LMFDB - Embedded newform 230.6.a.g.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("230.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$36.8882785570$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 772x^{3} - 255x^{2} + 13416x + 10080 $ x^5 - 772x^3 - 255x^2 + 13416*x + 10080
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-3.96404$ of defining polynomial
Character	$\chi$	$=$	230.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.00000 q^{2} -2.96404 q^{3} +16.0000 q^{4} -25.0000 q^{5} +11.8561 q^{6} -147.425 q^{7} -64.0000 q^{8} -234.214 q^{9} +O(q^{10})$	\(q-4.00000 q^{2} -2.96404 q^{3} +16.0000 q^{4} -25.0000 q^{5} +11.8561 q^{6} -147.425 q^{7} -64.0000 q^{8} -234.214 q^{9} +100.000 q^{10} +234.603 q^{11} -47.4246 q^{12} -797.505 q^{13} +589.698 q^{14} +74.1009 q^{15} +256.000 q^{16} -1606.49 q^{17} +936.858 q^{18} +1286.86 q^{19} -400.000 q^{20} +436.972 q^{21} -938.414 q^{22} +529.000 q^{23} +189.698 q^{24} +625.000 q^{25} +3190.02 q^{26} +1414.48 q^{27} -2358.79 q^{28} -4798.50 q^{29} -296.404 q^{30} +2775.71 q^{31} -1024.00 q^{32} -695.373 q^{33} +6425.97 q^{34} +3685.61 q^{35} -3747.43 q^{36} -10525.9 q^{37} -5147.43 q^{38} +2363.83 q^{39} +1600.00 q^{40} -6564.06 q^{41} -1747.89 q^{42} -7421.61 q^{43} +3753.65 q^{44} +5855.36 q^{45} -2116.00 q^{46} +7494.70 q^{47} -758.793 q^{48} +4926.99 q^{49} -2500.00 q^{50} +4761.70 q^{51} -12760.1 q^{52} +36324.5 q^{53} -5657.92 q^{54} -5865.09 q^{55} +9435.17 q^{56} -3814.29 q^{57} +19194.0 q^{58} +10050.8 q^{59} +1185.61 q^{60} +8352.67 q^{61} -11102.8 q^{62} +34529.0 q^{63} +4096.00 q^{64} +19937.6 q^{65} +2781.49 q^{66} +56632.1 q^{67} -25703.9 q^{68} -1567.97 q^{69} -14742.5 q^{70} +74905.4 q^{71} +14989.7 q^{72} -4917.21 q^{73} +42103.7 q^{74} -1852.52 q^{75} +20589.7 q^{76} -34586.3 q^{77} -9455.33 q^{78} -80923.7 q^{79} -6400.00 q^{80} +52721.6 q^{81} +26256.3 q^{82} -42110.0 q^{83} +6991.55 q^{84} +40162.3 q^{85} +29686.4 q^{86} +14222.9 q^{87} -15014.6 q^{88} +72516.4 q^{89} -23421.4 q^{90} +117572. q^{91} +8464.00 q^{92} -8227.29 q^{93} -29978.8 q^{94} -32171.4 q^{95} +3035.17 q^{96} +116045. q^{97} -19708.0 q^{98} -54947.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 20 q^{2} + 5 q^{3} + 80 q^{4} - 125 q^{5} - 20 q^{6} + 130 q^{7} - 320 q^{8} + 334 q^{9}+O(q^{10}) $ 5 * q - 20 * q^2 + 5 * q^3 + 80 * q^4 - 125 * q^5 - 20 * q^6 + 130 * q^7 - 320 * q^8 + 334 * q^9	\( 5 q - 20 q^{2} + 5 q^{3} + 80 q^{4} - 125 q^{5} - 20 q^{6} + 130 q^{7} - 320 q^{8} + 334 q^{9} + 500 q^{10} + 81 q^{11} + 80 q^{12} - 753 q^{13} - 520 q^{14} - 125 q^{15} + 1280 q^{16} - 1780 q^{17} - 1336 q^{18} + 1933 q^{19} - 2000 q^{20} - 2526 q^{21} - 324 q^{22} + 2645 q^{23} - 320 q^{24} + 3125 q^{25} + 3012 q^{26} + 2972 q^{27} + 2080 q^{28} + 3527 q^{29} + 500 q^{30} + 1816 q^{31} - 5120 q^{32} - 21947 q^{33} + 7120 q^{34} - 3250 q^{35} + 5344 q^{36} + 11683 q^{37} - 7732 q^{38} + 12580 q^{39} + 8000 q^{40} - 9602 q^{41} + 10104 q^{42} - 2232 q^{43} + 1296 q^{44} - 8350 q^{45} - 10580 q^{46} - 14552 q^{47} + 1280 q^{48} + 25889 q^{49} - 12500 q^{50} + 31351 q^{51} - 12048 q^{52} - 23069 q^{53} - 11888 q^{54} - 2025 q^{55} - 8320 q^{56} + 95210 q^{57} - 14108 q^{58} + 43917 q^{59} - 2000 q^{60} + 107483 q^{61} - 7264 q^{62} + 119033 q^{63} + 20480 q^{64} + 18825 q^{65} + 87788 q^{66} + 133125 q^{67} - 28480 q^{68} + 2645 q^{69} + 13000 q^{70} + 103326 q^{71} - 21376 q^{72} + 125870 q^{73} - 46732 q^{74} + 3125 q^{75} + 30928 q^{76} + 110422 q^{77} - 50320 q^{78} + 274892 q^{79} - 32000 q^{80} + 316657 q^{81} + 38408 q^{82} + 106201 q^{83} - 40416 q^{84} + 44500 q^{85} + 8928 q^{86} + 23782 q^{87} - 5184 q^{88} + 57800 q^{89} + 33400 q^{90} + 272163 q^{91} + 42320 q^{92} + 198110 q^{93} + 58208 q^{94} - 48325 q^{95} - 5120 q^{96} - 24935 q^{97} - 103556 q^{98} + 362547 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + 5 * q^3 + 80 * q^4 - 125 * q^5 - 20 * q^6 + 130 * q^7 - 320 * q^8 + 334 * q^9 + 500 * q^10 + 81 * q^11 + 80 * q^12 - 753 * q^13 - 520 * q^14 - 125 * q^15 + 1280 * q^16 - 1780 * q^17 - 1336 * q^18 + 1933 * q^19 - 2000 * q^20 - 2526 * q^21 - 324 * q^22 + 2645 * q^23 - 320 * q^24 + 3125 * q^25 + 3012 * q^26 + 2972 * q^27 + 2080 * q^28 + 3527 * q^29 + 500 * q^30 + 1816 * q^31 - 5120 * q^32 - 21947 * q^33 + 7120 * q^34 - 3250 * q^35 + 5344 * q^36 + 11683 * q^37 - 7732 * q^38 + 12580 * q^39 + 8000 * q^40 - 9602 * q^41 + 10104 * q^42 - 2232 * q^43 + 1296 * q^44 - 8350 * q^45 - 10580 * q^46 - 14552 * q^47 + 1280 * q^48 + 25889 * q^49 - 12500 * q^50 + 31351 * q^51 - 12048 * q^52 - 23069 * q^53 - 11888 * q^54 - 2025 * q^55 - 8320 * q^56 + 95210 * q^57 - 14108 * q^58 + 43917 * q^59 - 2000 * q^60 + 107483 * q^61 - 7264 * q^62 + 119033 * q^63 + 20480 * q^64 + 18825 * q^65 + 87788 * q^66 + 133125 * q^67 - 28480 * q^68 + 2645 * q^69 + 13000 * q^70 + 103326 * q^71 - 21376 * q^72 + 125870 * q^73 - 46732 * q^74 + 3125 * q^75 + 30928 * q^76 + 110422 * q^77 - 50320 * q^78 + 274892 * q^79 - 32000 * q^80 + 316657 * q^81 + 38408 * q^82 + 106201 * q^83 - 40416 * q^84 + 44500 * q^85 + 8928 * q^86 + 23782 * q^87 - 5184 * q^88 + 57800 * q^89 + 33400 * q^90 + 272163 * q^91 + 42320 * q^92 + 198110 * q^93 + 58208 * q^94 - 48325 * q^95 - 5120 * q^96 - 24935 * q^97 - 103556 * q^98 + 362547 * 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
$3$	−2.96404	−0.190143	−0.0950715	−	0.995470i	$-0.530308\pi$
$3$	−2.96404	−0.190143	−0.0950715	+	0.995470i	$0.530308\pi$
$4$	16.0000	0.500000
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	11.8561	0.134451
$7$	−147.425	−1.13717	−0.568584	−	0.822625i	$-0.692509\pi$
$7$	−147.425	−1.13717	−0.568584	+	0.822625i	$0.692509\pi$
$8$	−64.0000	−0.353553
$9$	−234.214	−0.963846
$10$	100.000	0.316228
$11$	234.603	0.584592	0.292296	−	0.956328i	$-0.405581\pi$
$11$	234.603	0.584592	0.292296	+	0.956328i	$0.405581\pi$
$12$	−47.4246	−0.0950715
$13$	−797.505	−1.30880	−0.654402	−	0.756147i	$-0.727080\pi$
$13$	−797.505	−1.30880	−0.654402	+	0.756147i	$0.727080\pi$
$14$	589.698	0.804099
$15$	74.1009	0.0850345
$16$	256.000	0.250000
$17$	−1606.49	−1.34821	−0.674104	−	0.738637i	$-0.735470\pi$
$17$	−1606.49	−1.34821	−0.674104	+	0.738637i	$0.735470\pi$
$18$	936.858	0.681542
$19$	1286.86	0.817799	0.408899	−	0.912579i	$-0.365913\pi$
$19$	1286.86	0.817799	0.408899	+	0.912579i	$0.365913\pi$
$20$	−400.000	−0.223607
$21$	436.972	0.216225
$22$	−938.414	−0.413369
$23$	529.000	0.208514
$23$	529.000	0.208514
$24$	189.698	0.0672257
