LMFDB - Embedded newform 165.6.a.g.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [165,6,Mod(1,165)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(165, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("165.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 165 = 3 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	165.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:	$26.4633302691$
Analytic rank:	$1$
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} - x^{4} - 143x^{3} + 71x^{2} + 4216x - 3740 $ x^5 - x^4 - 143x^3 + 71x^2 + 4216*x - 3740
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-9.46271$ of defining polynomial
Character	$\chi$	$=$	165.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+9.46271 q^{2} -9.00000 q^{3} +57.5429 q^{4} -25.0000 q^{5} -85.1644 q^{6} -112.299 q^{7} +241.706 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+9.46271 q^{2} -9.00000 q^{3} +57.5429 q^{4} -25.0000 q^{5} -85.1644 q^{6} -112.299 q^{7} +241.706 q^{8} +81.0000 q^{9} -236.568 q^{10} -121.000 q^{11} -517.887 q^{12} -648.794 q^{13} -1062.65 q^{14} +225.000 q^{15} +445.816 q^{16} +1348.51 q^{17} +766.480 q^{18} -2867.47 q^{19} -1438.57 q^{20} +1010.69 q^{21} -1144.99 q^{22} -3743.93 q^{23} -2175.35 q^{24} +625.000 q^{25} -6139.35 q^{26} -729.000 q^{27} -6461.99 q^{28} +5855.76 q^{29} +2129.11 q^{30} -8298.66 q^{31} -3515.95 q^{32} +1089.00 q^{33} +12760.5 q^{34} +2807.46 q^{35} +4660.98 q^{36} +14919.6 q^{37} -27134.0 q^{38} +5839.15 q^{39} -6042.64 q^{40} +2265.88 q^{41} +9563.84 q^{42} +5071.47 q^{43} -6962.70 q^{44} -2025.00 q^{45} -35427.8 q^{46} -11106.0 q^{47} -4012.35 q^{48} -4196.05 q^{49} +5914.20 q^{50} -12136.6 q^{51} -37333.5 q^{52} -23344.7 q^{53} -6898.32 q^{54} +3025.00 q^{55} -27143.2 q^{56} +25807.2 q^{57} +55411.4 q^{58} +27290.1 q^{59} +12947.2 q^{60} +32700.8 q^{61} -78527.8 q^{62} -9096.18 q^{63} -47536.5 q^{64} +16219.9 q^{65} +10304.9 q^{66} -13606.6 q^{67} +77597.1 q^{68} +33695.4 q^{69} +26566.2 q^{70} +43172.8 q^{71} +19578.2 q^{72} -89295.2 q^{73} +141180. q^{74} -5625.00 q^{75} -165003. q^{76} +13588.1 q^{77} +55254.2 q^{78} +54655.2 q^{79} -11145.4 q^{80} +6561.00 q^{81} +21441.4 q^{82} +120570. q^{83} +58157.9 q^{84} -33712.7 q^{85} +47989.9 q^{86} -52701.9 q^{87} -29246.4 q^{88} +35614.7 q^{89} -19162.0 q^{90} +72858.6 q^{91} -215437. q^{92} +74687.9 q^{93} -105093. q^{94} +71686.8 q^{95} +31643.5 q^{96} -16522.4 q^{97} -39706.0 q^{98} -9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9}+O(q^{10}) $ 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9	\( 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9} + 25 q^{10} - 605 q^{11} - 1143 q^{12} - 926 q^{13} + 368 q^{14} + 1125 q^{15} + 1891 q^{16} - 246 q^{17} - 81 q^{18} + 3420 q^{19} - 3175 q^{20} - 1044 q^{21} + 121 q^{22} - 4244 q^{23} + 1377 q^{24} + 3125 q^{25} - 8862 q^{26} - 3645 q^{27} - 4904 q^{28} - 2922 q^{29} - 225 q^{30} - 6112 q^{31} - 24757 q^{32} + 5445 q^{33} + 10866 q^{34} - 2900 q^{35} + 10287 q^{36} + 6654 q^{37} - 45692 q^{38} + 8334 q^{39} + 3825 q^{40} - 14934 q^{41} - 3312 q^{42} + 10804 q^{43} - 15367 q^{44} - 10125 q^{45} - 101500 q^{46} - 41460 q^{47} - 17019 q^{48} - 12099 q^{49} - 625 q^{50} + 2214 q^{51} - 97742 q^{52} - 62398 q^{53} + 729 q^{54} + 15125 q^{55} - 74368 q^{56} - 30780 q^{57} - 27822 q^{58} + 8524 q^{59} + 28575 q^{60} + 59010 q^{61} - 142624 q^{62} + 9396 q^{63} + 13799 q^{64} + 23150 q^{65} - 1089 q^{66} - 15772 q^{67} - 83686 q^{68} + 38196 q^{69} - 9200 q^{70} + 88124 q^{71} - 12393 q^{72} - 118358 q^{73} + 67194 q^{74} - 28125 q^{75} + 100668 q^{76} - 14036 q^{77} + 79758 q^{78} + 57324 q^{79} - 47275 q^{80} + 32805 q^{81} + 29102 q^{82} - 7268 q^{83} + 44136 q^{84} + 6150 q^{85} - 35288 q^{86} + 26298 