LMFDB - Embedded newform 115.6.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,6,Mod(1,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, 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("115.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	115.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:	$18.4441392785$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2 x^{9} - 220 x^{8} + 541 x^{7} + 15887 x^{6} - 50180 x^{5} - 417450 x^{4} + 1703213 x^{3} + \cdots + 15136200 $ x^10 - 2x^9 - 220x^8 + 541x^7 + 15887x^6 - 50180x^5 - 417450x^4 + 1703213x^3 + 2235790x^2 - 15551780*x + 15136200
Coefficient ring:	$\Z[a_1, a_2, a_3]$
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			$3.17438$ of defining polynomial
Character	$\chi$	$=$	115.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.17438 q^{2} -2.37223 q^{3} -14.5746 q^{4} -25.0000 q^{5} +9.90260 q^{6} +115.757 q^{7} +194.420 q^{8} -237.373 q^{9} +O(q^{10})$	\(q-4.17438 q^{2} -2.37223 q^{3} -14.5746 q^{4} -25.0000 q^{5} +9.90260 q^{6} +115.757 q^{7} +194.420 q^{8} -237.373 q^{9} +104.359 q^{10} +539.278 q^{11} +34.5743 q^{12} +116.796 q^{13} -483.214 q^{14} +59.3059 q^{15} -345.195 q^{16} +283.187 q^{17} +990.882 q^{18} -1935.09 q^{19} +364.365 q^{20} -274.603 q^{21} -2251.15 q^{22} -529.000 q^{23} -461.209 q^{24} +625.000 q^{25} -487.549 q^{26} +1139.56 q^{27} -1687.11 q^{28} -1811.62 q^{29} -247.565 q^{30} -1602.67 q^{31} -4780.46 q^{32} -1279.29 q^{33} -1182.13 q^{34} -2893.93 q^{35} +3459.61 q^{36} +7108.55 q^{37} +8077.78 q^{38} -277.067 q^{39} -4860.50 q^{40} -18391.4 q^{41} +1146.30 q^{42} -23389.6 q^{43} -7859.75 q^{44} +5934.31 q^{45} +2208.25 q^{46} -24977.0 q^{47} +818.883 q^{48} -3407.27 q^{49} -2608.99 q^{50} -671.787 q^{51} -1702.25 q^{52} -5302.06 q^{53} -4756.94 q^{54} -13481.9 q^{55} +22505.5 q^{56} +4590.48 q^{57} +7562.37 q^{58} +30543.4 q^{59} -864.358 q^{60} +44040.3 q^{61} +6690.16 q^{62} -27477.6 q^{63} +31001.7 q^{64} -2919.89 q^{65} +5340.25 q^{66} -20711.7 q^{67} -4127.34 q^{68} +1254.91 q^{69} +12080.4 q^{70} +37127.9 q^{71} -46149.9 q^{72} +23277.2 q^{73} -29673.8 q^{74} -1482.65 q^{75} +28203.1 q^{76} +62425.3 q^{77} +1156.58 q^{78} -53752.1 q^{79} +8629.87 q^{80} +54978.2 q^{81} +76772.6 q^{82} -114591. q^{83} +4002.23 q^{84} -7079.69 q^{85} +97637.1 q^{86} +4297.58 q^{87} +104846. q^{88} +40980.7 q^{89} -24772.1 q^{90} +13519.9 q^{91} +7709.95 q^{92} +3801.92 q^{93} +104263. q^{94} +48377.2 q^{95} +11340.4 q^{96} +429.764 q^{97} +14223.2 q^{98} -128010. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 12 q^{2} - 18 q^{3} + 138 q^{4} - 250 q^{5} + 78 q^{6} - 15 q^{7} - 285 q^{8} + 788 q^{9}+O(q^{10}) $ 10 * q - 12 * q^2 - 18 * q^3 + 138 * q^4 - 250 * q^5 + 78 * q^6 - 15 * q^7 - 285 * q^8 + 788 * q^9	\( 10 q - 12 q^{2} - 18 q^{3} + 138 q^{4} - 250 q^{5} + 78 q^{6} - 15 q^{7} - 285 q^{8} + 788 q^{9} + 300 q^{10} - 594 q^{11} - 1698 q^{12} - 1048 q^{13} + 639 q^{14} + 450 q^{15} + 234 q^{16} - 851 q^{17} - 6534 q^{18} - 178 q^{19} - 3450 q^{20} - 3116 q^{21} - 6103 q^{22} - 5290 q^{23} + 1689 q^{24} + 6250 q^{25} - 8914 q^{26} + 1800 q^{27} - 10177 q^{28} - 5527 q^{29} - 1950 q^{30} - 14999 q^{31} - 44832 q^{32} - 27368 q^{33} - 14369 q^{34} + 375 q^{35} - 34128 q^{36} - 25503 q^{37} - 53451 q^{38} - 41640 q^{39} + 7125 q^{40} - 7147 q^{41} - 52736 q^{42} + 5652 q^{43} - 3135 q^{44} - 19700 q^{45} + 6348 q^{46} - 57752 q^{47} - 51470 q^{48} + 19617 q^{49} - 7500 q^{50} + 13956 q^{51} + 46680 q^{52} - 74635 q^{53} - 5901 q^{54} + 14850 q^{55} + 6825 q^{56} - 55844 q^{57} + 46373 q^{58} - 58843 q^{59} + 42450 q^{60} + 43344 q^{61} + 40430 q^{62} - 55165 q^{63} + 223597 q^{64} + 26200 q^{65} + 273973 q^{66} + 68051 q^{67} + 53021 q^{68} + 9522 q^{69} - 15975 q^{70} - 19237 q^{71} + 253050 q^{72} - 9160 q^{73} + 92210 q^{74} - 11250 q^{75} + 309393 q^{76} - 238146 q^{77} + 184189 q^{78} - 61112 q^{79} - 5850 q^{80} + 107738 q^{81} - 57922 q^{82} - 106785 q^{83} + 235538 q^{84} + 21275 q^{85} + 175458 q^{86} - 149624 q^{87} + 20709 q^{88} - 172774 q^{89} + 163350 q^{90} + 314634 q^{91} - 73002 q^{92} - 82480 q^{93} + 328193 q^{94} + 4450 q^{95} + 724596 q^{96} + 120712 q^{97} + 515589 q^{98} - 244126 q^{99}+O(q^{100}) \) 10 * q - 12 * q^2 - 18 * q^3 + 138 * q^4 - 250 * q^5 + 78 * q^6 - 15 * q^7 - 285 * q^8 + 788 * q^9 + 300 * q^10 - 594 * q^11 - 1698 * q^12 - 1048 * q^13 + 639 * q^14 + 450 * q^15 + 234 * q^16 - 851 * q^17 - 6534 * q^18 - 178 * q^19 - 3450 * q^20 - 3116 * q^21 - 6103 * q^22 - 5290 * q^23 + 1689 * q^24 + 6250 * q^25 - 8914 * q^26 + 1800 * q^27 - 10177 * q^28 - 5527 * q^29 - 1950 * q^30 - 14999 * q^31 - 44832 * q^32 - 27368 * q^33 - 14369 * q^34 + 375 * q^35 - 34128 * q^36 - 25503 * q^37 - 53451 * q^38 - 41640 * q^39 + 7125 * q^40 - 7147 * q^41 - 52736 * q^42 + 5652 * q^43 - 3135 * q^44 - 19700 * q^45 + 6348 * q^46 - 57752 * q^47 - 51470 * q^48 + 19617 * q^49 - 7500 * q^50 + 13956 * q^51 + 46680 * q^52 - 74635 * q^53 - 5901 * q^54 + 14850 * q^55 + 6825 * q^56 - 55844 * q^57 + 46373 * q^58 - 58843 * q^59 + 42450 * q^60 + 43344 * q^61 + 40430 * q^62 - 55165 * q^63 + 223597 * q^64 + 26200 * q^65 + 273973 * q^66 + 68051 * q^67 + 53021 * q^68 + 9522 * q^69 - 15975 * q^70 - 19237 * q^71 + 253050 * q^72 - 9160 * q^73 + 92210 * q^74 - 11250 * q^75 + 309393 * q^76 - 238146 * q^77 + 184189 * q^78 - 61112 * q^79 - 5850 * q^80 + 107738 * q^81 - 57922 * q^82 - 106785 * q^83 + 235538 * q^84 + 21275 * q^85 + 175458 * q^86 - 149624 * q^87 + 20709 * q^88 - 172774 * q^89 + 163350 * q^90 + 314634 * q^91 - 73002 * q^92 - 82480 * q^93 + 328193 * q^94 + 4450 * q^95 + 724596 * q^96 + 120712 * q^97 + 515589 * q^98 - 244126 * 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 $

$2$	−4.17438	−0.737932	−0.368966	−	0.929443i	$-0.620288\pi$
$2$	−4.17438	−0.737932	−0.368966	+	0.929443i	$0.620288\pi$
$3$	−2.37223	−0.152179	−0.0760894	−	0.997101i	$-0.524243\pi$
$3$	−2.37223	−0.152179	−0.0760894	+	0.997101i	$0.524243\pi$
$4$	−14.5746	−0.455456
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	9.90260	0.112298
$7$	115.757	0.892900	0.446450	−	0.894809i	$-0.352688\pi$
$7$	115.757	0.892900	0.446450	+	0.894809i	$0.352688\pi$
$8$	194.420	1.07403
$9$	−237.373	−0.976842
$10$	104.359	0.330013
$11$	539.278	1.34379	0.671894	−	0.740647i	$-0.265481\pi$
$11$	539.278	1.34379	0.671894	+	0.740647i	$0.265481\pi$
$12$	34.5743	0.0693107
$13$	116.796	0.191676	0.0958381	−	0.995397i	$-0.469447\pi$
$13$	116.796	0.191676	0.0958381	+	0.995397i	$0.469447\pi$
$14$	−483.214	−0.658900
$15$	59.3059	0.0680565