$25$	625.000	0.200000
$26$	3190.02	0.925465
$27$	1414.48	0.373411
$28$	−2358.79	−0.568584
$29$	−4798.50	−1.05952	−0.529762	−	0.848146i	$-0.677719\pi$
$29$	−4798.50	−1.05952	−0.529762	+	0.848146i	$0.677719\pi$
$30$	−296.404	−0.0601285
$31$	2775.71	0.518763	0.259382	−	0.965775i	$-0.416481\pi$
$31$	2775.71	0.518763	0.259382	+	0.965775i	$0.416481\pi$
$32$	−1024.00	−0.176777
$33$	−695.373	−0.111156
$34$	6425.97	0.953327
$35$	3685.61	0.508557
$36$	−3747.43	−0.481923
$37$	−10525.9	−1.26403	−0.632013	−	0.774957i	$-0.717771\pi$
$37$	−10525.9	−1.26403	−0.632013	+	0.774957i	$0.717771\pi$
$38$	−5147.43	−0.578271
$39$	2363.83	0.248860
$40$	1600.00	0.158114
$41$	−6564.06	−0.609836	−0.304918	−	0.952379i	$-0.598629\pi$
$41$	−6564.06	−0.609836	−0.304918	+	0.952379i	$0.598629\pi$
$42$	−1747.89	−0.152894
$43$	−7421.61	−0.612106	−0.306053	−	0.952014i	$-0.599009\pi$
$43$	−7421.61	−0.612106	−0.306053	+	0.952014i	$0.599009\pi$
$44$	3753.65	0.292296
$45$	5855.36	0.431045
$46$	−2116.00	−0.147442
$47$	7494.70	0.494891	0.247445	−	0.968902i	$-0.420409\pi$
$47$	7494.70	0.494891	0.247445	+	0.968902i	$0.420409\pi$
$48$	−758.793	−0.0475357
$49$	4926.99	0.293151
$50$	−2500.00	−0.141421
$51$	4761.70	0.256352
$52$	−12760.1	−0.654402
$53$	36324.5	1.77627	0.888137	−	0.459579i	$-0.152000\pi$
$53$	36324.5	1.77627	0.888137	+	0.459579i	$0.152000\pi$
$54$	−5657.92	−0.264042
$55$	−5865.09	−0.261437
$56$	9435.17	0.402050
$57$	−3814.29	−0.155499
$58$	19194.0	0.749197
$59$	10050.8	0.375899	0.187950	−	0.982179i	$-0.439816\pi$
$59$	10050.8	0.375899	0.187950	+	0.982179i	$0.439816\pi$
$60$	1185.61	0.0425173
$61$	8352.67	0.287409	0.143705	−	0.989621i	$-0.454098\pi$
$61$	8352.67	0.287409	0.143705	+	0.989621i	$0.454098\pi$
$62$	−11102.8	−0.366821
$63$	34529.0	1.09605
$64$	4096.00	0.125000
$65$	19937.6	0.585315
$66$	2781.49	0.0785992
$67$	56632.1	1.54126	0.770630	−	0.637283i	$-0.219942\pi$
$67$	56632.1	1.54126	0.770630	+	0.637283i	$0.219942\pi$
$68$	−25703.9	−0.674104
$69$	−1567.97	−0.0396476
$70$	−14742.5	−0.359604
$71$	74905.4	1.76347	0.881733	−	0.471749i	$-0.156377\pi$
$71$	74905.4	1.76347	0.881733	+	0.471749i	$0.156377\pi$
$72$	14989.7	0.340771
$73$	−4917.21	−0.107997	−0.0539985	−	0.998541i	$-0.517197\pi$
$73$	−4917.21	−0.107997	−0.0539985	+	0.998541i	$0.517197\pi$
$74$	42103.7	0.893802
$75$	−1852.52	−0.0380286
$76$	20589.7	0.408899
$77$	−34586.3	−0.664779
$78$	−9455.33	−0.175971
$79$	−80923.7	−1.45884	−0.729421	−	0.684065i	$-0.760210\pi$
$79$	−80923.7	−1.45884	−0.729421	+	0.684065i	$0.760210\pi$
$80$	−6400.00	−0.111803
$81$	52721.6	0.892844
$82$	26256.3	0.431219
$83$	−42110.0	−0.670951	−0.335475	−	0.942049i	$-0.608897\pi$
$83$	−42110.0	−0.670951	−0.335475	+	0.942049i	$0.608897\pi$
$84$	6991.55	0.108112
$85$	40162.3	0.602937
$86$	29686.4	0.432825
$87$	14222.9	0.201461
$88$	−15014.6	−0.206684
$89$	72516.4	0.970424	0.485212	−	0.874397i	$-0.338743\pi$
$89$	72516.4	0.970424	0.485212	+	0.874397i	$0.338743\pi$
$90$	−23421.4	−0.304795
$91$	117572.	1.48833
$92$	8464.00	0.104257
$93$	−8227.29	−0.0986392
$94$	−29978.8	−0.349941
$95$	−32171.4	−0.365731
$96$	3035.17	0.0336128
$97$	116045.	1.25227	0.626133	−	0.779716i	$-0.284637\pi$
$97$	116045.	1.25227	0.626133	+	0.779716i	$0.284637\pi$
$98$	−19708.0	−0.207289
$99$	−54947.5	−0.563456
$100$	10000.0	0.100000
$101$	157470.	1.53601	0.768005	−	0.640444i	$-0.221250\pi$
$101$	157470.	1.53601	0.768005	+	0.640444i	$0.221250\pi$
$102$	−19046.8	−0.181268
$103$	29421.0	0.273253	0.136626	−	0.990623i	$-0.456374\pi$
$103$	29421.0	0.273253	0.136626	+	0.990623i	$0.456374\pi$
$104$	51040.3	0.462732
$105$	−10924.3	−0.0966985
$106$	−145298.	−1.25602
$107$	−201445.	−1.70097	−0.850485	−	0.526000i	$-0.823691\pi$
$107$	−201445.	−1.70097	−0.850485	+	0.526000i	$0.823691\pi$
$108$	22631.7	0.186706
$109$	152404.	1.22865	0.614326	−	0.789052i	$-0.289428\pi$
$109$	152404.	1.22865	0.614326	+	0.789052i	$0.289428\pi$
$110$	23460.3	0.184864
$111$	31199.2	0.240346
$112$	−37740.7	−0.284292
$113$	−79435.2	−0.585217	−0.292608	−	0.956232i	$-0.594523\pi$
$113$	−79435.2	−0.585217	−0.292608	+	0.956232i	$0.594523\pi$
$114$	15257.2	0.109954
$115$	−13225.0	−0.0932505
$116$	−76776.1	−0.529762
$117$	186787.	1.26149
$118$	−40203.3	−0.265801
$119$	236837.	1.53314
$120$	−4742.46	−0.0300642
$121$	−106012.	−0.658253
$122$	−33410.7	−0.203229
$123$	19456.1	0.115956
$124$	44411.3	0.259382
$125$	−15625.0	−0.0894427
$126$	−138116.	−0.775028
$127$	66621.5	0.366526	0.183263	−	0.983064i	$-0.441334\pi$
$127$	66621.5	0.366526	0.183263	+	0.983064i	$0.441334\pi$
$128$	−16384.0	−0.0883883
$129$	21997.9	0.116388
$130$	−79750.5	−0.413880
$131$	−289579.	−1.47431	−0.737155	−	0.675724i	$-0.763831\pi$
$131$	−289579.	−1.47431	−0.737155	+	0.675724i	$0.763831\pi$
$132$	−11126.0	−0.0555780
$133$	−189714.	−0.929975
$134$	−226528.	−1.08983
$135$	−35362.0	−0.166995
$136$	102816.	0.476663
$137$	−270174.	−1.22982	−0.614911	−	0.788597i	$-0.710808\pi$
$137$	−270174.	−1.22982	−0.614911	+	0.788597i	$0.710808\pi$
$138$	6271.90	0.0280351
$139$	101859.	0.447158	0.223579	−	0.974686i	$-0.428226\pi$
$139$	101859.	0.447158	0.223579	+	0.974686i	$0.428226\pi$
$140$	58969.8	0.254279
$141$	−22214.6	−0.0941000
$142$	−299621.	−1.24696
$143$	−187097.	−0.765116
$144$	−59958.9	−0.240961
$145$	119963.	0.473834
$146$	19668.9	0.0763655
$147$	−14603.8	−0.0557407
$148$	−168415.	−0.632013
$149$	−450491.	−1.66234	−0.831171	−	0.556017i	$-0.812329\pi$
$149$	−450491.	−1.66234	−0.831171	+	0.556017i	$0.812329\pi$
$150$	7410.09	0.0268903
$151$	409995.	1.46331	0.731654	−	0.681676i	$-0.238749\pi$
$151$	409995.	1.46331	0.731654	+	0.681676i	$0.238749\pi$
$152$	−82358.9	−0.289136
$153$	376264.	1.29946
$154$	138345.	0.470070
$155$	−69392.6	−0.231998
$156$	37821.3	0.124430
$157$	105518.	0.341648	0.170824	−	0.985302i	$-0.445357\pi$
$157$	105518.	0.341648	0.170824	+	0.985302i	$0.445357\pi$
$158$	323695.	1.03156
$159$	−107667.	−0.337746
$160$	25600.0	0.0790569
$161$	−77987.6	−0.237116
$162$	−210886.	−0.631336
$163$	352888.	1.04032	0.520161	−	0.854068i	$-0.325872\pi$
$163$	352888.	1.04032	0.520161	+	0.854068i	$0.325872\pi$
$164$	−105025.	−0.304918
$165$	17384.3	0.0497105
$166$	168440.	0.474434
$167$	−242662.	−0.673304	−0.336652	−	0.941629i	$-0.609295\pi$
$167$	−242662.	−0.673304	−0.336652	+	0.941629i	$0.609295\pi$
$168$	−27966.2	−0.0764469
$169$	264720.	0.712969
$170$	−160649.	−0.426341
$171$	−301401.	−0.788232
$172$	−118746.	−0.306053
$173$	−285907.	−0.726290	−0.363145	−	0.931733i	$-0.618297\pi$