q^{87} + 18513 q^{88} + 72978 q^{89} + 2025 q^{90} - 1464 q^{91} + 62148 q^{92} + 55008 q^{93} + 344836 q^{94} - 85500 q^{95} + 222813 q^{96} - 59174 q^{97} + 272767 q^{98} - 49005 q^{99}+O(q^{100}) \) 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9 + 25 * q^10 - 605 * q^11 - 1143 * q^12 - 926 * q^13 + 368 * q^14 + 1125 * q^15 + 1891 * q^16 - 246 * q^17 - 81 * q^18 + 3420 * q^19 - 3175 * q^20 - 1044 * q^21 + 121 * q^22 - 4244 * q^23 + 1377 * q^24 + 3125 * q^25 - 8862 * q^26 - 3645 * q^27 - 4904 * q^28 - 2922 * q^29 - 225 * q^30 - 6112 * q^31 - 24757 * q^32 + 5445 * q^33 + 10866 * q^34 - 2900 * q^35 + 10287 * q^36 + 6654 * q^37 - 45692 * q^38 + 8334 * q^39 + 3825 * q^40 - 14934 * q^41 - 3312 * q^42 + 10804 * q^43 - 15367 * q^44 - 10125 * q^45 - 101500 * q^46 - 41460 * q^47 - 17019 * q^48 - 12099 * q^49 - 625 * q^50 + 2214 * q^51 - 97742 * q^52 - 62398 * q^53 + 729 * q^54 + 15125 * q^55 - 74368 * q^56 - 30780 * q^57 - 27822 * q^58 + 8524 * q^59 + 28575 * q^60 + 59010 * q^61 - 142624 * q^62 + 9396 * q^63 + 13799 * q^64 + 23150 * q^65 - 1089 * q^66 - 15772 * q^67 - 83686 * q^68 + 38196 * q^69 - 9200 * q^70 + 88124 * q^71 - 12393 * q^72 - 118358 * q^73 + 67194 * q^74 - 28125 * q^75 + 100668 * q^76 - 14036 * q^77 + 79758 * q^78 + 57324 * q^79 - 47275 * q^80 + 32805 * q^81 + 29102 * q^82 - 7268 * q^83 + 44136 * q^84 + 6150 * q^85 - 35288 * q^86 + 26298 * q^87 + 18513 * q^88 + 72978 * q^89 + 2025 * q^90 - 1464 * q^91 + 62148 * q^92 + 55008 * q^93 + 344836 * q^94 - 85500 * q^95 + 222813 * q^96 - 59174 * q^97 + 272767 * q^98 - 49005 * 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 $

$2$	9.46271	1.67279	0.836394	−	0.548129i	$-0.184660\pi$
$2$	9.46271	1.67279	0.836394	+	0.548129i	$0.184660\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	57.5429	1.79822
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−85.1644	−0.965784
$7$	−112.299	−0.866221	−0.433111	−	0.901341i	$-0.642584\pi$
$7$	−112.299	−0.866221	−0.433111	+	0.901341i	$0.642584\pi$
$8$	241.706	1.33525
$9$	81.0000	0.333333
$10$	−236.568	−0.748093
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−517.887	−1.03820
$13$	−648.794	−1.06475	−0.532376	−	0.846508i	$-0.678701\pi$
$13$	−648.794	−1.06475	−0.532376	+	0.846508i	$0.678701\pi$
$14$	−1062.65	−1.44900
$15$	225.000	0.258199
$16$	445.816	0.435368
$17$	1348.51	1.13170	0.565850	−	0.824508i	$-0.308548\pi$
$17$	1348.51	1.13170	0.565850	+	0.824508i	$0.308548\pi$
$18$	766.480	0.557596
$19$	−2867.47	−1.82228	−0.911140	−	0.412098i	$-0.864796\pi$
$19$	−2867.47	−1.82228	−0.911140	+	0.412098i	$0.864796\pi$
$20$	−1438.57	−0.804187
$21$	1010.69	0.500113
$22$	−1144.99	−0.504364
$23$	−3743.93	−1.47574	−0.737868	−	0.674946i	$-0.764167\pi$
$23$	−3743.93	−1.47574	−0.737868	+	0.674946i	$0.764167\pi$
$24$	−2175.35	−0.770905
$25$	625.000	0.200000
$26$	−6139.35	−1.78110
$27$	−729.000	−0.192450
$28$	−6461.99	−1.55765
$29$	5855.76	1.29297	0.646485	−	0.762927i	$-0.276238\pi$
$29$	5855.76	1.29297	0.646485	+	0.762927i	$0.276238\pi$
$30$	2129.11	0.431912
$31$	−8298.66	−1.55097	−0.775486	−	0.631365i	$-0.782495\pi$
$31$	−8298.66	−1.55097	−0.775486	+	0.631365i	$0.782495\pi$
$32$	−3515.95	−0.606970
$33$	1089.00	0.174078
$34$	12760.5	1.89309
$35$	2807.46	0.387386
$36$	4660.98	0.599406
$37$	14919.6	1.79165	0.895823	−	0.444410i	$-0.146587\pi$
$37$	14919.6	1.79165	0.895823	+	0.444410i	$0.146587\pi$
$38$	−27134.0	−3.04829
$39$	5839.15	0.614735
$40$	−6042.64	−0.597141
$41$	2265.88	0.210512	0.105256	−	0.994445i	$-0.466434\pi$
$41$	2265.88	0.210512	0.105256	+	0.994445i	$0.466434\pi$
$42$	9563.84	0.836583
$43$	5071.47	0.418276	0.209138	−	0.977886i	$-0.432934\pi$
$43$	5071.47	0.418276	0.209138	+	0.977886i	$0.432934\pi$
$44$	−6962.70	−0.542183
$45$	−2025.00	−0.149071
$46$	−35427.8	−2.46859
