748$	3.32185e6			0.217083
$749$	6.77112e6	+	1.17279e7i	0.441018	+	0.763865i
$750$	1.11282e6	+	1.17862e7i	0.0722387	+	0.765101i
$751$	9.00409e6	−	1.55955e7i	0.582559	−	1.00902i	−0.412616	−	0.910905i	$-0.635385\pi$
$751$	9.00409e6	−	1.55955e7i	0.582559	−	1.00902i	0.995175	−	0.0981169i	$-0.0312819\pi$
$752$	−2.58826e6	+	4.48300e6i	−0.166903	+	0.289084i
$753$	1.37435e7	+	6.29409e6i	0.883303	+	0.404525i
$754$	−9.07575e6	−	1.57197e7i	−0.581372	−	1.00697i
$755$	7.00513e6			0.447248
$756$	−2.63668e6	−	9.08667e6i	−0.167785	−	0.578229i
$757$	−802525.			−0.0509001			−0.0254501	−	0.999676i	$-0.508102\pi$
$757$	−802525.			−0.0509001			−0.0254501	+	0.999676i	$0.508102\pi$
$758$	4.78746e6	+	8.29212e6i	0.302644	+	0.524195i
$759$	−5.98041e6	−	2.73884e6i	−0.376814	−	0.172569i
$760$	3.19379e6	−	5.53181e6i	0.200573	−	0.347403i
$761$	−6.32595e6	+	1.09569e7i	−0.395971	+	0.685843i	−0.993225	−	0.116210i	$-0.962925\pi$
$761$	−6.32595e6	+	1.09569e7i	−0.395971	+	0.685843i	0.597253	+	0.802053i	$0.296259\pi$
$762$	1.32632e6	+	1.40474e7i	0.0827485	+	0.876414i
$763$	−5.81655e6	−	1.00746e7i	−0.361704	−	0.626490i
$764$	−2.41810e6			−0.149879
$765$	1.93176e7	−	3.68063e6i	1.19344	−	0.227389i
$766$	−9.07340e6			−0.558725
$767$	−5.02200e6	−	8.69836e6i	−0.308239	−	0.533886i
$768$	−832804.	+	591705.i	−0.0509495	+	0.0361995i
$769$	1.24798e7	−	2.16157e7i	0.761014	−	1.31811i	−0.181314	−	0.983425i	$-0.558035\pi$
$769$	1.24798e7	−	2.16157e7i	0.761014	−	1.31811i	0.942328	−	0.334690i	$-0.108632\pi$
$770$	1.78181e6	−	3.08618e6i	0.108301	−	0.187583i
$771$	−2.03086e7	+	1.44292e7i	−1.23039	+	0.874191i
$772$	4.31690e6	+	7.47710e6i	0.260693	+	0.451533i
$773$	−2.40583e7			−1.44816			−0.724080	−	0.689716i	$-0.757735\pi$
$773$	−2.40583e7			−1.44816			−0.724080	+	0.689716i	$0.757735\pi$
$774$	−2.25514e6	+	429679.i	−0.135307	+	0.0257805i
$775$	−5.79080e6			−0.346325
$776$	−3.22771e6	−	5.59056e6i	−0.192416	−	0.333274i
$777$	1.38326e6	+	1.46506e7i	0.0821963	+	0.870565i
$778$	2.44548e6	−	4.23569e6i	0.144849	−	0.250885i
$779$	5.32310e6	−	9.21988e6i	0.314283	−	0.544355i
$780$	−6.20324e6	−	2.84089e6i	−0.365075	−	0.167193i
$781$	−4.03707e6	−	6.99240e6i	−0.236831	−	0.410203i
$782$	2.39344e7			1.39960
$783$	−2.05202e7	+	2.13842e7i	−1.19613	+	1.24649i
$784$	1.93618e6			0.112501
$785$	−1.34722e7	−	2.33345e7i	−0.780304	−	1.35153i
$786$	1.35366e7	+	6.19935e6i	0.781545	+	0.357923i
$787$	−3.03596e6	+	5.25843e6i	−0.174726	+	0.302635i	−0.940067	−	0.340991i	$-0.889237\pi$
$787$	−3.03596e6	+	5.25843e6i	−0.174726	+	0.302635i	0.765340	+	0.643626i	$0.222571\pi$
$788$	3.82181e6	−	6.61958e6i	0.219257	−	0.379765i
$789$	1.81680e6	+	1.92422e7i	0.103900	+	1.10043i
$790$	5.20963e6	+	9.02335e6i	0.296988	+	0.514399i
$791$	1.98477e7			1.12789
$792$	−619248.	+	1.77698e6i	−0.0350794	+	0.100663i
$793$	1.75708e7			0.992220