$173$	−285907.	−0.726290	−0.363145	+	0.931733i	$0.618297\pi$
$174$	−56891.7	−0.142454
$175$	−92140.3	−0.227434
$176$	60058.5	0.146148
$177$	−29791.0	−0.0714746
$178$	−290066.	−0.686193
$179$	−208121.	−0.485494	−0.242747	−	0.970090i	$-0.578048\pi$
$179$	−208121.	−0.485494	−0.242747	+	0.970090i	$0.578048\pi$
$180$	93685.8	0.215522
$181$	−412441.	−0.935763	−0.467882	−	0.883791i	$-0.654983\pi$
$181$	−412441.	−0.935763	−0.467882	+	0.883791i	$0.654983\pi$
$182$	−470287.	−1.05241
$183$	−24757.6	−0.0546488
$184$	−33856.0	−0.0737210
$185$	263148.	0.565290
$186$	32909.2	0.0697484
$187$	−376889.	−0.788151
$188$	119915.	0.247445
$189$	−208529.	−0.424632
$190$	128686.	0.258611
$191$	494628.	0.981060	0.490530	−	0.871424i	$-0.336803\pi$
$191$	494628.	0.981060	0.490530	+	0.871424i	$0.336803\pi$
$192$	−12140.7	−0.0237679
$193$	246797.	0.476921	0.238461	−	0.971152i	$-0.423357\pi$
$193$	246797.	0.476921	0.238461	+	0.971152i	$0.423357\pi$
$194$	−464179.	−0.885486
$195$	−59095.8	−0.111294
$196$	78831.9	0.146576
$197$	−627159.	−1.15136	−0.575681	−	0.817674i	$-0.695263\pi$
$197$	−627159.	−1.15136	−0.575681	+	0.817674i	$0.695263\pi$
$198$	219790.	0.398424
$199$	−81640.4	−0.146141	−0.0730706	−	0.997327i	$-0.523280\pi$
$199$	−81640.4	−0.146141	−0.0730706	+	0.997327i	$0.523280\pi$
$200$	−40000.0	−0.0707107
$201$	−167860.	−0.293060
$202$	−629879.	−1.08612
$203$	707417.	1.20486
$204$	76187.3	0.128176
$205$	164102.	0.272727
$206$	−117684.	−0.193219
$207$	−123899.	−0.200976
$208$	−204161.	−0.327201
$209$	301901.	0.478078
$210$	43697.2	0.0683762
$211$	323999.	0.501000	0.250500	−	0.968117i	$-0.419405\pi$
$211$	323999.	0.501000	0.250500	+	0.968117i	$0.419405\pi$
$212$	581192.	0.888137
$213$	−222022.	−0.335311
$214$	805779.	1.20277
$215$	185540.	0.273742
$216$	−90526.8	−0.132021
$217$	−409207.	−0.589921
$218$	−609614.	−0.868788
$219$	14574.8	0.0205349
$220$	−93841.4	−0.130719
$221$	1.28119e6	1.76454
$222$	−124797.	−0.169950
$223$	460682.	0.620353	0.310176	−	0.950679i	$-0.399612\pi$
$223$	460682.	0.620353	0.310176	+	0.950679i	$0.399612\pi$
$224$	150963.	0.201025
$225$	−146384.	−0.192769
$226$	317741.	0.413811
$227$	−1.51885e6	−1.95637	−0.978184	−	0.207740i	$-0.933389\pi$
$227$	−1.51885e6	−1.95637	−0.978184	+	0.207740i	$0.933389\pi$
$228$	−61028.7	−0.0777494
$229$	311694.	0.392771	0.196386	−	0.980527i	$-0.437080\pi$
$229$	311694.	0.392771	0.196386	+	0.980527i	$0.437080\pi$
$230$	52900.0	0.0659380
$231$	102515.	0.126403
$232$	307104.	0.374598
$233$	43520.0	0.0525169	0.0262584	−	0.999655i	$-0.491641\pi$
$233$	43520.0	0.0525169	0.0262584	+	0.999655i	$0.491641\pi$
$234$	−747148.	−0.892005
$235$	−187367.	−0.221322
$236$	160813.	0.187950
$237$	239861.	0.277389
$238$	−947346.	−1.08409
$239$	489628.	0.554461	0.277231	−	0.960803i	$-0.410583\pi$
$239$	489628.	0.554461	0.277231	+	0.960803i	$0.410583\pi$
$240$	18969.8	0.0212586
$241$	209318.	0.232147	0.116074	−	0.993241i	$-0.462969\pi$
$241$	209318.	0.232147	0.116074	+	0.993241i	$0.462969\pi$
$242$	424049.	0.465455
$243$	−499987.	−0.543179
$244$	133643.	0.143705
$245$	−123175.	−0.131101
$246$	−77824.5	−0.0819933
$247$	−1.02627e6	−1.07034
$248$	−177645.	−0.183410
$249$	124816.	0.127577
$250$	62500.0	0.0632456
$251$	−1.24474e6	−1.24708	−0.623542	−	0.781790i	$-0.714307\pi$
$251$	−1.24474e6	−1.24708	−0.623542	+	0.781790i	$0.714307\pi$
$252$	552463.	0.548027
$253$	124105.	0.121896
$254$	−266486.	−0.259173
$255$	−119043.	−0.114644
$256$	65536.0	0.0625000
$257$	−929224.	−0.877582	−0.438791	−	0.898589i	$-0.644593\pi$
$257$	−929224.	−0.877582	−0.438791	+	0.898589i	$0.644593\pi$
$258$	−87991.6	−0.0822985
$259$	1.55178e6	1.43741
$260$	319002.	0.292658
$261$	1.12388e6	1.02122
$262$	1.15832e6	1.04249
$263$	1.49616e6	1.33380	0.666899	−	0.745148i	$-0.267621\pi$
$263$	1.49616e6	1.33380	0.666899	+	0.745148i	$0.267621\pi$
$264$	44503.9	0.0392996
$265$	−908112.	−0.794374
$266$	758858.	0.657592
$267$	−214941.	−0.184519
$268$	906114.	0.770630
$269$	1.21865e6	1.02683	0.513415	−	0.858140i	$-0.328380\pi$
$269$	1.21865e6	1.02683	0.513415	+	0.858140i	$0.328380\pi$
$270$	141448.	0.118083
$271$	454292.	0.375761	0.187880	−	0.982192i	$-0.439838\pi$
$271$	454292.	0.375761	0.187880	+	0.982192i	$0.439838\pi$
$272$	−411262.	−0.337052
$273$	−348487.	−0.282996
$274$	1.08070e6	0.869615
$275$	146627.	0.116918
$276$	−25087.6	−0.0198238
$277$	−255823.	−0.200327	−0.100164	−	0.994971i	$-0.531937\pi$
$277$	−255823.	−0.200327	−0.100164	+	0.994971i	$0.531937\pi$
$278$	−407435.	−0.316189
$279$	−650111.	−0.500008
$280$	−235879.	−0.179802
$281$	85913.7	0.0649077	0.0324539	−	0.999473i	$-0.489668\pi$
$281$	85913.7	0.0649077	0.0324539	+	0.999473i	$0.489668\pi$
$282$	88858.2	0.0665388
$283$	1.89869e6	1.40925	0.704626	−	0.709579i	$-0.251115\pi$
$283$	1.89869e6	1.40925	0.704626	+	0.709579i	$0.251115\pi$
$284$	1.19849e6	0.881733
$285$	95357.3	0.0695411
$286$	748389.	0.541019
$287$	967704.	0.693486
$288$	239836.	0.170385
$289$	1.16096e6	0.817663
$290$	−479850.	−0.335051
$291$	−343961.	−0.238110
$292$	−78675.4	−0.0539985
$293$	1.13216e6	0.770442	0.385221	−	0.922824i	$-0.374125\pi$
$293$	1.13216e6	0.770442	0.385221	+	0.922824i	$0.374125\pi$
$294$	58415.2	0.0394146
$295$	−251270.	−0.168107
$296$	673660.	0.446901
$297$	331842.	0.218293
$298$	1.80196e6	1.17545
$299$	−421880.	−0.272905
$300$	−29640.4	−0.0190143
$301$	1.09413e6	0.696068
$302$	−1.63998e6	−1.03471
$303$	−466746.	−0.292061
$304$	329436.	0.204450
$305$	−208817.	−0.128533
$306$	−1.50506e6	−0.918860
$307$	−771639.	−0.467271	−0.233635	−	0.972324i	$-0.575062\pi$
$307$	−771639.	−0.467271	−0.233635	+	0.972324i	$0.575062\pi$
$308$	−553381.	−0.332390
$309$	−87204.9	−0.0519571
$310$	277571.	0.164047
$311$	−1.34160e6	−0.786540	−0.393270	−	0.919423i	$-0.628656\pi$
$311$	−1.34160e6	−0.786540	−0.393270	+	0.919423i	$0.628656\pi$
$312$	−151285.	−0.0879853
$313$	2.23311e6	1.28839	0.644197	−	0.764859i	$-0.277192\pi$
$313$	2.23311e6	1.28839	0.644197	+	0.764859i	$0.277192\pi$
$314$	−422073.	−0.241581
$315$	−863224.	−0.490170
$316$	−1.29478e6	−0.729421
$317$	−1.60238e6	−0.895609	−0.447804	−	0.894132i	$-0.647794\pi$
$317$	−1.60238e6	−0.895609	−0.447804	+	0.894132i	$0.647794\pi$
$318$	430668.	0.238822
$319$	−1.12575e6	−0.619389
$320$	−102400.	−0.0559017
$321$	597089.	0.323427
$322$	311950.	0.167666
$323$	−2.06733e6	−1.10256
$324$	843545.	0.446422
$325$	−498440.	−0.261761
$326$	−1.41155e6	−0.735619
$327$	−451730.	−0.233620
$328$	420100.	0.215610
$329$	−1.10490e6	−0.562774
$330$	−69537.3	−0.0351506
$331$	1.13681e6	0.570317	0.285158	−	0.958480i	$-0.407954\pi$