$16$	−345.195	−0.337104
$17$	283.187	0.237658	0.118829	−	0.992915i	$-0.462086\pi$
$17$	283.187	0.237658	0.118829	+	0.992915i	$0.462086\pi$
$18$	990.882	0.720843
$19$	−1935.09	−1.22975	−0.614875	−	0.788625i	$-0.710793\pi$
$19$	−1935.09	−1.22975	−0.614875	+	0.788625i	$0.710793\pi$
$20$	364.365	0.203686
$21$	−274.603	−0.135881
$22$	−2251.15	−0.991625
$23$	−529.000	−0.208514
$23$	−529.000	−0.208514
$24$	−461.209	−0.163444
$25$	625.000	0.200000
$26$	−487.549	−0.141444
$27$	1139.56	0.300834
$28$	−1687.11	−0.406676
$29$	−1811.62	−0.400010	−0.200005	−	0.979795i	$-0.564096\pi$
$29$	−1811.62	−0.400010	−0.200005	+	0.979795i	$0.564096\pi$
$30$	−247.565	−0.0502211
$31$	−1602.67	−0.299530	−0.149765	−	0.988722i	$-0.547852\pi$
$31$	−1602.67	−0.299530	−0.149765	+	0.988722i	$0.547852\pi$
$32$	−4780.46	−0.825268
$33$	−1279.29	−0.204496
$34$	−1182.13	−0.175375
$35$	−2893.93	−0.399317
$36$	3459.61	0.444908
$37$	7108.55	0.853644	0.426822	−	0.904336i	$-0.359633\pi$
$37$	7108.55	0.853644	0.426822	+	0.904336i	$0.359633\pi$
$38$	8077.78	0.907472
$39$	−277.067	−0.0291691
$40$	−4860.50	−0.480320
$41$	−18391.4	−1.70866	−0.854328	−	0.519734i	$-0.826031\pi$
$41$	−18391.4	−1.70866	−0.854328	+	0.519734i	$0.826031\pi$
$42$	1146.30	0.100271
$43$	−23389.6	−1.92909	−0.964545	−	0.263920i	$-0.914985\pi$
$43$	−23389.6	−1.92909	−0.964545	+	0.263920i	$0.914985\pi$
$44$	−7859.75	−0.612036
$45$	5934.31	0.436857
$46$	2208.25	0.153870
$47$	−24977.0	−1.64928	−0.824642	−	0.565655i	$-0.808623\pi$
$47$	−24977.0	−1.64928	−0.824642	+	0.565655i	$0.808623\pi$
$48$	818.883	0.0513002
$49$	−3407.27	−0.202729
$50$	−2608.99	−0.147586
$51$	−671.787	−0.0361665
$52$	−1702.25	−0.0873000
$53$	−5302.06	−0.259272	−0.129636	−	0.991562i	$-0.541381\pi$
$53$	−5302.06	−0.259272	−0.129636	+	0.991562i	$0.541381\pi$
$54$	−4756.94	−0.221995
$55$	−13481.9	−0.600960
$56$	22505.5	0.959000
$57$	4590.48	0.187142
$58$	7562.37	0.295181
$59$	30543.4	1.14232	0.571159	−	0.820839i	$-0.306494\pi$
$59$	30543.4	1.14232	0.571159	+	0.820839i	$0.306494\pi$
$60$	−864.358	−0.0309967
$61$	44040.3	1.51539	0.757697	−	0.652607i	$-0.226325\pi$
$61$	44040.3	1.51539	0.757697	+	0.652607i	$0.226325\pi$
$62$	6690.16	0.221033
$63$	−27477.6	−0.872222
$64$	31001.7	0.946096
$65$	−2919.89	−0.0857202
$66$	5340.25	0.150904
$67$	−20711.7	−0.563675	−0.281838	−	0.959462i	$-0.590944\pi$
$67$	−20711.7	−0.563675	−0.281838	+	0.959462i	$0.590944\pi$
$68$	−4127.34	−0.108242
$69$	1254.91	0.0317315
$70$	12080.4	0.294669
$71$	37127.9	0.874087	0.437044	−	0.899440i	$-0.356026\pi$
$71$	37127.9	0.874087	0.437044	+	0.899440i	$0.356026\pi$
$72$	−46149.9	−1.04916
$73$	23277.2	0.511238	0.255619	−	0.966778i	$-0.417721\pi$
$73$	23277.2	0.511238	0.255619	+	0.966778i	$0.417721\pi$
$74$	−29673.8	−0.629931
$75$	−1482.65	−0.0304358
$76$	28203.1	0.560096
$77$	62425.3	1.19987
$78$	1156.58	0.0215248
$79$	−53752.1	−0.969009	−0.484505	−	0.874789i	$-0.661000\pi$
$79$	−53752.1	−0.969009	−0.484505	+	0.874789i	$0.661000\pi$
$80$	8629.87	0.150758
$81$	54978.2	0.931061
$82$	76772.6	1.26087
$83$	−114591.	−1.82581	−0.912907	−	0.408167i	$-0.866168\pi$
$83$	−114591.	−1.82581	−0.912907	+	0.408167i	$0.866168\pi$
$84$	4002.23	0.0618876
$85$	−7079.69	−0.106284
$86$	97637.1	1.42354
$87$	4297.58	0.0608731
$88$	104846.	1.44327
$89$	40980.7	0.548409	0.274205	−	0.961671i	$-0.411585\pi$
$89$	40980.7	0.548409	0.274205	+	0.961671i	$0.411585\pi$
$90$	−24772.1	−0.322371
$91$	13519.9	0.171148
$92$	7709.95	0.0949691
$93$	3801.92	0.0455822
$94$	104263.	1.21706
$95$	48377.2	0.549961
$96$	11340.4	0.125588
$97$	429.764	0.00463768	0.00231884	−	0.999997i	$-0.499262\pi$
$97$	429.764	0.00463768	0.00231884	+	0.999997i	$0.499262\pi$
$98$	14223.2	0.149601
$99$	−128010.	−1.31267
$100$	−9109.11	−0.0910911
$101$	−174445.	−1.70159	−0.850794	−	0.525499i	$-0.823879\pi$
$101$	−174445.	−1.70159	−0.850794	+	0.525499i	$0.823879\pi$
$102$	2804.29	0.0266884
$103$	56582.0	0.525515	0.262757	−	0.964862i	$-0.415368\pi$
$103$	56582.0	0.525515	0.262757	+	0.964862i	$0.415368\pi$
$104$	22707.4	0.205866
$105$	6865.08	0.0607676
$106$	22132.8	0.191325
$107$	17063.3	0.144080	0.0720398	−	0.997402i	$-0.477049\pi$
$107$	17063.3	0.144080	0.0720398	+	0.997402i	$0.477049\pi$
$108$	−16608.6	−0.137016
$109$	−27832.2	−0.224378	−0.112189	−	0.993687i	$-0.535786\pi$
$109$	−27832.2	−0.224378	−0.112189	+	0.993687i	$0.535786\pi$
$110$	56278.7	0.443468
$111$	−16863.1	−0.129907
$112$	−39958.8	−0.301001
$113$	−235136.	−1.73230	−0.866149	−	0.499786i	$-0.833412\pi$
$113$	−235136.	−1.73230	−0.866149	+	0.499786i	$0.833412\pi$
$114$	−19162.4	−0.138098
$115$	13225.0	0.0932505
$116$	26403.5	0.182187
$117$	−27724.1	−0.187237
$118$	−127500.	−0.842954
$119$	32781.0	0.212204
$120$	11530.2	0.0730946
$121$	129769.	0.805766
$122$	−183841.	−1.11826
$123$	43628.7	0.260021
$124$	23358.3	0.136423
$125$	−15625.0	−0.0894427
$126$	114702.	0.643641
$127$	−117540.	−0.646659	−0.323329	−	0.946286i	$-0.604802\pi$
$127$	−117540.	−0.646659	−0.323329	+	0.946286i	$0.604802\pi$
$128$	23562.1	0.127113
$129$	55485.7	0.293567
$130$	12188.7	0.0632557
$131$	228906.	1.16541	0.582706	−	0.812683i	$-0.301994\pi$
$131$	228906.	1.16541	0.582706	+	0.812683i	$0.301994\pi$
$132$	18645.2	0.0931389
$133$	−224000.	−1.09804
$134$	86458.4	0.415954
$135$	−28488.9	−0.134537
$136$	55057.3	0.255251
$137$	−238305.	−1.08476	−0.542378	−	0.840135i	$-0.682476\pi$
$137$	−238305.	−1.08476	−0.542378	+	0.840135i	$0.682476\pi$
$138$	−5238.47	−0.0234157
$139$	−215507.	−0.946070	−0.473035	−	0.881044i	$-0.656842\pi$
$139$	−215507.	−0.946070	−0.473035	+	0.881044i	$0.656842\pi$
$140$	42177.8	0.181871
$141$	59251.3	0.250986
$142$	−154986.	−0.645017
$143$	62985.3	0.257572
$144$	81939.8	0.329298
$145$	45290.4	0.178890
$146$	−97167.7	−0.377259
$147$	8082.85	0.0308511
$148$	−103604.	−0.388797
$149$	−327077.	−1.20693	−0.603467	−	0.797388i	$-0.706215\pi$
$149$	−327077.	−1.20693	−0.603467	+	0.797388i	$0.706215\pi$
$150$	6189.12	0.0224595
$151$	119246.	0.425598	0.212799	−	0.977096i	$-0.431742\pi$
$151$	119246.	0.425598	0.212799	+	0.977096i	$0.431742\pi$
$152$	−376219.	−1.32079
$153$	−67220.9	−0.232154
$154$	−260587.	−0.885422
$155$	40066.8	0.133954
$156$	4038.13	0.0132852
$157$	175169.	0.567165	0.283582	−	0.958948i	$-0.408477\pi$
$157$	175169.	0.567165	0.283582	+	0.958948i	$0.408477\pi$
$158$	224382.	0.715063
$159$	12577.7	0.0394557
$160$	119512.	0.369071
$161$	−61235.6	−0.186183
$162$	−229500.	−0.687060
$163$	140575.	0.414418	0.207209	−	0.978297i	$-0.433562\pi$
$163$	140575.	0.414418	0.207209	+	0.978297i	$0.433562\pi$
$164$	268047.	0.778217
$165$	31982.3	0.0914535
$166$	478347.	1.34733
