LMFDB - Embedded newform 862.6.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [862,6,Mod(1,862)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(862, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("862.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 862 = 2 \cdot 431 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	862.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:	$138.250852679$
Analytic rank:	$1$
Dimension:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	862.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.00000 q^{2} -24.9834 q^{3} +16.0000 q^{4} -15.3750 q^{5} -99.9335 q^{6} -246.831 q^{7} +64.0000 q^{8} +381.169 q^{9} +O(q^{10})$	\(q+4.00000 q^{2} -24.9834 q^{3} +16.0000 q^{4} -15.3750 q^{5} -99.9335 q^{6} -246.831 q^{7} +64.0000 q^{8} +381.169 q^{9} -61.4999 q^{10} -106.505 q^{11} -399.734 q^{12} -657.993 q^{13} -987.323 q^{14} +384.119 q^{15} +256.000 q^{16} +804.524 q^{17} +1524.68 q^{18} +2408.77 q^{19} -246.000 q^{20} +6166.67 q^{21} -426.019 q^{22} +701.915 q^{23} -1598.94 q^{24} -2888.61 q^{25} -2631.97 q^{26} -3451.94 q^{27} -3949.29 q^{28} +4916.86 q^{29} +1536.48 q^{30} -4304.63 q^{31} +1024.00 q^{32} +2660.85 q^{33} +3218.10 q^{34} +3795.02 q^{35} +6098.71 q^{36} +10786.2 q^{37} +9635.07 q^{38} +16438.9 q^{39} -983.999 q^{40} -3688.68 q^{41} +24666.7 q^{42} +17436.3 q^{43} -1704.08 q^{44} -5860.47 q^{45} +2807.66 q^{46} -23928.9 q^{47} -6395.75 q^{48} +44118.5 q^{49} -11554.4 q^{50} -20099.7 q^{51} -10527.9 q^{52} +10602.9 q^{53} -13807.8 q^{54} +1637.51 q^{55} -15797.2 q^{56} -60179.2 q^{57} +19667.5 q^{58} -3313.19 q^{59} +6145.90 q^{60} -3038.70 q^{61} -17218.5 q^{62} -94084.4 q^{63} +4096.00 q^{64} +10116.6 q^{65} +10643.4 q^{66} -7633.16 q^{67} +12872.4 q^{68} -17536.2 q^{69} +15180.1 q^{70} +18941.1 q^{71} +24394.8 q^{72} -28666.8 q^{73} +43144.8 q^{74} +72167.2 q^{75} +38540.3 q^{76} +26288.7 q^{77} +65755.6 q^{78} -10554.6 q^{79} -3936.00 q^{80} -6383.04 q^{81} -14754.7 q^{82} +31763.1 q^{83} +98666.7 q^{84} -12369.5 q^{85} +69745.2 q^{86} -122840. q^{87} -6816.31 q^{88} +76821.6 q^{89} -23441.9 q^{90} +162413. q^{91} +11230.6 q^{92} +107544. q^{93} -95715.6 q^{94} -37034.7 q^{95} -25583.0 q^{96} +74960.0 q^{97} +176474. q^{98} -40596.4 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 176 q^{2} - 90 q^{3} + 704 q^{4} - 250 q^{5} - 360 q^{6} - 479 q^{7} + 2816 q^{8} + 3270 q^{9}+O(q^{10}) $ 44 * q + 176 * q^2 - 90 * q^3 + 704 * q^4 - 250 * q^5 - 360 * q^6 - 479 * q^7 + 2816 * q^8 + 3270 * q^9	\( 44 q + 176 q^{2} - 90 q^{3} + 704 q^{4} - 250 q^{5} - 360 q^{6} - 479 q^{7} + 2816 q^{8} + 3270 q^{9} - 1000 q^{10} - 1826 q^{11} - 1440 q^{12} - 2623 q^{13} - 1916 q^{14} - 4443 q^{15} + 11264 q^{16} - 6751 q^{17} + 13080 q^{18} - 7969 q^{19} - 4000 q^{20} - 8220 q^{21} - 7304 q^{22} - 17276 q^{23} - 5760 q^{24} + 21130 q^{25} - 10492 q^{26} - 27963 q^{27} - 7664 q^{28} - 22547 q^{29} - 17772 q^{30} - 34076 q^{31} + 45056 q^{32} - 19225 q^{33} - 27004 q^{34} - 35854 q^{35} + 52320 q^{36} - 26809 q^{37} - 31876 q^{38} - 33759 q^{39} - 16000 q^{40} - 47099 q^{41} - 32880 q^{42} - 44019 q^{43} - 29216 q^{44} - 83014 q^{45} - 69104 q^{46} - 80854 q^{47} - 23040 q^{48} + 98079 q^{49} + 84520 q^{50} - 54896 q^{51} - 41968 q^{52} - 86057 q^{53} - 111852 q^{54} - 111885 q^{55} - 30656 q^{56} - 65903 q^{57} - 90188 q^{58} - 157759 q^{59} - 71088 q^{60} - 163640 q^{61} - 136304 q^{62} - 172844 q^{63} + 180224 q^{64} - 81544 q^{65} - 76900 q^{66} - 106228 q^{67} - 108016 q^{68} - 162750 q^{69} - 143416 q^{70} - 188370 q^{71} + 209280 q^{72} - 135423 q^{73} - 107236 q^{74} - 359459 q^{75} - 127504 q^{76} - 259175 q^{77} - 135036 q^{78} - 194026 q^{79} - 64000 q^{80} + 219444 q^{81} - 188396 q^{82} - 466476 q^{83} - 131520 q^{84} - 92384 q^{85} - 176076 q^{86} - 377355 q^{87} - 116864 q^{88} - 219335 q^{89} - 332056 q^{90} - 483654 q^{91} - 276416 q^{92} - 247383 q^{93} - 323416 q^{94} - 395162 q^{95} - 92160 q^{96} - 290677 q^{97} + 392316 q^{98} - 516636 q^{99}+O(q^{100}) \) 44 * q + 176 * q^2 - 90 * q^3 + 704 * q^4 - 250 * q^5 - 360 * q^6 - 479 * q^7 + 2816 * q^8 + 3270 * q^9 - 1000 * q^10 - 1826 * q^11 - 1440 * q^12 - 2623 * q^13 - 1916 * q^14 - 4443 * q^15 + 11264 * q^16 - 6751 * q^17 + 13080 * q^18 - 7969 * q^19 - 4000 * q^20 - 8220 * q^21 - 7304 * q^22 - 17276 * q^23 - 5760 * q^24 + 21130 * q^25 - 10492 * q^26 - 27963 * q^27 - 7664 * q^28 - 22547 * q^29 - 17772 * q^30 - 34076 * q^31 + 45056 * q^32 - 19225 * q^33 - 27004 * q^34 - 35854 * q^35 + 52320 * q^36 - 26809 * q^37 - 31876 * q^38 - 33759 * q^39 - 16000 * q^40 - 47099 * q^41 - 32880 * q^42 - 44019 * q^43 - 29216 * q^44 - 83014 * q^45 - 69104 * q^46 - 80854 * q^47 - 23040 * q^48 + 98079 * q^49 + 84520 * q^50 - 54896 * q^51 - 41968 * q^52 - 86057 * q^53 - 111852 * q^54 - 111885 * q^55 - 30656 * q^56 - 65903 * q^57 - 90188 * q^58 - 157759 * q^59 - 71088 * q^60 - 163640 * q^61 - 136304 * q^62 - 172844 * q^63 + 180224 * q^64 - 81544 * q^65 - 76900 * q^66 - 106228 * q^67 - 108016 * q^68 - 162750 * q^69 - 143416 * q^70 - 188370 * q^71 + 209280 * q^72 - 135423 * q^73 - 107236 * q^74 - 359459 * q^75 - 127504 * q^76 - 259175 * q^77 - 135036 * q^78 - 194026 * q^79 - 64000 * q^80 + 219444 * q^81 - 188396 * q^82 - 466476 * q^83 - 131520 * q^84 - 92384 * q^85 - 176076 * q^86 - 377355 * q^87 - 116864 * q^88 - 219335 * q^89 - 332056 * q^90 - 483654 * q^91 - 276416 * q^92 - 247383 * q^93 - 323416 * q^94 - 395162 * q^95 - 92160 * q^96 - 290677 * q^97 + 392316 * q^98 - 516636 * 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
$3$	−24.9834	−1.60268	−0.801342	−	0.598206i	$-0.795880\pi$
$3$	−24.9834	−1.60268	−0.801342	+	0.598206i	$0.795880\pi$
$4$	16.0000	0.500000
$5$	−15.3750	−0.275036	−0.137518	−	0.990499i	$-0.543912\pi$
$5$	−15.3750	−0.275036	−0.137518	+	0.990499i	$0.543912\pi$
$6$	−99.9335	−1.13327
$7$	−246.831	−1.90394	−0.951972	−	0.306184i	$-0.900948\pi$
$7$	−246.831	−1.90394	−0.951972	+	0.306184i	$0.900948\pi$
$8$	64.0000	0.353553
$9$	381.169	1.56860
$10$	−61.4999	−0.194480
$11$	−106.505	−0.265392	−0.132696	−	0.991157i	$-0.542363\pi$
$11$	−106.505	−0.265392	−0.132696	+	0.991157i	$0.542363\pi$
$12$	−399.734	−0.801342
$13$	−657.993	−1.07985	−0.539925	−	0.841713i	$-0.681547\pi$
$13$	−657.993	−1.07985	−0.539925	+	0.841713i	$0.681547\pi$
$14$	−987.323	−1.34629
$15$	384.119	0.440796
$16$	256.000	0.250000
$17$	804.524	0.675175	0.337588	−	0.941294i	$-0.390389\pi$
$17$	804.524	0.675175	0.337588	+	0.941294i	$0.390389\pi$
$18$	1524.68	1.10917
