LMFDB - Embedded newform 230.6.a.i.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,6,Mod(1,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("230.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	230.a (trivial)

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:	yes
Analytic conductor:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} - 1156x^{4} + 593x^{3} + 338133x^{2} + 408388x - 13033476 $ x^6 - 3x^5 - 1156x^4 + 593x^3 + 338133x^2 + 408388*x - 13033476
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$20.8018$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} +22.8018 q^{3} +16.0000 q^{4} -25.0000 q^{5} +91.2074 q^{6} -73.3684 q^{7} +64.0000 q^{8} +276.924 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} +22.8018 q^{3} +16.0000 q^{4} -25.0000 q^{5} +91.2074 q^{6} -73.3684 q^{7} +64.0000 q^{8} +276.924 q^{9} -100.000 q^{10} +483.677 q^{11} +364.829 q^{12} -343.645 q^{13} -293.474 q^{14} -570.046 q^{15} +256.000 q^{16} +1938.38 q^{17} +1107.70 q^{18} +2178.12 q^{19} -400.000 q^{20} -1672.93 q^{21} +1934.71 q^{22} -529.000 q^{23} +1459.32 q^{24} +625.000 q^{25} -1374.58 q^{26} +773.531 q^{27} -1173.89 q^{28} +5333.02 q^{29} -2280.18 q^{30} +9915.55 q^{31} +1024.00 q^{32} +11028.7 q^{33} +7753.52 q^{34} +1834.21 q^{35} +4430.79 q^{36} -10504.0 q^{37} +8712.49 q^{38} -7835.73 q^{39} -1600.00 q^{40} +8725.73 q^{41} -6691.74 q^{42} -5711.81 q^{43} +7738.84 q^{44} -6923.10 q^{45} -2116.00 q^{46} -23538.2 q^{47} +5837.27 q^{48} -11424.1 q^{49} +2500.00 q^{50} +44198.6 q^{51} -5498.31 q^{52} -23884.2 q^{53} +3094.13 q^{54} -12091.9 q^{55} -4695.58 q^{56} +49665.2 q^{57} +21332.1 q^{58} +13345.8 q^{59} -9120.74 q^{60} -39892.8 q^{61} +39662.2 q^{62} -20317.5 q^{63} +4096.00 q^{64} +8591.11 q^{65} +44114.9 q^{66} -69345.4 q^{67} +31014.1 q^{68} -12062.2 q^{69} +7336.84 q^{70} +39019.4 q^{71} +17723.1 q^{72} +10955.4 q^{73} -42016.1 q^{74} +14251.2 q^{75} +34850.0 q^{76} -35486.6 q^{77} -31342.9 q^{78} -71745.1 q^{79} -6400.00 q^{80} -49654.6 q^{81} +34902.9 q^{82} +44582.3 q^{83} -26767.0 q^{84} -48459.5 q^{85} -22847.2 q^{86} +121603. q^{87} +30955.3 q^{88} +84970.6 q^{89} -27692.4 q^{90} +25212.6 q^{91} -8464.00 q^{92} +226093. q^{93} -94152.9 q^{94} -54453.1 q^{95} +23349.1 q^{96} +71729.4 q^{97} -45696.3 q^{98} +133942. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 24 q^{2} + 15 q^{3} + 96 q^{4} - 150 q^{5} + 60 q^{6} + 106 q^{7} + 384 q^{8} + 899 q^{9}+O(q^{10}) $ 6 * q + 24 * q^2 + 15 * q^3 + 96 * q^4 - 150 * q^5 + 60 * q^6 + 106 * q^7 + 384 * q^8 + 899 * q^9	\( 6 q + 24 q^{2} + 15 q^{3} + 96 q^{4} - 150 q^{5} + 60 q^{6} + 106 q^{7} + 384 q^{8} + 899 q^{9} - 600 q^{10} + 321 q^{11} + 240 q^{12} + 527 q^{13} + 424 q^{14} - 375 q^{15} + 1536 q^{16} - 660 q^{17} + 3596 q^{18} + 2749 q^{19} - 2400 q^{20} + 6002 q^{21} + 1284 q^{22} - 3174 q^{23} + 960 q^{24} + 3750 q^{25} + 2108 q^{26} + 15372 q^{27} + 1696 q^{28} + 3337 q^{29} - 1500 q^{30} + 31094 q^{31} + 6144 q^{32} + 15087 q^{33} - 2640 q^{34} - 2650 q^{35} + 14384 q^{36} + 27037 q^{37} + 10996 q^{38} + 38528 q^{39} - 9600 q^{40} + 33608 q^{41} + 24008 q^{42} + 17024 q^{43} + 5136 q^{44} - 22475 q^{45} - 12696 q^{46} + 16864 q^{47} + 3840 q^{48} + 6002 q^{49} + 15000 q^{50} + 5719 q^{51} + 8432 q^{52} - 8475 q^{53} + 61488 q^{54} - 8025 q^{55} + 6784 q^{56} + 9566 q^{57} + 13348 q^{58} + 7899 q^{59} - 6000 q^{60} + 25437 q^{61} + 124376 q^{62} - 13333 q^{63} + 24576 q^{64} - 13175 q^{65} + 60348 q^{66} - 25517 q^{67} - 10560 q^{68} - 7935 q^{69} - 10600 q^{70} + 17204 q^{71} + 57536 q^{72} + 760 q^{73} + 108148 q^{74} + 9375 q^{75} + 43984 q^{76} + 102330 q^{77} + 154112 q^{78} + 66972 q^{79} - 38400 q^{80} + 115874 q^{81} + 134432 q^{82} + 58523 q^{83} + 96032 q^{84} + 16500 q^{85} + 68096 q^{86} - 70854 q^{87} + 20544 q^{88} + 38406 q^{89} - 89900 q^{90} + 25111 q^{91} - 50784 q^{92} + 130338 q^{93} + 67456 q^{94} - 68725 q^{95} + 15360 q^{96} + 82861 q^{97} + 24008 q^{98} - 2973 q^{99}+O(q^{100}) \) 6 * q + 24 * q^2 + 15 * q^3 + 96 * q^4 - 150 * q^5 + 60 * q^6 + 106 * q^7 + 384 * q^8 + 899 * q^9 - 600 * q^10 + 321 * q^11 + 240 * q^12 + 527 * q^13 + 424 * q^14 - 375 * q^15 + 1536 * q^16 - 660 * q^17 + 3596 * q^18 + 2749 * q^19 - 2400 * q^20 + 6002 * q^21 + 1284 * q^22 - 3174 * q^23 + 960 * q^24 + 3750 * q^25 + 2108 * q^26 + 15372 * q^27 + 1696 * q^28 + 3337 * q^29 - 1500 * q^30 + 31094 * q^31 + 6144 * q^32 + 15087 * q^33 - 2640 * q^34 - 2650 * q^35 + 14384 * q^36 + 27037 * q^37 + 10996 * q^38 + 38528 * q^39 - 9600 * q^40 + 33608 * q^41 + 24008 * q^42 + 17024 * q^43 + 5136 * q^44 - 22475 * q^45 - 12696 * q^46 + 16864 * q^47 + 3840 * q^48 + 6002 * q^49 + 15000 * q^50 + 5719 * q^51 + 8432 * q^52 - 8475 * q^53 + 61488 * q^54 - 8025 * q^55 + 6784 * q^56 + 9566 * q^57 + 13348 * q^58 + 7899 * q^59 - 6000 * q^60 + 25437 * q^61 + 124376 * q^62 - 13333 * q^63 + 24576 * q^64 - 13175 * q^65 + 60348 * q^66 - 25517 * q^67 - 10560 * q^68 - 7935 * q^69 - 10600 * q^70 + 17204 * q^71 + 57536 * q^72 + 760 * q^73 + 108148 * q^74 + 9375 * q^75 + 43984 * q^76 + 102330 * q^77 + 154112 * q^78 + 66972 * q^79 - 38400 * q^80 + 115874 * q^81 + 134432 * q^82 + 58523 * q^83 + 96032 * q^84 + 16500 * q^85 + 68096 * q^86 - 70854 * q^87 + 20544 * q^88 + 38406 * q^89 - 89900 * q^90 + 25111 * q^91 - 50784 * q^92 + 130338 * q^93 + 67456 * q^94 - 68725 * q^95 + 15360 * q^96 + 82861 * q^97 + 24008 * q^98 - 2973 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	4.00000	0.707107
$2$	4.00000	0.707107
$3$	22.8018	1.46274	0.731369	−	0.681981i	$-0.238882\pi$
$3$	22.8018	1.46274	0.731369	+	0.681981i	$0.238882\pi$
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	91.2074	1.03431
$7$	−73.3684	−0.565931	−0.282966	−	0.959130i	$-0.591318\pi$
$7$	−73.3684	−0.565931	−0.282966	+	0.959130i	$0.591318\pi$
$8$	64.0000	0.353553
$9$	276.924	1.13961
$10$	−100.000	−0.316228
$11$	483.677	1.20524	0.602620	−	0.798028i	$-0.294123\pi$
$11$	483.677	1.20524	0.602620	+	0.798028i	$0.294123\pi$
$12$	364.829	0.731369
$13$	−343.645	−0.563964	−0.281982	−	0.959420i	$-0.590992\pi$
$13$	−343.645	−0.563964	−0.281982	+	0.959420i	$0.590992\pi$
$14$	−293.474	−0.400174
$15$	−570.046	−0.654157
$16$	256.000	0.250000
$17$	1938.38	1.62673	0.813367	−	0.581751i	$-0.197632\pi$
$17$	1938.38	1.62673	0.813367	+	0.581751i	$0.197632\pi$
$18$	1107.70	0.805823
$19$	2178.12	1.38420	0.692099	−	0.721802i	$-0.256686\pi$
$19$	2178.12	1.38420	0.692099	+	0.721802i	$0.256686\pi$
$20$	−400.000	−0.223607
$21$	−1672.93	−0.827810