$167$	−314621.	−0.872964	−0.436482	−	0.899713i	$-0.643776\pi$
$167$	−314621.	−0.872964	−0.436482	+	0.899713i	$0.643776\pi$
$168$	−53388.3	−0.145940
$169$	−357652.	−0.963260
$170$	29553.3	0.0784302
$171$	459337.	1.20127
$172$	340894.	0.878615
$173$	−173706.	−0.441264	−0.220632	−	0.975357i	$-0.570812\pi$
$173$	−173706.	−0.441264	−0.220632	+	0.975357i	$0.570812\pi$
$174$	−17939.7	−0.0449203
$175$	72348.2	0.178580
$176$	−186156.	−0.452997
$177$	−72456.1	−0.173837
$178$	−171069.	−0.404689
$179$	−126133.	−0.294235	−0.147118	−	0.989119i	$-0.547000\pi$
$179$	−126133.	−0.294235	−0.147118	+	0.989119i	$0.547000\pi$
$180$	−86490.1	−0.198969
$181$	362984.	0.823552	0.411776	−	0.911285i	$-0.364909\pi$
$181$	362984.	0.823552	0.411776	+	0.911285i	$0.364909\pi$
$182$	−56437.3	−0.126295
$183$	−104474.	−0.230611
$184$	−102848.	−0.223950
$185$	−177714.	−0.381761
$186$	−15870.6	−0.0336366
$187$	152717.	0.319361
$188$	364029.	0.751176
$189$	131912.	0.268614
$190$	−201945.	−0.405834
$191$	−573499.	−1.13749	−0.568747	−	0.822513i	$-0.692572\pi$
$191$	−573499.	−1.13749	−0.568747	+	0.822513i	$0.692572\pi$
$192$	−73543.2	−0.143976
$193$	358805.	0.693369	0.346685	−	0.937982i	$-0.387307\pi$
$193$	358805.	0.693369	0.346685	+	0.937982i	$0.387307\pi$
$194$	−1794.00	−0.00342229
$195$	6926.67	0.0130448
$196$	49659.6	0.0923342
$197$	−655906.	−1.20414	−0.602069	−	0.798444i	$-0.705657\pi$
$197$	−655906.	−1.20414	−0.602069	+	0.798444i	$0.705657\pi$
$198$	534361.	0.968660
$199$	−384463.	−0.688212	−0.344106	−	0.938931i	$-0.611818\pi$
$199$	−384463.	−0.688212	−0.344106	+	0.938931i	$0.611818\pi$
$200$	121512.	0.214806
$201$	49133.0	0.0857794
$202$	728198.	1.25566
$203$	−209708.	−0.357169
$204$	9791.01	0.0164722
$205$	459785.	0.764134
$206$	−236194.	−0.387795
$207$	125570.	0.203686
$208$	−40317.3	−0.0646149
$209$	−1.04355e6	−1.65252
$210$	−28657.4	−0.0448424
$211$	309387.	0.478405	0.239203	−	0.970970i	$-0.423114\pi$
$211$	309387.	0.478405	0.239203	+	0.970970i	$0.423114\pi$
$212$	77275.4	0.118087
$213$	−88076.1	−0.133018
$214$	−71228.4	−0.106321
$215$	584741.	0.862715
$216$	221552.	0.323104
$217$	−185521.	−0.267451
$218$	116182.	0.165576
$219$	−55218.9	−0.0777996
$220$	196494.	0.273711
$221$	33075.1	0.0455533
$222$	70393.1	0.0958623
$223$	1.30912e6	1.76286	0.881432	−	0.472311i	$-0.156580\pi$
$223$	1.30912e6	1.76286	0.881432	+	0.472311i	$0.156580\pi$
$224$	−553373.	−0.736882
$225$	−148358.	−0.195368
$226$	981545.	1.27832
$227$	−1.38190e6	−1.77996	−0.889981	−	0.455998i	$-0.849283\pi$
$227$	−1.38190e6	−1.77996	−0.889981	+	0.455998i	$0.849283\pi$
$228$	−66904.4	−0.0852349
$229$	1.23238e6	1.55294	0.776471	−	0.630153i	$-0.217008\pi$
$229$	1.23238e6	1.55294	0.776471	+	0.630153i	$0.217008\pi$
$230$	−55206.1	−0.0688126
$231$	−148087.	−0.182595
$232$	−352214.	−0.429622
$233$	1.05461e6	1.27263	0.636313	−	0.771431i	$-0.280459\pi$
$233$	1.05461e6	1.27263	0.636313	+	0.771431i	$0.280459\pi$
$234$	115731.	0.138168
$235$	624425.	0.737582
$236$	−445157.	−0.520275
$237$	127513.	0.147463
$238$	−136840.	−0.156593
$239$	1.07816e6	1.22093	0.610463	−	0.792045i	$-0.290983\pi$
$239$	1.07816e6	1.22093	0.610463	+	0.792045i	$0.290983\pi$
$240$	−20472.1	−0.0229421
$241$	−391545.	−0.434249	−0.217124	−	0.976144i	$-0.569668\pi$
$241$	−391545.	−0.434249	−0.217124	+	0.976144i	$0.569668\pi$
$242$	−541706.	−0.594601
$243$	−407333.	−0.442521
$244$	−641869.	−0.690195
$245$	85181.8	0.0906633
$246$	−182122.	−0.191878
$247$	−226010.	−0.235714
$248$	−311591.	−0.321704
$249$	271838.	0.277850
$250$	65224.6	0.0660027
$251$	919511.	0.921240	0.460620	−	0.887597i	$-0.347627\pi$
$251$	919511.	0.921240	0.460620	+	0.887597i	$0.347627\pi$
$252$	400474.	0.397258
$253$	−285278.	−0.280199
$254$	490655.	0.477191
$255$	16794.7	0.0161741
$256$	−1.09041e6	−1.03990
$257$	−286148.	−0.270245	−0.135123	−	0.990829i	$-0.543143\pi$
$257$	−286148.	−0.270245	−0.135123	+	0.990829i	$0.543143\pi$
$258$	−231618.	−0.216632
$259$	822866.	0.762219
$260$	42556.2	0.0390418
$261$	430028.	0.390747
$262$	−955542.	−0.859996
$263$	−557560.	−0.497052	−0.248526	−	0.968625i	$-0.579946\pi$
$263$	−557560.	−0.497052	−0.248526	+	0.968625i	$0.579946\pi$
$264$	−248720.	−0.219635
$265$	132552.	0.115950
$266$	935062.	0.810282
$267$	−97215.9	−0.0834563
$268$	301864.	0.256729
$269$	401010.	0.337890	0.168945	−	0.985626i	$-0.445964\pi$
$269$	401010.	0.337890	0.168945	+	0.985626i	$0.445964\pi$
$270$	118923.	0.0992791
$271$	2.08406e6	1.72380	0.861901	−	0.507077i	$-0.169274\pi$
$271$	2.08406e6	1.72380	0.861901	+	0.507077i	$0.169274\pi$
$272$	−97754.9	−0.0801154
$273$	−32072.5	−0.0260451
$274$	994776.	0.800477
$275$	337049.	0.268758
$276$	−18289.8	−0.0144523
$277$	1.30265e6	1.02007	0.510033	−	0.860155i	$-0.329633\pi$
$277$	1.30265e6	1.02007	0.510033	+	0.860155i	$0.329633\pi$
$278$	899605.	0.698136
$279$	380431.	0.292594
$280$	−562637.	−0.428878
$281$	−1.11215e6	−0.840232	−0.420116	−	0.907470i	$-0.638011\pi$
$281$	−1.11215e6	−0.840232	−0.420116	+	0.907470i	$0.638011\pi$
$282$	−247337.	−0.185211
$283$	−623456.	−0.462743	−0.231372	−	0.972865i	$-0.574321\pi$
$283$	−623456.	−0.462743	−0.231372	+	0.972865i	$0.574321\pi$
$284$	−541124.	−0.398108
$285$	−114762.	−0.0836924
$286$	−262924.	−0.190071
$287$	−2.12893e6	−1.52566
$288$	1.13475e6	0.806156
$289$	−1.33966e6	−0.943519
$290$	−189059.	−0.132009
$291$	−1019.50	−0.000705757 0
$292$	−339255.	−0.232846
$293$	−1.15557e6	−0.786371	−0.393186	−	0.919459i	$-0.628627\pi$
$293$	−1.15557e6	−0.786371	−0.393186	+	0.919459i	$0.628627\pi$
$294$	−33740.8	−0.0227660
$295$	−763585.	−0.510860
$296$	1.38204e6	0.916837
$297$	614537.	0.404257
$298$	1.36534e6	0.890636
$299$	−61784.9	−0.0399673
$300$	21609.0	0.0138621
$301$	−2.70752e6	−1.72248
$302$	−497776.	−0.314063
$303$	413824.	0.258946
$304$	667982.	0.414554
$305$	−1.10101e6	−0.677705
$306$	280605.	0.171314
$307$	2.53752e6	1.53661	0.768306	−	0.640082i	$-0.221100\pi$
$307$	2.53752e6	1.53661	0.768306	+	0.640082i	$0.221100\pi$
$308$	−909822.	−0.546487
$309$	−134226.	−0.0799723
$310$	−167254.	−0.0988490
$311$	−312766.	−0.183366	−0.0916829	−	0.995788i	$-0.529225\pi$
$311$	−312766.	−0.183366	−0.0916829	+	0.995788i	$0.529225\pi$
$312$	−53867.2	−0.0313284
$313$	−1.12347e6	−0.648187	−0.324093	−	0.946025i	$-0.605059\pi$
$313$	−1.12347e6	−0.648187	−0.324093	+	0.946025i	$0.605059\pi$
$314$	−731223.	−0.418529
$315$	686939.	0.390070
$316$	783415.	0.441341
$317$	1.48240e6	0.828545	0.414272	−	0.910153i	$-0.364036\pi$
$317$	1.48240e6	0.828545	0.414272	+	0.910153i	$0.364036\pi$
$318$	−52504.2	−0.0291156
$319$	−976964.	−0.537529
$320$	−775042.	−0.423107