$19$	2408.77	1.53077	0.765387	−	0.643571i	$-0.222548\pi$
$19$	2408.77	1.53077	0.765387	+	0.643571i	$0.222548\pi$
$20$	−246.000	−0.137518
$21$	6166.67	3.05142
$22$	−426.019	−0.187660
$23$	701.915	0.276672	0.138336	−	0.990385i	$-0.455825\pi$
$23$	701.915	0.276672	0.138336	+	0.990385i	$0.455825\pi$
$24$	−1598.94	−0.566635
$25$	−2888.61	−0.924355
$26$	−2631.97	−0.763569
$27$	−3451.94	−0.911284
$28$	−3949.29	−0.951972
$29$	4916.86	1.08566	0.542829	−	0.839843i	$-0.317353\pi$
$29$	4916.86	1.08566	0.542829	+	0.839843i	$0.317353\pi$
$30$	1536.48	0.311690
$31$	−4304.63	−0.804509	−0.402255	−	0.915528i	$-0.631773\pi$
$31$	−4304.63	−0.804509	−0.402255	+	0.915528i	$0.631773\pi$
$32$	1024.00	0.176777
$33$	2660.85	0.425339
$34$	3218.10	0.477421
$35$	3795.02	0.523653
$36$	6098.71	0.784299
$37$	10786.2	1.29528	0.647640	−	0.761946i	$-0.275756\pi$
$37$	10786.2	1.29528	0.647640	+	0.761946i	$0.275756\pi$
$38$	9635.07	1.08242
$39$	16438.9	1.73066
$40$	−983.999	−0.0972399
$41$	−3688.68	−0.342698	−0.171349	−	0.985210i	$-0.554813\pi$
$41$	−3688.68	−0.342698	−0.171349	+	0.985210i	$0.554813\pi$
$42$	24666.7	2.15768
$43$	17436.3	1.43808	0.719040	−	0.694969i	$-0.244582\pi$
$43$	17436.3	1.43808	0.719040	+	0.694969i	$0.244582\pi$
$44$	−1704.08	−0.132696
$45$	−5860.47	−0.431421
$46$	2807.66	0.195637
$47$	−23928.9	−1.58008	−0.790038	−	0.613058i	$-0.789939\pi$
$47$	−23928.9	−1.58008	−0.790038	+	0.613058i	$0.789939\pi$
$48$	−6395.75	−0.400671
$49$	44118.5	2.62501
$50$	−11554.4	−0.653618
$51$	−20099.7	−1.08209
$52$	−10527.9	−0.539925
$53$	10602.9	0.518481	0.259241	−	0.965813i	$-0.416528\pi$
$53$	10602.9	0.518481	0.259241	+	0.965813i	$0.416528\pi$
$54$	−13807.8	−0.644375
$55$	1637.51	0.0729923
$56$	−15797.2	−0.673146
$57$	−60179.2	−2.45335
$58$	19667.5	0.767676
$59$	−3313.19	−0.123913	−0.0619565	−	0.998079i	$-0.519734\pi$
$59$	−3313.19	−0.123913	−0.0619565	+	0.998079i	$0.519734\pi$
$60$	6145.90	0.220398
$61$	−3038.70	−0.104559	−0.0522797	−	0.998632i	$-0.516649\pi$
$61$	−3038.70	−0.104559	−0.0522797	+	0.998632i	$0.516649\pi$
$62$	−17218.5	−0.568874
$63$	−94084.4	−2.98652
$64$	4096.00	0.125000
$65$	10116.6	0.296997
$66$	10643.4	0.300760
$67$	−7633.16	−0.207739	−0.103869	−	0.994591i	$-0.533122\pi$
$67$	−7633.16	−0.207739	−0.103869	+	0.994591i	$0.533122\pi$
$68$	12872.4	0.337588
$69$	−17536.2	−0.443418
$70$	15180.1	0.370279
$71$	18941.1	0.445923	0.222961	−	0.974827i	$-0.428428\pi$
$71$	18941.1	0.445923	0.222961	+	0.974827i	$0.428428\pi$
$72$	24394.8	0.554583
$73$	−28666.8	−0.629611	−0.314806	−	0.949156i	$-0.601939\pi$
$73$	−28666.8	−0.629611	−0.314806	+	0.949156i	$0.601939\pi$
$74$	43144.8	0.915901
$75$	72167.2	1.48145
$76$	38540.3	0.765387
$77$	26288.7	0.505291
$78$	65755.6	1.22376
$79$	−10554.6	−0.190272	−0.0951359	−	0.995464i	$-0.530329\pi$
$79$	−10554.6	−0.190272	−0.0951359	+	0.995464i	$0.530329\pi$
$80$	−3936.00	−0.0687590
$81$	−6383.04	−0.108097
$82$	−14754.7	−0.242324
$83$	31763.1	0.506090	0.253045	−	0.967455i	$-0.418568\pi$
$83$	31763.1	0.506090	0.253045	+	0.967455i	$0.418568\pi$
$84$	98666.7	1.52571
$85$	−12369.5	−0.185698
$86$	69745.2	1.01688
$87$	−122840.	−1.73997
$88$	−6816.31	−0.0938302
$89$	76821.6	1.02804	0.514018	−	0.857779i	$-0.328156\pi$
$89$	76821.6	1.02804	0.514018	+	0.857779i	$0.328156\pi$
$90$	−23441.9	−0.305061
$91$	162413.	2.05597
$92$	11230.6	0.138336
$93$	107544.	1.28937
$94$	−95715.6	−1.11728
$95$	−37034.7	−0.421018
$96$	−25583.0	−0.283317
$97$	74960.0	0.808910	0.404455	−	0.914558i	$-0.367461\pi$
$97$	74960.0	0.808910	0.404455	+	0.914558i	$0.367461\pi$
$98$	176474.	1.85616
$99$	−40596.4	−0.416293
$100$	−46217.8	−0.462178
$101$	23934.8	0.233468	0.116734	−	0.993163i	$-0.462758\pi$
$101$	23934.8	0.233468	0.116734	+	0.993163i	$0.462758\pi$
$102$	−80398.9	−0.765155
$103$	−149676.	−1.39015	−0.695073	−	0.718939i	$-0.744628\pi$
$103$	−149676.	−1.39015	−0.695073	+	0.718939i	$0.744628\pi$
$104$	−42111.6	−0.381784
$105$	−94812.4	−0.839251
$106$	42411.4	0.366622
$107$	−36521.6	−0.308383	−0.154191	−	0.988041i	$-0.549277\pi$
$107$	−36521.6	−0.308383	−0.154191	+	0.988041i	$0.549277\pi$
$108$	−55231.0	−0.455642
$109$	135485.	1.09226	0.546130	−	0.837701i	$-0.316101\pi$
$109$	135485.	1.09226	0.546130	+	0.837701i	$0.316101\pi$
$110$	6550.04	0.0516133
$111$	−269476.	−2.07593
$112$	−63188.7	−0.475986
$113$	−125223.	−0.922550	−0.461275	−	0.887257i	$-0.652608\pi$
$113$	−125223.	−0.922550	−0.461275	+	0.887257i	$0.652608\pi$
$114$	−240717.	−1.73478
$115$	−10791.9	−0.0760947
$116$	78669.8	0.542829
$117$	−250807.	−1.69385
$118$	−13252.8	−0.0876197
$119$	−198581.	−1.28550
$120$	24583.6	0.155845
$121$	−149708.	−0.929567
$122$	−12154.8	−0.0739346
$123$	92155.8	0.549237
$124$	−68874.0	−0.402255
$125$	92459.1	0.529267
$126$	−376338.	−2.11179
$127$	−93937.3	−0.516808	−0.258404	−	0.966037i	$-0.583196\pi$
$127$	−93937.3	−0.516808	−0.258404	+	0.966037i	$0.583196\pi$
$128$	16384.0	0.0883883
$129$	−435618.	−2.30479
$130$	40466.5	0.210009
$131$	228805.	1.16490	0.582449	−	0.812867i	$-0.302095\pi$
$131$	228805.	1.16490	0.582449	+	0.812867i	$0.302095\pi$
$132$	42573.6	0.212670
$133$	−594558.	−2.91451
$134$	−30532.6	−0.146893
$135$	53073.5	0.250636
$136$	51489.5	0.238711
$137$	112213.	0.510789	0.255395	−	0.966837i	$-0.417795\pi$
$137$	112213.	0.510789	0.255395	+	0.966837i	$0.417795\pi$
$138$	−70144.9	−0.313544
$139$	17338.9	0.0761173	0.0380587	−	0.999276i	$-0.487883\pi$
$139$	17338.9	0.0761173	0.0380587	+	0.999276i	$0.487883\pi$
$140$	60720.3	0.261827
$141$	597825.	2.53236
$142$	75764.5	0.315315
$143$	70079.5	0.286583
$144$	97579.4	0.392150
$145$	−75596.7	−0.298595
$146$	−114667.	−0.445202
$147$	−1.10223e6	−4.20706
$148$	172579.	0.647640
$149$	233495.	0.861613	0.430806	−	0.902444i	$-0.358229\pi$
$149$	233495.	0.861613	0.430806	+	0.902444i	$0.358229\pi$
$150$	288669.	1.04754
$151$	53703.8	0.191674	0.0958369	−	0.995397i	$-0.469447\pi$
$151$	53703.8	0.191674	0.0958369	+	0.995397i	$0.469447\pi$
$152$	154161.	0.541210
$153$	306660.	1.05908
$154$	105155.	0.357295
$155$	66183.5	0.221269
$156$	263022.	0.865329
$157$	−287997.	−0.932477	−0.466239	−	0.884659i	$-0.654391\pi$
$157$	−287997.	−0.932477	−0.466239	+	0.884659i	$0.654391\pi$
$158$	−42218.4	−0.134542
$159$	−264895.	−0.830962
$160$	−15744.0	−0.0486200
$161$	−173254.	−0.526768
$162$	−25532.2	−0.0764364
$163$	−106175.	−0.313006	−0.156503	−	0.987678i	$-0.550022\pi$
$163$	−106175.	−0.313006	−0.156503	+	0.987678i	$0.550022\pi$
$164$	−59018.9	−0.171349
$165$	−40910.5	−0.116984
$166$	127052.	0.357860
$167$	−344469.	−0.955782	−0.477891	−	0.878419i	$-0.658599\pi$
$167$	−344469.	−0.955782	−0.477891	+	0.878419i	$0.658599\pi$