$331$	1.13681e6	0.570317	0.285158	+	0.958480i	$0.407954\pi$
$332$	−673761.	−0.335475
$333$	2.46533e6	1.21833
$334$	970649.	0.476098
$335$	−1.41580e6	−0.689272
$336$	111865.	0.0540561
$337$	648504.	0.311056	0.155528	−	0.987832i	$-0.450292\pi$
$337$	648504.	0.311056	0.155528	+	0.987832i	$0.450292\pi$
$338$	−1.05888e6	−0.504145
$339$	235449.	0.111275
$340$	642597.	0.301468
$341$	651190.	0.303265
$342$	1.20560e6	0.557364
$343$	1.75140e6	0.803806
$344$	474983.	0.216412
$345$	39199.4	0.0177309
$346$	1.14363e6	0.513565
$347$	−2.51173e6	−1.11982	−0.559911	−	0.828553i	$-0.689165\pi$
$347$	−2.51173e6	−1.11982	−0.559911	+	0.828553i	$0.689165\pi$
$348$	227567.	0.100731
$349$	−818604.	−0.359758	−0.179879	−	0.983689i	$-0.557571\pi$
$349$	−818604.	−0.359758	−0.179879	+	0.983689i	$0.557571\pi$
$350$	368561.	0.160820
$351$	−1.12805e6	−0.488723
$352$	−240234.	−0.103342
$353$	−4.62636e6	−1.97607	−0.988036	−	0.154224i	$-0.950712\pi$
$353$	−4.62636e6	−1.97607	−0.988036	+	0.154224i	$0.950712\pi$
$354$	119164.	0.0505402
$355$	−1.87263e6	−0.788646
$356$	1.16026e6	0.485212
$357$	−701992.	−0.291516
$358$	832485.	0.343296
$359$	1.01328e6	0.414949	0.207475	−	0.978240i	$-0.433476\pi$
$359$	1.01328e6	0.414949	0.207475	+	0.978240i	$0.433476\pi$
$360$	−374743.	−0.152397
$361$	−820096.	−0.331205
$362$	1.64977e6	0.661684
$363$	314224.	0.125162
$364$	1.88115e6	0.744165
$365$	122930.	0.0482978
$366$	99030.4	0.0386426
$367$	−2.33446e6	−0.904734	−0.452367	−	0.891832i	$-0.649420\pi$
$367$	−2.33446e6	−0.904734	−0.452367	+	0.891832i	$0.649420\pi$
$368$	135424.	0.0521286
$369$	1.53740e6	0.587788
$370$	−1.05259e6	−0.399720
$371$	−5.35512e6	−2.01992
$372$	−131637.	−0.0493196
$373$	−1.46765e6	−0.546198	−0.273099	−	0.961986i	$-0.588049\pi$
$373$	−1.46765e6	−0.546198	−0.273099	+	0.961986i	$0.588049\pi$
$374$	1.50756e6	0.557307
$375$	46313.1	0.0170069
$376$	−479661.	−0.174970
$377$	3.82683e6	1.38671
$378$	834117.	0.300260
$379$	−3.61367e6	−1.29226	−0.646130	−	0.763227i	$-0.723614\pi$
$379$	−3.61367e6	−1.29226	−0.646130	+	0.763227i	$0.723614\pi$
$380$	−514743.	−0.182865
$381$	−197468.	−0.0696924
$382$	−1.97851e6	−0.693714
$383$	3.80082e6	1.32398	0.661989	−	0.749514i	$-0.269713\pi$
$383$	3.80082e6	1.32398	0.661989	+	0.749514i	$0.269713\pi$
$384$	48562.8	0.0168064
$385$	864658.	0.297298
$386$	−987188.	−0.337234
$387$	1.73825e6	0.589976
$388$	1.85672e6	0.626133
$389$	4.90659e6	1.64401	0.822007	−	0.569477i	$-0.192854\pi$
$389$	4.90659e6	1.64401	0.822007	+	0.569477i	$0.192854\pi$
$390$	236383.	0.0786964
$391$	−849835.	−0.281121
$392$	−315328.	−0.103645
$393$	858322.	0.280330
$394$	2.50863e6	0.814136
$395$	2.02309e6	0.652414
$396$	−879160.	−0.281728
$397$	1.64255e6	0.523049	0.261524	−	0.965197i	$-0.415775\pi$
$397$	1.64255e6	0.523049	0.261524	+	0.965197i	$0.415775\pi$
$398$	326562.	0.103337
$399$	562320.	0.176828
$400$	160000.	0.0500000
$401$	3.66939e6	1.13955	0.569775	−	0.821801i	$-0.307030\pi$
$401$	3.66939e6	1.13955	0.569775	+	0.821801i	$0.307030\pi$
$402$	671438.	0.207224
$403$	−2.21364e6	−0.678960
$404$	2.51952e6	0.768005
$405$	−1.31804e6	−0.399292
$406$	−2.82967e6	−0.851962
$407$	−2.46942e6	−0.738940
$408$	−304749.	−0.0906342
$409$	539778.	0.159554	0.0797769	−	0.996813i	$-0.474579\pi$
$409$	539778.	0.159554	0.0797769	+	0.996813i	$0.474579\pi$
$410$	−656406.	−0.192847
$411$	800805.	0.233842
$412$	470736.	0.136626
$413$	−1.48174e6	−0.427461
$414$	495598.	0.142111
$415$	1.05275e6	0.300058
$416$	816645.	0.231366
$417$	−301913.	−0.0850240
$418$	−1.20761e6	−0.338053
$419$	−574974.	−0.159997	−0.0799987	−	0.996795i	$-0.525492\pi$
$419$	−574974.	−0.159997	−0.0799987	+	0.996795i	$0.525492\pi$
$420$	−174789.	−0.0483493
$421$	4.86690e6	1.33828	0.669141	−	0.743136i	$-0.266662\pi$
$421$	4.86690e6	1.33828	0.669141	+	0.743136i	$0.266662\pi$
$422$	−1.29600e6	−0.354261
$423$	−1.75537e6	−0.476999
$424$	−2.32477e6	−0.628008
$425$	−1.00406e6	−0.269641
$426$	888089.	0.237100
$427$	−1.23139e6	−0.326833
$428$	−3.22312e6	−0.850485
$429$	554563.	0.145481
$430$	−742161.	−0.193565
$431$	−2.95412e6	−0.766010	−0.383005	−	0.923746i	$-0.625111\pi$
$431$	−2.95412e6	−0.766010	−0.383005	+	0.923746i	$0.625111\pi$
$432$	362107.	0.0933529
$433$	−7.39274e6	−1.89490	−0.947448	−	0.319909i	$-0.896348\pi$
$433$	−7.39274e6	−1.89490	−0.947448	+	0.319909i	$0.896348\pi$
$434$	1.63683e6	0.417137
$435$	−355573.	−0.0900961
$436$	2.43846e6	0.614326
$437$	680748.	0.170523
$438$	−58299.2	−0.0145204
$439$	2.88199e6	0.713725	0.356863	−	0.934157i	$-0.383846\pi$
$439$	2.88199e6	0.713725	0.356863	+	0.934157i	$0.383846\pi$
$440$	375365.	0.0924321
$441$	−1.15397e6	−0.282553
$442$	−5.12474e6	−1.24772
$443$	6.47410e6	1.56736	0.783682	−	0.621162i	$-0.213339\pi$
$443$	6.47410e6	1.56736	0.783682	+	0.621162i	$0.213339\pi$
$444$	499188.	0.120173
$445$	−1.81291e6	−0.433987
$446$	−1.84273e6	−0.438656
$447$	1.33527e6	0.316083
$448$	−603851.	−0.142146
$449$	6.79313e6	1.59021	0.795104	−	0.606473i	$-0.207416\pi$
$449$	6.79313e6	1.59021	0.795104	+	0.606473i	$0.207416\pi$
$450$	585536.	0.136308
$451$	−1.53995e6	−0.356505
$452$	−1.27096e6	−0.292608
$453$	−1.21524e6	−0.278238
$454$	6.07540e6	1.38336
$455$	−2.93929e6	−0.665602
$456$	244115.	0.0549771
$457$	2.71737e6	0.608638	0.304319	−	0.952570i	$-0.401571\pi$
$457$	2.71737e6	0.608638	0.304319	+	0.952570i	$0.401571\pi$
$458$	−1.24678e6	−0.277731
$459$	−2.27235e6	−0.503436
$460$	−211600.	−0.0466252
$461$	−9.02639e6	−1.97816	−0.989081	−	0.147375i	$-0.952917\pi$
$461$	−9.02639e6	−1.97816	−0.989081	+	0.147375i	$0.952917\pi$
$462$	−410060.	−0.0893805
$463$	−2.31958e6	−0.502871	−0.251436	−	0.967874i	$-0.580903\pi$
$463$	−2.31958e6	−0.502871	−0.251436	+	0.967874i	$0.580903\pi$
$464$	−1.22842e6	−0.264881
$465$	205682.	0.0441128
$466$	−174080.	−0.0371351
$467$	−3.67003e6	−0.778712	−0.389356	−	0.921087i	$-0.627302\pi$
$467$	−3.67003e6	−0.778712	−0.389356	+	0.921087i	$0.627302\pi$
$468$	2.98859e6	0.630743
$469$	−8.34896e6	−1.75267
$470$	749470.	0.156498
$471$	−312760.	−0.0649619
$472$	−643252.	−0.132900
$473$	−1.74113e6	−0.357832
$474$	−959443.	−0.196143
$475$	804286.	0.163560
$476$	3.78939e6	0.766569
$477$	−8.50772e6	−1.71205
$478$	−1.95851e6	−0.392063
$479$	−7.04531e6	−1.40301	−0.701506	−	0.712664i	$-0.747489\pi$
$479$	−7.04531e6	−1.40301	−0.701506	+	0.712664i	$0.747489\pi$
$480$	−75879.3	−0.0150321
$481$	8.39448e6	1.65436
$482$	−837272.	−0.164153
$483$	231158.	0.0450859
$484$	−1.69620e6	−0.329126
$485$	−2.90112e6	−0.560030
$486$	1.99995e6	0.384086