$321$	−40478.0	−0.0219259
$322$	255620.	0.137390
$323$	−547993.	−0.292259
$324$	−801285.	−0.424057
$325$	72997.3	0.0383352
$326$	−586813.	−0.305813
$327$	66024.4	0.0341456
$328$	−3.57565e6	−1.83514
$329$	−2.89127e6	−1.47265
$330$	−133506.	−0.0674865
$331$	−3.32429e6	−1.66774	−0.833871	−	0.551960i	$-0.813880\pi$
$331$	−3.32429e6	−1.66774	−0.833871	+	0.551960i	$0.813880\pi$
$332$	1.67012e6	0.831578
$333$	−1.68737e6	−0.833875
$334$	1.31335e6	0.644188
$335$	517793.	0.252083
$336$	94791.6	0.0458059
$337$	3.09137e6	1.48278	0.741389	−	0.671075i	$-0.234167\pi$
$337$	3.09137e6	1.48278	0.741389	+	0.671075i	$0.234167\pi$
$338$	1.49297e6	0.710821
$339$	557797.	0.263619
$340$	103183.	0.0484075
$341$	−864286.	−0.402505
$342$	−1.91744e6	−0.886456
$343$	−2.33995e6	−1.07392
$344$	−4.54741e6	−2.07190
$345$	−31372.8	−0.0141908
$346$	725113.	0.325623
$347$	418312.	0.186499	0.0932494	−	0.995643i	$-0.470275\pi$
$347$	418312.	0.186499	0.0932494	+	0.995643i	$0.470275\pi$
$348$	−62635.4	−0.0277250
$349$	1.05103e6	0.461905	0.230953	−	0.972965i	$-0.425816\pi$
$349$	1.05103e6	0.461905	0.230953	+	0.972965i	$0.425816\pi$
$350$	−302009.	−0.131780
$351$	133095.	0.0576626
$352$	−2.57800e6	−1.10898
$353$	−169070.	−0.0722154	−0.0361077	−	0.999348i	$-0.511496\pi$
$353$	−169070.	−0.0722154	−0.0361077	+	0.999348i	$0.511496\pi$
$354$	302459.	0.128280
$355$	−928198.	−0.390904
$356$	−597277.	−0.249776
$357$	−77764.2	−0.0322930
$358$	526525.	0.217126
$359$	3.99005e6	1.63396	0.816982	−	0.576663i	$-0.195645\pi$
$359$	3.99005e6	1.63396	0.816982	+	0.576663i	$0.195645\pi$
$360$	1.15375e6	0.469196
$361$	1.26847e6	0.512284
$362$	−1.51523e6	−0.607726
$363$	−307843.	−0.122621
$364$	−197047.	−0.0779502
$365$	−581929.	−0.228633
$366$	436113.	0.170175
$367$	90469.6	0.0350621	0.0175310	−	0.999846i	$-0.494419\pi$
$367$	90469.6	0.0350621	0.0175310	+	0.999846i	$0.494419\pi$
$368$	182608.	0.0702911
$369$	4.36561e6	1.66909
$370$	741844.	0.281714
$371$	−613752.	−0.231504
$372$	−55411.3	−0.0207607
$373$	−1.13536e6	−0.422535	−0.211268	−	0.977428i	$-0.567759\pi$
$373$	−1.13536e6	−0.422535	−0.211268	+	0.977428i	$0.567759\pi$
$374$	−637497.	−0.235667
$375$	37066.2	0.0136113
$376$	−4.85602e6	−1.77138
$377$	−211589.	−0.0766725
$378$	−550650.	−0.198219
$379$	1.85101e6	0.661927	0.330963	−	0.943644i	$-0.392626\pi$
$379$	1.85101e6	0.661927	0.330963	+	0.943644i	$0.392626\pi$
$380$	−705077.	−0.250483
$381$	278832.	0.0984078
$382$	2.39400e6	0.839393
$383$	791473.	0.275701	0.137851	−	0.990453i	$-0.455981\pi$
$383$	791473.	0.275701	0.137851	+	0.990453i	$0.455981\pi$
$384$	−55894.8	−0.0193439
$385$	−1.56063e6	−0.536597
$386$	−1.49779e6	−0.511660
$387$	5.55206e6	1.88441
$388$	−6263.63	−0.00211226
$389$	−5.47609e6	−1.83483	−0.917417	−	0.397928i	$-0.869730\pi$
$389$	−5.47609e6	−1.83483	−0.917417	+	0.397928i	$0.869730\pi$
$390$	−28914.5	−0.00962619
$391$	−149806.	−0.0495550
$392$	−662441.	−0.217737
$393$	−543020.	−0.177351
$394$	2.73800e6	0.888572
$395$	1.34380e6	0.433354
$396$	1.86569e6	0.597862
$397$	856539.	0.272754	0.136377	−	0.990657i	$-0.456454\pi$
$397$	856539.	0.272754	0.136377	+	0.990657i	$0.456454\pi$
$398$	1.60489e6	0.507854
$399$	531381.	0.167099
$400$	−215747.	−0.0674209
$401$	4.82636e6	1.49885	0.749426	−	0.662088i	$-0.230330\pi$
$401$	4.82636e6	1.49885	0.749426	+	0.662088i	$0.230330\pi$
$402$	−205100.	−0.0632994
$403$	−187185.	−0.0574128
$404$	2.54246e6	0.774998
$405$	−1.37446e6	−0.416383
$406$	875398.	0.263567
$407$	3.83348e6	1.14712
$408$	−130609.	−0.0388438
$409$	−370285.	−0.109453	−0.0547265	−	0.998501i	$-0.517429\pi$
$409$	−370285.	−0.109453	−0.0547265	+	0.998501i	$0.517429\pi$
$410$	−1.91931e6	−0.563880
$411$	565316.	0.165077
$412$	−824659.	−0.239349
$413$	3.53562e6	1.01998
$414$	−524177.	−0.150306
$415$	2.86478e6	0.816529
$416$	−558337.	−0.158184
$417$	511232.	0.143972
$418$	4.35617e6	1.21945
$419$	5.03815e6	1.40196	0.700980	−	0.713181i	$-0.252746\pi$
$419$	5.03815e6	1.40196	0.700980	+	0.713181i	$0.252746\pi$
$420$	−100056.	−0.0276770
$421$	−1.39455e6	−0.383467	−0.191733	−	0.981447i	$-0.561411\pi$
$421$	−1.39455e6	−0.383467	−0.191733	+	0.981447i	$0.561411\pi$
$422$	−1.29150e6	−0.353031
$423$	5.92885e6	1.61109
$424$	−1.03083e6	−0.278465
$425$	176992.	0.0475315
$426$	367663.	0.0981580
$427$	5.09798e6	1.35310
$428$	−248690.	−0.0656218
$429$	−149416.	−0.0391971
$430$	−2.44093e6	−0.636625
$431$	2.53332e6	0.656897	0.328449	−	0.944522i	$-0.393474\pi$
$431$	2.53332e6	0.656897	0.328449	+	0.944522i	$0.393474\pi$
$432$	−393369.	−0.101412
$433$	2.45088e6	0.628205	0.314103	−	0.949389i	$-0.398296\pi$
$433$	2.45088e6	0.628205	0.314103	+	0.949389i	$0.398296\pi$
$434$	774434.	0.197360
$435$	−107439.	−0.0272233
$436$	405642.	0.102194
$437$	1.02366e6	0.256421
$438$	230505.	0.0574109
$439$	−5.83082e6	−1.44400	−0.722002	−	0.691891i	$-0.756778\pi$
$439$	−5.83082e6	−1.44400	−0.722002	+	0.691891i	$0.756778\pi$
$440$	−2.62116e6	−0.645448
$441$	808793.	0.198034
$442$	−138068.	−0.0336153
$443$	−4.81423e6	−1.16551	−0.582756	−	0.812647i	$-0.698026\pi$
$443$	−4.81423e6	−1.16551	−0.582756	+	0.812647i	$0.698026\pi$
$444$	245773.	0.0591667
$445$	−1.02452e6	−0.245256
$446$	−5.46478e6	−1.30087
$447$	775902.	0.183670
$448$	3.58867e6	0.844769
$449$	1.85298e6	0.433765	0.216882	−	0.976198i	$-0.430411\pi$
$449$	1.85298e6	0.433765	0.216882	+	0.976198i	$0.430411\pi$
$450$	619301.	0.144169
$451$	−9.91806e6	−2.29607
$452$	3.42701e6	0.788985
$453$	−282878.	−0.0647671
$454$	5.76855e6	1.31349
$455$	−337998.	−0.0765396
$456$	892481.	0.200996
$457$	208337.	0.0466634	0.0233317	−	0.999728i	$-0.492573\pi$
$457$	208337.	0.0466634	0.0233317	+	0.999728i	$0.492573\pi$
$458$	−5.14441e6	−1.14597
$459$	322708.	0.0714954
$460$	−192749.	−0.0424715
$461$	4.11958e6	0.902820	0.451410	−	0.892317i	$-0.350921\pi$
$461$	4.11958e6	0.902820	0.451410	+	0.892317i	$0.350921\pi$
$462$	618172.	0.134743
$463$	2.50227e6	0.542478	0.271239	−	0.962512i	$-0.412567\pi$
$463$	2.50227e6	0.542478	0.271239	+	0.962512i	$0.412567\pi$
$464$	625361.	0.134845
$465$	−95047.9	−0.0203850
$466$	−4.40232e6	−0.939112
$467$	−6.57630e6	−1.39537	−0.697685	−	0.716404i	$-0.745787\pi$
$467$	−6.57630e6	−1.39537	−0.697685	+	0.716404i	$0.745787\pi$
$468$	404067.	0.0852783
$469$	−2.39753e6	−0.503306
$470$	−2.60658e6	−0.544286
$471$	−415543.	−0.0863105
$472$	5.93824e6	1.22688
$473$	−1.26135e7	−2.59229
$474$	−532286.	−0.108818
$475$	−1.20943e6	−0.245950
$476$	−477769.	−0.0966497
$477$	1.25856e6	0.253268
$478$	−4.50065e6	−0.900961
$479$	4.62529e6	0.921086	0.460543	−	0.887637i	$-0.347655\pi$
$479$	4.62529e6	0.921086	0.460543	+	0.887637i	$0.347655\pi$