$168$	394667.	1.07884
$169$	61662.3	0.166074
$170$	−49478.2	−0.131308
$171$	918148.	2.40117
$172$	278981.	0.719040
$173$	199112.	0.505805	0.252902	−	0.967492i	$-0.418615\pi$
$173$	199112.	0.505805	0.252902	+	0.967492i	$0.418615\pi$
$174$	−491360.	−1.23034
$175$	712998.	1.75992
$176$	−27265.2	−0.0663479
$177$	82774.8	0.198593
$178$	307286.	0.726931
$179$	−230190.	−0.536974	−0.268487	−	0.963283i	$-0.586524\pi$
$179$	−230190.	−0.536974	−0.268487	+	0.963283i	$0.586524\pi$
$180$	−93767.6	−0.215711
$181$	−499296.	−1.13282	−0.566411	−	0.824123i	$-0.691669\pi$
$181$	−499296.	−1.13282	−0.566411	+	0.824123i	$0.691669\pi$
$182$	649652.	1.45379
$183$	75917.0	0.167576
$184$	44922.6	0.0978183
$185$	−165837.	−0.356249
$186$	430176.	0.911726
$187$	−85685.6	−0.179186
$188$	−382862.	−0.790038
$189$	852045.	1.73503
$190$	−148139.	−0.297704
$191$	−794101.	−1.57504	−0.787521	−	0.616288i	$-0.788636\pi$
$191$	−794101.	−1.57504	−0.787521	+	0.616288i	$0.788636\pi$
$192$	−102332.	−0.200336
$193$	242374.	0.468374	0.234187	−	0.972192i	$-0.424757\pi$
$193$	242374.	0.468374	0.234187	+	0.972192i	$0.424757\pi$
$194$	299840.	0.571986
$195$	−252748.	−0.475993
$196$	705896.	1.31250
$197$	−244572.	−0.448995	−0.224498	−	0.974475i	$-0.572074\pi$
$197$	−244572.	−0.448995	−0.224498	+	0.974475i	$0.572074\pi$
$198$	−162385.	−0.294364
$199$	−475919.	−0.851922	−0.425961	−	0.904741i	$-0.640064\pi$
$199$	−475919.	−0.851922	−0.425961	+	0.904741i	$0.640064\pi$
$200$	−184871.	−0.326809
$201$	190702.	0.332939
$202$	95739.3	0.165087
$203$	−1.21363e6	−2.06703
$204$	−321596.	−0.541047
$205$	56713.4	0.0942543
$206$	−598706.	−0.982981
$207$	267549.	0.433987
$208$	−168446.	−0.269962
$209$	−256545.	−0.406255
$210$	−379250.	−0.593440
$211$	−926876.	−1.43323	−0.716615	−	0.697469i	$-0.754309\pi$
$211$	−926876.	−1.43323	−0.716615	+	0.697469i	$0.754309\pi$
$212$	169646.	0.259241
$213$	−473213.	−0.714674
$214$	−146086.	−0.218060
$215$	−268083.	−0.395524
$216$	−220924.	−0.322188
$217$	1.06251e6	1.53174
$218$	541941.	0.772344
$219$	716194.	1.00907
$220$	26200.1	0.0364961
$221$	−529371.	−0.729088
$222$	−1.07790e6	−1.46790
$223$	374178.	0.503867	0.251933	−	0.967745i	$-0.418934\pi$
$223$	374178.	0.503867	0.251933	+	0.967745i	$0.418934\pi$
$224$	−252755.	−0.336573
$225$	−1.10105e6	−1.44994
$226$	−500894.	−0.652341
$227$	−1.38106e6	−1.77888	−0.889440	−	0.457053i	$-0.848905\pi$
$227$	−1.38106e6	−1.77888	−0.889440	+	0.457053i	$0.848905\pi$
$228$	−962866.	−1.22667
$229$	424763.	0.535251	0.267626	−	0.963523i	$-0.413761\pi$
$229$	424763.	0.535251	0.267626	+	0.963523i	$0.413761\pi$
$230$	−43167.7	−0.0538071
$231$	−656780.	−0.809823
$232$	314679.	0.383838
$233$	720683.	0.869670	0.434835	−	0.900510i	$-0.356807\pi$
$233$	720683.	0.869670	0.434835	+	0.900510i	$0.356807\pi$
$234$	−1.00323e6	−1.19773
$235$	367906.	0.434578
$236$	−53011.1	−0.0619565
$237$	263690.	0.304946
$238$	−794325.	−0.908983
$239$	736700.	0.834250	0.417125	−	0.908849i	$-0.363038\pi$
$239$	736700.	0.834250	0.417125	+	0.908849i	$0.363038\pi$
$240$	98334.5	0.110199
$241$	−1.55251e6	−1.72183	−0.860916	−	0.508748i	$-0.830109\pi$
$241$	−1.55251e6	−1.72183	−0.860916	+	0.508748i	$0.830109\pi$
$242$	−598831.	−0.657303
$243$	998291.	1.08453
$244$	−48619.2	−0.0522797
$245$	−678321.	−0.721971
$246$	368623.	0.388369
$247$	−1.58495e6	−1.65300
$248$	−275496.	−0.284437
$249$	−793550.	−0.811103
$250$	369837.	0.374248
$251$	1.58069e6	1.58366	0.791831	−	0.610740i	$-0.209128\pi$
$251$	1.58069e6	1.58366	0.791831	+	0.610740i	$0.209128\pi$
$252$	−1.50535e6	−1.49326
$253$	−74757.3	−0.0734264
$254$	−375749.	−0.365438
$255$	309033.	0.297615
$256$	65536.0	0.0625000
$257$	−307959.	−0.290844	−0.145422	−	0.989370i	$-0.546454\pi$
$257$	−307959.	−0.290844	−0.145422	+	0.989370i	$0.546454\pi$
$258$	−1.74247e6	−1.62973
$259$	−2.66236e6	−2.46614
$260$	161866.	0.148499
$261$	1.87416e6	1.70296
$262$	915221.	0.823707
$263$	1.45834e6	1.30008	0.650038	−	0.759902i	$-0.274753\pi$
$263$	1.45834e6	1.30008	0.650038	+	0.759902i	$0.274753\pi$
$264$	170294.	0.150380
$265$	−163019.	−0.142601
$266$	−2.37823e6	−2.06087
$267$	−1.91926e6	−1.64762
$268$	−122131.	−0.103869
$269$	1.32205e6	1.11395	0.556976	−	0.830529i	$-0.311962\pi$
$269$	1.32205e6	1.11395	0.556976	+	0.830529i	$0.311962\pi$
$270$	212294.	0.177226
$271$	95253.1	0.0787872	0.0393936	−	0.999224i	$-0.487457\pi$
$271$	95253.1	0.0787872	0.0393936	+	0.999224i	$0.487457\pi$
$272$	205958.	0.168794
$273$	−4.05763e6	−3.29508
$274$	448852.	0.361182
$275$	307651.	0.245316
$276$	−280579.	−0.221709
$277$	−819523.	−0.641743	−0.320872	−	0.947123i	$-0.603976\pi$
$277$	−819523.	−0.641743	−0.320872	+	0.947123i	$0.603976\pi$
$278$	69355.4	0.0538231
$279$	−1.64079e6	−1.26195
$280$	242881.	0.185139
$281$	989616.	0.747654	0.373827	−	0.927498i	$-0.378045\pi$
$281$	989616.	0.747654	0.373827	+	0.927498i	$0.378045\pi$
$282$	2.39130e6	1.79065
$283$	−1.55834e6	−1.15664	−0.578319	−	0.815811i	$-0.696291\pi$
$283$	−1.55834e6	−1.15664	−0.578319	+	0.815811i	$0.696291\pi$
$284$	303058.	0.222961
$285$	925253.	0.674759
$286$	280318.	0.202645
$287$	910481.	0.652478
$288$	390317.	0.277292
$289$	−772598.	−0.544138
$290$	−302387.	−0.211139
$291$	−1.87275e6	−1.29643
$292$	−458669.	−0.314806
$293$	168286.	0.114520	0.0572598	−	0.998359i	$-0.481764\pi$
$293$	168286.	0.114520	0.0572598	+	0.998359i	$0.481764\pi$
$294$	−4.40891e6	−2.97484
$295$	50940.3	0.0340805
$296$	690316.	0.457951
$297$	367648.	0.241847
$298$	933980.	0.609252
$299$	−461855.	−0.298764
$300$	1.15468e6	0.740725
$301$	−4.30382e6	−2.73802
$302$	214815.	0.135534
$303$	−597973.	−0.374175
$304$	616644.	0.382693
$305$	46719.9	0.0287576
$306$	1.22664e6	0.748882
$307$	−2.00610e6	−1.21481	−0.607403	−	0.794394i	$-0.707789\pi$
$307$	−2.00610e6	−1.21481	−0.607403	+	0.794394i	$0.707789\pi$
$308$	420619.	0.252646
$309$	3.73942e6	2.22797
$310$	264734.	0.156461
$311$	−808330.	−0.473901	−0.236951	−	0.971522i	$-0.576148\pi$
$311$	−808330.	−0.473901	−0.236951	+	0.971522i	$0.576148\pi$
$312$	1.05209e6	0.611880
$313$	−330552.	−0.190713	−0.0953563	−	0.995443i	$-0.530399\pi$
$313$	−330552.	−0.190713	−0.0953563	+	0.995443i	$0.530399\pi$
$314$	−1.15199e6	−0.659361
$315$	1.44655e6	0.821402
$316$	−168874.	−0.0951359
$317$	839033.	0.468955	0.234477	−	0.972122i	$-0.424662\pi$
$317$	839033.	0.468955	0.234477	+	0.972122i	$0.424662\pi$
$318$	−1.05958e6	−0.587579
$319$	−523670.	−0.288125
$320$	−62975.9	−0.0343795
$321$	912433.	0.494240
$322$	−693017.	−0.372481
$323$	1.93791e6	1.03354
$324$	−102129.	−0.0540487
$325$	1.90069e6	0.998164
$326$	−424699.	−0.221328