$794$	−1.11108e7	−	1.92445e7i	−0.625453	−	1.08332i
$795$	−1.72451e7	+	1.22526e7i	−0.967715	+	0.687559i
$796$	8.14104e6	−	1.41007e7i	0.455405	−	0.788784i
$797$	−2.70086e6	+	4.67802e6i	−0.150611	+	0.260865i	−0.931452	−	0.363864i	$-0.881457\pi$
$797$	−2.70086e6	+	4.67802e6i	−0.150611	+	0.260865i	0.780842	+	0.624729i	$0.214791\pi$
$798$	1.67917e7	−	1.19305e7i	0.933441	−	0.663208i
$799$	−1.73477e7	−	3.00471e7i	−0.961336	−	1.66508i
$800$	922123.			0.0509406
$801$	−1.90965e7	−	2.21333e7i	−1.05165	−	1.21889i
$802$	−8.33000e6			−0.457308
$803$	1.88259e6	+	3.26074e6i	0.103031	+	0.178454i
$804$	1.18077e6	+	1.25059e7i	0.0644208	+	0.682299i
$805$	1.28381e7	−	2.22363e7i	0.698253	−	1.20941i
$806$	7.45942e6	−	1.29201e7i	0.404453	−	0.700532i
$807$	−3.67008e6	−	1.68078e6i	−0.198377	−	0.0908505i
$808$	217721.	+	377104.i	0.0117320	+	0.0203204i
$809$	1.21897e7			0.654819			0.327410	−	0.944882i	$-0.393824\pi$
$809$	1.21897e7			0.654819			0.327410	+	0.944882i	$0.393824\pi$
$810$	−1.63221e6	+	1.10198e7i	−0.0874105	+	0.590151i
$811$	1.04536e7			0.558103			0.279051	−	0.960276i	$-0.409980\pi$
$811$	1.04536e7			0.558103			0.279051	+	0.960276i	$0.409980\pi$
$812$	−9.77117e6	−	1.69242e7i	−0.520064	−	0.900777i
$813$	−1.54350e7	−	7.06876e6i	−0.818995	−	0.375074i
$814$	1.46340e6	−	2.53469e6i	0.0774110	−	0.134080i
$815$	−1.95585e6	+	3.38763e6i	−0.103143	+	0.178650i
$816$	−643637.	−	6.81695e6i	−0.0338389	−	0.358397i
$817$	−2.49898e6	−	4.32836e6i	−0.130981	−	0.226865i
$818$	−9.76909e6			−0.510471
$819$	−1.43729e7	−	1.66585e7i	−0.748745	−	0.867814i
$820$	−3.79654e6			−0.197176
$821$	−1.23881e7	−	2.14568e7i	−0.641426	−	1.11098i	−0.985115	−	0.171899i	$-0.945010\pi$
$821$	−1.23881e7	−	2.14568e7i	−0.641426	−	1.11098i	0.343688	−	0.939084i	$-0.388324\pi$
$822$	1.79538e7	−	1.27561e7i	0.926778	−	0.658474i
$823$	−1.41684e7	+	2.45403e7i	−0.729156	+	1.26294i	0.228084	+	0.973641i	$0.426754\pi$
$823$	−1.41684e7	+	2.45403e7i	−0.729156	+	1.26294i	−0.957240	+	0.289294i	$0.906580\pi$
$824$	−6.51571e6	+	1.12855e7i	−0.334306	+	0.579034i
$825$	1.38464e6	−	983784.i	0.0708275	−	0.0503228i
$826$	−5.40681e6	−	9.36486e6i	−0.275734	−	0.477586i
$827$	2.86986e7			1.45914			0.729570	−	0.683906i	$-0.239720\pi$
$827$	2.86986e7			1.45914			0.729570	+	0.683906i	$0.239720\pi$
$828$	−4.46177e6	+	1.28034e7i	−0.226168	+	0.649008i
$829$	6.45414e6			0.326176			0.163088	−	0.986612i	$-0.447855\pi$
$829$	6.45414e6			0.326176			0.163088	+	0.986612i	$0.447855\pi$
$830$	241534.	+	418349.i	0.0121698	+	0.0210787i
$831$	−2.33954e6	−	2.47788e7i	−0.117525	−	1.24474i
$832$	−1.18783e6	+	2.05739e6i	−0.0594904	+	0.103040i
$833$	−6.48859e6	+	1.12386e7i	−0.323995	+	0.561176i
$834$	1.51477e7	+	6.93719e6i	0.754107	+	0.345357i
$835$	−2.95298e6	−	5.11472e6i	−0.146570	−	0.253867i
$836$	−4.09682e6			−0.202736