$480$	−283509.	−0.0561648
$481$	830248.	0.163623
$482$	1.63445e6	0.320446
$483$	145265.	0.0283331
$484$	−1.89133e6	−0.366991
$485$	−10744.1	−0.00207403
$486$	1.70036e6	0.326551
$487$	5.05164e6	0.965184	0.482592	−	0.875845i	$-0.339695\pi$
$487$	5.05164e6	0.965184	0.482592	+	0.875845i	$0.339695\pi$
$488$	8.56230e6	1.62758
$489$	−333477.	−0.0630657
$490$	−355581.	−0.0669034
$491$	−6.82168e6	−1.27699	−0.638495	−	0.769626i	$-0.720443\pi$
$491$	−6.82168e6	−1.27699	−0.638495	+	0.769626i	$0.720443\pi$
$492$	−635870.	−0.118428
$493$	−513027.	−0.0950655
$494$	943450.	0.173941
$495$	3.20024e6	0.587043
$496$	553235.	0.100973
$497$	4.29782e6	0.780473
$498$	−1.13475e6	−0.205035
$499$	3.98851e6	0.717066	0.358533	−	0.933517i	$-0.383277\pi$
$499$	3.98851e6	0.717066	0.358533	+	0.933517i	$0.383277\pi$
$500$	227728.	0.0407372
$501$	746354.	0.132847
$502$	−3.83839e6	−0.679813
$503$	4.90799e6	0.864935	0.432467	−	0.901650i	$-0.357643\pi$
$503$	4.90799e6	0.864935	0.432467	+	0.901650i	$0.357643\pi$
$504$	−5.34219e6	−0.936791
$505$	4.36112e6	0.760974
$506$	1.19086e6	0.206768
$507$	848434.	0.146588
$508$	1.71309e6	0.294524
$509$	1.74821e6	0.299089	0.149544	−	0.988755i	$-0.452219\pi$
$509$	1.74821e6	0.299089	0.149544	+	0.988755i	$0.452219\pi$
$510$	−70107.3	−0.0119354
$511$	2.69450e6	0.456485
$512$	3.79780e6	0.640261
$513$	−2.20514e6	−0.369950
$514$	1.19449e6	0.199423
$515$	−1.41455e6	−0.235017
$516$	−808681.	−0.133707
$517$	−1.34695e7	−2.21629
$518$	−3.43495e6	−0.562466
$519$	412071.	0.0671511
$520$	−567685.	−0.0920659
$521$	−1.06210e7	−1.71423	−0.857117	−	0.515121i	$-0.827747\pi$
$521$	−1.06210e7	−1.71423	−0.857117	+	0.515121i	$0.827747\pi$
$522$	−1.79510e6	−0.288345
$523$	2.43090e6	0.388609	0.194304	−	0.980941i	$-0.437755\pi$
$523$	2.43090e6	0.388609	0.194304	+	0.980941i	$0.437755\pi$
$524$	−3.33622e6	−0.530794
$525$	−171627.	−0.0271761
$526$	2.32746e6	0.366791
$527$	−453857.	−0.0711856
$528$	441605.	0.0689366
$529$	279841.	0.0434783
$530$	−553320.	−0.0855632
$531$	−7.25016e6	−1.11586
$532$	3.26471e6	0.500110
$533$	−2.14803e6	−0.327509
$534$	405816.	0.0615851
$535$	−426581.	−0.0644343
$536$	−4.02677e6	−0.605403
$537$	299216.	0.0447764
$538$	−1.67397e6	−0.249340
$539$	−1.83747e6	−0.272425
$540$	415214.	0.0612756
$541$	−1.85923e6	−0.273112	−0.136556	−	0.990632i	$-0.543603\pi$
$541$	−1.85923e6	−0.273112	−0.136556	+	0.990632i	$0.543603\pi$
$542$	−8.69966e6	−1.27205
$543$	−861083.	−0.125327
$544$	−1.35377e6	−0.196131
$545$	695804.	0.100345
$546$	133882.	0.0192195
$547$	−4.02968e6	−0.575841	−0.287920	−	0.957654i	$-0.592964\pi$
$547$	−4.02968e6	−0.575841	−0.287920	+	0.957654i	$0.592964\pi$
$548$	3.47320e6	0.494058
$549$	−1.04540e7	−1.48030
$550$	−1.40697e6	−0.198325
$551$	3.50564e6	0.491912
$552$	243980.	0.0340805
$553$	−6.22220e6	−0.865229
$554$	−5.43775e6	−0.752740
$555$	421579.	0.0580960
$556$	3.14092e6	0.430893
$557$	−1.74809e6	−0.238740	−0.119370	−	0.992850i	$-0.538088\pi$
$557$	−1.74809e6	−0.238740	−0.119370	+	0.992850i	$0.538088\pi$
$558$	−1.58806e6	−0.215914
$559$	−2.73181e6	−0.369761
$560$	998970.	0.134612
$561$	−362280.	−0.0486001
$562$	4.64255e6	0.620035
$563$	−5.57963e6	−0.741882	−0.370941	−	0.928657i	$-0.620965\pi$
$563$	−5.57963e6	−0.741882	−0.370941	+	0.928657i	$0.620965\pi$
$564$	−863562.	−0.114313
$565$	5.87839e6	0.774707
$566$	2.60254e6	0.341473
$567$	6.36413e6	0.831345
$568$	7.21840e6	0.938794
$569$	8.43793e6	1.09258	0.546292	−	0.837595i	$-0.316039\pi$
$569$	8.43793e6	1.09258	0.546292	+	0.837595i	$0.316039\pi$
$570$	479060.	0.0617593
$571$	3.61998e6	0.464639	0.232320	−	0.972640i	$-0.425368\pi$
$571$	3.61998e6	0.464639	0.232320	+	0.972640i	$0.425368\pi$
$572$	−917984.	−0.117313
$573$	1.36047e6	0.173102
$574$	8.88698e6	1.12583
$575$	−330625.	−0.0417029
$576$	−7.35895e6	−0.924186
$577$	−4.14606e6	−0.518438	−0.259219	−	0.965819i	$-0.583465\pi$
$577$	−4.14606e6	−0.518438	−0.259219	+	0.965819i	$0.583465\pi$
$578$	5.59225e6	0.696253
$579$	−851168.	−0.105516
$580$	−660089.	−0.0814765
$581$	−1.32648e7	−1.63027
$582$	4255.78	0.000520801 0
$583$	−2.85928e6	−0.348406
$584$	4.52554e6	0.549084
$585$	693102.	0.0837351
$586$	4.82379e6	0.580289
$587$	−5.69728e6	−0.682452	−0.341226	−	0.939981i	$-0.610842\pi$
$587$	−5.69728e6	−0.682452	−0.341226	+	0.939981i	$0.610842\pi$
$588$	−117804.	−0.0140513
$589$	3.10131e6	0.368347
$590$	3.18749e6	0.376980
$591$	1.55596e6	0.183244
$592$	−2.45383e6	−0.287767
$593$	5.12766e6	0.598801	0.299401	−	0.954127i	$-0.403213\pi$
$593$	5.12766e6	0.598801	0.299401	+	0.954127i	$0.403213\pi$
$594$	−2.56531e6	−0.298314
$595$	−819525.	−0.0949007
$596$	4.76701e6	0.549705
$597$	912037.	0.104731
$598$	257913.	0.0294931
$599$	9.56173e6	1.08885	0.544427	−	0.838808i	$-0.316747\pi$
$599$	9.56173e6	1.08885	0.544427	+	0.838808i	$0.316747\pi$
$600$	−288256.	−0.0326889
$601$	−1.68548e7	−1.90343	−0.951716	−	0.306981i	$-0.900681\pi$
$601$	−1.68548e7	−1.90343	−0.951716	+	0.306981i	$0.900681\pi$
$602$	1.13022e7	1.27108
$603$	4.91639e6	0.550621
$604$	−1.73795e6	−0.193841
$605$	−3.24423e6	−0.360349
$606$	−1.72746e6	−0.191085
$607$	−1.23664e7	−1.36229	−0.681147	−	0.732147i	$-0.738518\pi$
$607$	−1.23664e7	−1.36229	−0.681147	+	0.732147i	$0.738518\pi$
$608$	9.25061e6	1.01487
$609$	497476.	0.0543536
$610$	4.59602e6	0.500100
$611$	−2.91720e6	−0.316128
$612$	979717.	0.105736
$613$	−750283.	−0.0806443	−0.0403222	−	0.999187i	$-0.512838\pi$
$613$	−750283.	−0.0806443	−0.0403222	+	0.999187i	$0.512838\pi$
$614$	−1.05926e7	−1.13392
$615$	−1.09072e6	−0.116285
$616$	1.21367e7	1.28869
$617$	−3.25829e6	−0.344569	−0.172285	−	0.985047i	$-0.555115\pi$
$617$	−3.25829e6	−0.344569	−0.172285	+	0.985047i	$0.555115\pi$
$618$	560309.	0.0590141
$619$	1.16837e7	1.22562	0.612808	−	0.790232i	$-0.290040\pi$
$619$	1.16837e7	1.22562	0.612808	+	0.790232i	$0.290040\pi$
$620$	−583957.	−0.0610101
$621$	−602825.	−0.0627281
$622$	1.30560e6	0.135312
$623$	4.74381e6	0.489675
$624$	95642.0	0.00983302
$625$	390625.	0.0400000
$626$	4.68978e6	0.478318
$627$	2.47554e6	0.251479
$628$	−2.55302e6	−0.258318
$629$	2.01305e6	0.202875
$630$	−2.86754e6	−0.287845
$631$	−1.72370e7	−1.72341	−0.861706	−	0.507408i	$-0.830604\pi$
$631$	−1.72370e7	−1.72341	−0.861706	+	0.507408i	$0.830604\pi$
$632$	−1.04505e7	−1.04074
$633$	−733938.	−0.0728032
$634$	−6.18808e6	−0.611410
$635$	2.93849e6	0.289195
$636$	−183315.	−0.0179703
$637$	−397955.	−0.0388584
$638$	4.07822e6	0.396660
$639$	−8.81315e6	−0.853845
$640$	−589052.	−0.0568465
$641$	1.12975e7	1.08602	0.543011	−	0.839726i	$-0.317284\pi$
$641$	1.12975e7	1.08602	0.543011	+	0.839726i	$0.317284\pi$
$642$	168971.	0.0161798