$327$	−3.38488e6	−1.75055
$328$	−236076.	−0.121162
$329$	5.90639e6	3.00838
$330$	−163642.	−0.0827199
$331$	−1.93265e6	−0.969578	−0.484789	−	0.874631i	$-0.661104\pi$
$331$	−1.93265e6	−0.969578	−0.484789	+	0.874631i	$0.661104\pi$
$332$	508210.	0.253045
$333$	4.11137e6	2.03177
$334$	−1.37788e6	−0.675840
$335$	117360.	0.0571356
$336$	1.57867e6	0.762856
$337$	3.25743e6	1.56243	0.781214	−	0.624264i	$-0.214601\pi$
$337$	3.25743e6	1.56243	0.781214	+	0.624264i	$0.214601\pi$
$338$	246649.	0.117432
$339$	3.12851e6	1.47856
$340$	−197913.	−0.0928488
$341$	458463.	0.213510
$342$	3.67259e6	1.69788
$343$	−6.74131e6	−3.09392
$344$	1.11592e6	0.508438
$345$	269619.	0.121956
$346$	796449.	0.357658
$347$	−3.68410e6	−1.64251	−0.821255	−	0.570562i	$-0.806726\pi$
$347$	−3.68410e6	−1.64251	−0.821255	+	0.570562i	$0.806726\pi$
$348$	−1.96544e6	−0.869984
$349$	4.46717e6	1.96322	0.981610	−	0.190896i	$-0.0611393\pi$
$349$	4.46717e6	1.96322	0.981610	+	0.190896i	$0.0611393\pi$
$350$	2.85199e6	1.24445
$351$	2.27135e6	0.984049
$352$	−109061.	−0.0469151
$353$	2.02596e6	0.865352	0.432676	−	0.901549i	$-0.357569\pi$
$353$	2.02596e6	0.865352	0.432676	+	0.901549i	$0.357569\pi$
$354$	331099.	0.140427
$355$	−291219.	−0.122645
$356$	1.22915e6	0.514018
$357$	4.96123e6	2.06025
$358$	−920759.	−0.379698
$359$	1.04981e6	0.429908	0.214954	−	0.976624i	$-0.431040\pi$
$359$	1.04981e6	0.429908	0.214954	+	0.976624i	$0.431040\pi$
$360$	−375070.	−0.152530
$361$	3.32606e6	1.34327
$362$	−1.99719e6	−0.801027
$363$	3.74021e6	1.48980
$364$	2.59861e6	1.02799
$365$	440752.	0.173166
$366$	303668.	0.118494
$367$	−2.94854e6	−1.14272	−0.571362	−	0.820698i	$-0.693585\pi$
$367$	−2.94854e6	−1.14272	−0.571362	+	0.820698i	$0.693585\pi$
$368$	179690.	0.0691680
$369$	−1.40601e6	−0.537556
$370$	−663350.	−0.251906
$371$	−2.61711e6	−0.987160
$372$	1.72071e6	0.644687
$373$	77180.9	0.0287235	0.0143618	−	0.999897i	$-0.495428\pi$
$373$	77180.9	0.0287235	0.0143618	+	0.999897i	$0.495428\pi$
$374$	−342743.	−0.126704
$375$	−2.30994e6	−0.848248
$376$	−1.53145e6	−0.558641
$377$	−3.23526e6	−1.17235
$378$	3.40818e6	1.22685
$379$	784204.	0.280434	0.140217	−	0.990121i	$-0.455220\pi$
$379$	784204.	0.280434	0.140217	+	0.990121i	$0.455220\pi$
$380$	−592556.	−0.210509
$381$	2.34687e6	0.828280
$382$	−3.17640e6	−1.11372
$383$	−2.30075e6	−0.801444	−0.400722	−	0.916200i	$-0.631241\pi$
$383$	−2.30075e6	−0.801444	−0.400722	+	0.916200i	$0.631241\pi$
$384$	−409328.	−0.141659
$385$	−404188.	−0.138973
$386$	969496.	0.331190
$387$	6.64618e6	2.25577
$388$	1.19936e6	0.404455
$389$	3.57068e6	1.19640	0.598201	−	0.801346i	$-0.295882\pi$
$389$	3.57068e6	1.19640	0.598201	+	0.801346i	$0.295882\pi$
$390$	−1.01099e6	−0.336578
$391$	564707.	0.186802
$392$	2.82358e6	0.928080
$393$	−5.71633e6	−1.86696
$394$	−978290.	−0.317488
$395$	162277.	0.0523316
$396$	−649542.	−0.208147
$397$	−3.25279e6	−1.03581	−0.517904	−	0.855439i	$-0.673288\pi$
$397$	−3.25279e6	−1.03581	−0.517904	+	0.855439i	$0.673288\pi$
$398$	−1.90367e6	−0.602400
$399$	1.48541e7	4.67104
$400$	−739484.	−0.231089
$401$	3.54799e6	1.10185	0.550924	−	0.834555i	$-0.314275\pi$
$401$	3.54799e6	1.10185	0.550924	+	0.834555i	$0.314275\pi$
$402$	762808.	0.235424
$403$	2.83241e6	0.868749
$404$	382957.	0.116734
$405$	98139.2	0.0297307
$406$	−4.85453e6	−1.46161
$407$	−1.14878e6	−0.343757
$408$	−1.28638e6	−0.382578
$409$	−741312.	−0.219125	−0.109563	−	0.993980i	$-0.534945\pi$
$409$	−741312.	−0.219125	−0.109563	+	0.993980i	$0.534945\pi$
$410$	226854.	0.0666479
$411$	−2.80346e6	−0.818634
$412$	−2.39482e6	−0.695073
$413$	817799.	0.235924
$414$	1.07019e6	0.306875
$415$	−488357.	−0.139193
$416$	−673785.	−0.190892
$417$	−433183.	−0.121992
$418$	−1.02618e6	−0.287265
$419$	2.66074e6	0.740402	0.370201	−	0.928952i	$-0.379289\pi$
$419$	2.66074e6	0.740402	0.370201	+	0.928952i	$0.379289\pi$
$420$	−1.51700e6	−0.419626
$421$	−3.72813e6	−1.02515	−0.512574	−	0.858643i	$-0.671308\pi$
$421$	−3.72813e6	−1.02515	−0.512574	+	0.858643i	$0.671308\pi$
$422$	−3.70751e6	−1.01345
$423$	−9.12096e6	−2.47850
$424$	678583.	0.183311
$425$	−2.32396e6	−0.624102
$426$	−1.89285e6	−0.505351
$427$	750045.	0.199075
$428$	−584345.	−0.154191
$429$	−1.75082e6	−0.459302
$430$	−1.07233e6	−0.279678
$431$	185761.	0.0481683
$431$	185761.	0.0481683
$432$	−883696.	−0.227821
$433$	6.00536e6	1.53929	0.769644	−	0.638474i	$-0.220434\pi$
$433$	6.00536e6	1.53929	0.769644	+	0.638474i	$0.220434\pi$
$434$	4.25006e6	1.08310
$435$	1.88866e6	0.478554
$436$	2.16776e6	0.546130
$437$	1.69075e6	0.423522
$438$	2.86478e6	0.713519
$439$	6.66520e6	1.65064	0.825320	−	0.564666i	$-0.190995\pi$
$439$	6.66520e6	1.65064	0.825320	+	0.564666i	$0.190995\pi$
$440$	104801.	0.0258067
$441$	1.68166e7	4.11758
$442$	−2.11749e6	−0.515543
$443$	−370753.	−0.0897586	−0.0448793	−	0.998992i	$-0.514290\pi$
$443$	−370753.	−0.0897586	−0.0448793	+	0.998992i	$0.514290\pi$
$444$	−4.31161e6	−1.03796
$445$	−1.18113e6	−0.282747
$446$	1.49671e6	0.356288
$447$	−5.83350e6	−1.38089
$448$	−1.01102e6	−0.237993
$449$	386645.	0.0905101	0.0452550	−	0.998975i	$-0.485590\pi$
$449$	386645.	0.0905101	0.0452550	+	0.998975i	$0.485590\pi$
$450$	−4.40420e6	−1.02526
$451$	392862.	0.0909492
$452$	−2.00358e6	−0.461275
$453$	−1.34170e6	−0.307193
$454$	−5.52422e6	−1.25786
$455$	−2.49710e6	−0.565467
$456$	−3.85147e6	−0.867389
$457$	5.59179e6	1.25245	0.626225	−	0.779642i	$-0.284599\pi$
$457$	5.59179e6	1.25245	0.626225	+	0.779642i	$0.284599\pi$
$458$	1.69905e6	0.378480
$459$	−2.77717e6	−0.615277
$460$	−172671.	−0.0380474
$461$	−818931.	−0.179471	−0.0897356	−	0.995966i	$-0.528602\pi$
$461$	−818931.	−0.179471	−0.0897356	+	0.995966i	$0.528602\pi$
$462$	−2.62712e6	−0.572631
$463$	4.94352e6	1.07173	0.535864	−	0.844305i	$-0.319986\pi$
$463$	4.94352e6	1.07173	0.535864	+	0.844305i	$0.319986\pi$
$464$	1.25872e6	0.271415
$465$	−1.65349e6	−0.354625
$466$	2.88273e6	0.614950
$467$	−1.38442e6	−0.293748	−0.146874	−	0.989155i	$-0.546921\pi$
$467$	−1.38442e6	−0.293748	−0.146874	+	0.989155i	$0.546921\pi$
$468$	−4.01291e6	−0.846925
$469$	1.88410e6	0.395523
$470$	1.47163e6	0.307293
$471$	7.19513e6	1.49447
$472$	−212044.	−0.0438099
$473$	−1.85705e6	−0.381655
$474$	1.05476e6	0.215629
$475$	−6.95799e6	−1.41498
$476$	−3.17730e6	−0.642748
$477$	4.04148e6	0.813289
$478$	2.94680e6	0.589904
$479$	−8.70948e6	−1.73442	−0.867209	−	0.497945i	$-0.834088\pi$
$479$	−8.70948e6	−1.73442	−0.867209	+	0.497945i	$0.834088\pi$
$480$	393338.	0.0779225
$481$	−7.09724e6	−1.39871
$482$	−6.21002e6	−1.21752
$483$	4.32848e6	0.844243
$484$	−2.39532e6	−0.464784
$485$	−1.15251e6	−0.222479
$486$	3.99317e6	0.766879