$22$	1934.71	0.852234
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	1459.32	0.517156
$25$	625.000	0.200000
$26$	−1374.58	−0.398782
$27$	773.531	0.204206
$28$	−1173.89	−0.282966
$29$	5333.02	1.17755	0.588773	−	0.808298i	$-0.299611\pi$
$29$	5333.02	1.17755	0.588773	+	0.808298i	$0.299611\pi$
$30$	−2280.18	−0.462559
$31$	9915.55	1.85316	0.926579	−	0.376100i	$-0.122735\pi$
$31$	9915.55	1.85316	0.926579	+	0.376100i	$0.122735\pi$
$32$	1024.00	0.176777
$33$	11028.7	1.76295
$34$	7753.52	1.15027
$35$	1834.21	0.253092
$36$	4430.79	0.569803
$37$	−10504.0	−1.26140	−0.630698	−	0.776028i	$-0.717232\pi$
$37$	−10504.0	−1.26140	−0.630698	+	0.776028i	$0.717232\pi$
$38$	8712.49	0.978776
$39$	−7835.73	−0.824932
$40$	−1600.00	−0.158114
$41$	8725.73	0.810666	0.405333	−	0.914169i	$-0.367156\pi$
$41$	8725.73	0.810666	0.405333	+	0.914169i	$0.367156\pi$
$42$	−6691.74	−0.585350
$43$	−5711.81	−0.471088	−0.235544	−	0.971864i	$-0.575687\pi$
$43$	−5711.81	−0.471088	−0.235544	+	0.971864i	$0.575687\pi$
$44$	7738.84	0.602620
$45$	−6923.10	−0.509647
$46$	−2116.00	−0.147442
$47$	−23538.2	−1.55428	−0.777139	−	0.629329i	$-0.783330\pi$
$47$	−23538.2	−1.55428	−0.777139	+	0.629329i	$0.783330\pi$
$48$	5837.27	0.365685
$49$	−11424.1	−0.679722
$50$	2500.00	0.141421
$51$	44198.6	2.37949
$52$	−5498.31	−0.281982
$53$	−23884.2	−1.16794	−0.583971	−	0.811774i	$-0.698502\pi$
$53$	−23884.2	−1.16794	−0.583971	+	0.811774i	$0.698502\pi$
$54$	3094.13	0.144395
$55$	−12091.9	−0.539000
$56$	−4695.58	−0.200087
$57$	49665.2	2.02472
$58$	21332.1	0.832651
$59$	13345.8	0.499131	0.249565	−	0.968358i	$-0.419712\pi$
$59$	13345.8	0.499131	0.249565	+	0.968358i	$0.419712\pi$
$60$	−9120.74	−0.327078
$61$	−39892.8	−1.37268	−0.686341	−	0.727280i	$-0.740784\pi$
$61$	−39892.8	−1.37268	−0.686341	+	0.727280i	$0.740784\pi$
$62$	39662.2	1.31038
$63$	−20317.5	−0.644938
$64$	4096.00	0.125000
$65$	8591.11	0.252212
$66$	44114.9	1.24660
$67$	−69345.4	−1.88725	−0.943627	−	0.331009i	$-0.892611\pi$
$67$	−69345.4	−1.88725	−0.943627	+	0.331009i	$0.892611\pi$
$68$	31014.1	0.813367
$69$	−12062.2	−0.305002
$70$	7336.84	0.178963
$71$	39019.4	0.918618	0.459309	−	0.888276i	$-0.348097\pi$
$71$	39019.4	0.918618	0.459309	+	0.888276i	$0.348097\pi$
$72$	17723.1	0.402911
$73$	10955.4	0.240614	0.120307	−	0.992737i	$-0.461612\pi$
$73$	10955.4	0.240614	0.120307	+	0.992737i	$0.461612\pi$
$74$	−42016.1	−0.891942
$75$	14251.2	0.292548
$76$	34850.0	0.692099
$77$	−35486.6	−0.682084
$78$	−31342.9	−0.583315
$79$	−71745.1	−1.29338	−0.646688	−	0.762755i	$-0.723846\pi$
$79$	−71745.1	−1.29338	−0.646688	+	0.762755i	$0.723846\pi$
$80$	−6400.00	−0.111803
$81$	−49654.6	−0.840905
$82$	34902.9	0.573228
$83$	44582.3	0.710342	0.355171	−	0.934801i	$-0.384423\pi$
$83$	44582.3	0.710342	0.355171	+	0.934801i	$0.384423\pi$
$84$	−26767.0	−0.413905
$85$	−48459.5	−0.727498
$86$	−22847.2	−0.333110
$87$	121603.	1.72244
$88$	30955.3	0.426117
$89$	84970.6	1.13709	0.568543	−	0.822653i	$-0.307507\pi$
$89$	84970.6	1.13709	0.568543	+	0.822653i	$0.307507\pi$
$90$	−27692.4	−0.360375
$91$	25212.6	0.319165
$92$	−8464.00	−0.104257
$93$	226093.	2.71069
$94$	−94152.9	−1.09904
$95$	−54453.1	−0.619032
$96$	23349.1	0.258578
$97$	71729.4	0.774048	0.387024	−	0.922070i	$-0.373503\pi$
$97$	71729.4	0.774048	0.387024	+	0.922070i	$0.373503\pi$
$98$	−45696.3	−0.480636
$99$	133942.	1.37350
$100$	10000.0	0.100000
$101$	103187.	1.00652	0.503261	−	0.864135i	$-0.332133\pi$
$101$	103187.	1.00652	0.503261	+	0.864135i	$0.332133\pi$
$102$	176795.	1.68255
$103$	103379.	0.960150	0.480075	−	0.877227i	$-0.340609\pi$
$103$	103379.	0.960150	0.480075	+	0.877227i	$0.340609\pi$
$104$	−21993.3	−0.199391
$105$	41823.4	0.370208
$106$	−95536.9	−0.825860
$107$	−228901.	−1.93281	−0.966403	−	0.257032i	$-0.917255\pi$
$107$	−228901.	−1.93281	−0.966403	+	0.257032i	$0.917255\pi$
$108$	12376.5	0.102103
$109$	−20893.9	−0.168443	−0.0842215	−	0.996447i	$-0.526840\pi$
$109$	−20893.9	−0.168443	−0.0842215	+	0.996447i	$0.526840\pi$
$110$	−48367.7	−0.381131
$111$	−239511.	−1.84509
$112$	−18782.3	−0.141483
$113$	−88876.6	−0.654774	−0.327387	−	0.944890i	$-0.606168\pi$
$113$	−88876.6	−0.654774	−0.327387	+	0.944890i	$0.606168\pi$
$114$	198661.	1.43169
$115$	13225.0	0.0932505
$116$	85328.3	0.588773
$117$	−95163.4	−0.642696
$118$	53383.2	0.352939
$119$	−142216.	−0.920620
$120$	−36482.9	−0.231279
$121$	72892.6	0.452606
$122$	−159571.	−0.970633
$123$	198963.	1.18579
$124$	158649.	0.926579
$125$	−15625.0	−0.0894427
$126$	−81269.9	−0.456040
$127$	125677.	0.691425	0.345712	−	0.938341i	$-0.387637\pi$
$127$	125677.	0.691425	0.345712	+	0.938341i	$0.387637\pi$
$128$	16384.0	0.0883883
$129$	−130240.	−0.689079
$130$	34364.5	0.178341
$131$	20221.6	0.102952	0.0514762	−	0.998674i	$-0.483607\pi$
$131$	20221.6	0.102952	0.0514762	+	0.998674i	$0.483607\pi$
$132$	176460.	0.881476
$133$	−159805.	−0.783361
$134$	−277382.	−1.33449
$135$	−19338.3	−0.0913237
$136$	124056.	0.575137
$137$	388954.	1.77050	0.885251	−	0.465114i	$-0.153987\pi$
$137$	388954.	1.77050	0.885251	+	0.465114i	$0.153987\pi$
$138$	−48248.7	−0.215669
$139$	−135664.	−0.595563	−0.297781	−	0.954634i	$-0.596247\pi$
$139$	−135664.	−0.595563	−0.297781	+	0.954634i	$0.596247\pi$
$140$	29347.4	0.126546
$141$	−536715.	−2.27350
$142$	156078.	0.649561
$143$	−166213.	−0.679712
$144$	70892.6	0.284901
$145$	−133325.	−0.526615
$146$	43821.6	0.170140
$147$	−260490.	−0.994255
$148$	−168065.	−0.630698
$149$	46534.5	0.171716	0.0858578	−	0.996307i	$-0.472637\pi$
$149$	46534.5	0.171716	0.0858578	+	0.996307i	$0.472637\pi$
$150$	57004.6	0.206863
$151$	−109523.	−0.390898	−0.195449	−	0.980714i	$-0.562616\pi$
$151$	−109523.	−0.390898	−0.195449	+	0.980714i	$0.562616\pi$
$152$	139400.	0.489388
$153$	536784.	1.85384
$154$	−141946.	−0.482306
$155$	−247889.	−0.828757
$156$	−125372.	−0.412466
$157$	−163849.	−0.530510	−0.265255	−	0.964178i	$-0.585456\pi$
$157$	−163849.	−0.530510	−0.265255	+	0.964178i	$0.585456\pi$
$158$	−286980.	−0.914555
$159$	−544604.	−1.70840
$160$	−25600.0	−0.0790569
$161$	38811.9	0.118005
$162$	−198618.	−0.594610
$163$	50056.1	0.147567	0.0737833	−	0.997274i	$-0.476493\pi$
$163$	50056.1	0.147567	0.0737833	+	0.997274i	$0.476493\pi$
$164$	139612.	0.405333
$165$	−275718.	−0.788417
$166$	178329.	0.502288
$167$	−535735.	−1.48648	−0.743239	−	0.669026i	$-0.766711\pi$
$167$	−535735.	−1.48648	−0.743239	+	0.669026i	$0.766711\pi$
$168$	−107068.	−0.292675
$169$	−253201.	−0.681945
$170$	−193838.	−0.514419
$171$	603175.	1.57744
$172$	−91388.9	−0.235544
$173$	393143.	0.998700	0.499350	−	0.866400i	$-0.333572\pi$