$643$	1.03330e7	0.985598	0.492799	−	0.870143i	$-0.335974\pi$
$643$	1.03330e7	0.985598	0.492799	+	0.870143i	$0.335974\pi$
$644$	892483.	0.0847979
$645$	−1.38714e6	−0.131287
$646$	2.28753e6	0.215668
$647$	2.08740e6	0.196040	0.0980198	−	0.995184i	$-0.468749\pi$
$647$	2.08740e6	0.196040	0.0980198	+	0.995184i	$0.468749\pi$
$648$	1.06889e7	0.999986
$649$	1.64714e7	1.53503
$650$	−304718.	−0.0282888
$651$	440099.	0.0407003
$652$	−2.04882e6	−0.188749
$653$	−1.96369e7	−1.80214	−0.901072	−	0.433670i	$-0.857218\pi$
$653$	−1.96369e7	−1.80214	−0.901072	+	0.433670i	$0.857218\pi$
$654$	−275611.	−0.0251972
$655$	−5.72266e6	−0.521189
$656$	6.34861e6	0.575996
$657$	−5.52536e6	−0.499399
$658$	1.20692e7	1.08671
$659$	6.14484e6	0.551185	0.275592	−	0.961275i	$-0.411126\pi$
$659$	6.14484e6	0.551185	0.275592	+	0.961275i	$0.411126\pi$
$660$	−466129.	−0.0416530
$661$	−8.67957e6	−0.772671	−0.386335	−	0.922358i	$-0.626259\pi$
$661$	−8.67957e6	−0.772671	−0.386335	+	0.922358i	$0.626259\pi$
$662$	1.38768e7	1.23068
$663$	−78461.8	−0.00693225
$664$	−2.22788e7	−1.96098
$665$	5.60001e6	0.491060
$666$	7.04373e6	0.615343
$667$	958345.	0.0834079
$668$	4.58547e6	0.397596
$669$	−3.10555e6	−0.268271
$670$	−2.16146e6	−0.186020
$671$	2.37499e7	2.03637
$672$	1.31273e6	0.112138
$673$	−5.26147e6	−0.447785	−0.223893	−	0.974614i	$-0.571876\pi$
$673$	−5.26147e6	−0.447785	−0.223893	+	0.974614i	$0.571876\pi$
$674$	−1.29045e7	−1.09419
$675$	712223.	0.0601667
$676$	5.21263e6	0.438722
$677$	−1.16182e7	−0.974245	−0.487122	−	0.873334i	$-0.661953\pi$
$677$	−1.16182e7	−0.974245	−0.487122	+	0.873334i	$0.661953\pi$
$678$	−2.32846e6	−0.194533
$679$	49748.3	0.00414098
$680$	−1.37643e6	−0.114152
$681$	3.27818e6	0.270873
$682$	3.60785e6	0.297022
$683$	1.50356e7	1.23330	0.616651	−	0.787237i	$-0.288489\pi$
$683$	1.50356e7	1.23330	0.616651	+	0.787237i	$0.288489\pi$
$684$	−6.69464e6	−0.547125
$685$	5.95763e6	0.485118
$686$	9.76782e6	0.792478
$687$	−2.92349e6	−0.236325
$688$	8.07398e6	0.650304
$689$	−619258.	−0.0496962
$690$	130962.	0.0104718
$691$	1.50895e7	1.20221	0.601103	−	0.799171i	$-0.294728\pi$
$691$	1.50895e7	1.20221	0.601103	+	0.799171i	$0.294728\pi$
$692$	2.53169e6	0.200976
$693$	−1.48180e7	−1.17208
$694$	−1.74619e6	−0.137624
$695$	5.38766e6	0.423096
$696$	835534.	0.0653794
$697$	−5.20821e6	−0.406075
$698$	−4.38741e6	−0.340855
$699$	−2.50177e6	−0.193667
$700$	−1.05445e6	−0.0813353
$701$	8.96774e6	0.689268	0.344634	−	0.938737i	$-0.388003\pi$
$701$	8.96774e6	0.689268	0.344634	+	0.938737i	$0.388003\pi$
$702$	−555589.	−0.0425511
$703$	−1.37557e7	−1.04977
$704$	1.67185e7	1.27135
$705$	−1.48128e6	−0.112244
$706$	705762.	0.0532901
$707$	−2.01932e7	−1.51935
$708$	1.05602e6	0.0791750
$709$	−3.65113e6	−0.272779	−0.136390	−	0.990655i	$-0.543550\pi$
$709$	−3.65113e6	−0.272779	−0.136390	+	0.990655i	$0.543550\pi$
$710$	3.87465e6	0.288461
$711$	1.27593e7	0.946569
$712$	7.96747e6	0.589007
$713$	847814.	0.0624564
$714$	324617.	0.0238301
$715$	−1.57463e6	−0.115190
$716$	1.83833e6	0.134011
$717$	−2.55765e6	−0.185799
$718$	−1.66560e7	−1.20576
$719$	−1.69958e7	−1.22608	−0.613040	−	0.790052i	$-0.710053\pi$
$719$	−1.69958e7	−1.22608	−0.613040	+	0.790052i	$0.710053\pi$
$720$	−2.04849e6	−0.147266
$721$	6.54977e6	0.469232
$722$	−5.29505e6	−0.378031
$723$	928835.	0.0660835
$724$	−5.29034e6	−0.375091
$725$	−1.13226e6	−0.0800021
$726$	1.28505e6	0.0904857
$727$	2.07234e7	1.45420	0.727100	−	0.686531i	$-0.240868\pi$
$727$	2.07234e7	1.45420	0.727100	+	0.686531i	$0.240868\pi$
$728$	2.62854e6	0.183817
$729$	−1.23934e7	−0.863719
$730$	2.42919e6	0.168715
$731$	−6.62365e6	−0.458463
$732$	1.52266e6	0.105033
$733$	−9.13496e6	−0.627982	−0.313991	−	0.949426i	$-0.601666\pi$
$733$	−9.13496e6	−0.627982	−0.313991	+	0.949426i	$0.601666\pi$
$734$	−377654.	−0.0258734
$735$	−202071.	−0.0137970
$736$	2.52886e6	0.172080
$737$	−1.11694e7	−0.757460
$738$	−1.82237e7	−1.23167
$739$	9.40106e6	0.633236	0.316618	−	0.948553i	$-0.397453\pi$
$739$	9.40106e6	0.633236	0.316618	+	0.948553i	$0.397453\pi$
$740$	2.59010e6	0.173875
$741$	536148.	0.0358707
$742$	2.56203e6	0.170834
$743$	−1.23857e7	−0.823090	−0.411545	−	0.911389i	$-0.635011\pi$
$743$	−1.23857e7	−0.823090	−0.411545	+	0.911389i	$0.635011\pi$
$744$	739168.	0.0489565
$745$	8.17692e6	0.539758
$746$	4.73944e6	0.311803
$747$	2.72008e7	1.78353
$748$	−2.22578e6	−0.145455
$749$	1.97519e6	0.128649
$750$	−154728.	−0.0100442
$751$	1.44266e7	0.933391	0.466696	−	0.884418i	$-0.345444\pi$
$751$	1.44266e7	0.933391	0.466696	+	0.884418i	$0.345444\pi$
$752$	8.62193e6	0.555981
$753$	−2.18130e6	−0.140193
$754$	883252.	0.0565791
$755$	−2.98114e6	−0.190333
$756$	−1.92256e6	−0.122342
$757$	−2.02830e7	−1.28645	−0.643226	−	0.765677i	$-0.722404\pi$
$757$	−2.02830e7	−1.28645	−0.643226	+	0.765677i	$0.722404\pi$
$758$	−7.72680e6	−0.488457
$759$	676746.	0.0426404
$760$	9.40549e6	0.590673
$761$	1.56925e7	0.982271	0.491136	−	0.871083i	$-0.336582\pi$
$761$	1.56925e7	0.982271	0.491136	+	0.871083i	$0.336582\pi$
$762$	−1.16395e6	−0.0726183
$763$	−3.22177e6	−0.200347
$764$	8.35850e6	0.518078
$765$	1.68052e6	0.103822
$766$	−3.30391e6	−0.203449
$767$	3.56734e6	0.218955
$768$	2.58671e6	0.158250
$769$	−1.84834e6	−0.112711	−0.0563554	−	0.998411i	$-0.517948\pi$
$769$	−1.84834e6	−0.112711	−0.0563554	+	0.998411i	$0.517948\pi$
$770$	6.51466e6	0.395973
$771$	678810.	0.0411256
$772$	−5.22943e6	−0.315799
$773$	6.13309e6	0.369173	0.184587	−	0.982816i	$-0.440905\pi$
$773$	6.13309e6	0.369173	0.184587	+	0.982816i	$0.440905\pi$
$774$	−2.31764e7	−1.39057
$775$	−1.00167e6	−0.0599061
$776$	83554.6	0.00498100
$777$	−1.95203e6	−0.115994
$778$	2.28593e7	1.35398
$779$	3.55889e7	2.10122
$780$	−100953.	−0.00594133
$781$	2.00223e7	1.17459
$782$	625347.	0.0365683
$783$	−2.06444e6	−0.120337
$784$	1.17617e6	0.0683410
$785$	−4.37923e6	−0.253644
$786$	2.26677e6	0.130873
$787$	2.40217e6	0.138251	0.0691253	−	0.997608i	$-0.477979\pi$
$787$	2.40217e6	0.138251	0.0691253	+	0.997608i	$0.477979\pi$
$788$	9.55956e6	0.548431
$789$	1.32266e6	0.0756409
$790$	−5.60954e6	−0.319786
$791$	−2.72187e7	−1.54677
$792$	−2.48876e7	−1.40984
$793$	5.14371e6	0.290465
$794$	−3.57552e6	−0.201274
$795$	−314443.	−0.0176451
$796$	5.60339e6	0.313450
$797$	−2.29154e7	−1.27786	−0.638928	−	0.769266i	$-0.720622\pi$
$797$	−2.29154e7	−1.27786	−0.638928	+	0.769266i	$0.720622\pi$
$798$	−2.21819e6	−0.123308
$799$	−7.07317e6	−0.391965
$800$	−2.98779e6	−0.165054
$801$	−9.72770e6	−0.535709
$802$	−2.01470e7	−1.10605
$803$	1.25529e7	0.686995
$804$	−716093.	−0.0390687
$805$	1.53089e6	0.0832634
$806$	781382.	0.0423668
$807$	−951291.	−0.0514197
$808$	−3.39155e7	−1.82755