$487$	975276.	0.186340	0.0931698	−	0.995650i	$-0.470300\pi$
$487$	975276.	0.186340	0.0931698	+	0.995650i	$0.470300\pi$
$488$	−194477.	−0.0369673
$489$	2.65260e6	0.501649
$490$	−2.71328e6	−0.510511
$491$	−2.13615e6	−0.399878	−0.199939	−	0.979808i	$-0.564074\pi$
$491$	−2.13615e6	−0.399878	−0.199939	+	0.979808i	$0.564074\pi$
$492$	1.47449e6	0.274618
$493$	3.95573e6	0.733010
$494$	−6.33981e6	−1.16885
$495$	624168.	0.114496
$496$	−1.10198e6	−0.201127
$497$	−4.67525e6	−0.849012
$498$	−3.17420e6	−0.573536
$499$	9.62570e6	1.73054	0.865269	−	0.501308i	$-0.167148\pi$
$499$	9.62570e6	1.73054	0.865269	+	0.501308i	$0.167148\pi$
$500$	1.47935e6	0.264633
$501$	8.60600e6	1.53182
$502$	6.32276e6	1.11982
$503$	1.43913e6	0.253618	0.126809	−	0.991927i	$-0.459526\pi$
$503$	1.43913e6	0.253618	0.126809	+	0.991927i	$0.459526\pi$
$504$	−6.02140e6	−1.05590
$505$	−367997.	−0.0642120
$506$	−299029.	−0.0519203
$507$	−1.54053e6	−0.266165
$508$	−1.50300e6	−0.258404
$509$	9.28384e6	1.58830	0.794151	−	0.607721i	$-0.207916\pi$
$509$	9.28384e6	1.58830	0.794151	+	0.607721i	$0.207916\pi$
$510$	1.23613e6	0.210445
$511$	7.07586e6	1.19875
$512$	262144.	0.0441942
$513$	−8.31492e6	−1.39497
$514$	−1.23184e6	−0.205658
$515$	2.30127e6	0.382340
$516$	−6.96988e6	−1.15239
$517$	2.54854e6	0.419339
$518$	−1.06495e7	−1.74383
$519$	−4.97450e6	−0.810645
$520$	647465.	0.105004
$521$	−2.91993e6	−0.471280	−0.235640	−	0.971840i	$-0.575719\pi$
$521$	−2.91993e6	−0.471280	−0.235640	+	0.971840i	$0.575719\pi$
$522$	7.49663e6	1.20418
$523$	−7.10847e6	−1.13638	−0.568188	−	0.822899i	$-0.692355\pi$
$523$	−7.10847e6	−1.13638	−0.568188	+	0.822899i	$0.692355\pi$
$524$	3.66088e6	0.582449
$525$	−1.78131e7	−2.82060
$526$	5.83335e6	0.919293
$527$	−3.46317e6	−0.543185
$528$	681178.	0.106335
$529$	−5.94366e6	−0.923453
$530$	−652075.	−0.100834
$531$	−1.26289e6	−0.194370
$532$	−9.51293e6	−1.45725
$533$	2.42713e6	0.370062
$534$	−7.67705e6	−1.16504
$535$	561519.	0.0848164
$536$	−488522.	−0.0734467
$537$	5.75092e6	0.860601
$538$	5.28819e6	0.787683
$539$	−4.69883e6	−0.696655
$540$	849176.	0.125318
$541$	−7.86267e6	−1.15499	−0.577493	−	0.816396i	$-0.695969\pi$
$541$	−7.86267e6	−1.15499	−0.577493	+	0.816396i	$0.695969\pi$
$542$	381012.	0.0557110
$543$	1.24741e7	1.81556
$544$	823832.	0.119355
$545$	−2.08308e6	−0.300411
$546$	−1.62305e7	−2.32997
$547$	4.14364e6	0.592125	0.296063	−	0.955169i	$-0.404326\pi$
$547$	4.14364e6	0.592125	0.296063	+	0.955169i	$0.404326\pi$
$548$	1.79541e6	0.255395
$549$	−1.15826e6	−0.164012
$550$	1.23060e6	0.173465
$551$	1.18436e7	1.66190
$552$	−1.12232e6	−0.156772
$553$	2.60520e6	0.362267
$554$	−3.27809e6	−0.453781
$555$	4.14318e6	0.570954
$556$	277422.	0.0380587
$557$	−1.24627e7	−1.70205	−0.851027	−	0.525122i	$-0.824020\pi$
$557$	−1.24627e7	−1.70205	−0.851027	+	0.525122i	$0.824020\pi$
$558$	−6.56317e6	−0.892335
$559$	−1.14730e7	−1.55291
$560$	971525.	0.130913
$561$	2.14072e6	0.287179
$562$	3.95846e6	0.528671
$563$	1.29467e7	1.72143	0.860716	−	0.509086i	$-0.170017\pi$
$563$	1.29467e7	1.72143	0.860716	+	0.509086i	$0.170017\pi$
$564$	9.56520e6	1.26618
$565$	1.92531e6	0.253734
$566$	−6.23337e6	−0.817866
$567$	1.57553e6	0.205812
$568$	1.21223e6	0.157657
$569$	−6.76862e6	−0.876434	−0.438217	−	0.898869i	$-0.644390\pi$
$569$	−6.76862e6	−0.876434	−0.438217	+	0.898869i	$0.644390\pi$
$570$	3.70101e6	0.477126
$571$	4.90917e6	0.630112	0.315056	−	0.949073i	$-0.397977\pi$
$571$	4.90917e6	0.630112	0.315056	+	0.949073i	$0.397977\pi$
$572$	1.12127e6	0.143292
$573$	1.98393e7	2.52430
$574$	3.64192e6	0.461372
$575$	−2.02756e6	−0.255743
$576$	1.56127e6	0.196075
$577$	−9.46183e6	−1.18314	−0.591569	−	0.806254i	$-0.701491\pi$
$577$	−9.46183e6	−1.18314	−0.591569	+	0.806254i	$0.701491\pi$
$578$	−3.09039e6	−0.384764
$579$	−6.05532e6	−0.750656
$580$	−1.20955e6	−0.149298
$581$	−7.84012e6	−0.963568
$582$	−7.49102e6	−0.916713
$583$	−1.12925e6	−0.137601
$584$	−1.83468e6	−0.222601
$585$	3.85615e6	0.465870
$586$	673146.	0.0809776
$587$	−1.42379e6	−0.170549	−0.0852747	−	0.996357i	$-0.527177\pi$
$587$	−1.42379e6	−0.170549	−0.0852747	+	0.996357i	$0.527177\pi$
$588$	−1.76357e7	−2.10353
$589$	−1.03688e7	−1.23152
$590$	203761.	0.0240986
$591$	6.11025e6	0.719598
$592$	2.76126e6	0.323820
$593$	8.17755e6	0.954963	0.477481	−	0.878642i	$-0.341550\pi$
$593$	8.17755e6	0.954963	0.477481	+	0.878642i	$0.341550\pi$
$594$	1.47059e6	0.171012
$595$	3.05318e6	0.353558
$596$	3.73592e6	0.430806
$597$	1.18901e7	1.36536
$598$	−1.84742e6	−0.211258
$599$	6.54085e6	0.744847	0.372424	−	0.928063i	$-0.378527\pi$
$599$	6.54085e6	0.744847	0.372424	+	0.928063i	$0.378527\pi$
$600$	4.61870e6	0.523772
$601$	6.58358e6	0.743491	0.371745	−	0.928335i	$-0.378759\pi$
$601$	6.58358e6	0.743491	0.371745	+	0.928335i	$0.378759\pi$
$602$	−1.72153e7	−1.93608
$603$	−2.90953e6	−0.325858
$604$	859261.	0.0958369
$605$	2.30175e6	0.255664
$606$	−2.39189e6	−0.264582
$607$	−4.93248e6	−0.543367	−0.271683	−	0.962387i	$-0.587580\pi$
$607$	−4.93248e6	−0.543367	−0.271683	+	0.962387i	$0.587580\pi$
$608$	2.46658e6	0.270605
$609$	3.03207e7	3.31280
$610$	186880.	0.0203347
$611$	1.57451e7	1.70624
$612$	4.90656e6	0.529540
$613$	−3.02518e6	−0.325162	−0.162581	−	0.986695i	$-0.551982\pi$
$613$	−3.02518e6	−0.325162	−0.162581	+	0.986695i	$0.551982\pi$
$614$	−8.02441e6	−0.858998
$615$	−1.41689e6	−0.151060
$616$	1.68248e6	0.178647
$617$	5.26460e6	0.556740	0.278370	−	0.960474i	$-0.410206\pi$
$617$	5.26460e6	0.556740	0.278370	+	0.960474i	$0.410206\pi$
$618$	1.49577e7	1.57541
$619$	5.37928e6	0.564283	0.282142	−	0.959373i	$-0.408955\pi$
$619$	5.37928e6	0.564283	0.282142	+	0.959373i	$0.408955\pi$
$620$	1.05894e6	0.110635
$621$	−2.42297e6	−0.252127
$622$	−3.23332e6	−0.335099
$623$	−1.89619e7	−1.95732
$624$	4.20836e6	0.432664
$625$	7.60535e6	0.778788
$626$	−1.32221e6	−0.134854
$627$	6.40937e6	0.651098
$628$	−4.60795e6	−0.466239
$629$	8.67775e6	0.874541
$630$	5.78618e6	0.580819
$631$	−638448.	−0.0638341	−0.0319170	−	0.999491i	$-0.510161\pi$
$631$	−638448.	−0.0638341	−0.0319170	+	0.999491i	$0.510161\pi$
$632$	−675495.	−0.0672712
$633$	2.31565e7	2.29701
$634$	3.35613e6	0.331601
$635$	1.44428e6	0.142141
$636$	−4.23832e6	−0.415481
$637$	−2.90297e7	−2.83461
$638$	−2.09468e6	−0.203735
$639$	7.21977e6	0.699474
$640$	−251904.	−0.0243100
$641$	−1.14642e7	−1.10204	−0.551022	−	0.834491i	$-0.685762\pi$
$641$	−1.14642e7	−1.10204	−0.551022	+	0.834491i	$0.685762\pi$
$642$	3.64973e6	0.349481
$643$	−7.10661e6	−0.677852	−0.338926	−	0.940813i	$-0.610064\pi$
$643$	−7.10661e6	−0.677852	−0.338926	+	0.940813i	$0.610064\pi$
$644$	−2.77207e6	−0.263384