$173$	393143.	0.998700	0.499350	+	0.866400i	$0.333572\pi$
$174$	486411.	1.21795
$175$	−45855.2	−0.113186
$176$	123821.	0.301310
$177$	304309.	0.730098
$178$	339882.	0.804041
$179$	−261626.	−0.610307	−0.305153	−	0.952303i	$-0.598708\pi$
$179$	−261626.	−0.610307	−0.305153	+	0.952303i	$0.598708\pi$
$180$	−110770.	−0.254823
$181$	−172262.	−0.390835	−0.195417	−	0.980720i	$-0.562606\pi$
$181$	−172262.	−0.390835	−0.195417	+	0.980720i	$0.562606\pi$
$182$	100851.	0.225684
$183$	−909630.	−2.00788
$184$	−33856.0	−0.0737210
$185$	262601.	0.564114
$186$	904371.	1.91674
$187$	937550.	1.96061
$188$	−376611.	−0.777139
$189$	−56752.8	−0.115567
$190$	−217812.	−0.437722
$191$	−930319.	−1.84522	−0.922611	−	0.385732i	$-0.873949\pi$
$191$	−930319.	−1.84522	−0.922611	+	0.385732i	$0.873949\pi$
$192$	93396.4	0.182842
$193$	678348.	1.31087	0.655434	−	0.755252i	$-0.272486\pi$
$193$	678348.	1.31087	0.655434	+	0.755252i	$0.272486\pi$
$194$	286917.	0.547334
$195$	195893.	0.368921
$196$	−182785.	−0.339861
$197$	−475035.	−0.872088	−0.436044	−	0.899925i	$-0.643621\pi$
$197$	−475035.	−0.872088	−0.436044	+	0.899925i	$0.643621\pi$
$198$	535767.	0.971210
$199$	−396720.	−0.710153	−0.355076	−	0.934837i	$-0.615545\pi$
$199$	−396720.	−0.710153	−0.355076	+	0.934837i	$0.615545\pi$
$200$	40000.0	0.0707107
$201$	−1.58120e6	−2.76056
$202$	412750.	0.711718
$203$	−391275.	−0.666411
$204$	707178.	1.18974
$205$	−218143.	−0.362541
$206$	413516.	0.678929
$207$	−146493.	−0.237624
$208$	−87973.0	−0.140991
$209$	1.05351e6	1.66829
$210$	167293.	0.261777
$211$	431006.	0.666464	0.333232	−	0.942845i	$-0.391861\pi$
$211$	431006.	0.666464	0.333232	+	0.942845i	$0.391861\pi$
$212$	−382148.	−0.583971
$213$	889715.	1.34370
$214$	−915604.	−1.36670
$215$	142795.	0.210677
$216$	49506.0	0.0721977
$217$	−727488.	−1.04876
$218$	−83575.5	−0.119107
$219$	249803.	0.351956
$220$	−193471.	−0.269500
$221$	−666114.	−0.917419
$222$	−958045.	−1.30468
$223$	−941740.	−1.26814	−0.634072	−	0.773274i	$-0.718618\pi$
$223$	−941740.	−1.26814	−0.634072	+	0.773274i	$0.718618\pi$
$224$	−75129.2	−0.100043
$225$	173078.	0.227921
$226$	−355506.	−0.462995
$227$	−925424.	−1.19200	−0.596000	−	0.802985i	$-0.703244\pi$
$227$	−925424.	−1.19200	−0.596000	+	0.802985i	$0.703244\pi$
$228$	794643.	1.01236
$229$	721628.	0.909337	0.454669	−	0.890661i	$-0.349758\pi$
$229$	721628.	0.909337	0.454669	+	0.890661i	$0.349758\pi$
$230$	52900.0	0.0659380
$231$	−809160.	−0.997711
$232$	341313.	0.416326
$233$	1.40365e6	1.69383	0.846914	−	0.531730i	$-0.178458\pi$
$233$	1.40365e6	1.69383	0.846914	+	0.531730i	$0.178458\pi$
$234$	−380654.	−0.454455
$235$	588455.	0.695094
$236$	213533.	0.249565
$237$	−1.63592e6	−1.89187
$238$	−568863.	−0.650977
$239$	996800.	1.12879	0.564395	−	0.825505i	$-0.309109\pi$
$239$	996800.	1.12879	0.564395	+	0.825505i	$0.309109\pi$
$240$	−145932.	−0.163539
$241$	−320198.	−0.355121	−0.177560	−	0.984110i	$-0.556820\pi$
$241$	−320198.	−0.355121	−0.177560	+	0.984110i	$0.556820\pi$
$242$	291571.	0.320041
$243$	−1.32018e6	−1.43423
$244$	−638285.	−0.686341
$245$	285602.	0.303981
$246$	795851.	0.838482
$247$	−748500.	−0.780638
$248$	634595.	0.655190
$249$	1.01656e6	1.03905
$250$	−62500.0	−0.0632456
$251$	−1.89409e6	−1.89765	−0.948827	−	0.315795i	$-0.897729\pi$
$251$	−1.89409e6	−1.89765	−0.948827	+	0.315795i	$0.897729\pi$
$252$	−325080.	−0.322469
$253$	−255865.	−0.251310
$254$	502706.	0.488911
$255$	−1.10497e6	−1.06414
$256$	65536.0	0.0625000
$257$	−427835.	−0.404058	−0.202029	−	0.979380i	$-0.564754\pi$
$257$	−427835.	−0.404058	−0.202029	+	0.979380i	$0.564754\pi$
$258$	−520959.	−0.487253
$259$	770664.	0.713864
$260$	137458.	0.126106
$261$	1.47684e6	1.34194
$262$	80886.2	0.0727983
$263$	2.03973e6	1.81838	0.909188	−	0.416386i	$-0.136703\pi$
$263$	2.03973e6	1.81838	0.909188	+	0.416386i	$0.136703\pi$
$264$	705839.	0.623298
$265$	597106.	0.522320
$266$	−639221.	−0.553920
$267$	1.93749e6	1.66326
$268$	−1.10953e6	−0.943627
$269$	1.02723e6	0.865539	0.432769	−	0.901505i	$-0.357536\pi$
$269$	1.02723e6	0.865539	0.432769	+	0.901505i	$0.357536\pi$
$270$	−77353.1	−0.0645756
$271$	920534.	0.761406	0.380703	−	0.924697i	$-0.375682\pi$
$271$	920534.	0.761406	0.380703	+	0.924697i	$0.375682\pi$
$272$	496225.	0.406684
$273$	574895.	0.466855
$274$	1.55581e6	1.25193
$275$	302298.	0.241048
$276$	−192995.	−0.152501
$277$	−84402.7	−0.0660932	−0.0330466	−	0.999454i	$-0.510521\pi$
$277$	−84402.7	−0.0660932	−0.0330466	+	0.999454i	$0.510521\pi$
$278$	−542656.	−0.421127
$279$	2.74585e6	2.11187
$280$	117389.	0.0894816
$281$	−1.50165e6	−1.13450	−0.567248	−	0.823547i	$-0.691992\pi$
$281$	−1.50165e6	−1.13450	−0.567248	+	0.823547i	$0.691992\pi$
$282$	−2.14686e6	−1.60761
$283$	1.21354e6	0.900719	0.450359	−	0.892847i	$-0.351296\pi$
$283$	1.21354e6	0.900719	0.450359	+	0.892847i	$0.351296\pi$
$284$	624311.	0.459309
$285$	−1.24163e6	−0.905483
$286$	−664852.	−0.480629
$287$	−640193.	−0.458782
$288$	283570.	0.201456
$289$	2.33746e6	1.64626
$290$	−533302.	−0.372373
$291$	1.63556e6	1.13223
$292$	175286.	0.120307
$293$	−1.74980e6	−1.19074	−0.595372	−	0.803450i	$-0.702995\pi$
$293$	−1.74980e6	−1.19074	−0.595372	+	0.803450i	$0.702995\pi$
$294$	−1.04196e6	−0.703045
$295$	−333645.	−0.223218
$296$	−672258.	−0.445971
$297$	374140.	0.246117
$298$	186138.	0.121421
$299$	181788.	0.117595
$300$	228018.	0.146274
$301$	419066.	0.266604
$302$	−438092.	−0.276406
$303$	2.35286e6	1.47228
$304$	557599.	0.346050
$305$	997320.	0.613882
$306$	2.14714e6	1.31086
$307$	−1.96554e6	−1.19025	−0.595123	−	0.803635i	$-0.702897\pi$
$307$	−1.96554e6	−1.19025	−0.595123	+	0.803635i	$0.702897\pi$
$308$	−567786.	−0.341042
$309$	2.35723e6	1.40445
$310$	−991555.	−0.586020
$311$	2.68058e6	1.57155	0.785773	−	0.618515i	$-0.212265\pi$
$311$	2.68058e6	1.57155	0.785773	+	0.618515i	$0.212265\pi$
$312$	−501487.	−0.291657
$313$	−2.81291e6	−1.62291	−0.811456	−	0.584413i	$-0.801325\pi$
$313$	−2.81291e6	−1.62291	−0.811456	+	0.584413i	$0.801325\pi$
$314$	−655395.	−0.375127
$315$	507937.	0.288425
$316$	−1.14792e6	−0.646688
$317$	−2.68808e6	−1.50243	−0.751215	−	0.660058i	$-0.770532\pi$
$317$	−2.68808e6	−1.50243	−0.751215	+	0.660058i	$0.770532\pi$
$318$	−2.17842e6	−1.20802
$319$	2.57946e6	1.41923
$320$	−102400.	−0.0559017
$321$	−5.21936e6	−2.82719
$322$	155247.	0.0834420
$323$	4.22203e6	2.25172
$324$	−794474.	−0.420453
$325$	−214778.	−0.112793
$326$	200224.	0.104345
$327$	−476419.	−0.246388
$328$	558447.	0.286614
$329$	1.72696e6	0.879615
$330$	−1.10287e6	−0.557495
$331$	553276.	0.277570	0.138785	−	0.990323i	$-0.455680\pi$