$837$	−2.36539e7	−	5.81822e6i	−1.16705	−	0.287062i
$838$	1.80596e7			0.888377
$839$	1.18083e7	+	2.04525e7i	0.579138	+	1.00310i	0.995578	+	0.0939332i	$0.0299440\pi$
$839$	1.18083e7	+	2.04525e7i	0.579138	+	1.00310i	−0.416441	+	0.909163i	$0.636723\pi$
$840$	−6.67856e6	−	3.05857e6i	−0.326576	−	0.149562i
$841$	−2.03517e7	+	3.52501e7i	−0.992225	+	1.71858i
$842$	4.27315e6	−	7.40132e6i	0.207715	−	0.359773i
$843$	−51337.5	−	543731.i	−0.00248809	−	0.0263521i
$844$	−54137.8	−	93769.3i	−0.00261604	−	0.00453111i
$845$	1.64590e6			0.0792980
$846$	1.93073e7	−	3.67867e6i	0.927459	−	0.176711i
$847$	−2.28560e6			−0.109469
$848$	3.68296e6	+	6.37908e6i	0.175876	+	0.304627i
$849$	−2.88331e6	+	2.04859e6i	−0.137285	+	0.0975406i
$850$	−3.09025e6	+	5.35246e6i	−0.146705	+	0.254101i
$851$	1.05440e7	−	1.82628e7i	0.499094	−	0.864456i
$852$	−1.35673e7	+	9.63953e6i	−0.640316	+	0.454943i
$853$	−9.04842e6	−	1.56723e7i	−0.425795	−	0.737498i	0.570699	−	0.821159i	$-0.306672\pi$
$853$	−9.04842e6	−	1.56723e7i	−0.425795	−	0.737498i	−0.996494	+	0.0836607i	$0.973339\pi$
$854$	1.89171e7			0.887586
$855$	−2.38243e7	+	4.53931e6i	−1.11456	+	0.212361i
$856$	−5.55189e6			−0.258974
$857$	−2.02239e6	−	3.50287e6i	−0.0940615	−	0.162919i	0.815155	−	0.579243i	$-0.196652\pi$
$857$	−2.02239e6	−	3.50287e6i	−0.0940615	−	0.162919i	−0.909217	+	0.416324i	$0.863318\pi$
$858$	411337.	+	4.35659e6i	0.0190757	+	0.202036i
$859$	95082.3	−	164687.i	0.00439660	−	0.00761513i	−0.863819	−	0.503803i	$-0.831934\pi$
$859$	95082.3	−	164687.i	0.00439660	−	0.00761513i	0.868215	+	0.496188i	$0.165267\pi$
$860$	−891161.	+	1.54354e6i	−0.0410875	+	0.0711657i
$861$	−1.11312e7	−	5.09772e6i	−0.511721	−	0.234352i
$862$	−6.39566e6	−	1.10776e7i	−0.293168	−	0.507782i
$863$	−1.82273e7			−0.833098			−0.416549	−	0.909113i	$-0.636761\pi$
$863$	−1.82273e7			−0.833098			−0.416549	+	0.909113i	$0.636761\pi$
$864$	3.76663e6	+	926489.i	0.171660	+	0.0422236i
$865$	−3.80013e6			−0.172686
$866$	1.68922e6	+	2.92582e6i	0.0765406	+	0.132572i
$867$	2.16025e7	+	9.89328e6i	0.976016	+	0.446985i
$868$	8.03100e6	−	1.39101e7i	0.361801	−	0.626658i
$869$	3.34131e6	−	5.78733e6i	0.150096	−	0.259973i
$870$	2.16286e6	+	2.29075e7i	0.0968793	+	1.02608i
$871$	1.46054e7	+	2.52974e7i	0.652333	+	1.12987i
$872$	4.76920e6			0.212400
$873$	−8.06575e6	+	2.31453e7i	−0.358186	+	1.02784i
$874$	−2.95182e7			−1.30711
$875$	1.48196e7	+	2.56683e7i	0.654358	+	1.13338i
$876$	6.32678e6	−	4.49516e6i	0.278562	−	0.197918i
$877$	−5.12496e6	+	8.87669e6i	−0.225005	+	0.389720i	−0.956321	−	0.292319i	$-0.905573\pi$
$877$	−5.12496e6	+	8.87669e6i	−0.225005	+	0.389720i	0.731316	+	0.682039i	$0.238906\pi$
$878$	−3.32323e6	+	5.75601e6i	−0.145487	+	0.251991i
$879$	−2.82509e7	+	2.00722e7i	−1.23328	+	0.876240i
$880$	730484.	+	1.26523e6i	0.0317983	+	0.0550763i