$645$	6.69761e6	0.633900
$646$	7.75164e6	0.730823
$647$	−1.84244e7	−1.73034	−0.865172	−	0.501475i	$-0.832791\pi$
$647$	−1.84244e7	−1.73034	−0.865172	+	0.501475i	$0.832791\pi$
$648$	−408515.	−0.0382182
$649$	352871.	0.0328855
$650$	7.60274e6	0.705809
$651$	−2.65452e7	−2.45490
$652$	−1.69880e6	−0.156503
$653$	2.90292e6	0.266411	0.133206	−	0.991088i	$-0.457473\pi$
$653$	2.90292e6	0.266411	0.133206	+	0.991088i	$0.457473\pi$
$654$	−1.35395e7	−1.23782
$655$	−3.51788e6	−0.320389
$656$	−944303.	−0.0856745
$657$	−1.09269e7	−0.987607
$658$	2.36256e7	2.12724
$659$	1.73634e6	0.155748	0.0778738	−	0.996963i	$-0.475187\pi$
$659$	1.73634e6	0.155748	0.0778738	+	0.996963i	$0.475187\pi$
$660$	−654568.	−0.0584918
$661$	−1.22092e7	−1.08688	−0.543441	−	0.839447i	$-0.682879\pi$
$661$	−1.22092e7	−1.08688	−0.543441	+	0.839447i	$0.682879\pi$
$662$	−7.73059e6	−0.685595
$663$	1.32255e7	1.16850
$664$	2.03284e6	0.178930
$665$	9.14132e6	0.801595
$666$	1.64455e7	1.43668
$667$	3.45122e6	0.300371
$668$	−5.51150e6	−0.477891
$669$	−9.34823e6	−0.807540
$670$	469439.	0.0404010
$671$	323636.	0.0277492
$672$	6.31467e6	0.539421
$673$	−1.07595e7	−0.915701	−0.457850	−	0.889029i	$-0.651380\pi$
$673$	−1.07595e7	−0.915701	−0.457850	+	0.889029i	$0.651380\pi$
$674$	1.30297e7	1.10480
$675$	9.97131e6	0.842350
$676$	986597.	0.0830372
$677$	−2.30801e7	−1.93538	−0.967690	−	0.252143i	$-0.918865\pi$
$677$	−2.30801e7	−1.93538	−0.967690	+	0.252143i	$0.918865\pi$
$678$	1.25140e7	1.04550
$679$	−1.85024e7	−1.54012
$680$	−791650.	−0.0656540
$681$	3.45034e7	2.85098
$682$	1.83385e6	0.150974
$683$	−1.77668e7	−1.45733	−0.728663	−	0.684872i	$-0.759858\pi$
$683$	−1.77668e7	−1.45733	−0.728663	+	0.684872i	$0.759858\pi$
$684$	1.46904e7	1.20058
$685$	−1.72527e6	−0.140485
$686$	−2.69653e7	−2.18773
$687$	−1.06120e7	−0.857839
$688$	4.46369e6	0.359520
$689$	−6.97661e6	−0.559882
$690$	1.07848e6	0.0862358
$691$	5.07974e6	0.404712	0.202356	−	0.979312i	$-0.435140\pi$
$691$	5.07974e6	0.404712	0.202356	+	0.979312i	$0.435140\pi$
$692$	3.18580e6	0.252902
$693$	1.00204e7	0.792599
$694$	−1.47364e7	−1.16143
$695$	−266585.	−0.0209350
$696$	−7.86175e6	−0.615172
$697$	−2.96763e6	−0.231381
$698$	1.78687e7	1.38821
$699$	−1.80051e7	−1.39381
$700$	1.14080e7	0.879961
$701$	9.21489e6	0.708264	0.354132	−	0.935195i	$-0.384776\pi$
$701$	9.21489e6	0.708264	0.354132	+	0.935195i	$0.384776\pi$
$702$	9.08541e6	0.695828
$703$	2.59814e7	1.98278
$704$	−436244.	−0.0331740
$705$	−9.19154e6	−0.696491
$706$	8.10382e6	0.611897
$707$	−5.90785e6	−0.444510
$708$	1.32440e6	0.0992967
$709$	−1.63974e7	−1.22507	−0.612533	−	0.790445i	$-0.709849\pi$
$709$	−1.63974e7	−1.22507	−0.612533	+	0.790445i	$0.709849\pi$
$710$	−1.16488e6	−0.0867230
$711$	−4.02309e6	−0.298460
$712$	4.91658e6	0.363466
$713$	−3.02148e6	−0.222585
$714$	1.98449e7	1.45681
$715$	−1.07747e6	−0.0788207
$716$	−3.68304e6	−0.268487
$717$	−1.84053e7	−1.33704
$718$	4.19925e6	0.303991
$719$	1.01966e7	0.735587	0.367794	−	0.929907i	$-0.380113\pi$
$719$	1.01966e7	0.735587	0.367794	+	0.929907i	$0.380113\pi$
$720$	−1.50028e6	−0.107855
$721$	3.69448e7	2.64676
$722$	1.33042e7	0.949833
$723$	3.87868e7	2.75955
$724$	−7.98874e6	−0.566411
$725$	−1.42029e7	−1.00353
$726$	1.49608e7	1.05345
$727$	−3.59924e6	−0.252566	−0.126283	−	0.991994i	$-0.540305\pi$
$727$	−3.59924e6	−0.252566	−0.126283	+	0.991994i	$0.540305\pi$
$728$	1.03944e7	0.726896
$729$	−2.33896e7	−1.63006
$730$	1.76301e6	0.122447
$731$	1.40279e7	0.970956
$732$	1.21467e6	0.0837879
$733$	−1.24936e7	−0.858872	−0.429436	−	0.903097i	$-0.641288\pi$
$733$	−1.24936e7	−0.858872	−0.429436	+	0.903097i	$0.641288\pi$
$734$	−1.17942e7	−0.808028
$735$	1.69467e7	1.15709
$736$	718761.	0.0489091
$737$	812968.	0.0551321
$738$	−5.62405e6	−0.380109
$739$	1.98498e6	0.133704	0.0668522	−	0.997763i	$-0.478704\pi$
$739$	1.98498e6	0.133704	0.0668522	+	0.997763i	$0.478704\pi$
$740$	−2.65340e6	−0.178124
$741$	3.95975e7	2.64924
$742$	−1.04684e7	−0.698027
$743$	−1.63105e7	−1.08392	−0.541958	−	0.840406i	$-0.682317\pi$
$743$	−1.63105e7	−1.08392	−0.541958	+	0.840406i	$0.682317\pi$
$744$	6.88282e6	0.455863
$745$	−3.58998e6	−0.236974
$746$	308724.	0.0203106
$747$	1.21071e7	0.793852
$748$	−1.37097e6	−0.0895930
$749$	9.01465e6	0.587144
$750$	−9.23977e6	−0.599802
$751$	−1.82809e7	−1.18276	−0.591380	−	0.806393i	$-0.701417\pi$
$751$	−1.82809e7	−1.18276	−0.591380	+	0.806393i	$0.701417\pi$
$752$	−6.12580e6	−0.395019
$753$	−3.94910e7	−2.53811
$754$	−1.29411e7	−0.828975
$755$	−825695.	−0.0527172
$756$	1.36327e7	0.867517
$757$	1.82234e7	1.15582	0.577909	−	0.816101i	$-0.303869\pi$
$757$	1.82234e7	1.15582	0.577909	+	0.816101i	$0.303869\pi$
$758$	3.13682e6	0.198297
$759$	1.86769e6	0.117679
$760$	−2.37022e6	−0.148852
$761$	−1.14984e7	−0.719742	−0.359871	−	0.933002i	$-0.617179\pi$
$761$	−1.14984e7	−0.719742	−0.359871	+	0.933002i	$0.617179\pi$
$762$	9.38749e6	0.585682
$763$	−3.34419e7	−2.07960
$764$	−1.27056e7	−0.787521
$765$	−4.71489e6	−0.291285
$766$	−9.20302e6	−0.566707
$767$	2.18006e6	0.133807
$768$	−1.63731e6	−0.100168
$769$	−1.21819e7	−0.742845	−0.371422	−	0.928464i	$-0.621130\pi$
$769$	−1.21819e7	−0.742845	−0.371422	+	0.928464i	$0.621130\pi$
$770$	−1.61675e6	−0.0982690
$771$	7.69387e6	0.466132
$772$	3.87798e6	0.234187
$773$	−1.80943e7	−1.08916	−0.544582	−	0.838707i	$-0.683312\pi$
$773$	−1.80943e7	−1.08916	−0.544582	+	0.838707i	$0.683312\pi$
$774$	2.65847e7	1.59507
$775$	1.24344e7	0.743652
$776$	4.79744e6	0.285993
$777$	6.65149e7	3.95245
$778$	1.42827e7	0.845984
$779$	−8.88518e6	−0.524593
$780$	−4.04396e6	−0.237997
$781$	−2.01732e6	−0.118344
$782$	2.25883e6	0.132089
$783$	−1.69727e7	−0.989343
$784$	1.12943e7	0.656251
$785$	4.42794e6	0.256465
$786$	−2.28653e7	−1.32014
$787$	1.41526e7	0.814515	0.407258	−	0.913313i	$-0.366485\pi$
$787$	1.41526e7	0.814515	0.407258	+	0.913313i	$0.366485\pi$
$788$	−3.91316e6	−0.224498
$789$	−3.64342e7	−2.08361
$790$	649107.	0.0370040
$791$	3.09090e7	1.75648
$792$	−2.59817e6	−0.147182
$793$	1.99944e6	0.112908
$794$	−1.30111e7	−0.732427
$795$	4.07276e6	0.228545
$796$	−7.61470e6	−0.425961
$797$	−6.34577e6	−0.353866	−0.176933	−	0.984223i	$-0.556618\pi$
$797$	−6.34577e6	−0.353866	−0.176933	+	0.984223i	$0.556618\pi$
$798$	5.94163e7	3.30292
$799$	−1.92514e7	−1.06683
$800$	−2.95794e6	−0.163404
$801$	2.92820e7	1.61258
$802$	1.41920e7	0.779125
$803$	3.05315e6	0.167094
$804$	3.05123e6	0.166470
$805$	2.66378e6	0.144880
$806$	1.13297e7	0.614298
$807$	−3.30292e7	−1.78531
$808$	1.53183e6	0.0825433
$809$	1.03652e7	0.556812	0.278406	−	0.960464i	$-0.410194\pi$
$809$	1.03652e7	0.556812	0.278406	+	0.960464i	$0.410194\pi$