$809$	9.72366e6	0.522346	0.261173	−	0.965292i	$-0.415891\pi$
$809$	9.72366e6	0.522346	0.261173	+	0.965292i	$0.415891\pi$
$810$	5.73749e6	0.307263
$811$	−6.87112e6	−0.366839	−0.183420	−	0.983035i	$-0.558717\pi$
$811$	−6.87112e6	−0.366839	−0.183420	+	0.983035i	$0.558717\pi$
$812$	3.05640e6	0.162675
$813$	−4.94388e6	−0.262326
$814$	−1.60024e7	−0.846494
$815$	−3.51437e6	−0.185334
$816$	231897.	0.0121919
$817$	4.52610e7	2.37230
$818$	1.54571e6	0.0807689
$819$	−3.20926e6	−0.167184
$820$	−6.70117e6	−0.348029
$821$	3.42232e7	1.77200	0.885998	−	0.463688i	$-0.153474\pi$
$821$	3.42232e7	1.77200	0.885998	+	0.463688i	$0.153474\pi$
$822$	−2.35984e6	−0.121816
$823$	−1.78367e7	−0.917941	−0.458971	−	0.888451i	$-0.651782\pi$
$823$	−1.78367e7	−0.917941	−0.458971	+	0.888451i	$0.651782\pi$
$824$	1.10007e7	0.564418
$825$	−799558.	−0.0408992
$826$	−1.47590e7	−0.752674
$827$	−1.64998e7	−0.838909	−0.419454	−	0.907776i	$-0.637779\pi$
$827$	−1.64998e7	−0.838909	−0.419454	+	0.907776i	$0.637779\pi$
$828$	−1.83013e6	−0.0927697
$829$	2.49879e7	1.26283	0.631413	−	0.775447i	$-0.282475\pi$
$829$	2.49879e7	1.26283	0.631413	+	0.775447i	$0.282475\pi$
$830$	−1.19587e7	−0.602543
$831$	−3.09019e6	−0.155232
$832$	3.62086e6	0.181344
$833$	−964897.	−0.0481802
$834$	−2.13407e6	−0.106242
$835$	7.86552e6	0.390401
$836$	1.52093e7	0.752651
$837$	−1.82634e6	−0.0901088
$838$	−2.10311e7	−1.03455
$839$	−5.69219e6	−0.279174	−0.139587	−	0.990210i	$-0.544577\pi$
$839$	−5.69219e6	−0.279174	−0.139587	+	0.990210i	$0.544577\pi$
$840$	1.33471e6	0.0652661
$841$	−1.72292e7	−0.839992
$842$	5.82136e6	0.282972
$843$	2.63829e6	0.127866
$844$	−4.50919e6	−0.217892
$845$	8.94129e6	0.430783
$846$	−2.47493e7	−1.18887
$847$	1.50217e7	0.719468
$848$	1.83025e6	0.0874017
$849$	1.47898e6	0.0704197
$850$	−738832.	−0.0350750
$851$	−3.76042e6	−0.177997
$852$	1.28367e6	0.0605836
$853$	−6.00174e6	−0.282426	−0.141213	−	0.989979i	$-0.545100\pi$
$853$	−6.00174e6	−0.282426	−0.141213	+	0.989979i	$0.545100\pi$
$854$	−2.12809e7	−0.998493
$855$	−1.14834e7	−0.537224
$856$	3.31743e6	0.154745
$857$	−3.62438e7	−1.68571	−0.842853	−	0.538144i	$-0.819126\pi$
$857$	−3.62438e7	−1.68571	−0.842853	+	0.538144i	$0.819126\pi$
$858$	623718.	0.0289248
$859$	1.55995e7	0.721318	0.360659	−	0.932698i	$-0.382552\pi$
$859$	1.55995e7	0.721318	0.360659	+	0.932698i	$0.382552\pi$
$860$	−8.52235e6	−0.392928
$861$	5.05033e6	0.232173
$862$	−1.05750e7	−0.484746
$863$	9.26097e6	0.423282	0.211641	−	0.977348i	$-0.432119\pi$
$863$	9.26097e6	0.423282	0.211641	+	0.977348i	$0.432119\pi$
$864$	−5.44760e6	−0.248268
$865$	4.34264e6	0.197339
$866$	−1.02309e7	−0.463573
$867$	3.17799e6	0.143584
$868$	2.70389e6	0.121812
$869$	−2.89873e7	−1.30214
$870$	448493.	0.0200889
$871$	−2.41904e6	−0.108043
$872$	−5.41112e6	−0.240988
$873$	−102014.	−0.00453028
$874$	−4.27315e6	−0.189221
$875$	−1.80871e6	−0.0798634
$876$	804793.	0.0354343
$877$	−4.39210e7	−1.92829	−0.964147	−	0.265367i	$-0.914507\pi$
$877$	−4.39210e7	−1.92829	−0.964147	+	0.265367i	$0.914507\pi$
$878$	2.43400e7	1.06558
$879$	2.74129e6	0.119669
$880$	4.65390e6	0.202586
$881$	−2.95441e6	−0.128242	−0.0641210	−	0.997942i	$-0.520424\pi$
$881$	−2.95441e6	−0.128242	−0.0641210	+	0.997942i	$0.520424\pi$
$882$	−3.37620e6	−0.146136
$883$	−4.34926e7	−1.87721	−0.938606	−	0.344992i	$-0.887882\pi$
$883$	−4.34926e7	−1.87721	−0.938606	+	0.344992i	$0.887882\pi$
$884$	−482055.	−0.0207475
$885$	1.81140e6	0.0777422
$886$	2.00964e7	0.860070
$887$	−2.36867e7	−1.01087	−0.505436	−	0.862864i	$-0.668668\pi$
$887$	−2.36867e7	−1.01087	−0.505436	+	0.862864i	$0.668668\pi$
$888$	−3.27853e6	−0.139523
$889$	−1.36061e7	−0.577402
$890$	4.27672e6	0.180982
$891$	2.96485e7	1.25115
$892$	−1.90799e7	−0.802907
$893$	4.83327e7	2.02821
$894$	−3.23891e6	−0.135536
$895$	3.15331e6	0.131586
$896$	2.72748e6	0.113499
$897$	146568.	0.00608217
$898$	−7.73502e6	−0.320089
$899$	2.90343e6	0.119815
$900$	2.16225e6	0.0889816
$901$	−1.50148e6	−0.0616179
$902$	4.14017e7	1.69435
$903$	6.42287e6	0.262126
$904$	−4.57151e7	−1.86054
$905$	−9.07460e6	−0.368304
$906$	1.18084e6	0.0477937
$907$	1.45385e7	0.586815	0.293408	−	0.955987i	$-0.405211\pi$
$907$	1.45385e7	0.586815	0.293408	+	0.955987i	$0.405211\pi$
$908$	2.01406e7	0.810694
$909$	4.14084e7	1.66218
$910$	1.41093e6	0.0564810
$911$	3.72476e7	1.48697	0.743486	−	0.668752i	$-0.233171\pi$
$911$	3.72476e7	1.48697	0.743486	+	0.668752i	$0.233171\pi$
$912$	−1.58461e6	−0.0630864
$913$	−6.17966e7	−2.45351
$914$	−869677.	−0.0344344
$915$	2.61185e6	0.103132
$916$	−1.79614e7	−0.707296
$917$	2.64976e7	1.04060
$918$	−1.34710e6	−0.0527588
$919$	1.31283e7	0.512766	0.256383	−	0.966575i	$-0.417469\pi$
$919$	1.31283e7	0.512766	0.256383	+	0.966575i	$0.417469\pi$
$920$	2.57120e6	0.100154
$921$	−6.01960e6	−0.233840
$922$	−1.71967e7	−0.666220
$923$	4.33638e6	0.167542
$924$	2.15831e6	0.0831638
$925$	4.44284e6	0.170729
$926$	−1.04454e7	−0.400312
$927$	−1.34310e7	−0.513345
$928$	8.66036e6	0.330116
$929$	2.79278e7	1.06169	0.530845	−	0.847469i	$-0.321875\pi$
$929$	2.79278e7	1.06169	0.530845	+	0.847469i	$0.321875\pi$
$930$	396766.	0.0150427
$931$	6.59337e6	0.249306
$932$	−1.53704e7	−0.579625
$933$	741953.	0.0279044
$934$	2.74520e7	1.02969
$935$	−3.81792e6	−0.142823
$936$	−5.39011e6	−0.201098
$937$	1.21452e7	0.451915	0.225958	−	0.974137i	$-0.427449\pi$
$937$	1.21452e7	0.451915	0.225958	+	0.974137i	$0.427449\pi$
$938$	1.00082e7	0.371405
$939$	2.66513e6	0.0986404
$940$	−9.10073e6	−0.335936
$941$	−2.41588e7	−0.889408	−0.444704	−	0.895678i	$-0.646691\pi$
$941$	−2.41588e7	−0.889408	−0.444704	+	0.895678i	$0.646691\pi$
$942$	1.73463e6	0.0636913
$943$	9.72904e6	0.356279
$944$	−1.05434e7	−0.385081
$945$	−3.29780e6	−0.120128
$946$	5.26535e7	1.91293
$947$	2.45375e6	0.0889110	0.0444555	−	0.999011i	$-0.485845\pi$
$947$	2.45375e6	0.0889110	0.0444555	+	0.999011i	$0.485845\pi$
$948$	−1.85844e6	−0.0671628
$949$	2.71867e6	0.0979922
$950$	5.04862e6	0.181494
$951$	−3.51659e6	−0.126087
$952$	6.37327e6	0.227914
$953$	3.13851e7	1.11942	0.559708	−	0.828690i	$-0.310913\pi$
$953$	3.13851e7	1.11942	0.559708	+	0.828690i	$0.310913\pi$
$954$	−5.25372e6	−0.186894
$955$	1.43375e7	0.508703
$956$	−1.57138e7	−0.556078
$957$	2.31759e6	0.0818006
$958$	−1.93077e7	−0.679699
$959$	−2.75855e7	−0.968579
$960$	1.83858e6	0.0643880
$961$	−2.60606e7	−0.910282
$962$	−3.46577e6	−0.120743
$963$	−4.05035e6	−0.140743
$964$	5.70660e6	0.197781
$965$	−8.97011e6	−0.310084
$966$	−606391.	−0.0209079
$967$	−1.52177e7	−0.523339	−0.261669	−	0.965158i	$-0.584273\pi$
$967$	−1.52177e7	−0.523339	−0.261669	+	0.965158i	$0.584273\pi$
$968$	2.52297e7	0.865415