$331$	553276.	0.277570	0.138785	+	0.990323i	$0.455680\pi$
$332$	713317.	0.355171
$333$	−2.90882e6	−1.43749
$334$	−2.14294e6	−1.05110
$335$	1.73363e6	0.844006
$336$	−428271.	−0.206953
$337$	1.56218e6	0.749302	0.374651	−	0.927166i	$-0.377763\pi$
$337$	1.56218e6	0.749302	0.374651	+	0.927166i	$0.377763\pi$
$338$	−1.01281e6	−0.482208
$339$	−2.02655e6	−0.957763
$340$	−775352.	−0.363749
$341$	4.79592e6	2.23350
$342$	2.41270e6	1.11542
$343$	2.07127e6	0.950607
$344$	−365556.	−0.166555
$345$	301554.	0.136401
$346$	1.57257e6	0.706188
$347$	3.21668e6	1.43412	0.717058	−	0.697013i	$-0.245488\pi$
$347$	3.21668e6	1.43412	0.717058	+	0.697013i	$0.245488\pi$
$348$	1.94564e6	0.861222
$349$	−63855.8	−0.0280632	−0.0140316	−	0.999902i	$-0.504467\pi$
$349$	−63855.8	−0.0280632	−0.0140316	+	0.999902i	$0.504467\pi$
$350$	−183421.	−0.0800348
$351$	−265820.	−0.115165
$352$	495285.	0.213059
$353$	−2.73425e6	−1.16789	−0.583944	−	0.811794i	$-0.698491\pi$
$353$	−2.73425e6	−1.16789	−0.583944	+	0.811794i	$0.698491\pi$
$354$	1.21723e6	0.516257
$355$	−975486.	−0.410819
$356$	1.35953e6	0.568543
$357$	−3.24278e6	−1.34663
$358$	−1.04650e6	−0.431552
$359$	537313.	0.220035	0.110017	−	0.993930i	$-0.464909\pi$
$359$	537313.	0.220035	0.110017	+	0.993930i	$0.464909\pi$
$360$	−443079.	−0.180187
$361$	2.26812e6	0.916006
$362$	−689048.	−0.276362
$363$	1.66209e6	0.662044
$364$	403402.	0.159582
$365$	−273885.	−0.107606
$366$	−3.63852e6	−1.41978
$367$	1.24579e6	0.482812	0.241406	−	0.970424i	$-0.422391\pi$
$367$	1.24579e6	0.482812	0.241406	+	0.970424i	$0.422391\pi$
$368$	−135424.	−0.0521286
$369$	2.41636e6	0.923840
$370$	1.05040e6	0.398889
$371$	1.75235e6	0.660975
$372$	3.61748e6	1.35534
$373$	−76868.2	−0.0286072	−0.0143036	−	0.999898i	$-0.504553\pi$
$373$	−76868.2	−0.0286072	−0.0143036	+	0.999898i	$0.504553\pi$
$374$	3.75020e6	1.38636
$375$	−356279.	−0.130831
$376$	−1.50645e6	−0.549520
$377$	−1.83266e6	−0.664093
$378$	−227011.	−0.0817179
$379$	1.55101e6	0.554646	0.277323	−	0.960777i	$-0.410553\pi$
$379$	1.55101e6	0.554646	0.277323	+	0.960777i	$0.410553\pi$
$380$	−871249.	−0.309516
$381$	2.86566e6	1.01137
$382$	−3.72128e6	−1.30477
$383$	673724.	0.234685	0.117342	−	0.993092i	$-0.462563\pi$
$383$	673724.	0.234685	0.117342	+	0.993092i	$0.462563\pi$
$384$	373585.	0.129289
$385$	887165.	0.305037
$386$	2.71339e6	0.926924
$387$	−1.58174e6	−0.536855
$388$	1.14767e6	0.387024
$389$	807964.	0.270719	0.135359	−	0.990797i	$-0.456781\pi$
$389$	807964.	0.270719	0.135359	+	0.990797i	$0.456781\pi$
$390$	783573.	0.260866
$391$	−1.02540e6	−0.339198
$392$	−731141.	−0.240318
$393$	461089.	0.150592
$394$	−1.90014e6	−0.616659
$395$	1.79363e6	0.578415
$396$	2.14307e6	0.686749
$397$	2.50880e6	0.798897	0.399448	−	0.916756i	$-0.369202\pi$
$397$	2.50880e6	0.798897	0.399448	+	0.916756i	$0.369202\pi$
$398$	−1.58688e6	−0.502154
$399$	−3.64386e6	−1.14585
$400$	160000.	0.0500000
$401$	−2.58452e6	−0.802636	−0.401318	−	0.915939i	$-0.631448\pi$
$401$	−2.58452e6	−0.802636	−0.401318	+	0.915939i	$0.631448\pi$
$402$	−6.32481e6	−1.95201
$403$	−3.40742e6	−1.04511
$404$	1.65100e6	0.503261
$405$	1.24137e6	0.376064
$406$	−1.56510e6	−0.471224
$407$	−5.08056e6	−1.52029
$408$	2.82871e6	0.841276
$409$	−2.96893e6	−0.877590	−0.438795	−	0.898587i	$-0.644595\pi$
$409$	−2.96893e6	−0.877590	−0.438795	+	0.898587i	$0.644595\pi$
$410$	−872573.	−0.256355
$411$	8.86886e6	2.58978
$412$	1.65406e6	0.480075
$413$	−979159.	−0.282474
$414$	−585971.	−0.168026
$415$	−1.11456e6	−0.317675
$416$	−351892.	−0.0996956
$417$	−3.09339e6	−0.871153
$418$	4.21403e6	1.17966
$419$	−3.22287e6	−0.896826	−0.448413	−	0.893827i	$-0.648011\pi$
$419$	−3.22287e6	−0.896826	−0.448413	+	0.893827i	$0.648011\pi$
$420$	669174.	0.185104
$421$	−4.44425e6	−1.22206	−0.611030	−	0.791607i	$-0.709245\pi$
$421$	−4.44425e6	−1.22206	−0.611030	+	0.791607i	$0.709245\pi$
$422$	1.72402e6	0.471261
$423$	−6.51830e6	−1.77126
$424$	−1.52859e6	−0.412930
$425$	1.21149e6	0.325347
$426$	3.55886e6	0.950139
$427$	2.92687e6	0.776844
$428$	−3.66242e6	−0.966403
$429$	−3.78996e6	−0.994241
$430$	571181.	0.148971
$431$	−2.12387e6	−0.550725	−0.275362	−	0.961340i	$-0.588798\pi$
$431$	−2.12387e6	−0.550725	−0.275362	+	0.961340i	$0.588798\pi$
$432$	198024.	0.0510515
$433$	315893.	0.0809693	0.0404846	−	0.999180i	$-0.487110\pi$
$433$	315893.	0.0809693	0.0404846	+	0.999180i	$0.487110\pi$
$434$	−2.90995e6	−0.741586
$435$	−3.04007e6	−0.770300
$436$	−334302.	−0.0842215
$437$	−1.15223e6	−0.288625
$438$	999213.	0.248870
$439$	−1.31617e6	−0.325949	−0.162975	−	0.986630i	$-0.552109\pi$
$439$	−1.31617e6	−0.325949	−0.162975	+	0.986630i	$0.552109\pi$
$440$	−773884.	−0.190565
$441$	−3.16360e6	−0.774614
$442$	−2.66446e6	−0.648713
$443$	2.36493e6	0.572544	0.286272	−	0.958148i	$-0.407584\pi$
$443$	2.36493e6	0.572544	0.286272	+	0.958148i	$0.407584\pi$
$444$	−3.83218e6	−0.922547
$445$	−2.12426e6	−0.508520
$446$	−3.76696e6	−0.896714
$447$	1.06107e6	0.251175
$448$	−300517.	−0.0707414
$449$	−1.56989e6	−0.367496	−0.183748	−	0.982973i	$-0.558823\pi$
$449$	−1.56989e6	−0.367496	−0.183748	+	0.982973i	$0.558823\pi$
$450$	692310.	0.161165
$451$	4.22044e6	0.977048
$452$	−1.42203e6	−0.327387
$453$	−2.49733e6	−0.571781
$454$	−3.70169e6	−0.842871
$455$	−630316.	−0.142735
$456$	3.17857e6	0.715847
$457$	−1.36978e6	−0.306803	−0.153402	−	0.988164i	$-0.549023\pi$
$457$	−1.36978e6	−0.306803	−0.153402	+	0.988164i	$0.549023\pi$
$458$	2.88651e6	0.642998
$459$	1.49940e6	0.332189
$460$	211600.	0.0466252
$461$	−445213.	−0.0975699	−0.0487850	−	0.998809i	$-0.515535\pi$
$461$	−445213.	−0.0975699	−0.0487850	+	0.998809i	$0.515535\pi$
$462$	−3.23664e6	−0.705488
$463$	−771842.	−0.167331	−0.0836654	−	0.996494i	$-0.526663\pi$
$463$	−771842.	−0.167331	−0.0836654	+	0.996494i	$0.526663\pi$
$464$	1.36525e6	0.294387
$465$	−5.65232e6	−1.21226
$466$	5.61460e6	1.19772
$467$	−8.50391e6	−1.80437	−0.902186	−	0.431347i	$-0.858039\pi$
$467$	−8.50391e6	−1.80437	−0.902186	+	0.431347i	$0.858039\pi$
$468$	−1.52262e6	−0.321348
$469$	5.08776e6	1.06806
$470$	2.35382e6	0.491506
$471$	−3.73605e6	−0.775998
$472$	854131.	0.176469
$473$	−2.76267e6	−0.567775
$474$	−6.54368e6	−1.33775
$475$	1.36133e6	0.276840
$476$	−2.27545e6	−0.460310
$477$	−6.61412e6	−1.33099
$478$	3.98720e6	0.798175
$479$	−2.76172e6	−0.549972	−0.274986	−	0.961448i	$-0.588673\pi$
$479$	−2.76172e6	−0.549972	−0.274986	+	0.961448i	$0.588673\pi$
$480$	−583727.	−0.115640
$481$	3.60965e6	0.711382
$482$	−1.28079e6	−0.251108
$483$	884982.	0.172610
$484$	1.16628e6	0.226303
$485$	−1.79323e6	−0.346165