$810$	392557.	0.0210228
$811$	1.72634e7	0.921670	0.460835	−	0.887486i	$-0.347550\pi$
$811$	1.72634e7	0.921670	0.460835	+	0.887486i	$0.347550\pi$
$812$	−1.94181e7	−1.03352
$813$	−2.37974e6	−0.126271
$814$	−4.59512e6	−0.243073
$815$	1.63243e6	0.0860878
$816$	−5.14553e6	−0.270523
$817$	4.20000e7	2.20137
$818$	−2.96525e6	−0.154945
$819$	6.19069e7	3.22500
$820$	907415.	0.0471272
$821$	3.77910e7	1.95673	0.978365	−	0.206887i	$-0.0663334\pi$
$821$	3.77910e7	1.95673	0.978365	+	0.206887i	$0.0663334\pi$
$822$	−1.12138e7	−0.578862
$823$	−1.20621e7	−0.620757	−0.310379	−	0.950613i	$-0.600456\pi$
$823$	−1.20621e7	−0.620757	−0.310379	+	0.950613i	$0.600456\pi$
$824$	−9.57929e6	−0.491491
$825$	−7.68616e6	−0.393165
$826$	3.27119e6	0.166823
$827$	4.72117e6	0.240041	0.120021	−	0.992771i	$-0.461704\pi$
$827$	4.72117e6	0.240041	0.120021	+	0.992771i	$0.461704\pi$
$828$	4.28078e6	0.216994
$829$	2.47944e7	1.25305	0.626523	−	0.779403i	$-0.284478\pi$
$829$	2.47944e7	1.25305	0.626523	+	0.779403i	$0.284478\pi$
$830$	−1.95343e6	−0.0984243
$831$	2.04744e7	1.02851
$832$	−2.69514e6	−0.134981
$833$	3.54944e7	1.77234
$834$	−1.73273e6	−0.0862614
$835$	5.29620e6	0.262874
$836$	−4.10472e6	−0.203127
$837$	1.48593e7	0.733137
$838$	1.06430e7	0.523543
$839$	−1.94749e7	−0.955149	−0.477574	−	0.878591i	$-0.658484\pi$
$839$	−1.94749e7	−0.955149	−0.477574	+	0.878591i	$0.658484\pi$
$840$	−6.06800e6	−0.296720
$841$	3.66440e6	0.178654
$842$	−1.49125e7	−0.724888
$843$	−2.47239e7	−1.19825
$844$	−1.48300e7	−0.716615
$845$	−948056.	−0.0456765
$846$	−3.64838e7	−1.75257
$847$	3.69525e7	1.76984
$848$	2.71433e6	0.129620
$849$	3.89327e7	1.85372
$850$	−9.29582e6	−0.441307
$851$	7.57099e6	0.358368
$852$	−7.57141e6	−0.357337
$853$	−2.90713e7	−1.36802	−0.684010	−	0.729473i	$-0.739765\pi$
$853$	−2.90713e7	−1.36802	−0.684010	+	0.729473i	$0.739765\pi$
$854$	3.00018e6	0.140767
$855$	−1.41165e7	−0.660408
$856$	−2.33738e6	−0.109030
$857$	2.53554e7	1.17928	0.589642	−	0.807664i	$-0.299269\pi$
$857$	2.53554e7	1.17928	0.589642	+	0.807664i	$0.299269\pi$
$858$	−7.00329e6	−0.324776
$859$	2.55311e7	1.18056	0.590278	−	0.807200i	$-0.299018\pi$
$859$	2.55311e7	1.18056	0.590278	+	0.807200i	$0.299018\pi$
$860$	−4.28932e6	−0.197762
$861$	−2.27469e7	−1.04572
$862$	743044.	0.0340601
$863$	4.11780e7	1.88208	0.941041	−	0.338292i	$-0.109849\pi$
$863$	4.11780e7	1.88208	0.941041	+	0.338292i	$0.109849\pi$
$864$	−3.53479e6	−0.161094
$865$	−3.06135e6	−0.139114
$866$	2.40215e7	1.08844
$867$	1.93021e7	0.872082
$868$	1.70002e7	0.765871
$869$	1.12412e6	0.0504965
$870$	7.55464e6	0.338389
$871$	5.02257e6	0.224326
$872$	8.67106e6	0.386172
$873$	2.85725e7	1.26886
$874$	6.76300e6	0.299475
$875$	−2.28218e7	−1.00770
$876$	1.14591e7	0.504534
$877$	−4.42390e7	−1.94225	−0.971127	−	0.238565i	$-0.923323\pi$
$877$	−4.42390e7	−1.94225	−0.971127	+	0.238565i	$0.923323\pi$
$878$	2.66608e7	1.16718
$879$	−4.20437e6	−0.183539
$880$	419202.	0.0182481
$881$	4.33012e6	0.187958	0.0939788	−	0.995574i	$-0.470041\pi$
$881$	4.33012e6	0.187958	0.0939788	+	0.995574i	$0.470041\pi$
$882$	6.72665e7	2.91157
$883$	−1.65049e7	−0.712379	−0.356189	−	0.934414i	$-0.615924\pi$
$883$	−1.65049e7	−0.712379	−0.356189	+	0.934414i	$0.615924\pi$
$884$	−8.46994e6	−0.364544
$885$	−1.27266e6	−0.0546204
$886$	−1.48301e6	−0.0634689
$887$	−1.30518e7	−0.557010	−0.278505	−	0.960435i	$-0.589839\pi$
$887$	−1.30518e7	−0.557010	−0.278505	+	0.960435i	$0.589839\pi$
$888$	−1.72464e7	−0.733951
$889$	2.31866e7	0.983973
$890$	−4.72452e6	−0.199932
$891$	679825.	0.0286882
$892$	5.98684e6	0.251933
$893$	−5.76391e7	−2.41874
$894$	−2.33340e7	−0.976439
$895$	3.53916e6	0.147687
$896$	−4.04408e6	−0.168287
$897$	1.15387e7	0.478824
$898$	1.54658e6	0.0640003
$899$	−2.11653e7	−0.873422
$900$	−1.76168e7	−0.724971
$901$	8.53025e6	0.350066
$902$	1.57145e6	0.0643108
$903$	1.07524e8	4.38819
$904$	−8.01430e6	−0.326171
$905$	7.67667e6	0.311567
$906$	−5.36681e6	−0.217218
$907$	−4.73814e7	−1.91245	−0.956225	−	0.292633i	$-0.905469\pi$
$907$	−4.73814e7	−1.91245	−0.956225	+	0.292633i	$0.905469\pi$
$908$	−2.20969e7	−0.889440
$909$	9.12322e6	0.366217
$910$	−9.98839e6	−0.399845
$911$	−3.63499e6	−0.145113	−0.0725567	−	0.997364i	$-0.523116\pi$
$911$	−3.63499e6	−0.145113	−0.0725567	+	0.997364i	$0.523116\pi$
$912$	−1.54059e7	−0.613337
$913$	−3.38292e6	−0.134312
$914$	2.23672e7	0.885616
$915$	−1.16722e6	−0.0460894
$916$	6.79620e6	0.267626
$917$	−5.64762e7	−2.21790
$918$	−1.11087e7	−0.435066
$919$	−3.11886e7	−1.21817	−0.609084	−	0.793105i	$-0.708463\pi$
$919$	−3.11886e7	−1.21817	−0.609084	+	0.793105i	$0.708463\pi$
$920$	−690684.	−0.0269035
$921$	5.01192e7	1.94695
$922$	−3.27572e6	−0.126905
$923$	−1.24631e7	−0.481529
$924$	−1.05085e7	−0.404911
$925$	−3.11571e7	−1.19730
$926$	1.97741e7	0.757826
$927$	−5.70521e7	−2.18058
$928$	5.03487e6	0.191919
$929$	−2.86968e7	−1.09092	−0.545462	−	0.838136i	$-0.683646\pi$
$929$	−2.86968e7	−1.09092	−0.545462	+	0.838136i	$0.683646\pi$
$930$	−6.61395e6	−0.250757
$931$	1.06271e8	4.01829
$932$	1.15309e7	0.434835
$933$	2.01948e7	0.759514
$934$	−5.53768e6	−0.207711
$935$	1.31742e6	0.0492826
$936$	−1.60516e7	−0.598866
$937$	4.49911e7	1.67408	0.837042	−	0.547139i	$-0.184283\pi$
$937$	4.49911e7	1.67408	0.837042	+	0.547139i	$0.184283\pi$
$938$	7.53639e6	0.279677
$939$	8.25831e6	0.305652
$940$	5.88650e6	0.217289
$941$	2.59905e7	0.956842	0.478421	−	0.878131i	$-0.341209\pi$
$941$	2.59905e7	0.956842	0.478421	+	0.878131i	$0.341209\pi$
$942$	2.87805e7	1.05675
$943$	−2.58914e6	−0.0948149
$944$	−848178.	−0.0309783
$945$	−1.31002e7	−0.477197
$946$	−7.42820e6	−0.269871
$947$	−3.94362e7	−1.42896	−0.714480	−	0.699656i	$-0.753337\pi$
$947$	−3.94362e7	−1.42896	−0.714480	+	0.699656i	$0.753337\pi$
$948$	4.21904e6	0.152473
$949$	1.88626e7	0.679885
$950$	−2.78320e7	−1.00054
$951$	−2.09619e7	−0.751587
$952$	−1.27092e7	−0.454492
$953$	5.52116e7	1.96924	0.984618	−	0.174720i	$-0.0559021\pi$
$953$	5.52116e7	1.96924	0.984618	+	0.174720i	$0.0559021\pi$
$954$	1.61659e7	0.575082
$955$	1.22093e7	0.433193
$956$	1.17872e7	0.417125
$957$	1.30830e7	0.461773
$958$	−3.48379e7	−1.22642
$959$	−2.76976e7	−0.972514
$960$	1.57335e6	0.0550995
$961$	−1.00994e7	−0.352765
$962$	−2.83890e7	−0.989036
$963$	−1.39209e7	−0.483729
$964$	−2.48401e7	−0.860916
$965$	−3.72650e6	−0.128820
$966$	1.73139e7	0.596970
$967$	3.37470e7	1.16056	0.580282	−	0.814415i	$-0.302942\pi$
$967$	3.37470e7	1.16056	0.580282	+	0.814415i	$0.302942\pi$
$968$	−9.58129e6	−0.328652
$969$	−4.84156e7	−1.65644
$970$	−4.61004e6	−0.157317
$971$	−4.59211e7	−1.56302	−0.781509	−	0.623894i	$-0.785550\pi$