$47$	−11106.0	−0.733351	−0.366676	−	0.930349i	$-0.619504\pi$
$47$	−11106.0	−0.733351	−0.366676	+	0.930349i	$0.619504\pi$
$48$	−4012.35	−0.251360
$49$	−4196.05	−0.249661
$50$	5914.20	0.334557
$51$	−12136.6	−0.653387
$52$	−37333.5	−1.91466
$53$	−23344.7	−1.14156	−0.570781	−	0.821103i	$-0.693359\pi$
$53$	−23344.7	−1.14156	−0.570781	+	0.821103i	$0.693359\pi$
$54$	−6898.32	−0.321928
$55$	3025.00	0.134840
$56$	−27143.2	−1.15662
$57$	25807.2	1.05209
$58$	55411.4	2.16286
$59$	27290.1	1.02064	0.510322	−	0.859983i	$-0.329526\pi$
$59$	27290.1	1.02064	0.510322	+	0.859983i	$0.329526\pi$
$60$	12947.2	0.464298
$61$	32700.8	1.12521	0.562605	−	0.826726i	$-0.309799\pi$
$61$	32700.8	1.12521	0.562605	+	0.826726i	$0.309799\pi$
$62$	−78527.8	−2.59444
$63$	−9096.18	−0.288740
$64$	−47536.5	−1.45070
$65$	16219.9	0.476172
$66$	10304.9	0.291195
$67$	−13606.6	−0.370308	−0.185154	−	0.982710i	$-0.559278\pi$
$67$	−13606.6	−0.370308	−0.185154	+	0.982710i	$0.559278\pi$
$68$	77597.1	2.03504
$69$	33695.4	0.852016
$70$	26566.2	0.648014
$71$	43172.8	1.01640	0.508200	−	0.861239i	$-0.330311\pi$
$71$	43172.8	1.01640	0.508200	+	0.861239i	$0.330311\pi$
$72$	19578.2	0.445082
$73$	−89295.2	−1.96120	−0.980598	−	0.196032i	$-0.937194\pi$
$73$	−89295.2	−1.96120	−0.980598	+	0.196032i	$0.937194\pi$
$74$	141180.	2.99704
$75$	−5625.00	−0.115470
$76$	−165003.	−3.27685
$77$	13588.1	0.261176
$78$	55254.2	1.02832
$79$	54655.2	0.985289	0.492644	−	0.870231i	$-0.336030\pi$
$79$	54655.2	0.985289	0.492644	+	0.870231i	$0.336030\pi$
$80$	−11145.4	−0.194702
$81$	6561.00	0.111111
$82$	21441.4	0.352142
$83$	120570.	1.92108	0.960540	−	0.278142i	$-0.0897185\pi$
$83$	120570.	1.92108	0.960540	+	0.278142i	$0.0897185\pi$
$84$	58157.9	0.899312
$85$	−33712.7	−0.506111
$86$	47989.9	0.699687
$87$	−52701.9	−0.746497
$88$	−29246.4	−0.402592
$89$	35614.7	0.476600	0.238300	−	0.971192i	$-0.423410\pi$
$89$	35614.7	0.476600	0.238300	+	0.971192i	$0.423410\pi$
$90$	−19162.0	−0.249364
$91$	72858.6	0.922311
$92$	−215437.	−2.65369
$93$	74687.9	0.895454
$94$	−105093.	−1.22674
$95$	71686.8	0.814948
$96$	31643.5	0.350434
$97$	−16522.4	−0.178297	−0.0891485	−	0.996018i	$-0.528415\pi$
$97$	−16522.4	−0.178297	−0.0891485	+	0.996018i	$0.528415\pi$
$98$	−39706.0	−0.417629
$99$	−9801.00	−0.100504
$100$	35964.3	0.359643
$101$	−100164.	−0.977028	−0.488514	−	0.872556i	$-0.662461\pi$
$101$	−100164.	−0.977028	−0.488514	+	0.872556i	$0.662461\pi$
$102$	−114845.	−1.09298
$103$	−11112.8	−0.103212	−0.0516059	−	0.998668i	$-0.516434\pi$
$103$	−11112.8	−0.103212	−0.0516059	+	0.998668i	$0.516434\pi$
$104$	−156817.	−1.42171
$105$	−25267.2	−0.223657
$106$	−220905.	−1.90959
$107$	−229112.	−1.93458	−0.967292	−	0.253665i	$-0.918364\pi$
$107$	−229112.	−1.93458	−0.967292	+	0.253665i	$0.918364\pi$
$108$	−41948.8	−0.346067
$109$	32296.0	0.260365	0.130182	−	0.991490i	$-0.458444\pi$
$109$	32296.0	0.260365	0.130182	+	0.991490i	$0.458444\pi$
$110$	28624.7	0.225559
$111$	−134276.	−1.03441
$112$	−50064.5	−0.377125
$113$	106328.	0.783341	0.391671	−	0.920106i	$-0.371897\pi$
$113$	106328.	0.783341	0.391671	+	0.920106i	$0.371897\pi$
$114$	244206.	1.75993
$115$	93598.3	0.659969
$116$	336958.	2.32504
$117$	−52552.3	−0.354917
$118$	258238.	1.70732
$119$	−151435.	−0.980302
$120$	54383.8	0.344759
$121$	14641.0	0.0909091
$122$	309438.	1.88224
$123$	−20392.9	−0.121539
$124$	−477529.	−2.78898
$125$	−15625.0	−0.0894427
$126$	−86074.5	−0.483001
$127$	56641.4	0.311619	0.155810	−	0.987787i	$-0.450201\pi$
$127$	56641.4	0.311619	0.155810	+	0.987787i	$0.450201\pi$
$128$	−337314.	−1.81974
$129$	−45643.2	−0.241492
$130$	153484.	0.796534
$131$	−175193.	−0.891947	−0.445973	−	0.895046i	$-0.647142\pi$
$131$	−175193.	−0.891947	−0.445973	+	0.895046i	$0.647142\pi$
$132$	62664.3	0.313029
$133$	322013.	1.57850
$134$	−128756.	−0.619447