$486$	−5.28074e6	−1.01415
$487$	−7.56023e6	−1.44448	−0.722242	−	0.691641i	$-0.756888\pi$
$487$	−7.56023e6	−1.44448	−0.722242	+	0.691641i	$0.756888\pi$
$488$	−2.55314e6	−0.485316
$489$	1.14137e6	0.215851
$490$	1.14241e6	0.214947
$491$	−942948.	−0.176516	−0.0882580	−	0.996098i	$-0.528130\pi$
$491$	−942948.	−0.176516	−0.0882580	+	0.996098i	$0.528130\pi$
$492$	3.18340e6	0.592897
$493$	1.03374e7	1.91556
$494$	−2.99400e6	−0.551994
$495$	−3.34855e6	−0.614247
$496$	2.53838e6	0.463289
$497$	−2.86279e6	−0.519875
$498$	4.06624e6	0.734716
$499$	5.88410e6	1.05786	0.528931	−	0.848665i	$-0.322593\pi$
$499$	5.88410e6	1.05786	0.528931	+	0.848665i	$0.322593\pi$
$500$	−250000.	−0.0447214
$501$	−1.22157e7	−2.17433
$502$	−7.57638e6	−1.34184
$503$	7.17915e6	1.26518	0.632591	−	0.774486i	$-0.281991\pi$
$503$	7.17915e6	1.26518	0.632591	+	0.774486i	$0.281991\pi$
$504$	−1.30032e6	−0.228020
$505$	−2.57968e6	−0.450130
$506$	−1.02346e6	−0.177703
$507$	−5.77346e6	−0.997508
$508$	2.01082e6	0.345712
$509$	7.09009e6	1.21299	0.606495	−	0.795087i	$-0.292575\pi$
$509$	7.09009e6	1.21299	0.606495	+	0.795087i	$0.292575\pi$
$510$	−4.41986e6	−0.752460
$511$	−803780.	−0.136171
$512$	262144.	0.0441942
$513$	1.68485e6	0.282662
$514$	−1.71134e6	−0.285712
$515$	−2.58447e6	−0.429392
$516$	−2.08384e6	−0.344540
$517$	−1.13849e7	−1.87328
$518$	3.08266e6	0.504778
$519$	8.96438e6	1.46084
$520$	549831.	0.0891705
$521$	3.59327e6	0.579957	0.289979	−	0.957033i	$-0.406352\pi$
$521$	3.59327e6	0.579957	0.289979	+	0.957033i	$0.406352\pi$
$522$	5.90737e6	0.948894
$523$	8.04859e6	1.28666	0.643332	−	0.765587i	$-0.277551\pi$
$523$	8.04859e6	1.28666	0.643332	+	0.765587i	$0.277551\pi$
$524$	323545.	0.0514762
$525$	−1.04558e6	−0.165562
$526$	8.15893e6	1.28579
$527$	1.92201e7	3.01460
$528$	2.82336e6	0.440738
$529$	279841.	0.0434783
$530$	2.38842e6	0.369336
$531$	3.69577e6	0.568812
$532$	−2.55689e6	−0.391681
$533$	−2.99855e6	−0.457186
$534$	7.74994e6	1.17610
$535$	5.72252e6	0.864377
$536$	−4.43810e6	−0.667245
$537$	−5.96555e6	−0.892720
$538$	4.10891e6	0.612028
$539$	−5.52557e6	−0.819228
$540$	−309413.	−0.0456619
$541$	−2.63301e6	−0.386776	−0.193388	−	0.981122i	$-0.561948\pi$
$541$	−2.63301e6	−0.386776	−0.193388	+	0.981122i	$0.561948\pi$
$542$	3.68214e6	0.538396
$543$	−3.92789e6	−0.571689
$544$	1.98490e6	0.287569
$545$	522347.	0.0753300
$546$	2.29958e6	0.330116
$547$	1.16772e7	1.66867	0.834336	−	0.551256i	$-0.185851\pi$
$547$	1.16772e7	1.66867	0.834336	+	0.551256i	$0.185851\pi$
$548$	6.22326e6	0.885251
$549$	−1.10473e7	−1.56432
$550$	1.20919e6	0.170447
$551$	1.16160e7	1.62996
$552$	−771979.	−0.107835
$553$	5.26382e6	0.731962
$554$	−337611.	−0.0467350
$555$	5.98778e6	0.825151
$556$	−2.17062e6	−0.297781
$557$	−4.81350e6	−0.657389	−0.328695	−	0.944436i	$-0.606609\pi$
$557$	−4.81350e6	−0.657389	−0.328695	+	0.944436i	$0.606609\pi$
$558$	1.09834e7	1.49332
$559$	1.96283e6	0.265677
$560$	469558.	0.0632731
$561$	2.13779e7	2.86786
$562$	−6.00660e6	−0.802210
$563$	6.96537e6	0.926133	0.463066	−	0.886324i	$-0.346749\pi$
$563$	6.96537e6	0.926133	0.463066	+	0.886324i	$0.346749\pi$
$564$	−8.58743e6	−1.13675
$565$	2.22192e6	0.292824
$566$	4.85417e6	0.636904
$567$	3.64308e6	0.475895
$568$	2.49724e6	0.324781
$569$	−5.52686e6	−0.715645	−0.357822	−	0.933790i	$-0.616481\pi$
$569$	−5.52686e6	−0.715645	−0.357822	+	0.933790i	$0.616481\pi$
$570$	−4.96652e6	−0.640273
$571$	3.66678e6	0.470646	0.235323	−	0.971917i	$-0.424385\pi$
$571$	3.66678e6	0.470646	0.235323	+	0.971917i	$0.424385\pi$
$572$	−2.65941e6	−0.339856
$573$	−2.12130e7	−2.69908
$574$	−2.56077e6	−0.324408
$575$	−330625.	−0.0417029
$576$	1.13428e6	0.142451
$577$	1.57468e6	0.196903	0.0984515	−	0.995142i	$-0.468611\pi$
$577$	1.57468e6	0.196903	0.0984515	+	0.995142i	$0.468611\pi$
$578$	9.34984e6	1.16408
$579$	1.54676e7	1.91746
$580$	−2.13321e6	−0.263307
$581$	−3.27093e6	−0.402005
$582$	6.54225e6	0.800607
$583$	−1.15523e7	−1.40765
$584$	701145.	0.0850699
$585$	2.37909e6	0.287422
$586$	−6.99918e6	−0.841983
$587$	4.53054e6	0.542694	0.271347	−	0.962482i	$-0.412531\pi$
$587$	4.53054e6	0.542694	0.271347	+	0.962482i	$0.412531\pi$
$588$	−4.16784e6	−0.497128
$589$	2.15973e7	2.56514
$590$	−1.33458e6	−0.157839
$591$	−1.08317e7	−1.27564
$592$	−2.68903e6	−0.315349
$593$	−1.47456e7	−1.72197	−0.860984	−	0.508633i	$-0.830151\pi$
$593$	−1.47456e7	−1.72197	−0.860984	+	0.508633i	$0.830151\pi$
$594$	1.49656e6	0.174031
$595$	3.55540e6	0.411714
$596$	744552.	0.0858578
$597$	−9.04595e6	−1.03877
$598$	727152.	0.0831519
$599$	3.44657e6	0.392482	0.196241	−	0.980556i	$-0.437126\pi$
$599$	3.44657e6	0.392482	0.196241	+	0.980556i	$0.437126\pi$
$600$	912074.	0.103431
$601$	−1.26760e6	−0.143152	−0.0715759	−	0.997435i	$-0.522803\pi$
$601$	−1.26760e6	−0.143152	−0.0715759	+	0.997435i	$0.522803\pi$
$602$	1.67626e6	0.188517
$603$	−1.92034e7	−2.15073
$604$	−1.75237e6	−0.195449
$605$	−1.82232e6	−0.202411
$606$	9.41145e6	1.04106
$607$	1.72388e7	1.89904	0.949522	−	0.313700i	$-0.101569\pi$
$607$	1.72388e7	1.89904	0.949522	+	0.313700i	$0.101569\pi$
$608$	2.23040e6	0.244694
$609$	−8.92179e6	−0.974785
$610$	3.98928e6	0.434080
$611$	8.08878e6	0.876557
$612$	8.58855e6	0.926918
$613$	1.18149e7	1.26993	0.634964	−	0.772542i	$-0.281015\pi$
$613$	1.18149e7	1.26993	0.634964	+	0.772542i	$0.281015\pi$
$614$	−7.86217e6	−0.841631
$615$	−4.97407e6	−0.530303
$616$	−2.27114e6	−0.241153
$617$	−7.90373e6	−0.835832	−0.417916	−	0.908486i	$-0.637239\pi$
$617$	−7.90373e6	−0.835832	−0.417916	+	0.908486i	$0.637239\pi$
$618$	9.42893e6	0.993095
$619$	−3.08483e6	−0.323598	−0.161799	−	0.986824i	$-0.551730\pi$
$619$	−3.08483e6	−0.323598	−0.161799	+	0.986824i	$0.551730\pi$
$620$	−3.96622e6	−0.414379
$621$	−409198.	−0.0425799
$622$	1.07223e7	1.11125
$623$	−6.23415e6	−0.643513
$624$	−2.00595e6	−0.206233
$625$	390625.	0.0400000
$626$	−1.12516e7	−1.14757
$627$	2.40219e7	2.44028
$628$	−2.62158e6	−0.265255
$629$	−2.03608e7	−2.05196
$630$	2.03175e6	0.203947
$631$	−1.58650e6	−0.158623	−0.0793114	−	0.996850i	$-0.525272\pi$
$631$	−1.58650e6	−0.158623	−0.0793114	+	0.996850i	$0.525272\pi$
$632$	−4.59169e6	−0.457277
$633$	9.82772e6	0.974863
$634$	−1.07523e7	−1.06238
$635$	−3.14191e6	−0.309214
$636$	−8.71367e6	−0.854198
$637$	3.92582e6	0.383338
$638$	1.03178e7	1.00355
$639$	1.08054e7	1.04686
$640$	−409600.	−0.0395285
$641$	837342.	0.0804929	0.0402465	−	0.999190i	$-0.487186\pi$
$641$	837342.	0.0804929	0.0402465	+	0.999190i	$0.487186\pi$
$642$	−2.08775e7	−1.99913
$643$	6.50224e6	0.620206	0.310103	−	0.950703i	$-0.399636\pi$
$643$	6.50224e6	0.620206	0.310103	+	0.950703i	$0.399636\pi$