$971$	−4.59211e7	−1.56302	−0.781509	+	0.623894i	$0.785550\pi$
$972$	1.59727e7	0.542265
$973$	−4.27976e6	−0.144923
$974$	3.90111e6	0.131762
$975$	−4.74856e7	−1.59974
$976$	−777907.	−0.0261398
$977$	−1.48245e6	−0.0496869	−0.0248435	−	0.999691i	$-0.507909\pi$
$977$	−1.48245e6	−0.0496869	−0.0248435	+	0.999691i	$0.507909\pi$
$978$	1.06104e7	0.354720
$979$	−8.18187e6	−0.272832
$980$	−1.08531e7	−0.360986
$981$	5.16428e7	1.71332
$982$	−8.54459e6	−0.282756
$983$	−2.65901e7	−0.877680	−0.438840	−	0.898565i	$-0.644611\pi$
$983$	−2.65901e7	−0.877680	−0.438840	+	0.898565i	$0.644611\pi$
$984$	5.89797e6	0.194185
$985$	3.76030e6	0.123490
$986$	1.58229e7	0.518316
$987$	−1.47562e8	−4.82148
$988$	−2.53592e7	−0.826502
$989$	1.22388e7	0.397876
$990$	2.49667e6	0.0809606
$991$	−426092.	−0.0137822	−0.00689112	−	0.999976i	$-0.502194\pi$
$991$	−426092.	−0.0137822	−0.00689112	+	0.999976i	$0.502194\pi$
$992$	−4.40794e6	−0.142219
$993$	4.82841e7	1.55393
$994$	−1.87010e7	−0.600342
$995$	7.31724e6	0.234309
$996$	−1.26968e7	−0.405551
$997$	−4.85213e7	−1.54595	−0.772974	−	0.634438i	$-0.781231\pi$
$997$	−4.85213e7	−1.54595	−0.772974	+	0.634438i	$0.781231\pi$
$998$	3.85028e7	1.22368
$999$	−3.72333e7	−1.18037

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	862.6.a.b.1.5	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
862.6.a.b.1.5	✓	44	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:	\( N \)	\(=\)	\( 862 = 2 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	862.a (trivial)

\(f(q)\)	\(=\)	\(q+4.00000 q^{2} -24.9834 q^{3} +16.0000 q^{4} -15.3750 q^{5} -99.9335 q^{6} -246.831 q^{7} +64.0000 q^{8} +381.169 q^{9} +O(q^{10})\)	\(q+4.00000 q^{2} -24.9834 q^{3} +16.0000 q^{4} -15.3750 q^{5} -99.9335 q^{6} -246.831 q^{7} +64.0000 q^{8} +381.169 q^{9} -61.4999 q^{10} -106.505 q^{11} -399.734 q^{12} -657.993 q^{13} -987.323 q^{14} +384.119 q^{15} +256.000 q^{16} +804.524 q^{17} +1524.68 q^{18} +2408.77 q^{19} -246.000 q^{20} +6166.67 q^{21} -426.019 q^{22} +701.915 q^{23} -1598.94 q^{24} -2888.61 q^{25} -2631.97 q^{26} -3451.94 q^{27} -3949.29 q^{28} +4916.86 q^{29} +1536.48 q^{30} -4304.63 q^{31} +1024.00 q^{32} +2660.85 q^{33} +3218.10 q^{34} +3795.02 q^{35} +6098.71 q^{36} +10786.2 q^{37} +9635.07 q^{38} +16438.9 q^{39} -983.999 q^{40} -3688.68 q^{41} +24666.7 q^{42} +17436.3 q^{43} -1704.08 q^{44} -5860.47 q^{45} +2807.66 q^{46} -23928.9 q^{47} -6395.75 q^{48} +44118.5 q^{49} -11554.4 q^{50} -20099.7 q^{51} -10527.9 q^{52} +10602.9 q^{53} -13807.8 q^{54} +1637.51 q^{55} -15797.2 q^{56} -60179.2 q^{57} +19667.5 q^{58} -3313.19 q^{59} +6145.90 q^{60} -3038.70 q^{61} -17218.5 q^{62} -94084.4 q^{63} +4096.00 q^{64} +10116.6 q^{65} +10643.4 q^{66} -7633.16 q^{67} +12872.4 q^{68} -17536.2 q^{69} +15180.1 q^{70} +18941.1 q^{71} +24394.8 q^{72} -28666.8 q^{73} +43144.8 q^{74} +72167.2 q^{75} +38540.3 q^{76} +26288.7 q^{77} +65755.6 q^{78} -10554.6 q^{79} -3936.00 q^{80} -6383.04 q^{81} -14754.7 q^{82} +31763.1 q^{83} +98666.7 q^{84} -12369.5 q^{85} +69745.2 q^{86} -122840. q^{87} -6816.31 q^{88} +76821.6 q^{89} -23441.9 q^{90} +162413. q^{91} +11230.6 q^{92} +107544. q^{93} -95715.6 q^{94} -37034.7 q^{95} -25583.0 q^{96} +74960.0 q^{97} +176474. q^{98} -40596.4 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 176 q^{2} - 90 q^{3} + 704 q^{4} - 250 q^{5} - 360 q^{6} - 479 q^{7} + 2816 q^{8} + 3270 q^{9}+O(q^{10}) \) 44 * q + 176 * q^2 - 90 * q^3 + 704 * q^4 - 250 * q^5 - 360 * q^6 - 479 * q^7 + 2816 * q^8 + 3270 * q^9	\( 44 q + 176 q^{2} - 90 q^{3} + 704 q^{4} - 250 q^{5} - 360 q^{6} - 479 q^{7} + 2816 q^{8} + 3270 q^{9} - 1000 q^{10} - 1826 q^{11} - 1440 q^{12} - 2623 q^{13} - 1916 q^{14} - 4443 q^{15} + 11264 q^{16} - 6751 q^{17} + 13080 q^{18} - 7969 q^{19} - 4000 q^{20} - 8220 q^{21} - 7304 q^{22} - 17276 q^{23} - 5760 q^{24} + 21130 q^{25} - 10492 q^{26} - 27963 q^{27} - 7664 q^{28} - 22547 q^{29} - 17772 q^{30} - 34076 q^{31} + 45056 q^{32} - 19225 q^{33} - 27004 q^{34} - 35854 q^{35} + 52320 q^{36} - 26809 q^{37} - 31876 q^{38} - 33759 q^{39} - 16000 q^{40} - 47099 q^{41} - 32880 q^{42} - 44019 q^{43} - 29216 q^{44} - 83014 q^{45} - 69104 q^{46} - 80854 q^{47} - 23040 q^{48} + 98079 q^{49} + 84520 q^{50} - 54896 q^{51} - 41968 q^{52} - 86057 q^{53} - 111852 q^{54} - 111885 q^{55} - 30656 q^{56} - 65903 q^{57} - 90188 q^{58} - 157759 q^{59} - 71088 q^{60} - 163640 q^{61} - 136304 q^{62} - 172844 q^{63} + 180224 q^{64} - 81544 q^{65} - 76900 q^{66} - 106228 q^{67} - 108016 q^{68} - 162750 q^{69} - 143416 q^{70} - 188370 q^{71} + 209280 q^{72} - 135423 q^{73} - 107236 q^{74} - 359459 q^{75} - 127504 q^{76} - 259175 q^{77} - 135036 q^{78} - 194026 q^{79} - 64000 q^{80} + 219444 q^{81} - 188396 q^{82} - 466476 q^{83} - 131520 q^{84} - 92384 q^{85} - 176076 q^{86} - 377355 q^{87} - 116864 q^{88} - 219335 q^{89} - 332056 q^{90} - 483654 q^{91} - 276416 q^{92} - 247383 q^{93} - 323416 q^{94} - 395162 q^{95} - 92160 q^{96} - 290677 q^{97} + 392316 q^{98} - 516636 q^{99}+O(q^{100}) \) 44 * q + 176 * q^2 - 90 * q^3 + 704 * q^4 - 250 * q^5 - 360 * q^6 - 479 * q^7 + 2816 * q^8 + 3270 * q^9 - 1000 * q^10 - 1826 * q^11 - 1440 * q^12 - 2623 * q^13 - 1916 * q^14 - 4443 * q^15 + 11264 * q^16 - 6751 * q^17 + 13080 * q^18 - 7969 * q^19 - 4000 * q^20 - 8220 * q^21 - 7304 * q^22 - 17276 * q^23 - 5760 * q^24 + 21130 * q^25 - 10492 * q^26 - 27963 * q^27 - 7664 * q^28 - 22547 * q^29 - 17772 * q^30 - 34076 * q^31 + 45056 * q^32 - 19225 * q^33 - 27004 * q^34 - 35854 * q^35 + 52320 * q^36 - 26809 * q^37 - 31876 * q^38 - 33759 * q^39 - 16000 * q^40 - 47099 * q^41 - 32880 * q^42 - 44019 * q^43 - 29216 * q^44 - 83014 * q^45 - 69104 * q^46 - 80854 * q^47 - 23040 * q^48 + 98079 * q^49 + 84520 * q^50 - 54896 * q^51 - 41968 * q^52 - 86057 * q^53 - 111852 * q^54 - 111885 * q^55 - 30656 * q^56 - 65903 * q^57 - 90188 * q^58 - 157759 * q^59 - 71088 * q^60 - 163640 * q^61 - 136304 * q^62 - 172844 * q^63 + 180224 * q^64 - 81544 * q^65 - 76900 * q^66 - 106228 * q^67 - 108016 * q^68 - 162750 * q^69 - 143416 * q^70 - 188370 * q^71 + 209280 * q^72 - 135423 * q^73 - 107236 * q^74 - 359459 * q^75 - 127504 * q^76 - 259175 * q^77 - 135036 * q^78 - 194026 * q^79 - 64000 * q^80 + 219444 * q^81 - 188396 * q^82 - 466476 * q^83 - 131520 * q^84 - 92384 * q^85 - 176076 * q^86 - 377355 * q^87 - 116864 * q^88 - 219335 * q^89 - 332056 * q^90 - 483654 * q^91 - 276416 * q^92 - 247383 * q^93 - 323416 * q^94 - 395162 * q^95 - 92160 * q^96 - 290677 * q^97 + 392316 * q^98 - 516636 * q^99

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