$135$	18225.0	0.0860663
$136$	325942.	1.51110
$137$	11120.6	0.0506204	0.0253102	−	0.999680i	$-0.491943\pi$
$137$	11120.6	0.0506204	0.0253102	+	0.999680i	$0.491943\pi$
$138$	318850.	1.42524
$139$	−137839.	−0.605109	−0.302555	−	0.953132i	$-0.597840\pi$
$139$	−137839.	−0.605109	−0.302555	+	0.953132i	$0.597840\pi$
$140$	161550.	0.696604
$141$	99953.7	0.423400
$142$	408532.	1.70022
$143$	78504.1	0.321035
$144$	36111.1	0.145123
$145$	−146394.	−0.578234
$146$	−844975.	−3.28066
$147$	37764.4	0.144142
$148$	858517.	3.22177
$149$	−54653.5	−0.201675	−0.100838	−	0.994903i	$-0.532152\pi$
$149$	−54653.5	−0.201675	−0.100838	+	0.994903i	$0.532152\pi$
$150$	−53227.8	−0.193157
$151$	233622.	0.833817	0.416909	−	0.908948i	$-0.363114\pi$
$151$	233622.	0.833817	0.416909	+	0.908948i	$0.363114\pi$
$152$	−693084.	−2.43319
$153$	109229.	0.377233
$154$	128580.	0.436891
$155$	207467.	0.693615
$156$	336002.	1.10543
$157$	100987.	0.326976	0.163488	−	0.986545i	$-0.447726\pi$
$157$	100987.	0.326976	0.163488	+	0.986545i	$0.447726\pi$
$158$	517186.	1.64818
$159$	210103.	0.659081
$160$	87898.6	0.271445
$161$	420438.	1.27831
$162$	62084.9	0.185865
$163$	−206753.	−0.609514	−0.304757	−	0.952430i	$-0.598575\pi$
$163$	−206753.	−0.609514	−0.304757	+	0.952430i	$0.598575\pi$
$164$	130386.	0.378547
$165$	−27225.0	−0.0778499
$166$	1.14092e6	3.21356
$167$	−320361.	−0.888892	−0.444446	−	0.895806i	$-0.646599\pi$
$167$	−320361.	−0.888892	−0.444446	+	0.895806i	$0.646599\pi$
$168$	244289.	0.667775
$169$	49640.8	0.133697
$170$	−319014.	−0.846617
$171$	−232265.	−0.607426
$172$	291827.	0.752151
$173$	910.609	0.00231322	0.00115661	−	0.999999i	$-0.499632\pi$
$173$	910.609	0.00231322	0.00115661	+	0.999999i	$0.499632\pi$
$174$	−498703.	−1.24873
$175$	−70186.6	−0.173244
$176$	−53943.8	−0.131268
$177$	−245611.	−0.589270
$178$	337011.	0.797250
$179$	−86236.3	−0.201167	−0.100584	−	0.994929i	$-0.532071\pi$
$179$	−86236.3	−0.201167	−0.100584	+	0.994929i	$0.532071\pi$
$180$	−116524.	−0.268062
$181$	−233433.	−0.529622	−0.264811	−	0.964300i	$-0.585310\pi$
$181$	−233433.	−0.529622	−0.264811	+	0.964300i	$0.585310\pi$
$182$	689440.	1.54283
$183$	−294307.	−0.649640
$184$	−904929.	−1.97047
$185$	−372990.	−0.801249
$186$	706751.	1.49790
$187$	−163169.	−0.341220
$188$	−639070.	−1.31872
$189$	81865.6	0.166704
$190$	678351.	1.36323
$191$	−790492.	−1.56789	−0.783943	−	0.620833i	$-0.786794\pi$
$191$	−790492.	−1.56789	−0.783943	+	0.620833i	$0.786794\pi$
$192$	427829.	0.837562
$193$	53420.1	0.103231	0.0516156	−	0.998667i	$-0.483563\pi$
$193$	53420.1	0.103231	0.0516156	+	0.998667i	$0.483563\pi$
$194$	−156347.	−0.298253
$195$	−145979.	−0.274918
$196$	−241453.	−0.448944
$197$	−735355.	−1.34999	−0.674997	−	0.737821i	$-0.735855\pi$
$197$	−735355.	−1.34999	−0.674997	+	0.737821i	$0.735855\pi$
$198$	−92744.1	−0.168121
$199$	636293.	1.13900	0.569501	−	0.821991i	$-0.307136\pi$
$199$	636293.	1.13900	0.569501	+	0.821991i	$0.307136\pi$
$200$	151066.	0.267049
$201$	122460.	0.213797
$202$	−947821.	−1.63436
$203$	−657593.	−1.12000
$204$	−698374.	−1.17493
$205$	−56647.0	−0.0941440
$206$	−105157.	−0.172651
$207$	−303259.	−0.491912
$208$	−289243.	−0.463559
$209$	346964.	0.549438
$210$	−239096.	−0.374131
$211$	−704627.	−1.08956	−0.544782	−	0.838578i	$-0.683388\pi$
$211$	−704627.	−1.08956	−0.544782	+	0.838578i	$0.683388\pi$
$212$	−1.34332e6	−2.05278
$213$	−388555.	−0.586818
$214$	−2.16802e6	−3.23615
$215$	−126787.	−0.187059
$216$	−176203.	−0.256968
$217$	931927.	1.34348
$218$	305607.	0.435535
$219$	803656.	1.13230
$220$	174067.	0.242472
$221$	−874904.	−1.20498
$222$	−1.27062e6	−1.73034
$223$	−393682.	−0.530132	−0.265066	−	0.964230i	$-0.585394\pi$
$223$	−393682.	−0.530132	−0.265066	+	0.964230i	$0.585394\pi$
$224$	394835.	0.525770
$225$	50625.0	0.0666667
$226$	1.00615e6	1.31036