$487$	1.43773e6	0.274699	0.137349	−	0.990523i	$-0.456142\pi$
$487$	1.43773e6	0.274699	0.137349	+	0.990523i	$0.456142\pi$
$488$	−534571.	−0.101615
$489$	−1.04597e6	−0.197810
$490$	492699.	0.0927026
$491$	3.90623e6	0.731230	0.365615	−	0.930766i	$-0.380859\pi$
$491$	3.90623e6	0.731230	0.365615	+	0.930766i	$0.380859\pi$
$492$	311298.	0.0579780
$493$	7.70876e6	1.42846
$494$	4.10510e6	0.756844
$495$	1.37369e6	0.251985
$496$	710581.	0.129691
$497$	−1.10429e7	−2.00536
$498$	−499263.	−0.0902102
$499$	−7.99603e6	−1.43755	−0.718775	−	0.695243i	$-0.755297\pi$
$499$	−7.99603e6	−1.43755	−0.718775	+	0.695243i	$0.755297\pi$
$500$	−250000.	−0.0447214
$501$	719260.	0.128024
$502$	4.97897e6	0.881821
$503$	397938.	0.0701286	0.0350643	−	0.999385i	$-0.488836\pi$
$503$	397938.	0.0701286	0.0350643	+	0.999385i	$0.488836\pi$
$504$	−2.20985e6	−0.387514
$505$	−3.93675e6	−0.686925
$506$	−496421.	−0.0861933
$507$	−784641.	−0.135566
$508$	1.06594e6	0.183263
$509$	9.84432e6	1.68419	0.842096	−	0.539328i	$-0.181322\pi$
$509$	9.84432e6	1.68419	0.842096	+	0.539328i	$0.181322\pi$
$510$	476170.	0.0810657
$511$	724918.	0.122811
$512$	−262144.	−0.0441942
$513$	1.82024e6	0.305376
$514$	3.71690e6	0.620544
$515$	−735525.	−0.122202
$516$	351967.	0.0581939
$517$	1.75828e6	0.289309
$518$	−6.20712e6	−1.01640
$519$	847440.	0.138099
$520$	−1.27601e6	−0.206940
$521$	−5.84655e6	−0.943638	−0.471819	−	0.881696i	$-0.656402\pi$
$521$	−5.84655e6	−0.943638	−0.471819	+	0.881696i	$0.656402\pi$
$522$	−4.49552e6	−0.722110
$523$	1.13800e7	1.81923	0.909614	−	0.415454i	$-0.136377\pi$
$523$	1.13800e7	1.81923	0.909614	+	0.415454i	$0.136377\pi$
$524$	−4.63326e6	−0.737155
$525$	273107.	0.0432449
$526$	−5.98466e6	−0.943137
$527$	−4.45915e6	−0.699400
$528$	−178015.	−0.0277890
$529$	279841.	0.0434783
$530$	3.63245e6	0.561707
$531$	−2.35405e6	−0.362309
$532$	−3.03543e6	−0.464987
$533$	5.23487e6	0.798156
$534$	859765.	0.130475
$535$	5.03612e6	0.760697
$536$	−3.62445e6	−0.544917
$537$	616878.	0.0923132
$538$	−4.87461e6	−0.726079
$539$	1.15589e6	0.171374
$540$	−565792.	−0.0834973
$541$	−1.45493e6	−0.213722	−0.106861	−	0.994274i	$-0.534080\pi$
$541$	−1.45493e6	−0.213722	−0.106861	+	0.994274i	$0.534080\pi$
$542$	−1.81717e6	−0.265703
$543$	1.22249e6	0.177929
$544$	1.64505e6	0.238332
$545$	−3.81009e6	−0.549470
$546$	1.39395e6	0.200108
$547$	9.90566e6	1.41552	0.707759	−	0.706454i	$-0.249706\pi$
$547$	9.90566e6	1.41552	0.707759	+	0.706454i	$0.249706\pi$
$548$	−4.32278e6	−0.614911
$549$	−1.95632e6	−0.277018
$550$	−586509.	−0.0826738
$551$	−6.17499e6	−0.866478
$552$	100350.	0.0140175
$553$	1.19301e7	1.65895
$554$	1.02329e6	0.141653
$555$	−779981.	−0.107486
$556$	1.62974e6	0.223579
$557$	4.97064e6	0.678851	0.339426	−	0.940633i	$-0.389767\pi$
$557$	4.97064e6	0.678851	0.339426	+	0.940633i	$0.389767\pi$
$558$	2.60044e6	0.353559
$559$	5.91877e6	0.801128
$560$	943517.	0.127139
$561$	1.11711e6	0.149861
$562$	−343655.	−0.0458967
$563$	−373457.	−0.0496558	−0.0248279	−	0.999692i	$-0.507904\pi$
$563$	−373457.	−0.0496558	−0.0248279	+	0.999692i	$0.507904\pi$
$564$	−355433.	−0.0470500
$565$	1.98588e6	0.261717
$566$	−7.59478e6	−0.996492
$567$	−7.77245e6	−1.01531
$568$	−4.79394e6	−0.623479
$569$	−1.74520e6	−0.225977	−0.112989	−	0.993596i	$-0.536042\pi$
$569$	−1.74520e6	−0.225977	−0.112989	+	0.993596i	$0.536042\pi$
$570$	−381429.	−0.0491730
$571$	−3.52701e6	−0.452706	−0.226353	−	0.974045i	$-0.572680\pi$
$571$	−3.52701e6	−0.452706	−0.226353	+	0.974045i	$0.572680\pi$
$572$	−2.99356e6	−0.382558
$573$	−1.46610e6	−0.186542
$574$	−3.87082e6	−0.490369
$575$	330625.	0.0417029
$576$	−959343.	−0.120481
$577$	1.24533e7	1.55720	0.778599	−	0.627522i	$-0.215931\pi$
$577$	1.24533e7	1.55720	0.778599	+	0.627522i	$0.215931\pi$
$578$	−4.64386e6	−0.578175
$579$	−731515.	−0.0906832
$580$	1.91940e6	0.236917
$581$	6.20805e6	0.762984
$582$	1.37584e6	0.168369
$583$	8.52185e6	1.03839
$584$	314702.	0.0381827
$585$	−4.66968e6	−0.564153
$586$	−4.52865e6	−0.544785
$587$	3.90424e6	0.467672	0.233836	−	0.972276i	$-0.424872\pi$
$587$	3.90424e6	0.467672	0.233836	+	0.972276i	$0.424872\pi$
$588$	−233661.	−0.0278703
$589$	3.57194e6	0.424244
$590$	1.00508e6	0.118870
$591$	1.85892e6	0.218923
$592$	−2.69464e6	−0.316007
$593$	−2.64803e6	−0.309233	−0.154617	−	0.987975i	$-0.549414\pi$
$593$	−2.64803e6	−0.309233	−0.154617	+	0.987975i	$0.549414\pi$
$594$	−1.32737e6	−0.154357
$595$	−5.92091e6	−0.685640
$596$	−7.20785e6	−0.831171
$597$	241985.	0.0277877
$598$	1.68752e6	0.192973
$599$	−7.39845e6	−0.842507	−0.421254	−	0.906943i	$-0.638410\pi$
$599$	−7.39845e6	−0.842507	−0.421254	+	0.906943i	$0.638410\pi$
$600$	118561.	0.0134451
$601$	1.04575e6	0.118098	0.0590490	−	0.998255i	$-0.481193\pi$
$601$	1.04575e6	0.118098	0.0590490	+	0.998255i	$0.481193\pi$
$602$	−4.37651e6	−0.492194
$603$	−1.32641e7	−1.48554
$604$	6.55991e6	0.731654
$605$	2.65031e6	0.294379
$606$	1.86699e6	0.206519
$607$	7.82522e6	0.862035	0.431018	−	0.902344i	$-0.358155\pi$
$607$	7.82522e6	0.862035	0.431018	+	0.902344i	$0.358155\pi$
$608$	−1.31774e6	−0.144568
$609$	−2.09681e6	−0.229095
$610$	835267.	0.0908868
$611$	−5.97706e6	−0.647716
$612$	6.02023e6	0.649732
$613$	1.20113e7	1.29104	0.645519	−	0.763744i	$-0.276641\pi$
$613$	1.20113e7	1.29104	0.645519	+	0.763744i	$0.276641\pi$
$614$	3.08656e6	0.330410
$615$	−486403.	−0.0518571
$616$	2.21352e6	0.235035
$617$	8.99246e6	0.950967	0.475483	−	0.879725i	$-0.342273\pi$
$617$	8.99246e6	0.950967	0.475483	+	0.879725i	$0.342273\pi$
$618$	348820.	0.0367392
$619$	7.28210e6	0.763889	0.381944	−	0.924185i	$-0.375255\pi$
$619$	7.28210e6	0.763889	0.381944	+	0.924185i	$0.375255\pi$
$620$	−1.11028e6	−0.115999
$621$	748260.	0.0778617
$622$	5.36639e6	0.556168
$623$	−1.06907e7	−1.10353
$624$	605141.	0.0622150
$625$	390625.	0.0400000
$626$	−8.93243e6	−0.911033
$627$	−894846.	−0.0909033
$628$	1.68829e6	0.170824
$629$	1.69098e7	1.70417
$630$	3.45290e6	0.346603
$631$	1.66750e7	1.66722	0.833611	−	0.552352i	$-0.186269\pi$
$631$	1.66750e7	1.66722	0.833611	+	0.552352i	$0.186269\pi$
$632$	5.17912e6	0.515778
$633$	−960346.	−0.0952617
$634$	6.40953e6	0.633291
$635$	−1.66554e6	−0.163915
$636$	−1.72267e6	−0.168873
$637$	−3.92930e6	−0.383678
$638$	4.50298e6	0.437974
$639$	−1.75439e7	−1.69971
$640$	409600.	0.0395285
$641$	1.31658e7	1.26561	0.632807	−	0.774309i	$-0.281903\pi$
$641$	1.31658e7	1.26561	0.632807	+	0.774309i	$0.281903\pi$
$642$	−2.38836e6	−0.228698
$643$	7.57027e6	0.722078	0.361039	−	0.932551i	$-0.382422\pi$
$643$	7.57027e6	0.722078	0.361039	+	0.932551i	$0.382422\pi$