$881$	2.10164e7			0.912261			0.456131	−	0.889913i	$-0.349235\pi$
$881$	2.10164e7			0.912261			0.456131	+	0.889913i	$0.349235\pi$
$882$	−4.80236e6	−	5.56606e6i	−0.207866	−	0.240922i
$883$	1.06683e7			0.460460			0.230230	−	0.973136i	$-0.426052\pi$
$883$	1.06683e7			0.460460			0.230230	+	0.973136i	$0.426052\pi$
$884$	−7.96141e6	−	1.37896e7i	−0.342657	−	0.593499i
$885$	1.19680e6	+	1.26757e7i	0.0513647	+	0.544019i
$886$	1.52935e7	−	2.64891e7i	0.654520	−	1.13366i
$887$	1.17542e7	−	2.03588e7i	0.501629	−	0.868847i	−0.498369	−	0.866965i	$-0.666067\pi$
$887$	1.17542e7	−	2.03588e7i	0.501629	−	0.868847i	0.999998	−	0.00188236i	$-0.000599175\pi$
$888$	−5.48512e6	−	2.51201e6i	−0.233429	−	0.106903i
$889$	1.76628e7	+	3.05929e7i	0.749559	+	1.29827i
$890$	−2.26955e7			−0.960427
$891$	6.64434e6	−	2.62731e6i	0.280387	−	0.110871i
$892$	6.38815e6			0.268821
$893$	2.13949e7	+	3.70570e7i	0.897803	+	1.55504i
$894$	−572347.	−	262117.i	−0.0239505	−	0.0109686i
$895$	8.46664e6	−	1.46646e7i	0.353308	−	0.611947i
$896$	−1.27885e6	+	2.21503e6i	−0.0532169	+	0.0921744i
$897$	2.96374e6	+	3.13898e7i	0.122987	+	1.30259i
$898$	−2.41680e6	−	4.18603e6i	−0.100012	−	0.173225i
$899$	−5.03126e7			−2.07624
$900$	−2.28716e6	−	2.65088e6i	−0.0941220	−	0.109090i
$901$	−4.93698e7			−2.02605
$902$	1.21750e6	+	2.10877e6i	0.0498256	+	0.0863004i
$903$	−4.68536e6	+	3.32894e6i	−0.191216	+	0.135859i
$904$	−4.06845e6	+	7.04677e6i	−0.165580	+	0.286793i
$905$	−1.53149e6	+	2.65262e6i	−0.0621575	+	0.107660i
$906$	−7.54960e6	+	5.36397e6i	−0.305565	+	0.217103i
$907$	8.51983e6	+	1.47568e7i	0.343885	+	0.595626i	0.985150	−	0.171693i	$-0.0549237\pi$
$907$	8.51983e6	+	1.47568e7i	0.343885	+	0.595626i	−0.641266	+	0.767319i	$0.721590\pi$
$908$	−2.89411e6			−0.116493
$909$	544065.	−	1.56124e6i	0.0218394	−	0.0626699i
$910$	−1.70817e7			−0.683796
$911$	−1.45646e7	−	2.52266e7i	−0.581436	−	1.00708i	−0.995309	−	0.0967422i	$-0.969158\pi$
$911$	−1.45646e7	−	2.52266e7i	−0.581436	−	1.00708i	0.413874	−	0.910334i	$-0.364176\pi$
$912$	793795.	+	8.40732e6i	0.0316025	+	0.334711i
$913$	154913.	−	268318.i	0.00615052	−	0.0106530i
$914$	−1.40216e7	+	2.42862e7i	−0.555179	+	0.961598i
$915$	−2.02506e7	−	9.27415e6i	−0.799624	−	0.366203i
$916$	105115.	+	182065.i	0.00413931	+	0.00716950i
$917$	3.72754e7			1.46386
$918$	−1.80007e7	+	1.87586e7i	−0.704988	+	0.734671i
$919$	1.97677e7			0.772088			0.386044	−	0.922480i	$-0.373841\pi$
$919$	1.97677e7			0.772088			0.386044	+	0.922480i	$0.373841\pi$
$920$	5.26323e6	+	9.11619e6i	0.205014	+	0.355094i
$921$	9.78739e6	+	4.48231e6i	0.380205	+	0.174122i
$922$	8.50244e6	−	1.47267e7i	0.329394	−	0.570528i
$923$	−1.93511e7	+	3.35171e7i	−0.747656	+	1.29498i
$924$	442855.	+	4.69041e6i	0.0170640	+	0.180730i
$925$	2.72275e6	+	4.71593e6i	0.104629	+	0.181223i
$926$	2.03873e7			0.781326