$644$	620990.	0.0590024
$645$	3.25599e6	0.308166
$646$	1.68881e7	1.59221
$647$	−9.60343e6	−0.901915	−0.450957	−	0.892545i	$-0.648917\pi$
$647$	−9.60343e6	−0.901915	−0.450957	+	0.892545i	$0.648917\pi$
$648$	−3.17789e6	−0.297305
$649$	6.45505e6	0.601573
$650$	−859111.	−0.0797565
$651$	−1.65881e7	−1.53406
$652$	800898.	0.0737833
$653$	4.74506e6	0.435471	0.217735	−	0.976008i	$-0.430133\pi$
$653$	4.74506e6	0.435471	0.217735	+	0.976008i	$0.430133\pi$
$654$	−1.90568e6	−0.174223
$655$	−505539.	−0.0460417
$656$	2.23379e6	0.202667
$657$	3.03381e6	0.274205
$658$	6.90784e6	0.621982
$659$	308617.	0.0276826	0.0138413	−	0.999904i	$-0.495594\pi$
$659$	308617.	0.0276826	0.0138413	+	0.999904i	$0.495594\pi$
$660$	−4.41149e6	−0.394208
$661$	2.09256e7	1.86284	0.931418	−	0.363951i	$-0.118572\pi$
$661$	2.09256e7	1.86284	0.931418	+	0.363951i	$0.118572\pi$
$662$	2.21310e6	0.196271
$663$	−1.51886e7	−1.34194
$664$	2.85327e6	0.251144
$665$	3.99513e6	0.350330
$666$	−1.16353e7	−1.01646
$667$	−2.82117e6	−0.245535
$668$	−8.57175e6	−0.743239
$669$	−2.14734e7	−1.85496
$670$	6.93454e6	0.596802
$671$	−1.92952e7	−1.65441
$672$	−1.71308e6	−0.146338
$673$	3.46487e6	0.294883	0.147441	−	0.989071i	$-0.452896\pi$
$673$	3.46487e6	0.294883	0.147441	+	0.989071i	$0.452896\pi$
$674$	6.24873e6	0.529836
$675$	483457.	0.0408412
$676$	−4.05122e6	−0.340973
$677$	4.25269e6	0.356608	0.178304	−	0.983975i	$-0.442939\pi$
$677$	4.25269e6	0.356608	0.178304	+	0.983975i	$0.442939\pi$
$678$	−8.10620e6	−0.677241
$679$	−5.26267e6	−0.438058
$680$	−3.10141e6	−0.257209
$681$	−2.11014e7	−1.74358
$682$	1.91837e7	1.57932
$683$	−1.14195e7	−0.936693	−0.468346	−	0.883545i	$-0.655150\pi$
$683$	−1.14195e7	−0.936693	−0.468346	+	0.883545i	$0.655150\pi$
$684$	9.65079e6	0.788720
$685$	−9.72384e6	−0.791792
$686$	8.28507e6	0.672181
$687$	1.64545e7	1.33012
$688$	−1.46222e6	−0.117772
$689$	8.20768e6	0.658677
$690$	1.20622e6	0.0964502
$691$	2.18181e6	0.173829	0.0869144	−	0.996216i	$-0.472299\pi$
$691$	2.18181e6	0.173829	0.0869144	+	0.996216i	$0.472299\pi$
$692$	6.29028e6	0.499350
$693$	−9.82710e6	−0.777306
$694$	1.28667e7	1.01407
$695$	3.39160e6	0.266344
$696$	7.78257e6	0.608976
$697$	1.69138e7	1.31874
$698$	−255423.	−0.0198437
$699$	3.20058e7	2.47763
$700$	−733684.	−0.0565931
$701$	−4.68411e6	−0.360024	−0.180012	−	0.983664i	$-0.557614\pi$
$701$	−4.68411e6	−0.360024	−0.180012	+	0.983664i	$0.557614\pi$
$702$	−1.06328e6	−0.0814338
$703$	−2.28791e7	−1.74602
$704$	1.98114e6	0.150655
$705$	1.34179e7	1.01674
$706$	−1.09370e7	−0.825821
$707$	−7.57069e6	−0.569622
$708$	4.86894e6	0.365049
$709$	5.19567e6	0.388173	0.194087	−	0.980984i	$-0.437826\pi$
$709$	5.19567e6	0.388173	0.194087	+	0.980984i	$0.437826\pi$
$710$	−3.90194e6	−0.290493
$711$	−1.98680e7	−1.47394
$712$	5.43812e6	0.402021
$713$	−5.24532e6	−0.386410
$714$	−1.29711e7	−0.952209
$715$	4.15533e6	0.303976
$716$	−4.18601e6	−0.305153
$717$	2.27289e7	1.65113
$718$	2.14925e6	0.155588
$719$	6.38476e6	0.460598	0.230299	−	0.973120i	$-0.426030\pi$
$719$	6.38476e6	0.460598	0.230299	+	0.973120i	$0.426030\pi$
$720$	−1.77231e6	−0.127412
$721$	−7.58475e6	−0.543379
$722$	9.07248e6	0.647714
$723$	−7.30110e6	−0.519449
$724$	−2.75619e6	−0.195417
$725$	3.33314e6	0.235509
$726$	6.64835e6	0.468136
$727$	1.12450e7	0.789087	0.394543	−	0.918877i	$-0.370903\pi$
$727$	1.12450e7	0.789087	0.394543	+	0.918877i	$0.370903\pi$
$728$	1.61361e6	0.112842
$729$	−1.80366e7	−1.25700
$730$	−1.09554e6	−0.0760888
$731$	−1.10717e7	−0.766336
$732$	−1.45541e7	−1.00394
$733$	1.91800e7	1.31852	0.659261	−	0.751914i	$-0.270869\pi$
$733$	1.91800e7	1.31852	0.659261	+	0.751914i	$0.270869\pi$
$734$	4.98314e6	0.341400
$735$	6.51225e6	0.444644
$736$	−541696.	−0.0368605
$737$	−3.35408e7	−2.27460
$738$	9.66546e6	0.653253
$739$	−2.47987e7	−1.67039	−0.835195	−	0.549954i	$-0.814645\pi$
$739$	−2.47987e7	−1.67039	−0.835195	+	0.549954i	$0.814645\pi$
$740$	4.20161e6	0.282057
$741$	−1.70672e7	−1.14187
$742$	7.00939e6	0.467380
$743$	−7.68160e6	−0.510481	−0.255240	−	0.966878i	$-0.582155\pi$
$743$	−7.68160e6	−0.510481	−0.255240	+	0.966878i	$0.582155\pi$
$744$	1.44699e7	0.958372
$745$	−1.16336e6	−0.0767935
$746$	−307473.	−0.0202283
$747$	1.23459e7	0.809510
$748$	1.50008e7	0.980303
$749$	1.67941e7	1.09384
$750$	−1.42512e6	−0.0925117
$751$	1.47507e7	0.954362	0.477181	−	0.878805i	$-0.341659\pi$
$751$	1.47507e7	0.954362	0.477181	+	0.878805i	$0.341659\pi$
$752$	−6.02578e6	−0.388570
$753$	−4.31888e7	−2.77577
$754$	−7.33065e6	−0.469585
$755$	2.73808e6	0.174815
$756$	−908044.	−0.0577833
$757$	455339.	0.0288799	0.0144399	−	0.999896i	$-0.495403\pi$
$757$	455339.	0.0288799	0.0144399	+	0.999896i	$0.495403\pi$
$758$	6.20404e6	0.392194
$759$	−5.83420e6	−0.367601
$760$	−3.48500e6	−0.218861
$761$	−1.93519e7	−1.21133	−0.605666	−	0.795719i	$-0.707093\pi$
$761$	−1.93519e7	−1.21133	−0.605666	+	0.795719i	$0.707093\pi$
$762$	1.14626e7	0.715149
$763$	1.53295e6	0.0953272
$764$	−1.48851e7	−0.922611
$765$	−1.34196e7	−0.829060
$766$	2.69489e6	0.165947
$767$	−4.58621e6	−0.281492
$768$	1.49434e6	0.0914212
$769$	−1.23939e7	−0.755775	−0.377887	−	0.925852i	$-0.623349\pi$
$769$	−1.23939e7	−0.755775	−0.377887	+	0.925852i	$0.623349\pi$
$770$	3.54866e6	0.215694
$771$	−9.75543e6	−0.591031
$772$	1.08536e7	0.655434
$773$	−6.98655e6	−0.420547	−0.210273	−	0.977643i	$-0.567435\pi$
$773$	−6.98655e6	−0.420547	−0.210273	+	0.977643i	$0.567435\pi$
$774$	−6.32695e6	−0.379614
$775$	6.19722e6	0.370632
$776$	4.59068e6	0.273667
$777$	1.75726e7	1.04420
$778$	3.23186e6	0.191427
$779$	1.90057e7	1.12212
$780$	3.13429e6	0.184460
$781$	1.88728e7	1.10716
$782$	−4.10161e6	−0.239849
$783$	4.12526e6	0.240462
$784$	−2.92456e6	−0.169930
$785$	4.09622e6	0.237251
$786$	1.84435e6	0.106485
$787$	−2.04562e6	−0.117730	−0.0588650	−	0.998266i	$-0.518748\pi$
$787$	−2.04562e6	−0.117730	−0.0588650	+	0.998266i	$0.518748\pi$
$788$	−7.60056e6	−0.436044
$789$	4.65096e7	2.65981
$790$	7.17451e6	0.409001
$791$	6.52073e6	0.370557
$792$	8.57228e6	0.485605
$793$	1.37089e7	0.774143
$794$	1.00352e7	0.564905
$795$	1.36151e7	0.764018
$796$	−6.34752e6	−0.355076
$797$	−2.43488e7	−1.35779	−0.678895	−	0.734236i	$-0.737541\pi$
$797$	−2.43488e7	−1.35779	−0.678895	+	0.734236i	$0.737541\pi$
$798$	−1.45754e7	−0.810241
$799$	−4.56260e7	−2.52840
$800$	640000.	0.0353553
$801$	2.35304e7	1.29583
$802$	−1.03381e7	−0.567550
$803$	5.29888e6	0.289998
$804$	−2.52992e7	−1.38028
$805$	−970297.	−0.0527734
$806$	−1.36297e7	−0.739007
$807$	2.34227e7	1.26606
$808$	6.60399e6	0.355859
$809$	2.57882e7	1.38532	0.692660	−	0.721264i	$-0.256439\pi$