$227$	−1.44133e6	−1.85652	−0.928261	−	0.371929i	$-0.878697\pi$
$227$	−1.44133e6	−1.85652	−0.928261	+	0.371929i	$0.878697\pi$
$228$	1.48502e6	1.89189
$229$	−619133.	−0.780181	−0.390091	−	0.920776i	$-0.627556\pi$
$229$	−619133.	−0.780181	−0.390091	+	0.920776i	$0.627556\pi$
$230$	885694.	1.10399
$231$	−122293.	−0.150790
$232$	1.41537e6	1.72643
$233$	−586616.	−0.707887	−0.353943	−	0.935267i	$-0.615159\pi$
$233$	−586616.	−0.707887	−0.353943	+	0.935267i	$0.615159\pi$
$234$	−497288.	−0.593701
$235$	277649.	0.327965
$236$	1.57035e6	1.83534
$237$	−491896.	−0.568857
$238$	−1.43299e6	−1.63984
$239$	1.36791e6	1.54904	0.774521	−	0.632548i	$-0.217991\pi$
$239$	1.36791e6	1.54904	0.774521	+	0.632548i	$0.217991\pi$
$240$	100309.	0.112411
$241$	−302011.	−0.334950	−0.167475	−	0.985876i	$-0.553561\pi$
$241$	−302011.	−0.334950	−0.167475	+	0.985876i	$0.553561\pi$
$242$	138544.	0.152072
$243$	−59049.0	−0.0641500
$244$	1.88170e6	2.02337
$245$	104901.	0.111652
$246$	−192972.	−0.203309
$247$	1.86040e6	1.94028
$248$	−2.00583e6	−2.07093
$249$	−1.08513e6	−1.10914
$250$	−147855.	−0.149619
$251$	−603365.	−0.604499	−0.302250	−	0.953229i	$-0.597738\pi$
$251$	−603365.	−0.604499	−0.302250	+	0.953229i	$0.597738\pi$
$252$	−523421.	−0.519218
$253$	453016.	0.444951
$254$	535981.	0.521273
$255$	303414.	0.292204
$256$	−1.67074e6	−1.59334
$257$	−233950.	−0.220948	−0.110474	−	0.993879i	$-0.535237\pi$
$257$	−233950.	−0.220948	−0.110474	+	0.993879i	$0.535237\pi$
$258$	−431909.	−0.403964
$259$	−1.67545e6	−1.55196
$260$	933338.	0.856260
$261$	474317.	0.430990
$262$	−1.65780e6	−1.49204
$263$	507997.	0.452868	0.226434	−	0.974027i	$-0.427293\pi$
$263$	507997.	0.452868	0.226434	+	0.974027i	$0.427293\pi$
$264$	263217.	0.232437
$265$	583618.	0.510522
$266$	3.04711e6	2.64049
$267$	−320532.	−0.275165
$268$	−782965.	−0.665894
$269$	−695260.	−0.585823	−0.292912	−	0.956140i	$-0.594624\pi$
$269$	−695260.	−0.585823	−0.292912	+	0.956140i	$0.594624\pi$
$270$	172458.	0.143971
$271$	2.40572e6	1.98985	0.994927	−	0.100604i	$-0.0320775\pi$
$271$	2.40572e6	1.98985	0.994927	+	0.100604i	$0.0320775\pi$
$272$	601187.	0.492705
$273$	−655727.	−0.532496
$274$	105231.	0.0846772
$275$	−75625.0	−0.0603023
$276$	1.93893e6	1.53211
$277$	975903.	0.764200	0.382100	−	0.924121i	$-0.375201\pi$
$277$	975903.	0.764200	0.382100	+	0.924121i	$0.375201\pi$
$278$	−1.30433e6	−1.01222
$279$	−672191.	−0.516990
$280$	678579.	0.517256
$281$	605666.	0.457580	0.228790	−	0.973476i	$-0.426523\pi$
$281$	605666.	0.457580	0.228790	+	0.973476i	$0.426523\pi$
$282$	945834.	0.708259
$283$	−1.34478e6	−0.998126	−0.499063	−	0.866566i	$-0.666322\pi$
$283$	−1.34478e6	−0.998126	−0.499063	+	0.866566i	$0.666322\pi$
$284$	2.48429e6	1.82771
$285$	−645181.	−0.470510
$286$	742862.	0.537023
$287$	−254455.	−0.182350
$288$	−284792.	−0.202323
$289$	398616.	0.280744
$290$	−1.38529e6	−0.967262
$291$	148702.	0.102940
$292$	−5.13831e6	−3.52665
$293$	−1.69403e6	−1.15280	−0.576399	−	0.817168i	$-0.695543\pi$
$293$	−1.69403e6	−1.15280	−0.576399	+	0.817168i	$0.695543\pi$
$294$	357354.	0.241118
$295$	−682252.	−0.456446
$296$	3.60615e6	2.39229
$297$	88209.0	0.0580259
$298$	−517171.	−0.337360
$299$	2.42904e6	1.57129
$300$	−323679.	−0.207640
$301$	−569519.	−0.362319
$302$	2.21070e6	1.39480
$303$	901474.	0.564087
$304$	−1.27837e6	−0.793361
$305$	−817519.	−0.503209
$306$	1.03360e6	0.631031
$307$	−2.34161e6	−1.41797	−0.708986	−	0.705222i	$-0.750847\pi$
$307$	−2.34161e6	−1.41797	−0.708986	+	0.705222i	$0.750847\pi$
$308$	781900.	0.469650
$309$	100015.	0.0595894
$310$	1.96320e6	1.16027
$311$	−1.09707e6	−0.643182	−0.321591	−	0.946879i	$-0.604218\pi$
$311$	−1.09707e6	−0.643182	−0.321591	+	0.946879i	$0.604218\pi$
$312$	1.41135e6	0.820823
$313$	−1.94983e6	−1.12496	−0.562478	−	0.826812i	$-0.690152\pi$