$927$	4.86043e7	−	9.26071e6i	1.85770	−	0.353953i
$928$	8.01174e6			0.305392
$929$	1.32211e7	+	2.28996e7i	0.502606	+	0.870538i	0.999995	+	0.00301121i	$0.000958499\pi$
$929$	1.32211e7	+	2.28996e7i	0.502606	+	0.870538i	−0.497390	+	0.867527i	$0.665708\pi$
$930$	−1.54166e7	+	1.09534e7i	−0.584494	+	0.415282i
$931$	8.00236e6	−	1.38605e7i	0.302583	−	0.524088i
$932$	−7.21422e6	+	1.24954e7i	−0.272051	+	0.471205i
$933$	−2.97031e7	+	2.11040e7i	−1.11712	+	0.793708i
$934$	201926.	+	349746.i	0.00757398	+	0.0131185i
$935$	−9.79208e6			−0.366308
$936$	8.86071e6	−	1.68826e6i	0.330582	−	0.0629867i
$937$	5.39424e6			0.200716			0.100358	−	0.994951i	$-0.468001\pi$
$937$	5.39424e6			0.200716			0.100358	+	0.994951i	$0.468001\pi$
$938$	1.57246e7	+	2.72358e7i	0.583541	+	1.01072i
$939$	−225633.	−	2.38975e6i	−0.00835102	−	0.0884481i
$940$	7.62962e6	−	1.32149e7i	0.281633	−	0.487802i
$941$	−5.43423e6	+	9.41237e6i	−0.200062	+	0.346517i	−0.948548	−	0.316633i	$-0.897448\pi$
$941$	−5.43423e6	+	9.41237e6i	−0.200062	+	0.346517i	0.748486	+	0.663150i	$0.230781\pi$
$942$	3.23870e7	+	1.48322e7i	1.18917	+	0.544601i
$943$	8.77224e6	+	1.51940e7i	0.321241	+	0.556406i
$944$	4.43324e6			0.161917
$945$	7.77235e6	+	2.67855e7i	0.283122	+	0.975709i
$946$	1.14313e6			0.0415306
$947$	−1.43823e7	−	2.49109e7i	−0.521140	−	0.902641i	−0.999698	−	0.0245849i	$-0.992174\pi$
$947$	−1.43823e7	−	2.49109e7i	−0.521140	−	0.902641i	0.478558	−	0.878056i	$-0.341160\pi$
$948$	−1.25239e7	−	5.73556e6i	−0.452605	−	0.207279i
$949$	9.02392e6	−	1.56299e7i	0.325259	−	0.563366i
$950$	3.81119e6	−	6.60117e6i	0.137010	−	0.237308i
$951$	−3.13359e6	−	3.31887e7i	−0.112354	−	1.18998i
$952$	−8.57144e6	−	1.48462e7i	−0.306522	−	0.530912i
$953$	−9.23014e6			−0.329212			−0.164606	−	0.986359i	$-0.552635\pi$
$953$	−9.23014e6			−0.329212			−0.164606	+	0.986359i	$0.552635\pi$
$954$	9.20337e6	−	2.64098e7i	0.327398	−	0.939495i
$955$	7.12802e6			0.252907
$956$	1.14279e7	+	1.97936e7i	0.404408	+	0.700455i
$957$	1.20303e7	−	8.54748e6i	0.424615	−	0.301688i
$958$	−5.23408e6	+	9.06569e6i	−0.184258	+	0.319144i
$959$	2.75697e7	−	4.77522e7i	0.968023	−	1.67667i
$960$	2.45492e6	−	1.74422e6i	0.0859725	−	0.0610833i
$961$	−6.36158e6	−	1.10186e7i	−0.222206	−	0.384873i
$962$	−1.40292e7			−0.488760
$963$	1.37705e7	+	1.59603e7i	0.478502	+	0.554596i
$964$	1.99825e7			0.692559
$965$	−1.27253e7	−	2.20408e7i	−0.439895	−	0.761921i
$966$	3.19083e6	+	3.37951e7i	0.110017	+	1.16523i
$967$	−2.04985e7	+	3.55045e7i	−0.704947	+	1.22100i	0.261764	+	0.965132i	$0.415696\pi$
$967$	−2.04985e7	+	3.55045e7i	−0.704947	+	1.22100i	−0.966711	+	0.255872i	$0.917637\pi$
$968$	468512.	−	811487.i	0.0160706	−	0.0278351i
$969$	−5.14605e7	−	2.35673e7i	−1.76062	−	0.806307i
$970$	9.51459e6	+	1.64798e7i	0.324684	+	0.562369i
$971$	−3.06547e7			−1.04340			−0.521698	−	0.853130i	$-0.674701\pi$