$644$	−1.24780e6	−0.118558
$645$	−549948.	−0.0520502
$646$	8.26932e6	0.779630
$647$	1.47861e7	1.38865	0.694326	−	0.719661i	$-0.255703\pi$
$647$	1.47861e7	1.38865	0.694326	+	0.719661i	$0.255703\pi$
$648$	−3.37418e6	−0.315668
$649$	2.35796e6	0.219748
$650$	1.99376e6	0.185093
$651$	1.21290e6	0.112169
$652$	5.64621e6	0.520161
$653$	1.88068e7	1.72596	0.862982	−	0.505234i	$-0.168594\pi$
$653$	1.88068e7	1.72596	0.862982	+	0.505234i	$0.168594\pi$
$654$	1.80692e6	0.165194
$655$	7.23947e6	0.659331
$656$	−1.68040e6	−0.152459
$657$	1.15168e6	0.104093
$658$	4.41961e6	0.397941
$659$	1.80829e7	1.62201	0.811005	−	0.585039i	$-0.198921\pi$
$659$	1.80829e7	1.62201	0.811005	+	0.585039i	$0.198921\pi$
$660$	278149.	0.0248552
$661$	−9.97343e6	−0.887852	−0.443926	−	0.896063i	$-0.646415\pi$
$661$	−9.97343e6	−0.887852	−0.443926	+	0.896063i	$0.646415\pi$
$662$	−4.54722e6	−0.403275
$663$	−3.79748e6	−0.335515
$664$	2.69504e6	0.237217
$665$	4.74286e6	0.415897
$666$	−9.86130e6	−0.861487
$667$	−2.53841e6	−0.220926
$668$	−3.88260e6	−0.336652
$669$	−1.36548e6	−0.117956
$670$	5.66321e6	0.487389
$671$	1.95956e6	0.168017
$672$	−447459.	−0.0382235
$673$	−1.04689e7	−0.890968	−0.445484	−	0.895290i	$-0.646968\pi$
$673$	−1.04689e7	−0.890968	−0.445484	+	0.895290i	$0.646968\pi$
$674$	−2.59402e6	−0.219950
$675$	884050.	0.0746823
$676$	4.23553e6	0.356485
$677$	2.35650e6	0.197604	0.0988020	−	0.995107i	$-0.468499\pi$
$677$	2.35650e6	0.197604	0.0988020	+	0.995107i	$0.468499\pi$
$678$	−941795.	−0.0786832
$679$	−1.71079e7	−1.42404
$680$	−2.57039e6	−0.213170
$681$	4.50193e6	0.371990
$682$	−2.60476e6	−0.214441
$683$	9.69086e6	0.794896	0.397448	−	0.917625i	$-0.369896\pi$
$683$	9.69086e6	0.794896	0.397448	+	0.917625i	$0.369896\pi$
$684$	−4.82241e6	−0.394116
$685$	6.75435e6	0.549993
$686$	−7.00562e6	−0.568376
$687$	−923872.	−0.0746827
$688$	−1.89993e6	−0.153027
$689$	−2.89689e7	−2.32479
$690$	−156797.	−0.0125377
$691$	7.71127e6	0.614371	0.307185	−	0.951650i	$-0.400613\pi$
$691$	7.71127e6	0.614371	0.307185	+	0.951650i	$0.400613\pi$
$692$	−4.57452e6	−0.363145
$693$	8.10061e6	0.640744
$694$	1.00469e7	0.791833
$695$	−2.54647e6	−0.199975
$696$	−910268.	−0.0712272
$697$	1.05451e7	0.822186
$698$	3.27442e6	0.254387
$699$	−128995.	−0.00998572
$700$	−1.47425e6	−0.113717
$701$	8.37287e6	0.643546	0.321773	−	0.946817i	$-0.395721\pi$
$701$	8.37287e6	0.643546	0.321773	+	0.946817i	$0.395721\pi$
$702$	4.51222e6	0.345579
$703$	−1.35454e7	−1.03372
$704$	960936.	0.0730740
$705$	555364.	0.0420828
$706$	1.85054e7	1.39729
$707$	−2.32149e7	−1.74670
$708$	−476656.	−0.0357373
$709$	−3.19310e6	−0.238559	−0.119280	−	0.992861i	$-0.538059\pi$
$709$	−3.19310e6	−0.238559	−0.119280	+	0.992861i	$0.538059\pi$
$710$	7.49054e6	0.557657
$711$	1.89535e7	1.40610
$712$	−4.64105e6	−0.343097
$713$	1.46835e6	0.108170
$714$	2.80797e6	0.206133
$715$	4.67743e6	0.342170
$716$	−3.32994e6	−0.242747
$717$	−1.45127e6	−0.105427
$718$	−4.05313e6	−0.293413
$719$	−2.26047e7	−1.63071	−0.815356	−	0.578959i	$-0.803459\pi$
$719$	−2.26047e7	−1.63071	−0.815356	+	0.578959i	$0.803459\pi$
$720$	1.49897e6	0.107761
$721$	−4.33738e6	−0.310734
$722$	3.28038e6	0.234197
$723$	−620426.	−0.0441412
$724$	−6.59906e6	−0.467882
$725$	−2.99906e6	−0.211905
$726$	−1.25690e6	−0.0885030
$727$	−2.03585e7	−1.42860	−0.714299	−	0.699841i	$-0.753254\pi$
$727$	−2.03585e7	−1.42860	−0.714299	+	0.699841i	$0.753254\pi$
$728$	−7.52459e6	−0.526204
$729$	−1.13294e7	−0.789562
$730$	−491721.	−0.0341517
$731$	1.19228e7	0.825246
$732$	−396122.	−0.0273244
$733$	2.59412e7	1.78333	0.891663	−	0.452701i	$-0.149539\pi$
$733$	2.59412e7	1.78333	0.891663	+	0.452701i	$0.149539\pi$
$734$	9.33783e6	0.639744
$735$	365095.	0.0249280
$736$	−541696.	−0.0368605
$737$	1.32861e7	0.901007
$738$	−6.14960e6	−0.415629
$739$	6.63716e6	0.447066	0.223533	−	0.974696i	$-0.428241\pi$
$739$	6.63716e6	0.447066	0.223533	+	0.974696i	$0.428241\pi$
$740$	4.21037e6	0.282645
$741$	3.04192e6	0.203517
$742$	2.14205e7	1.42830
$743$	−1.02506e7	−0.681207	−0.340603	−	0.940207i	$-0.610631\pi$
$743$	−1.02506e7	−0.681207	−0.340603	+	0.940207i	$0.610631\pi$
$744$	526547.	0.0348742
$745$	1.12623e7	0.743422
$746$	5.87059e6	0.386220
$747$	9.86278e6	0.646693
$748$	−6.03022e6	−0.394075
$749$	2.96979e7	1.93429
$750$	−185252.	−0.0120257
$751$	−6.11090e6	−0.395371	−0.197686	−	0.980265i	$-0.563343\pi$
$751$	−6.11090e6	−0.395371	−0.197686	+	0.980265i	$0.563343\pi$
$752$	1.91864e6	0.123723
$753$	3.68946e6	0.237124
$754$	−1.53073e7	−0.980552
$755$	−1.02499e7	−0.654411
$756$	−3.33647e6	−0.212316
$757$	−7.56413e6	−0.479755	−0.239877	−	0.970803i	$-0.577107\pi$
$757$	−7.56413e6	−0.479755	−0.239877	+	0.970803i	$0.577107\pi$
$758$	1.44547e7	0.913766
$759$	−367852.	−0.0231776
$760$	2.05897e6	0.129305
$761$	2.55006e7	1.59620	0.798102	−	0.602522i	$-0.205838\pi$
$761$	2.55006e7	1.59620	0.798102	+	0.602522i	$0.205838\pi$
$762$	789874.	0.0492799
$763$	−2.24680e7	−1.39718
$764$	7.91405e6	0.490530
$765$	−9.40660e6	−0.581138
$766$	−1.52033e7	−0.936194
$767$	−8.01557e6	−0.491979
$768$	−194251.	−0.0118839
$769$	−9.54748e6	−0.582201	−0.291100	−	0.956692i	$-0.594021\pi$
$769$	−9.54748e6	−0.582201	−0.291100	+	0.956692i	$0.594021\pi$
$770$	−3.45863e6	−0.210222
$771$	2.75425e6	0.166866
$772$	3.94875e6	0.238461
$773$	−2.12468e6	−0.127893	−0.0639463	−	0.997953i	$-0.520369\pi$
$773$	−2.12468e6	−0.127893	−0.0639463	+	0.997953i	$0.520369\pi$
$774$	−6.95299e6	−0.417176
$775$	1.73482e6	0.103753
$776$	−7.42687e6	−0.442743
$777$	−4.59953e6	−0.273314
$778$	−1.96263e7	−1.16249
$779$	−8.44702e6	−0.498723
$780$	−945533.	−0.0556468
$781$	1.75731e7	1.03091
$782$	3.39934e6	0.198782
$783$	−6.78739e6	−0.395638
$784$	1.26131e6	0.0732878
$785$	−2.63796e6	−0.152789
$786$	−3.43329e6	−0.198223
$787$	−2.72330e6	−0.156732	−0.0783661	−	0.996925i	$-0.524970\pi$
$787$	−2.72330e6	−0.156732	−0.0783661	+	0.996925i	$0.524970\pi$
$788$	−1.00345e7	−0.575681
$789$	−4.43468e6	−0.253612
$790$	−8.09237e6	−0.461326
$791$	1.17107e7	0.665490
$792$	3.51664e6	0.199212
$793$	−6.66129e6	−0.376162
$794$	−6.57020e6	−0.369851
$795$	2.69168e6	0.151045
$796$	−1.30625e6	−0.0730706
$797$	1.57351e7	0.877455	0.438728	−	0.898620i	$-0.355429\pi$
$797$	1.57351e7	0.877455	0.438728	+	0.898620i	$0.355429\pi$
$798$	−2.24928e6	−0.125036
$799$	−1.20402e7	−0.667216
$800$	−640000.	−0.0353553
$801$	−1.69844e7	−0.935339
$802$	−1.46776e7	−0.805784
$803$	−1.15360e6	−0.0631342
$804$	−2.68575e6	−0.146530
$805$	1.94969e6	0.106041
$806$	8.85455e6	0.480097