$809$	2.57882e7	1.38532	0.692660	+	0.721264i	$0.256439\pi$
$810$	4.96546e6	0.265918
$811$	2.65254e6	0.141615	0.0708077	−	0.997490i	$-0.477442\pi$
$811$	2.65254e6	0.141615	0.0708077	+	0.997490i	$0.477442\pi$
$812$	−6.26040e6	−0.333205
$813$	2.09899e7	1.11374
$814$	−2.03222e7	−1.07501
$815$	−1.25140e6	−0.0659938
$816$	1.13149e7	0.594872
$817$	−1.24410e7	−0.652080
$818$	−1.18757e7	−0.620550
$819$	6.98199e6	0.363722
$820$	−3.49029e6	−0.181270
$821$	2.45460e7	1.27093	0.635467	−	0.772128i	$-0.280808\pi$
$821$	2.45460e7	1.27093	0.635467	+	0.772128i	$0.280808\pi$
$822$	3.54754e7	1.83125
$823$	2.64349e7	1.36043	0.680217	−	0.733011i	$-0.261885\pi$
$823$	2.64349e7	1.36043	0.680217	+	0.733011i	$0.261885\pi$
$824$	6.61625e6	0.339464
$825$	6.89296e6	0.352591
$826$	−3.91664e6	−0.199739
$827$	−2.02482e7	−1.02949	−0.514746	−	0.857343i	$-0.672114\pi$
$827$	−2.02482e7	−1.02949	−0.514746	+	0.857343i	$0.672114\pi$
$828$	−2.34389e6	−0.118812
$829$	1.48166e7	0.748794	0.374397	−	0.927269i	$-0.377850\pi$
$829$	1.48166e7	0.748794	0.374397	+	0.927269i	$0.377850\pi$
$830$	−4.45823e6	−0.224630
$831$	−1.92454e6	−0.0966772
$832$	−1.40757e6	−0.0704955
$833$	−2.21442e7	−1.10573
$834$	−1.23736e7	−0.615998
$835$	1.33934e7	0.664773
$836$	1.68561e7	0.834146
$837$	7.66999e6	0.378426
$838$	−1.28915e7	−0.634152
$839$	−314733.	−0.0154361	−0.00771804	−	0.999970i	$-0.502457\pi$
$839$	−314733.	−0.0154361	−0.00771804	+	0.999970i	$0.502457\pi$
$840$	2.67670e6	0.130888
$841$	7.92994e6	0.386616
$842$	−1.77770e7	−0.864128
$843$	−3.42404e7	−1.65947
$844$	6.89609e6	0.333232
$845$	6.33004e6	0.304975
$846$	−2.60732e7	−1.25247
$847$	−5.34801e6	−0.256144
$848$	−6.11436e6	−0.291986
$849$	2.76710e7	1.31752
$850$	4.84595e6	0.230055
$851$	5.55663e6	0.263019
$852$	1.42354e7	0.671850
$853$	−8.40932e6	−0.395720	−0.197860	−	0.980230i	$-0.563399\pi$
$853$	−8.40932e6	−0.395720	−0.197860	+	0.980230i	$0.563399\pi$
$854$	1.17075e7	0.549312
$855$	−1.50794e7	−0.705453
$856$	−1.46497e7	−0.683350
$857$	6.21845e6	0.289221	0.144611	−	0.989489i	$-0.453807\pi$
$857$	6.21845e6	0.289221	0.144611	+	0.989489i	$0.453807\pi$
$858$	−1.51599e7	−0.703035
$859$	1.50382e7	0.695367	0.347684	−	0.937612i	$-0.386968\pi$
$859$	1.50382e7	0.695367	0.347684	+	0.937612i	$0.386968\pi$
$860$	2.28472e6	0.105339
$861$	−1.45976e7	−0.671078
$862$	−8.49548e6	−0.389421
$863$	−3.65576e7	−1.67090	−0.835450	−	0.549567i	$-0.814793\pi$
$863$	−3.65576e7	−1.67090	−0.835450	+	0.549567i	$0.814793\pi$
$864$	792096.	0.0360989
$865$	−9.82857e6	−0.446632
$866$	1.26357e6	0.0572539
$867$	5.32984e7	2.40806
$868$	−1.16398e7	−0.524380
$869$	−3.47015e7	−1.55883
$870$	−1.21603e7	−0.544684
$871$	2.38302e7	1.06434
$872$	−1.33721e6	−0.0595536
$873$	1.98636e7	0.882109
$874$	−4.60891e6	−0.204089
$875$	1.14638e6	0.0506184
$876$	3.99685e6	0.175978
$877$	−2.73603e7	−1.20122	−0.600609	−	0.799543i	$-0.705075\pi$
$877$	−2.73603e7	−1.20122	−0.600609	+	0.799543i	$0.705075\pi$
$878$	−5.26467e6	−0.230481
$879$	−3.98986e7	−1.74175
$880$	−3.09553e6	−0.134750
$881$	8.02204e6	0.348213	0.174107	−	0.984727i	$-0.444296\pi$
$881$	8.02204e6	0.348213	0.174107	+	0.984727i	$0.444296\pi$
$882$	−1.26544e7	−0.547735
$883$	−1.53018e7	−0.660453	−0.330227	−	0.943902i	$-0.607125\pi$
$883$	−1.53018e7	−0.660453	−0.330227	+	0.943902i	$0.607125\pi$
$884$	−1.06578e7	−0.458709
$885$	−7.60772e6	−0.326510
$886$	9.45972e6	0.404850
$887$	−1.50376e7	−0.641753	−0.320877	−	0.947121i	$-0.603978\pi$
$887$	−1.50376e7	−0.641753	−0.320877	+	0.947121i	$0.603978\pi$
$888$	−1.53287e7	−0.652339
$889$	−9.22068e6	−0.391299
$890$	−8.49706e6	−0.359578
$891$	−2.40168e7	−1.01349
$892$	−1.50678e7	−0.634072
$893$	−5.12691e7	−2.15143
$894$	4.24429e6	0.177608
$895$	6.54065e6	0.272937
$896$	−1.20207e6	−0.0500217
$897$	4.14510e6	0.172010
$898$	−6.27954e6	−0.259859
$899$	5.28798e7	2.18218
$900$	2.76924e6	0.113961
$901$	−4.62967e7	−1.89993
$902$	1.68817e7	0.690877
$903$	9.55548e6	0.389972
$904$	−5.68810e6	−0.231498
$905$	4.30655e6	0.174787
$906$	−9.98931e6	−0.404310
$907$	6.45562e6	0.260567	0.130284	−	0.991477i	$-0.458411\pi$
$907$	6.45562e6	0.260567	0.130284	+	0.991477i	$0.458411\pi$
$908$	−1.48068e7	−0.596000
$909$	2.85751e7	1.14704
$910$	−2.52126e6	−0.100929
$911$	1.58554e7	0.632968	0.316484	−	0.948598i	$-0.397498\pi$
$911$	1.58554e7	0.632968	0.316484	+	0.948598i	$0.397498\pi$
$912$	1.27143e7	0.506180
$913$	2.15635e7	0.856134
$914$	−5.47912e6	−0.216943
$915$	2.27407e7	0.897949
$916$	1.15461e7	0.454669
$917$	−1.48362e6	−0.0582640
$918$	5.99759e6	0.234893
$919$	−3.18992e7	−1.24592	−0.622961	−	0.782253i	$-0.714070\pi$
$919$	−3.18992e7	−1.24592	−0.622961	+	0.782253i	$0.714070\pi$
$920$	846400.	0.0329690
$921$	−4.48180e7	−1.74102
$922$	−1.78085e6	−0.0689924
$923$	−1.34088e7	−0.518067
$924$	−1.29466e7	−0.498855
$925$	−6.56502e6	−0.252279
$926$	−3.08737e6	−0.118321
$927$	2.86281e7	1.09419
$928$	5.46101e6	0.208163
$929$	−3.80146e7	−1.44514	−0.722571	−	0.691296i	$-0.757040\pi$
$929$	−3.80146e7	−1.44514	−0.722571	+	0.691296i	$0.757040\pi$
$930$	−2.26093e7	−0.857194
$931$	−2.48831e7	−0.940870
$932$	2.24584e7	0.846914
$933$	6.11221e7	2.29876
$934$	−3.40156e7	−1.27588
$935$	−2.34388e7	−0.876810
$936$	−6.09046e6	−0.227227
$937$	−4.31888e6	−0.160702	−0.0803512	−	0.996767i	$-0.525604\pi$
$937$	−4.31888e6	−0.160702	−0.0803512	+	0.996767i	$0.525604\pi$
$938$	2.03510e7	0.755230
$939$	−6.41396e7	−2.37390
$940$	9.41529e6	0.347547
$941$	−4.90716e7	−1.80658	−0.903289	−	0.429033i	$-0.858854\pi$
$941$	−4.90716e7	−1.80658	−0.903289	+	0.429033i	$0.858854\pi$
$942$	−1.49442e7	−0.548714
$943$	−4.61591e6	−0.169036
$944$	3.41652e6	0.124783
$945$	1.41882e6	0.0516830
$946$	−1.10507e7	−0.401478
$947$	4.17918e7	1.51431	0.757157	−	0.653233i	$-0.226588\pi$
$947$	4.17918e7	1.51431	0.757157	+	0.653233i	$0.226588\pi$
$948$	−2.61747e7	−0.945935
$949$	−3.76476e6	−0.135698
$950$	5.44531e6	0.195755
$951$	−6.12932e7	−2.19766
$952$	−9.10181e6	−0.325488
$953$	3.06645e7	1.09371	0.546856	−	0.837227i	$-0.315824\pi$
$953$	3.06645e7	1.09371	0.546856	+	0.837227i	$0.315824\pi$
$954$	−2.64565e7	−0.941155
$955$	2.32580e7	0.825208
$956$	1.59488e7	0.564395
$957$	5.88164e7	2.07596
$958$	−1.10469e7	−0.388889
$959$	−2.85369e7	−1.00198
$960$	−2.33491e6	−0.0817696
$961$	6.96889e7	2.43419
$962$	1.44386e7	0.503023
$963$	−6.33882e7	−2.20264
$964$	−5.12317e6	−0.177560
$965$	−1.69587e7	−0.586238
$966$	3.53993e6	0.122054
$967$	2.28736e6	0.0786627	0.0393314	−	0.999226i	$-0.487477\pi$
$967$	2.28736e6	0.0786627	0.0393314	+	0.999226i	$0.487477\pi$
$968$	4.66513e6	0.160020