$971$	−3.06547e7			−1.04340			−0.521698	+	0.853130i	$0.674701\pi$
$972$	−6.67905e6	−	1.31262e7i	−0.226751	−	0.445628i
$973$	4.17119e7			1.41246
$974$	−5.77123e6	−	9.99606e6i	−0.194926	−	0.337623i
$975$	−7.40239e6	−	3.39006e6i	−0.249379	−	0.114208i
$976$	−3.87771e6	+	6.71639e6i	−0.130302	+	0.225690i
$977$	1.68449e7	−	2.91762e7i	0.564589	−	0.977897i	−0.432499	−	0.901634i	$-0.642368\pi$
$977$	1.68449e7	−	2.91762e7i	0.564589	−	0.977897i	0.997088	−	0.0762621i	$-0.0242986\pi$
$978$	−486113.	−	5.14856e6i	−0.0162514	−	0.172123i
$979$	7.27813e6	+	1.26061e7i	0.242696	+	0.420362i
$980$	−5.70744e6			−0.189835
$981$	−1.18292e7	−	1.37103e7i	−0.392448	−	0.454857i
$982$	−4.21792e7			−1.39579
$983$	−1.67943e6	−	2.90885e6i	−0.0554341	−	0.0960147i	0.836977	−	0.547239i	$-0.184321\pi$
$983$	−1.67943e6	−	2.90885e6i	−0.0554341	−	0.0960147i	−0.892411	+	0.451224i	$0.850988\pi$
$984$	4.09162e6	−	2.90709e6i	0.134713	−	0.0957130i
$985$	−1.12659e7	+	1.95131e7i	−0.369977	+	0.640818i
$986$	−2.68492e7	+	4.65042e7i	−0.879507	+	1.52335i
$987$	4.01135e7	−	2.85005e7i	1.31068	−	0.931236i
$988$	9.81877e6	+	1.70066e7i	0.320011	+	0.554275i
$989$	8.23642e6			0.267761
$990$	1.82541e6	−	5.23816e6i	0.0591932	−	0.169860i
$991$	−2.97153e7			−0.961160			−0.480580	−	0.876951i	$-0.659574\pi$
$991$	−2.97153e7			−0.961160			−0.480580	+	0.876951i	$0.659574\pi$
$992$	3.29245e6	+	5.70270e6i	0.106228	+	0.183993i
$993$	−782773.	−	8.29058e6i	−0.0251920	−	0.266816i
$994$	−2.08339e7	+	3.60853e7i	−0.668812	+	1.15842i
$995$	−2.39980e7	+	4.15658e7i	−0.768454	+	1.33100i
$996$	−580646.	−	265917.i	−0.0185465	−	0.00849373i
$997$	−2.10859e7	−	3.65219e7i	−0.671823	−	1.16363i	−0.977387	−	0.211459i	$-0.932178\pi$
$997$	−2.10859e7	−	3.65219e7i	−0.671823	−	1.16363i	0.305564	−	0.952171i	$-0.401155\pi$
$998$	−3.94412e7			−1.25350
$999$	6.38346e6	+	2.19990e7i	0.202368	+	0.697412i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	198.6.e.b.67.11	✓	24
3.2	odd	2		594.6.e.a.199.4		24
9.2	odd	6		594.6.e.a.397.4		24
9.7	even	3	inner	198.6.e.b.133.11	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
198.6.e.b.67.11	✓	24	1.1	even	1	trivial
198.6.e.b.133.11	yes	24	9.7	even	3	inner
594.6.e.a.199.4		24	3.2	odd	2
594.6.e.a.397.4		24	9.2	odd	6

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:	\( N \)	\(=\)	\( 198 = 2 \cdot 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	198.