$807$	−3.61213e6	−0.195245
$808$	−1.00781e7	−0.543062
$809$	−3.58237e7	−1.92442	−0.962208	−	0.272316i	$-0.912211\pi$
$809$	−3.58237e7	−1.92442	−0.962208	+	0.272316i	$0.912211\pi$
$810$	5.27216e6	0.282342
$811$	−2.05177e6	−0.109541	−0.0547706	−	0.998499i	$-0.517443\pi$
$811$	−2.05177e6	−0.109541	−0.0547706	+	0.998499i	$0.517443\pi$
$812$	1.13187e7	0.602428
$813$	−1.34654e6	−0.0714483
$814$	9.87768e6	0.522509
$815$	−8.82220e6	−0.465246
$816$	1.21900e6	0.0640880
$817$	−9.55055e6	−0.500580
$818$	−2.15911e6	−0.112822
$819$	−2.75370e7	−1.43452
$820$	2.62563e6	0.136363
$821$	1.07269e6	0.0555414	0.0277707	−	0.999614i	$-0.491159\pi$
$821$	1.07269e6	0.0555414	0.0277707	+	0.999614i	$0.491159\pi$
$822$	−3.20322e6	−0.165351
$823$	−1.41813e7	−0.729822	−0.364911	−	0.931042i	$-0.618901\pi$
$823$	−1.41813e7	−0.729822	−0.364911	+	0.931042i	$0.618901\pi$
$824$	−1.88294e6	−0.0966094
$825$	−434608.	−0.0222312
$826$	5.92695e6	0.302260
$827$	2.06129e7	1.04804	0.524018	−	0.851707i	$-0.324432\pi$
$827$	2.06129e7	1.04804	0.524018	+	0.851707i	$0.324432\pi$
$828$	−1.98239e6	−0.100488
$829$	489390.	0.0247326	0.0123663	−	0.999924i	$-0.496064\pi$
$829$	489390.	0.0247326	0.0123663	+	0.999924i	$0.496064\pi$
$830$	−4.21100e6	−0.212173
$831$	758268.	0.0380908
$832$	−3.26658e6	−0.163601
$833$	−7.91519e6	−0.395229
$834$	1.20765e6	0.0601210
$835$	6.06656e6	0.301111
$836$	4.83042e6	0.239039
$837$	3.92618e6	0.193712
$838$	2.29990e6	0.113135
$839$	−1.49768e7	−0.734539	−0.367269	−	0.930115i	$-0.619707\pi$
$839$	−1.49768e7	−0.734539	−0.367269	+	0.930115i	$0.619707\pi$
$840$	699155.	0.0341881
$841$	2.51448e6	0.122591
$842$	−1.94676e7	−0.946308
$843$	−254651.	−0.0123418
$844$	5.18399e6	0.250500
$845$	−6.61801e6	−0.318849
$846$	7.02147e6	0.337289
$847$	1.56288e7	0.748544
$848$	9.29907e6	0.444068
$849$	−5.62780e6	−0.267959
$850$	4.01623e6	0.190665
$851$	−5.56822e6	−0.263568
$852$	−3.55235e6	−0.167655
$853$	2.49247e7	1.17289	0.586446	−	0.809989i	$-0.300527\pi$
$853$	2.49247e7	1.17289	0.586446	+	0.809989i	$0.300527\pi$
$854$	4.92555e6	0.231106
$855$	7.53502e6	0.352508
$856$	1.28925e7	0.601384
$857$	−7.26039e6	−0.337682	−0.168841	−	0.985643i	$-0.554002\pi$
$857$	−7.26039e6	−0.337682	−0.168841	+	0.985643i	$0.554002\pi$
$858$	−2.21825e6	−0.102871
$859$	−2.73298e7	−1.26373	−0.631865	−	0.775079i	$-0.717710\pi$
$859$	−2.73298e7	−1.26373	−0.631865	+	0.775079i	$0.717710\pi$
$860$	2.96864e6	0.136871
$861$	−2.86831e6	−0.131862
$862$	1.18165e7	0.541651
$863$	−2.38536e7	−1.09025	−0.545127	−	0.838354i	$-0.683519\pi$
$863$	−2.38536e7	−1.09025	−0.545127	+	0.838354i	$0.683519\pi$
$864$	−1.44843e6	−0.0660104
$865$	7.14768e6	0.324807
$866$	2.95709e7	1.33989
$867$	−3.44114e6	−0.155473
$868$	−6.54731e6	−0.294961
$869$	−1.89850e7	−0.852827
$870$	1.42229e6	0.0637076
$871$	−4.51644e7	−2.01721
$872$	−9.75383e6	−0.434394
$873$	−2.71794e7	−1.20699
$874$	−2.72299e6	−0.120578
$875$	2.30351e6	0.101711
$876$	233197.	0.0102674
$877$	−1.64235e7	−0.721050	−0.360525	−	0.932750i	$-0.617402\pi$
$877$	−1.64235e7	−0.721050	−0.360525	+	0.932750i	$0.617402\pi$
$878$	−1.15280e7	−0.504680
$879$	−3.35577e6	−0.146494
$880$	−1.50146e6	−0.0653593
$881$	5.15209e6	0.223637	0.111819	−	0.993729i	$-0.464332\pi$
$881$	5.15209e6	0.223637	0.111819	+	0.993729i	$0.464332\pi$
$882$	4.61589e6	0.199795
$883$	3.28007e7	1.41573	0.707866	−	0.706346i	$-0.249658\pi$
$883$	3.28007e7	1.41573	0.707866	+	0.706346i	$0.249658\pi$
$884$	2.04990e7	0.882270
$885$	744775.	0.0319644
$886$	−2.58964e7	−1.10829
$887$	6.09094e6	0.259941	0.129971	−	0.991518i	$-0.458512\pi$
$887$	6.09094e6	0.259941	0.129971	+	0.991518i	$0.458512\pi$
$888$	−1.99675e6	−0.0849751
$889$	−9.82164e6	−0.416802
$890$	7.25164e6	0.306875
$891$	1.23687e7	0.521949
$892$	7.37091e6	0.310176
$893$	9.64461e6	0.404721
$894$	−5.34108e6	−0.223504
$895$	5.20303e6	0.217119
$896$	2.41540e6	0.100512
$897$	1.25047e6	0.0518909
$898$	−2.71725e7	−1.12445
$899$	−1.33192e7	−0.549642
$900$	−2.34214e6	−0.0963846
$901$	−5.83551e7	−2.39479
$902$	6.15981e6	0.252087
$903$	−3.24303e6	−0.132352
$904$	5.08385e6	0.206905
$905$	1.03110e7	0.418486
$906$	4.86095e6	0.196744
$907$	1.31981e7	0.532712	0.266356	−	0.963875i	$-0.414180\pi$
$907$	1.31981e7	0.532712	0.266356	+	0.963875i	$0.414180\pi$
$908$	−2.43016e7	−0.978184
$909$	−3.68817e7	−1.48048
$910$	1.17572e7	0.470651
$911$	−3.59681e7	−1.43589	−0.717946	−	0.696099i	$-0.754917\pi$
$911$	−3.59681e7	−1.43589	−0.717946	+	0.696099i	$0.754917\pi$
$912$	−976459.	−0.0388747
$913$	−9.87916e6	−0.392232
$914$	−1.08695e7	−0.430372
$915$	618940.	0.0244397
$916$	4.98710e6	0.196386
$917$	4.26910e7	1.67654
$918$	9.08942e6	0.355983
$919$	2.34478e7	0.915827	0.457914	−	0.888997i	$-0.348597\pi$
$919$	2.34478e7	0.915827	0.457914	+	0.888997i	$0.348597\pi$
$920$	846400.	0.0329690
$921$	2.28717e6	0.0888482
$922$	3.61056e7	1.39877
$923$	−5.97374e7	−2.30803
$924$	1.64024e6	0.0632015
$925$	−6.57871e6	−0.252805
$926$	9.27832e6	0.355584
$927$	−6.89082e6	−0.263373
$928$	4.91367e6	0.187299
$929$	−3.71881e7	−1.41373	−0.706863	−	0.707351i	$-0.749890\pi$
$929$	−3.71881e7	−1.41373	−0.706863	+	0.707351i	$0.749890\pi$
$930$	−822729.	−0.0311924
$931$	6.34034e6	0.239739
$932$	696320.	0.0262584
$933$	3.97654e6	0.149555
$934$	1.46801e7	0.550633
$935$	9.42222e6	0.352472
$936$	−1.19544e7	−0.446002
$937$	2.46209e7	0.916124	0.458062	−	0.888920i	$-0.348544\pi$
$937$	2.46209e7	0.916124	0.458062	+	0.888920i	$0.348544\pi$
$938$	3.33959e7	1.23933
$939$	−6.61901e6	−0.244979
$940$	−2.99788e6	−0.110661
$941$	−7.31579e6	−0.269332	−0.134666	−	0.990891i	$-0.542996\pi$
$941$	−7.31579e6	−0.269332	−0.134666	+	0.990891i	$0.542996\pi$
$942$	1.25104e6	0.0459350
$943$	−3.47239e6	−0.127160
$944$	2.57301e6	0.0939748
$945$	5.21323e6	0.189901
$946$	6.96454e6	0.253026
$947$	−3.14462e7	−1.13945	−0.569723	−	0.821837i	$-0.692949\pi$
$947$	−3.14462e7	−1.13945	−0.569723	+	0.821837i	$0.692949\pi$
$948$	3.83777e6	0.138694
$949$	3.92150e6	0.141347
$950$	−3.21714e6	−0.115654
$951$	4.74952e6	0.170294
$952$	−1.51575e7	−0.542046
$953$	4.36999e7	1.55865	0.779324	−	0.626621i	$-0.215563\pi$
$953$	4.36999e7	1.55865	0.779324	+	0.626621i	$0.215563\pi$
$954$	3.40309e7	1.21060
$955$	−1.23657e7	−0.438743
$956$	7.83404e6	0.277231
$957$	3.33675e6	0.117772
$958$	2.81812e7	0.992079
$959$	3.98303e7	1.39851
$960$	303517.	0.0106293
$961$	−2.09246e7	−0.730885
$962$	−3.35779e7	−1.16981
$963$	4.71813e7	1.63947
$964$	3.34909e6	0.116074
$965$	−6.16992e6	−0.213286
$966$	−924632.	−0.0318806
$967$	1.20059e7	0.412886	0.206443	−	0.978459i	$-0.433811\pi$