$313$	−1.94983e6	−1.12496	−0.562478	+	0.826812i	$0.690152\pi$
$314$	955609.	0.546960
$315$	227404.	0.129129
$316$	3.14502e6	1.77176
$317$	−568478.	−0.317736	−0.158868	−	0.987300i	$-0.550784\pi$
$317$	−568478.	−0.317736	−0.158868	+	0.987300i	$0.550784\pi$
$318$	1.98814e6	1.10250
$319$	−708547.	−0.389845
$320$	1.18841e6	0.648772
$321$	2.06200e6	1.11693
$322$	3.97848e6	2.13835
$323$	−3.86681e6	−2.06227
$324$	377539.	0.199802
$325$	−405496.	−0.212950
$326$	−1.95645e6	−1.01959
$327$	−290664.	−0.150322
$328$	547676.	0.281086
$329$	1.24718e6	0.635244
$330$	−257622.	−0.130226
$331$	1.45692e6	0.730911	0.365455	−	0.930829i	$-0.380913\pi$
$331$	1.45692e6	0.730911	0.365455	+	0.930829i	$0.380913\pi$
$332$	6.93798e6	3.45452
$333$	1.20849e6	0.597216
$334$	−3.03149e6	−1.48693
$335$	340165.	0.165607
$336$	450581.	0.217733
$337$	538155.	0.258127	0.129063	−	0.991636i	$-0.458803\pi$
$337$	538155.	0.258127	0.129063	+	0.991636i	$0.458803\pi$
$338$	469736.	0.223647
$339$	−956951.	−0.452262
$340$	−1.93993e6	−0.910098
$341$	1.00414e6	0.467635
$342$	−2.19786e6	−1.01610
$343$	2.35861e6	1.08248
$344$	1.22580e6	0.558502
$345$	−842385.	−0.381033
$346$	8616.84	0.00386952
$347$	−217696.	−0.0970569	−0.0485284	−	0.998822i	$-0.515453\pi$
$347$	−217696.	−0.0970569	−0.0485284	+	0.998822i	$0.515453\pi$
$348$	−3.03262e6	−1.34236
$349$	1.43197e6	0.629317	0.314658	−	0.949205i	$-0.398110\pi$
$349$	1.43197e6	0.629317	0.314658	+	0.949205i	$0.398110\pi$
$350$	−664155.	−0.289801
$351$	472971.	0.204912
$352$	425429.	0.183008
$353$	−2.20348e6	−0.941181	−0.470590	−	0.882352i	$-0.655959\pi$
$353$	−2.20348e6	−0.941181	−0.470590	+	0.882352i	$0.655959\pi$
$354$	−2.32414e6	−0.985723
$355$	−1.07932e6	−0.454548
$356$	2.04937e6	0.857030
$357$	1.36292e6	0.565978
$358$	−816029.	−0.336510
$359$	2.40488e6	0.984821	0.492410	−	0.870363i	$-0.336116\pi$
$359$	2.40488e6	0.984821	0.492410	+	0.870363i	$0.336116\pi$
$360$	−489454.	−0.199047
$361$	5.74629e6	2.32070
$362$	−2.20891e6	−0.885944
$363$	−131769.	−0.0524864
$364$	4.19250e6	1.65852
$365$	2.23238e6	0.877073
$366$	−2.78494e6	−1.08671
$367$	−5.09240e6	−1.97359	−0.986797	−	0.161964i	$-0.948217\pi$
$367$	−5.09240e6	−1.97359	−0.986797	+	0.161964i	$0.948217\pi$
$368$	−1.66911e6	−0.642487
$369$	183536.	0.0701708
$370$	−3.52949e6	−1.34032
$371$	2.62158e6	0.988845
$372$	4.29776e6	1.61022
$373$	2.55571e6	0.951129	0.475565	−	0.879681i	$-0.342244\pi$
$373$	2.55571e6	0.951129	0.475565	+	0.879681i	$0.342244\pi$
$374$	−1.54403e6	−0.570789
$375$	140625.	0.0516398
$376$	−2.68438e6	−0.979205
$377$	−3.79918e6	−1.37669
$378$	774671.	0.278861
$379$	1.82150e6	0.651375	0.325687	−	0.945478i	$-0.394404\pi$
$379$	1.82150e6	0.651375	0.325687	+	0.945478i	$0.394404\pi$
$380$	4.12507e6	1.46545
$381$	−509772.	−0.179914
$382$	−7.48020e6	−2.62274
$383$	221105.	0.0770198	0.0385099	−	0.999258i	$-0.487739\pi$
$383$	221105.	0.0770198	0.0385099	+	0.999258i	$0.487739\pi$
$384$	3.03583e6	1.05063
$385$	−339703.	−0.116801
$386$	505499.	0.172684
$387$	410789.	0.139425
$388$	−950748.	−0.320617
$389$	3.43904e6	1.15229	0.576147	−	0.817346i	$-0.304556\pi$
$389$	3.43904e6	1.15229	0.576147	+	0.817346i	$0.304556\pi$
$390$	−1.38135e6	−0.459879
$391$	−5.04872e6	−1.67009
$392$	−1.01421e6	−0.333359
$393$	1.57674e6	0.514966
$394$	−6.95845e6	−2.25825
$395$	−1.36638e6	−0.440634
$396$	−563978.	−0.180728
$397$	3.63169e6	1.15646	0.578232	−	0.815872i	$-0.303743\pi$
$397$	3.63169e6	1.15646	0.578232	+	0.815872i	$0.303743\pi$
$398$	6.02106e6	1.90531
$399$	−2.89811e6	−0.911346
$400$	278635.	0.0870735
$401$	2.17412e6	0.675185	0.337593	−	0.941292i	$-0.390387\pi$
$401$	2.17412e6	0.675185	0.337593	+	0.941292i	$0.390387\pi$
$402$	1.15880e6	0.357638
$403$	5.38412e6	1.65140
$404$	−5.76372e6	−1.75691
$405$	−164025.	−0.0496904
$406$	−6.22262e6	−1.87352
$407$	−1.80527e6	−0.540202