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 + 3.46410i) q^{2} +(14.1729 + 6.49073i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(23.5822 - 40.8457i) q^{5} +(5.86120 + 62.0777i) q^{6} +(78.0548 + 135.195i) q^{7} -64.0000 q^{8} +(158.741 + 183.985i) q^{9} +O(q^{10})\)	\(q+(2.00000 + 3.46410i) q^{2} +(14.1729 + 6.49073i) q^{3} +(-8.00000 + 13.8564i) q^{4} +(23.5822 - 40.8457i) q^{5} +(5.86120 + 62.0777i) q^{6} +(78.0548 + 135.195i) q^{7} -64.0000 q^{8} +(158.741 + 183.985i) q^{9} +188.658 q^{10} +(-60.5000 - 104.789i) q^{11} +(-203.321 + 144.459i) q^{12} +(-289.998 + 502.292i) q^{13} +(-312.219 + 540.780i) q^{14} +(599.346 - 425.834i) q^{15} +(-128.000 - 221.703i) q^{16} +1715.83 q^{17} +(-319.860 + 917.864i) q^{18} -2116.13 q^{19} +(377.316 + 653.530i) q^{20} +(228.748 + 2422.73i) q^{21} +(242.000 - 419.156i) q^{22} +(1743.64 - 3020.08i) q^{23} +(-907.064 - 415.407i) q^{24} +(450.255 + 779.865i) q^{25} -2319.99 q^{26} +(1055.62 + 3637.94i) q^{27} -2497.75 q^{28} +(3911.98 + 6775.76i) q^{29} +(2673.83 + 1224.53i) q^{30} +(-3215.29 + 5569.04i) q^{31} +(512.000 - 886.810i) q^{32} +(-177.301 - 1877.85i) q^{33} +(3431.66 + 5943.81i) q^{34} +7362.83 q^{35} +(-3819.29 + 727.701i) q^{36} +6047.12 q^{37} +(-4232.25 - 7330.48i) q^{38} +(-7370.35 + 5236.62i) q^{39} +(-1509.26 + 2614.12i) q^{40} +(-2515.49 + 4356.96i) q^{41} +(-7935.10 + 5637.87i) q^{42} +(1180.92 + 2045.42i) q^{43} +1936.00 q^{44} +(11258.4 - 2145.10i) q^{45} +13949.1 q^{46} +(-10110.4 - 17511.7i) q^{47} +(-375.117 - 3972.98i) q^{48} +(-3781.61 + 6549.93i) q^{49} +(-1801.02 + 3119.46i) q^{50} +(24318.3 + 11137.0i) q^{51} +(-4639.97 - 8036.67i) q^{52} -28773.1 q^{53} +(-10490.9 + 10932.6i) q^{54} -5706.90 q^{55} +(-4995.51 - 8652.47i) q^{56} +(-29991.6 - 13735.2i) q^{57} +(-15647.9 + 27103.0i) q^{58} +(-8658.67 + 14997.3i) q^{59} +(1105.76 + 11711.5i) q^{60} +(-15147.3 - 26235.9i) q^{61} -25722.3 q^{62} +(-12483.3 + 35821.8i) q^{63} +4096.00 q^{64} +(13677.6 + 23690.3i) q^{65} +(6150.47 - 4369.89i) q^{66} +(25181.9 - 43616.4i) q^{67} +(-13726.6 + 23775.2i) q^{68} +(44315.0 - 31485.7i) q^{69} +(14725.7 + 25505.6i) q^{70} +66728.4 q^{71} +(-10159.4 - 11775.0i) q^{72} -31117.1 q^{73} +(12094.2 + 20947.8i) q^{74} +(1319.52 + 13975.4i) q^{75} +(16929.0 - 29321.9i) q^{76} +(9444.63 - 16358.6i) q^{77} +(-32880.9 - 15058.4i) q^{78} +(27614.2 + 47829.1i) q^{79} -12074.1 q^{80} +(-8651.69 + 58411.8i) q^{81} -20123.9 q^{82} +(1280.27 + 2217.50i) q^{83} +(-35400.4 - 16212.2i) q^{84} +(40463.1 - 70084.2i) q^{85} +(-4723.69 + 8181.67i) q^{86} +(11464.5 + 121424. i) q^{87} +(3872.00 + 6706.50i) q^{88} -120300. q^{89} +(29947.7 + 34710.2i) q^{90} -90543.0 q^{91} +(27898.3 + 48321.3i) q^{92} +(-81717.0 + 58059.8i) q^{93} +(40441.5 - 70046.8i) q^{94} +(-49903.0 + 86434.6i) q^{95} +(13012.6 - 9245.39i) q^{96} +(50433.0 + 87352.6i) q^{97} -30252.8 q^{98} +(9675.76 - 27765.4i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9}+O(q^{10}) \) 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9	\( 24 q + 48 q^{2} + 21 q^{3} - 192 q^{4} - 7 q^{5} + 168 q^{6} + 24 q^{7} - 1536 q^{8} - 543 q^{9} - 56 q^{10} - 1452 q^{11} + 336 q^{12} - 688 q^{13} - 96 q^{14} - 1500 q^{15} - 