$969$	1.29997e6	0.0444757
$970$	44849.9	0.00153050
$971$	1.30611e7	0.444562	0.222281	−	0.974983i	$-0.428650\pi$
$971$	1.30611e7	0.444562	0.222281	+	0.974983i	$0.428650\pi$
$972$	5.93671e6	0.201549
$973$	−2.49464e7	−0.844746
$974$	−2.10874e7	−0.712240
$975$	−173167.	−0.00583382
$976$	−1.52025e7	−0.510846
$977$	5.15862e7	1.72901	0.864504	−	0.502626i	$-0.167633\pi$
$977$	5.15862e7	1.72901	0.864504	+	0.502626i	$0.167633\pi$
$978$	1.39206e6	0.0465383
$979$	2.21000e7	0.736945
$980$	−1.24149e6	−0.0412931
$981$	6.60659e6	0.219182
$982$	2.84763e7	0.942332
$983$	−2.00691e7	−0.662437	−0.331219	−	0.943554i	$-0.607460\pi$
$983$	−2.00691e7	−0.662437	−0.331219	+	0.943554i	$0.607460\pi$
$984$	8.48228e6	0.279270
$985$	1.63976e7	0.538507
$986$	2.14157e6	0.0701519
$987$	6.85876e6	0.224106
$988$	3.29400e6	0.107357
$989$	1.23731e7	0.402243
$990$	−1.33590e7	−0.433198
$991$	2.53926e7	0.821339	0.410669	−	0.911784i	$-0.365295\pi$
$991$	2.53926e7	0.821339	0.410669	+	0.911784i	$0.365295\pi$
$992$	7.66152e6	0.247193
$993$	7.88599e6	0.253795
$994$	−1.79407e7	−0.575936
$995$	9.61158e6	0.307778
$996$	−3.96192e6	−0.126549
$997$	5.48564e6	0.174779	0.0873895	−	0.996174i	$-0.472148\pi$
$997$	5.48564e6	0.174779	0.0873895	+	0.996174i	$0.472148\pi$
$998$	−1.66495e7	−0.529146
$999$	8.10059e6	0.256805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.6.a.d.1.5	✓	10
3.2	odd	2		1035.6.a.j.1.6		10
5.4	even	2		575.6.a.f.1.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.6.a.d.1.5	✓	10	1.1	even	1	trivial
575.6.a.f.1.6		10	5.4	even	2
1035.6.a.j.1.6		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	115.a (trivial)

\(f(q)\)	\(=\)	\(q-4.17438 q^{2} -2.37223 q^{3} -14.5746 q^{4} -25.0000 q^{5} +9.90260 q^{6} +115.757 q^{7} +194.420 q^{8} -237.373 q^{9} +O(q^{10})\)	\(q-4.17438 q^{2} -2.37223 q^{3} -14.5746 q^{4} -25.0000 q^{5} +9.90260 q^{6} +115.757 q^{7} +194.420 q^{8} -237.373 q^{9} +104.359 q^{10} +539.278 q^{11} +34.5743 q^{12} +116.796 q^{13} -483.214 q^{14} +59.3059 q^{15} -345.195 q^{16} +283.187 q^{17} +990.882 q^{18} -1935.09 q^{19} +364.365 q^{20} -274.603 q^{21} -2251.15 q^{22} -529.000 q^{23} -461.209 q^{24} +625.000 q^{25} -487.549 q^{26} +1139.56 q^{27} -1687.11 q^{28} -1811.62 q^{29} -247.565 q^{30} -1602.67 q^{31} -4780.46 q^{32} -1279.29 q^{33} -1182.13 q^{34} -2893.93 q^{35} +3459.61 q^{36} +7108.55 q^{37} +8077.78 q^{38} -277.067 q^{39} -4860.50 q^{40} -18391.4 q^{41} +1146.30 q^{42} -23389.6 q^{43} -7859.75 q^{44} +5934.31 q^{45} +2208.25 q^{46} -24977.0 q^{47} +818.883 q^{48} -3407.27 q^{49} -2608.99 q^{50} -671.787 q^{51} -1702.25 q^{52} -5302.06 q^{53} -4756.94 q^{54} -13481.9 q^{55} +22505.5 q^{56} +4590.48 q^{57} +7562.37 q^{58} +30543.4 q^{59} -864.358 q^{60} +44040.3 q^{61} +6690.16 q^{62} -27477.6 q^{63} +31001.7 q^{64} -2919.89 q^{65} +5340.25 q^{66} -20711.7 q^{67} -4127.34 q^{68} +1254.91 q^{69} +12080.4 q^{70} +37127.9 q^{71} -46149.9 q^{72} +23277.2 q^{73} -29673.8 q^{74} -1482.65 q^{75} +28203.1 q^{76} +62425.3 q^{77} +1156.58 q^{78} -53752.1 q^{79} +8629.87 q^{80} +54978.2 q^{81} +76772.6 q^{82} -114591. q^{83} +4002.23 q^{84} -7079.69 q^{85} +97637.1 q^{86} +4297.58 q^{87} +104846. q^{88} +40980.7 q^{89} -24772.1 q^{90} +13519.9 q^{91} +7709.95 q^{92} +3801.92 q^{93} +104263. q^{94} +48377.2 q^{95} +11340.4 q^{96} +429.764 q^{97} +14223.2 q^{98} -128010. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 12 q^{2} - 18 q^{3} + 138 q^{4} - 250 q^{5} + 78 q^{6} - 15 q^{7} - 285 q^{8} + 788 q^{9}+O(q^{10}) \) 10 * q - 12 * q^2 - 18 * q^3 + 138 * q^4 - 250 * q^5 + 78 * q^6 - 15 * q^7 - 285 * q^8 + 788 * q^9	\( 10 q - 12 q^{2} - 18 q^{3} + 138 q^{4} - 250 q^{5} + 78 q^{6} - 15 q^{7} - 285 q^{8} + 788 q^{9} + 300 q^{10} - 594 q^{11} - 1698 q^{12} - 1048 q^{13} + 639 q^{14} + 450 q^{15} + 234 q^{16} - 851 q^{17} - 6534 q^{18} - 178 q^{19} - 3450 q^{20} - 3116 q^{21} - 6103 q^{22} - 5290 q^{23} + 1689 q^{24} + 6250 q^{25} - 8914 q^{26} + 1800 q^{27} - 10177 q^{28} - 5527 q^{29} - 1950 q^{30} - 14999 q^{31} - 44832 q^{32} - 27368 q^{33} - 14369 q^{34} + 375 q^{35} - 34128 q^{36} - 25503 q^{37} - 53451 q^{38} - 41640 q^{39} + 7125 q^{40} - 7147 q^{41} - 52736 q^{42} + 5652 q^{43} - 3135 q^{44} - 19700 q^{45} + 6348 q^{46} - 57752 q^{47} - 51470 q^{48} + 19617 q^{49} - 7500 q^{50} + 13956 q^{51} + 46680 q^{52} - 74635 q^{53} - 5901 q^{54} + 14850 q^{55} + 6825 q^{56} - 55844 q^{57} + 46373 q^{58} - 58843 q^{59} + 42450 q^{60} + 43344 q^{61} + 40430 q^{62} - 55165 q^{63} + 223597 q^{64} + 26200 q^{65} + 273973 q^{66} + 68051 q^{67} + 53021 q^{68} + 9522 q^{69} - 15975 q^{70} - 19237 q^{71} + 253050 q^{72} - 9160 q^{73} + 92210 q^{74} - 11250 q^{75} + 309393 q^{76} - 238146 q^{77} + 184189 q^{78} - 61112 q^{79} - 5850 q^{80} + 107738 q^{81} - 57922 q^{82} - 106785 q^{83} + 235538 q^{84} + 21275 q^{85} + 175458 q^{86} - 149624 q^{87} + 20709 q^{88} - 172774 q^{89} + 163350 q^{90} + 314634 q^{91} - 73002 q^{92} - 82480 q^{93} + 328193 q^{94} + 4450 q^{95} + 724596 q^{96} + 120712 q^{97} + 515589 q^{98} - 244126 q^{99}+O(q^{100}) \) 10 * q - 12 * q^2 - 18 * q^3 + 138 * q^4 - 250 * q^5 + 78 * q^6 - 15 * q^7 - 285 * q^8 + 788 * q^9 + 300 * q^10 - 594 * q^11 - 1698 * q^12 - 1048 * q^13 + 639 * q^14 + 450 * q^15 + 234 * q^16 - 851 * q^17 - 6534 * q^18 - 178 * q^19 - 3450 * q^20 - 3116 * q^21 - 6103 * q^22 - 5290 * q^23 + 1689 * q^24 + 6250 * q^25 - 8914 * q^26 + 1800 * q^27 - 10177 * q^28 - 5527 * q^29 - 1950 * q^30 - 14999 * q^31 - 44832 * q^32 - 27368 * q^33 - 14369 * q^34 + 375 * q^35 - 34128 * q^36 - 25503 * q^37 - 53451 * q^38 - 41640 * q^39 + 7125 * q^40 - 7147 * q^41 - 52736 * q^42 + 5652 * q^43 - 3135 * q^44 - 19700 * q^45 + 6348 * q^46 - 57752 * q^47 - 51470 * q^48 + 19617 * q^49 - 7500 * q^50 + 13956 * q^51 + 46680 * q^52 - 74635 * q^53 - 5901 * q^54 + 14850 * q^55 + 6825 * q^56 - 55844 * q^57 + 46373 * q^58 - 58843 * q^59 + 42450 * q^60 + 43344 * q^61 + 40430 * q^62 - 55165 * q^63 + 223597 * q^64 + 26200 * q^65 + 273973 * q^66 + 68051 * q^67 + 53021 * q^68 + 9522 * q^69 - 15975 * q^70 - 19237 * q^71 + 253050 * q^72 - 9160 * q^73 + 92210 * q^74 - 11250 * q^75 + 309393 * q^76 - 238146 * q^77 + 184189 * q^78 - 61112 * q^79 - 5850 * q^80 + 107738 * q^81 - 57922 * q^82 - 106785 * q^83 + 235538 * q^84 + 21275 * q^85 + 175458 * q^86 - 149624 * q^87 + 20709 * q^88 - 172774 * q^89 + 163350 * q^90 + 314634 * q^91 - 73002 * q^92 - 82480 * q^93 + 328193 * q^94 + 4450 * q^95 + 724596 * q^96 + 120712 * q^97 + 515589 * q^98 - 244126 * q^99

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