$408$	−2.93348e6	−0.872433
$409$	3.02714e6	0.894796	0.447398	−	0.894335i	$-0.352351\pi$
$409$	3.02714e6	0.894796	0.447398	+	0.894335i	$0.352351\pi$
$410$	−536035.	−0.157483
$411$	−100085.	−0.0292257
$412$	−639462.	−0.185597
$413$	−3.06463e6	−0.884104
$414$	−2.86965e6	−0.822864
$415$	−3.01426e6	−0.859133
$416$	2.28112e6	0.646273
$417$	1.24055e6	0.349360
$418$	3.28322e6	0.919093
$419$	−4.92856e6	−1.37147	−0.685733	−	0.727853i	$-0.740518\pi$
$419$	−4.92856e6	−1.37147	−0.685733	+	0.727853i	$0.740518\pi$
$420$	−1.45395e6	−0.402185
$421$	3.23644e6	0.889945	0.444972	−	0.895544i	$-0.353214\pi$
$421$	3.23644e6	0.889945	0.444972	+	0.895544i	$0.353214\pi$
$422$	−6.66768e6	−1.82261
$423$	−899584.	−0.244450
$424$	−5.64255e6	−1.52427
$425$	842817.	0.226340
$426$	−3.67679e6	−0.981622
$427$	−3.67225e6	−0.974681
$428$	−1.31838e7	−3.47880
$429$	−706537.	−0.185350
$430$	−1.19975e6	−0.312909
$431$	−4.48720e6	−1.16354	−0.581771	−	0.813353i	$-0.697640\pi$
$431$	−4.48720e6	−1.16354	−0.581771	+	0.813353i	$0.697640\pi$
$432$	−325000.	−0.0837865
$433$	4.96059e6	1.27149	0.635746	−	0.771898i	$-0.280693\pi$
$433$	4.96059e6	1.27149	0.635746	+	0.771898i	$0.280693\pi$
$434$	8.81856e6	2.24736
$435$	1.31755e6	0.333843
$436$	1.85840e6	0.468192
$437$	1.07356e7	2.68920
$438$	7.60477e6	1.89409
$439$	2.50896e6	0.621345	0.310672	−	0.950517i	$-0.399446\pi$
$439$	2.50896e6	0.621345	0.310672	+	0.950517i	$0.399446\pi$
$440$	731159.	0.180045
$441$	−339880.	−0.0832202
$442$	−8.27896e6	−2.01567
$443$	5.30137e6	1.28345	0.641725	−	0.766935i	$-0.278219\pi$
$443$	5.30137e6	1.28345	0.641725	+	0.766935i	$0.278219\pi$
$444$	−7.72665e6	−1.86009
$445$	−890367.	−0.213142
$446$	−3.72530e6	−0.886798
$447$	491882.	0.116437
$448$	5.33828e6	1.25663
$449$	−3.96929e6	−0.929173	−0.464587	−	0.885528i	$-0.653797\pi$
$449$	−3.96929e6	−0.929173	−0.464587	+	0.885528i	$0.653797\pi$
$450$	479050.	0.111519
$451$	−274172.	−0.0634719
$452$	6.11842e6	1.40862
$453$	−2.10260e6	−0.481405
$454$	−1.36389e7	−3.10557
$455$	−1.82147e6	−0.412470
$456$	6.23775e6	1.40480
$457$	1.81191e6	0.405832	0.202916	−	0.979196i	$-0.434958\pi$
$457$	1.81191e6	0.405832	0.202916	+	0.979196i	$0.434958\pi$
$458$	−5.85868e6	−1.30508
$459$	−983062.	−0.217796
$460$	5.38592e6	1.18677
$461$	2.27993e6	0.499654	0.249827	−	0.968291i	$-0.419626\pi$
$461$	2.27993e6	0.499654	0.249827	+	0.968291i	$0.419626\pi$
$462$	−1.15722e6	−0.252239
$463$	5.35762e6	1.16150	0.580750	−	0.814082i	$-0.302759\pi$
$463$	5.35762e6	1.16150	0.580750	+	0.814082i	$0.302759\pi$
$464$	2.61060e6	0.562917
$465$	−1.86720e6	−0.400459
$466$	−5.55098e6	−1.18414
$467$	4.42170e6	0.938203	0.469102	−	0.883144i	$-0.344578\pi$
$467$	4.42170e6	0.938203	0.469102	+	0.883144i	$0.344578\pi$
$468$	−3.02402e6	−0.638218
$469$	1.52800e6	0.320769
$470$	2.62732e6	0.548615
$471$	−908881.	−0.188779
$472$	6.59616e6	1.36281
$473$	−613648.	−0.126115
$474$	−4.65468e6	−0.951576
$475$	−1.79217e6	−0.364456
$476$	−8.71404e6	−1.76280
$477$	−1.89092e6	−0.380520
$478$	1.29442e7	2.59122
$479$	3.07932e6	0.613220	0.306610	−	0.951835i	$-0.400805\pi$
$479$	3.07932e6	0.613220	0.306610	+	0.951835i	$0.400805\pi$
$480$	−791088.	−0.156719
$481$	−9.67974e6	−1.90766
$482$	−2.85784e6	−0.560299
$483$	−3.78394e6	−0.738034
$484$	842486.	0.163474
$485$	413060.	0.0797368
$486$	−558764.	−0.107309
$487$	3.40370e6	0.650322	0.325161	−	0.945659i	$-0.394582\pi$
$487$	3.40370e6	0.650322	0.325161	+	0.945659i	$0.394582\pi$
$488$	7.90396e6	1.50243
$489$	1.86078e6	0.351903
$490$	992650.	0.186769
$491$	1.17756e6	0.220435	0.110217	−	0.993908i	$-0.464845\pi$
$491$	1.17756e6	0.220435	0.110217	+	0.993908i	$0.464845\pi$
$492$	−1.17347e6	−0.218554
$493$	7.89654e6	1.46325
$494$	1.76044e7	3.24567
$495$	245025.	0.0449467
$496$	−3.69968e6	−0.675243
$497$	−4.84824e6	−0.880427