3072 q^{16} + 3512 q^{17} + 1164 q^{18} - 3836 q^{19} - 112 q^{20} + 1842 q^{21} + 5808 q^{22} - 680 q^{23} - 1344 q^{24} - 7759 q^{25} - 5504 q^{26} + 3024 q^{27} - 768 q^{28} - 3210 q^{29} - 4596 q^{30} + 857 q^{31} + 12288 q^{32} - 5082 q^{33} + 7024 q^{34} + 29824 q^{35} + 13344 q^{36} + 7166 q^{37} - 7672 q^{38} - 23076 q^{39} + 448 q^{40} - 27726 q^{41} - 10680 q^{42} - 15092 q^{43} + 46464 q^{44} + 38667 q^{45} - 5440 q^{46} - 28938 q^{47} - 10752 q^{48} + 17322 q^{49} + 31036 q^{50} + 37032 q^{51} - 11008 q^{52} - 12652 q^{53} + 59832 q^{54} + 1694 q^{55} - 1536 q^{56} - 168660 q^{57} + 12840 q^{58} - 33123 q^{59} + 5616 q^{60} + 36262 q^{61} + 6856 q^{62} + 47496 q^{63} + 98304 q^{64} - 31470 q^{65} - 10164 q^{66} + 35563 q^{67} - 28096 q^{68} + 123459 q^{69} + 59648 q^{70} + 295146 q^{71} + 34752 q^{72} + 12056 q^{73} + 14332 q^{74} - 244221 q^{75} + 30688 q^{76} + 2904 q^{77} - 64200 q^{78} + 128058 q^{79} + 3584 q^{80} + 90621 q^{81} - 221808 q^{82} - 209888 q^{83} - 72192 q^{84} + 228182 q^{85} + 60368 q^{86} - 89802 q^{87} + 92928 q^{88} - 46724 q^{89} + 96972 q^{90} - 305924 q^{91} - 10880 q^{92} - 187767 q^{93} + 115752 q^{94} - 118660 q^{95} - 21504 q^{96} + 240799 q^{97} + 138576 q^{98} - 35211 q^{99}+O(q^{100}) \) 24 * q + 48 * q^2 + 21 * q^3 - 192 * q^4 - 7 * q^5 + 168 * q^6 + 24 * q^7 - 1536 * q^8 - 543 * q^9 - 56 * q^10 - 1452 * q^11 + 336 * q^12 - 688 * q^13 - 96 * q^14 - 1500 * q^15 - 3072 * q^16 + 3512 * q^17 + 1164 * q^18 - 3836 * q^19 - 112 * q^20 + 1842 * q^21 + 5808 * q^22 - 680 * q^23 - 1344 * q^24 - 7759 * q^25 - 5504 * q^26 + 3024 * q^27 - 768 * q^28 - 3210 * q^29 - 4596 * q^30 + 857 * q^31 + 12288 * q^32 - 5082 * q^33 + 7024 * q^34 + 29824 * q^35 + 13344 * q^36 + 7166 * q^37 - 7672 * q^38 - 23076 * q^39 + 448 * q^40 - 27726 * q^41 - 10680 * q^42 - 15092 * q^43 + 46464 * q^44 + 38667 * q^45 - 5440 * q^46 - 28938 * q^47 - 10752 * q^48 + 17322 * q^49 + 31036 * q^50 + 37032 * q^51 - 11008 * q^52 - 12652 * q^53 + 59832 * q^54 + 1694 * q^55 - 1536 * q^56 - 168660 * q^57 + 12840 * q^58 - 33123 * q^59 + 5616 * q^60 + 36262 * q^61 + 6856 * q^62 + 47496 * q^63 + 98304 * q^64 - 31470 * q^65 - 10164 * q^66 + 35563 * q^67 - 28096 * q^68 + 123459 * q^69 + 59648 * q^70 + 295146 * q^71 + 34752 * q^72 + 12056 * q^73 + 14332 * q^74 - 244221 * q^75 + 30688 * q^76 + 2904 * q^77 - 64200 * q^78 + 128058 * q^79 + 3584 * q^80 + 90621 * q^81 - 221808 * q^82 - 209888 * q^83 - 72192 * q^84 + 228182 * q^85 + 60368 * q^86 - 89802 * q^87 + 92928 * q^88 - 46724 * q^89 + 96972 * q^90 - 305924 * q^91 - 10880 * q^92 - 187767 * q^93 + 115752 * q^94 - 118660 * q^95 - 21504 * q^96 + 240799 * q^97 + 138576 * q^98 - 35211 * q^99

Introduction

L-functions

Modular forms

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