$967$	1.20059e7	0.412886	0.206443	+	0.978459i	$0.433811\pi$
$968$	6.78478e6	0.232727
$969$	6.12764e6	0.209645
$970$	1.16045e7	0.396001
$971$	1.05403e7	0.358760	0.179380	−	0.983780i	$-0.442591\pi$
$971$	1.05403e7	0.358760	0.179380	+	0.983780i	$0.442591\pi$
$972$	−7.99980e6	−0.271590
$973$	−1.50165e7	−0.508494
$974$	−5.75094e6	−0.194241
$975$	1.47739e6	0.0497720
$976$	2.13828e6	0.0718523
$977$	2.51063e6	0.0841483	0.0420742	−	0.999114i	$-0.486603\pi$
$977$	2.51063e6	0.0841483	0.0420742	+	0.999114i	$0.486603\pi$
$978$	4.18389e6	0.139873
$979$	1.70126e7	0.567302
$980$	−1.97080e6	−0.0655506
$981$	−3.56951e7	−1.18423
$982$	−1.56249e7	−0.517058
$983$	2.31997e7	0.765772	0.382886	−	0.923796i	$-0.374930\pi$
$983$	2.31997e7	0.765772	0.382886	+	0.923796i	$0.374930\pi$
$984$	−1.24519e6	−0.0409967
$985$	1.56790e7	0.514905
$986$	−3.08351e7	−1.01007
$987$	3.27497e6	0.107008
$988$	−1.64204e7	−0.535169
$989$	−3.92603e6	−0.127633
$990$	−5.49475e6	−0.178180
$991$	1.70288e7	0.550807	0.275403	−	0.961329i	$-0.411189\pi$
$991$	1.70288e7	0.550807	0.275403	+	0.961329i	$0.411189\pi$
$992$	−2.84232e6	−0.0917052
$993$	−3.36953e6	−0.108442
$994$	4.41716e7	1.41800
$995$	2.04101e6	0.0653563
$996$	1.99705e6	0.0637883
$997$	4.01656e7	1.27972	0.639862	−	0.768490i	$-0.278992\pi$
$997$	4.01656e7	1.27972	0.639862	+	0.768490i	$0.278992\pi$
$998$	3.19841e7	1.01650
$999$	−1.48887e7	−0.472002

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.6.a.g.1.2	✓	5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.6.a.g.1.2	✓	5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.00000 q^{2} -2.96404 q^{3} +16.0000 q^{4} -25.0000 q^{5} +11.8561 q^{6} -147.425 q^{7} -64.0000 q^{8} -234.214 q^{9} +O(q^{10})\)	\(q-4.00000 q^{2} -2.96404 q^{3} +16.0000 q^{4} -25.0000 q^{5} +11.8561 q^{6} -147.425 q^{7} -64.0000 q^{8} -234.214 q^{9} +100.000 q^{10} +234.603 q^{11} -47.4246 q^{12} -797.505 q^{13} +589.698 q^{14} +74.1009 q^{15} +256.000 q^{16} -1606.49 q^{17} +936.858 q^{18} +1286.86 q^{19} -400.000 q^{20} +436.972 q^{21} -938.414 q^{22} +529.000 q^{23} +189.698 q^{24} +625.000 q^{25} +3190.02 q^{26} +1414.48 q^{27} -2358.79 q^{28} -4798.50 q^{29} -296.404 q^{30} +2775.71 q^{31} -1024.00 q^{32} -695.373 q^{33} +6425.97 q^{34} +3685.61 q^{35} -3747.43 q^{36} -10525.9 q^{37} -5147.43 q^{38} +2363.83 q^{39} +1600.00 q^{40} -6564.06 q^{41} -1747.89 q^{42} -7421.61 q^{43} +3753.65 q^{44} +5855.36 q^{45} -2116.00 q^{46} +7494.70 q^{47} -758.793 q^{48} +4926.99 q^{49} -2500.00 q^{50} +4761.70 q^{51} -12760.1 q^{52} +36324.5 q^{53} -5657.92 q^{54} -5865.09 q^{55} +9435.17 q^{56} -3814.29 q^{57} +19194.0 q^{58} +10050.8 q^{59} +1185.61 q^{60} +8352.67 q^{61} -11102.8 q^{62} +34529.0 q^{63} +4096.00 q^{64} +19937.6 q^{65} +2781.49 q^{66} +56632.1 q^{67} -25703.9 q^{68} -1567.97 q^{69} -14742.5 q^{70} +74905.4 q^{71} +14989.7 q^{72} -4917.21 q^{73} +42103.7 q^{74} -1852.52 q^{75} +20589.7 q^{76} -34586.3 q^{77} -9455.33 q^{78} -80923.7 q^{79} -6400.00 q^{80} +52721.6 q^{81} +26256.3 q^{82} -42110.0 q^{83} +6991.55 q^{84} +40162.3 q^{85} +29686.4 q^{86} +14222.9 q^{87} -15014.6 q^{88} +72516.4 q^{89} -23421.4 q^{90} +117572. q^{91} +8464.00 q^{92} -8227.29 q^{93} -29978.8 q^{94} -32171.4 q^{95} +3035.17 q^{96} +116045. q^{97} -19708.0 q^{98} -54947.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 20 q^{2} + 5 q^{3} + 80 q^{4} - 125 q^{5} - 20 q^{6} + 130 q^{7} - 320 q^{8} + 334 q^{9}+O(q^{10}) \) 5 * q - 20 * q^2 + 5 * q^3 + 80 * q^4 - 125 * q^5 - 20 * q^6 + 130 * q^7 - 320 * q^8 + 334 * q^9	\( 5 q - 20 q^{2} + 5 q^{3} + 80 q^{4} - 125 q^{5} - 20 q^{6} + 130 q^{7} - 320 q^{8} + 334 q^{9} + 500 q^{10} + 81 q^{11} + 80 q^{12} - 753 q^{13} - 520 q^{14} - 125 q^{15} + 1280 q^{16} - 1780 q^{17} - 1336 q^{18} + 1933 q^{19} - 2000 q^{20} - 2526 q^{21} - 324 q^{22} + 2645 q^{23} - 320 q^{24} + 3125 q^{25} + 3012 q^{26} + 2972 q^{27} + 2080 q^{28} + 3527 q^{29} + 500 q^{30} + 1816 q^{31} - 5120 q^{32} - 21947 q^{33} + 7120 q^{34} - 3250 q^{35} + 5344 q^{36} + 11683 q^{37} - 7732 q^{38} + 12580 q^{39} + 8000 q^{40} - 9602 q^{41} + 10104 q^{42} - 2232 q^{43} + 1296 q^{44} - 8350 q^{45} - 10580 q^{46} - 14552 q^{47} + 1280 q^{48} + 25889 q^{49} - 12500 q^{50} + 31351 q^{51} - 12048 q^{52} - 23069 q^{53} - 11888 q^{54} - 2025 q^{55} - 8320 q^{56} + 95210 q^{57} - 14108 q^{58} + 43917 q^{59} - 2000 q^{60} + 107483 q^{61} - 7264 q^{62} + 119033 q^{63} + 20480 q^{64} + 18825 q^{65} + 87788 q^{66} + 133125 q^{67} - 28480 q^{68} + 2645 q^{69} + 13000 q^{70} + 103326 q^{71} - 21376 q^{72} + 125870 q^{73} - 46732 q^{74} + 3125 q^{75} + 30928 q^{76} + 110422 q^{77} - 50320 q^{78} + 274892 q^{79} - 32000 q^{80} + 316657 q^{81} + 38408 q^{82} + 106201 q^{83} - 40416 q^{84} + 44500 q^{85} + 8928 q^{86} + 23782 q^{87} - 5184 q^{88} + 57800 q^{89} + 33400 q^{90} + 272163 q^{91} + 42320 q^{92} + 198110 q^{93} + 58208 q^{94} - 48325 q^{95} - 5120 q^{96} - 24935 q^{97} - 103556 q^{98} + 362547 q^{99}+O(q^{100}) \) 5 * q - 20 * q^2 + 5 * q^3 + 80 * q^4 - 125 * q^5 - 20 * q^6 + 130 * q^7 - 320 * q^8 + 334 * q^9 + 500 * q^10 + 81 * q^11 + 80 * q^12 - 753 * q^13 - 520 * q^14 - 125 * q^15 + 1280 * q^16 - 1780 * q^17 - 1336 * q^18 + 1933 * q^19 - 2000 * q^20 - 2526 * q^21 - 324 * q^22 + 2645 * q^23 - 320 * q^24 + 3125 * q^25 + 3012 * q^26 + 2972 * q^27 + 2080 * q^28 + 3527 * q^29 + 500 * q^30 + 1816 * q^31 - 5120 * q^32 - 21947 * q^33 + 7120 * q^34 - 3250 * q^35 + 5344 * q^36 + 11683 * q^37 - 7732 * q^38 + 12580 * q^39 + 8000 * q^40 - 9602 * q^41 + 10104 * q^42 - 2232 * q^43 + 1296 * q^44 - 8350 * q^45 - 10580 * q^46 - 14552 * q^47 + 1280 * q^48 + 25889 * q^49 - 12500 * q^50 + 31351 * q^51 - 12048 * q^52 - 23069 * q^53 - 11888 * q^54 - 2025 * q^55 - 8320 * q^56 + 95210 * q^57 - 14108 * q^58 + 43917 * q^59 - 2000 * q^60 + 107483 * q^61 - 7264 * q^62 + 119033 * q^63 + 20480 * q^64 + 18825 * q^65 + 87788 * q^66 + 133125 * q^67 - 28480 * q^68 + 2645 * q^69 + 13000 * q^70 + 103326 * q^71 - 21376 * q^72 + 125870 * q^73 - 46732 * q^74 + 3125 * q^75 + 30928 * q^76 + 110422 * q^77 - 50320 * q^78 + 274892 * q^79 - 32000 * q^80 + 316657 * q^81 + 38408 * q^82 + 106201 * q^83 - 40416 * q^84 + 44500 * q^85 + 8928 * q^86 + 23782 * q^87 - 5184 * q^88 + 57800 * q^89 + 33400 * q^90 + 272163 * q^91 + 42320 * q^92 + 198110 * q^93 + 58208 * q^94 - 48325 * q^95 - 5120 * q^96 - 24935 * q^97 - 103556 * q^98 + 362547 * q^99

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