$969$	9.62701e7	3.29368
$970$	−7.17294e6	−0.244775
$971$	−9.55908e6	−0.325363	−0.162681	−	0.986679i	$-0.552014\pi$
$971$	−9.55908e6	−0.325363	−0.162681	+	0.986679i	$0.552014\pi$
$972$	−2.11230e7	−0.717115
$973$	9.95345e6	0.337048
$974$	−3.02409e7	−1.02140
$975$	−4.89733e6	−0.164986
$976$	−1.02126e7	−0.343171
$977$	2.89873e7	0.971563	0.485782	−	0.874080i	$-0.338535\pi$
$977$	2.89873e7	0.971563	0.485782	+	0.874080i	$0.338535\pi$
$978$	4.56549e6	0.152630
$979$	4.10983e7	1.37046
$980$	4.56963e6	0.151990
$981$	−5.78602e6	−0.191958
$982$	−3.77179e6	−0.124816
$983$	4.43231e7	1.46301	0.731504	−	0.681837i	$-0.238819\pi$
$983$	4.43231e7	1.46301	0.731504	+	0.681837i	$0.238819\pi$
$984$	1.27336e7	0.419241
$985$	1.18759e7	0.390010
$986$	4.13497e7	1.35450
$987$	3.93779e7	1.28665
$988$	−1.19760e7	−0.390319
$989$	3.02155e6	0.0982287
$990$	−1.33942e7	−0.434339
$991$	−2.58365e7	−0.835698	−0.417849	−	0.908516i	$-0.637216\pi$
$991$	−2.58365e7	−0.835698	−0.417849	+	0.908516i	$0.637216\pi$
$992$	1.01535e7	0.327595
$993$	1.26157e7	0.406012
$994$	−1.14512e7	−0.367607
$995$	9.91801e6	0.317590
$996$	1.62650e7	0.519523
$997$	−1.73962e7	−0.554263	−0.277131	−	0.960832i	$-0.589384\pi$
$997$	−1.73962e7	−0.554263	−0.277131	+	0.960832i	$0.589384\pi$
$998$	2.35364e7	0.748021
$999$	−8.12520e6	−0.257585

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.a.i.1.5	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.a.i.1.5	✓	6	1.1	even	1	trivial

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:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	230.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} +22.8018 q^{3} +16.0000 q^{4} -25.0000 q^{5} +91.2074 q^{6} -73.3684 q^{7} +64.0000 q^{8} +276.924 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} +22.8018 q^{3} +16.0000 q^{4} -25.0000 q^{5} +91.2074 q^{6} -73.3684 q^{7} +64.0000 q^{8} +276.924 q^{9} -100.000 q^{10} +483.677 q^{11} +364.829 q^{12} -343.645 q^{13} -293.474 q^{14} -570.046 q^{15} +256.000 q^{16} +1938.38 q^{17} +1107.70 q^{18} +2178.12 q^{19} -400.000 q^{20} -1672.93 q^{21} +1934.71 q^{22} -529.000 q^{23} +1459.32 q^{24} +625.000 q^{25} -1374.58 q^{26} +773.531 q^{27} -1173.89 q^{28} +5333.02 q^{29} -2280.18 q^{30} +9915.55 q^{31} +1024.00 q^{32} +11028.7 q^{33} +7753.52 q^{34} +1834.21 q^{35} +4430.79 q^{36} -10504.0 q^{37} +8712.49 q^{38} -7835.73 q^{39} -1600.00 q^{40} +8725.73 q^{41} -6691.74 q^{42} -5711.81 q^{43} +7738.84 q^{44} -6923.10 q^{45} -2116.00 q^{46} -23538.2 q^{47} +5837.27 q^{48} -11424.1 q^{49} +2500.00 q^{50} +44198.6 q^{51} -5498.31 q^{52} -23884.2 q^{53} +3094.13 q^{54} -12091.9 q^{55} -4695.58 q^{56} +49665.2 q^{57} +21332.1 q^{58} +13345.8 q^{59} -9120.74 q^{60} -39892.8 q^{61} +39662.2 q^{62} -20317.5 q^{63} +4096.00 q^{64} +8591.11 q^{65} +44114.9 q^{66} -69345.4 q^{67} +31014.1 q^{68} -12062.2 q^{69} +7336.84 q^{70} +39019.4 q^{71} +17723.1 q^{72} +10955.4 q^{73} -42016.1 q^{74} +14251.2 q^{75} +34850.0 q^{76} -35486.6 q^{77} -31342.9 q^{78} -71745.1 q^{79} -6400.00 q^{80} -49654.6 q^{81} +34902.9 q^{82} +44582.3 q^{83} -26767.0 q^{84} -48459.5 q^{85} -22847.2 q^{86} +121603. q^{87} +30955.3 q^{88} +84970.6 q^{89} -27692.4 q^{90} +25212.6 q^{91} -8464.00 q^{92} +226093. q^{93} -94152.9 q^{94} -54453.1 q^{95} +23349.1 q^{96} +71729.4 q^{97} -45696.3 q^{98} +133942. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 24 q^{2} + 15 q^{3} + 96 q^{4} - 150 q^{5} + 60 q^{6} + 106 q^{7} + 384 q^{8} + 899 q^{9}+O(q^{10}) \) 6 * q + 24 * q^2 + 15 * q^3 + 96 * q^4 - 150 * q^5 + 60 * q^6 + 106 * q^7 + 384 * q^8 + 899 * q^9	\( 6 q + 24 q^{2} + 15 q^{3} + 96 q^{4} - 150 q^{5} + 60 q^{6} + 106 q^{7} + 384 q^{8} + 899 q^{9} - 600 q^{10} + 321 q^{11} + 240 q^{12} + 527 q^{13} + 424 q^{14} - 375 q^{15} + 1536 q^{16} - 660 q^{17} + 3596 q^{18} + 2749 q^{19} - 2400 q^{20} + 6002 q^{21} + 1284 q^{22} - 3174 q^{23} + 960 q^{24} + 3750 q^{25} + 2108 q^{26} + 15372 q^{27} + 1696 q^{28} + 3337 q^{29} - 1500 q^{30} + 31094 q^{31} + 6144 q^{32} + 15087 q^{33} - 2640 q^{34} - 2650 q^{35} + 14384 q^{36} + 27037 q^{37} + 10996 q^{38} + 38528 q^{39} - 9600 q^{40} + 33608 q^{41} + 24008 q^{42} + 17024 q^{43} + 5136 q^{44} - 22475 q^{45} - 12696 q^{46} + 16864 q^{47} + 3840 q^{48} + 6002 q^{49} + 15000 q^{50} + 5719 q^{51} + 8432 q^{52} - 8475 q^{53} + 61488 q^{54} - 8025 q^{55} + 6784 q^{56} + 9566 q^{57} + 13348 q^{58} + 7899 q^{59} - 6000 q^{60} + 25437 q^{61} + 124376 q^{62} - 13333 q^{63} + 24576 q^{64} - 13175 q^{65} + 60348 q^{66} - 25517 q^{67} - 10560 q^{68} - 7935 q^{69} - 10600 q^{70} + 17204 q^{71} + 57536 q^{72} + 760 q^{73} + 108148 q^{74} + 9375 q^{75} + 43984 q^{76} + 102330 q^{77} + 154112 q^{78} + 66972 q^{79} - 38400 q^{80} + 115874 q^{81} + 134432 q^{82} + 58523 q^{83} + 96032 q^{84} + 16500 q^{85} + 68096 q^{86} - 70854 q^{87} + 20544 q^{88} + 38406 q^{89} - 89900 q^{90} + 25111 q^{91} - 50784 q^{92} + 130338 q^{93} + 67456 q^{94} - 68725 q^{95} + 15360 q^{96} + 82861 q^{97} + 24008 q^{98} - 2973 q^{99}+O(q^{100}) \) 6 * q + 24 * q^2 + 15 * q^3 + 96 * q^4 - 150 * q^5 + 60 * q^6 + 106 * q^7 + 384 * q^8 + 899 * q^9 - 600 * q^10 + 321 * q^11 + 240 * q^12 + 527 * q^13 + 424 * q^14 - 375 * q^15 + 1536 * q^16 - 660 * q^17 + 3596 * q^18 + 2749 * q^19 - 2400 * q^20 + 6002 * q^21 + 1284 * q^22 - 3174 * q^23 + 960 * q^24 + 3750 * q^25 + 2108 * q^26 + 15372 * q^27 + 1696 * q^28 + 3337 * q^29 - 1500 * q^30 + 31094 * q^31 + 6144 * q^32 + 15087 * q^33 - 2640 * q^34 - 2650 * q^35 + 14384 * q^36 + 27037 * q^37 + 10996 * q^38 + 38528 * q^39 - 9600 * q^40 + 33608 * q^41 + 24008 * q^42 + 17024 * q^43 + 5136 * q^44 - 22475 * q^45 - 12696 * q^46 + 16864 * q^47 + 3840 * q^48 + 6002 * q^49 + 15000 * q^50 + 5719 * q^51 + 8432 * q^52 - 8475 * q^53 + 61488 * q^54 - 8025 * q^55 + 6784 * q^56 + 9566 * q^57 + 13348 * q^58 + 7899 * q^59 - 6000 * q^60 + 25437 * q^61 + 124376 * q^62 - 13333 * q^63 + 24576 * q^64 - 13175 * q^65 + 60348 * q^66 - 25517 * q^67 - 10560 * q^68 - 7935 * q^69 - 10600 * q^70 + 17204 * q^71 + 57536 * q^72 + 760 * q^73 + 108148 * q^74 + 9375 * q^75 + 43984 * q^76 + 102330 * q^77 + 154112 * q^78 + 66972 * q^79 - 38400 * q^80 + 115874 * q^81 + 134432 * q^82 + 58523 * q^83 + 96032 * q^84 + 16500 * q^85 + 68096 * q^86 - 70854 * q^87 + 20544 * q^88 + 38406 * q^89 - 89900 * q^90 + 25111 * q^91 - 50784 * q^92 + 130338 * q^93 + 67456 * q^94 - 68725 * q^95 + 15360 * q^96 + 82861 * q^97 + 24008 * q^98 - 2973 * q^99

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