$498$	−1.02683e7	−1.85535
$499$	9.86746e6	1.77400	0.887000	−	0.461769i	$-0.152785\pi$
$499$	9.86746e6	1.77400	0.887000	+	0.461769i	$0.152785\pi$
$500$	−899109.	−0.160837
$501$	2.88325e6	0.513202
$502$	−5.70947e6	−1.01120
$503$	6.89093e6	1.21439	0.607194	−	0.794553i	$-0.292295\pi$
$503$	6.89093e6	1.21439	0.607194	+	0.794553i	$0.292295\pi$
$504$	−2.19860e6	−0.385540
$505$	2.50409e6	0.436940
$506$	4.28676e6	0.744308
$507$	−446767.	−0.0771900
$508$	3.25931e6	0.560359
$509$	4.91822e6	0.841421	0.420710	−	0.907195i	$-0.361781\pi$
$509$	4.91822e6	0.841421	0.420710	+	0.907195i	$0.361781\pi$
$510$	2.87112e6	0.488794
$511$	1.00277e7	1.69883
$512$	−5.01567e6	−0.845579
$513$	2.09039e6	0.350698
$514$	−2.21380e6	−0.369599
$515$	277819.	0.0461577
$516$	−2.62645e6	−0.434254
$517$	1.34382e6	0.221114
$518$	−1.58543e7	−2.59610
$519$	−8195.49	−0.00133554
$520$	3.92043e6	0.635807
$521$	531474.	0.0857803	0.0428901	−	0.999080i	$-0.486343\pi$
$521$	531474.	0.0857803	0.0428901	+	0.999080i	$0.486343\pi$
$522$	4.48832e6	0.720955
$523$	−8.78862e6	−1.40497	−0.702484	−	0.711699i	$-0.747926\pi$
$523$	−8.78862e6	−1.40497	−0.702484	+	0.711699i	$0.747926\pi$
$524$	−1.00811e7	−1.60391
$525$	631679.	0.100023
$526$	4.80703e6	0.757552
$527$	−1.11908e7	−1.75523
$528$	485494.	0.0757878
$529$	7.58069e6	1.17779
$530$	5.52261e6	0.853994
$531$	2.21050e6	0.340215
$532$	1.85296e7	2.83848
$533$	−1.47009e6	−0.224143
$534$	−3.03310e6	−0.460293
$535$	5.72779e6	0.865172
$536$	−3.28880e6	−0.494453
$537$	776126.	0.116144
$538$	−6.57904e6	−0.979957
$539$	507722.	0.0752755
$540$	1.04872e6	0.154766
$541$	−5.53762e6	−0.813449	−0.406724	−	0.913551i	$-0.633329\pi$
$541$	−5.53762e6	−0.813449	−0.406724	+	0.913551i	$0.633329\pi$
$542$	2.27646e7	3.32860
$543$	2.10090e6	0.305777
$544$	−4.74128e6	−0.686908
$545$	−807399.	−0.116439
$546$	−6.20496e6	−0.890753
$547$	−1.23738e7	−1.76822	−0.884108	−	0.467282i	$-0.845233\pi$
$547$	−1.23738e7	−1.76822	−0.884108	+	0.467282i	$0.845233\pi$
$548$	639911.	0.0910265
$549$	2.64876e6	0.375070
$550$	−715618.	−0.100873
$551$	−1.67912e7	−2.35615
$552$	8.14436e6	1.13765
$553$	−6.13769e6	−0.853478
$554$	9.23469e6	1.27834
$555$	3.35691e6	0.462601
$556$	−7.93164e6	−1.08812
$557$	−1.13874e7	−1.55521	−0.777603	−	0.628755i	$-0.783565\pi$
$557$	−1.13874e7	−1.55521	−0.777603	+	0.628755i	$0.783565\pi$
$558$	−6.36076e6	−0.864815
$559$	−3.29034e6	−0.445360
$560$	1.25161e6	0.168655
$561$	1.46852e6	0.197004
$562$	5.73124e6	0.765435
$563$	−2.98437e6	−0.396810	−0.198405	−	0.980120i	$-0.563576\pi$
$563$	−2.98437e6	−0.396810	−0.198405	+	0.980120i	$0.563576\pi$
$564$	5.75163e6	0.761366
$565$	−2.65820e6	−0.350321
$566$	−1.27253e7	−1.66965
$567$	−736790.	−0.0962468
$568$	1.04351e7	1.35714
$569$	−1.35179e7	−1.75037	−0.875183	−	0.483792i	$-0.839259\pi$
$569$	−1.35179e7	−1.75037	−0.875183	+	0.483792i	$0.839259\pi$
$570$	−6.10516e6	−0.787064
$571$	−2.82364e6	−0.362426	−0.181213	−	0.983444i	$-0.558002\pi$
$571$	−2.82364e6	−0.362426	−0.181213	+	0.983444i	$0.558002\pi$
$572$	4.51736e6	0.577290
$573$	7.11443e6	0.905219
$574$	−2.40784e6	−0.305033
$575$	−2.33996e6	−0.295147
$576$	−3.85046e6	−0.483566
$577$	−5.87192e6	−0.734244	−0.367122	−	0.930173i	$-0.619657\pi$
$577$	−5.87192e6	−0.734244	−0.367122	+	0.930173i	$0.619657\pi$
$578$	3.77199e6	0.469625
$579$	−480781.	−0.0596006
$580$	−8.42395e6	−1.03979
$581$	−1.35399e7	−1.66408
$582$	1.40712e6	0.172196
$583$	2.82471e6	0.344194
$584$	−2.15831e7	−2.61868
$585$	1.31381e6	0.158724
$586$	−1.60302e7	−1.92839
$587$	9.77315e6	1.17068	0.585342	−	0.810787i	$-0.300960\pi$
$587$	9.77315e6	1.17068	0.585342	+	0.810787i	$0.300960\pi$
$588$	2.17308e6	0.259198
$589$	2.37962e7	2.82630
$590$	−6.45595e6	−0.763537
$591$	6.61820e6	0.779419
$592$	6.65140e6	0.780025
$593$	−1.03889e7	−1.21320	−0.606602	−	0.795006i	$-0.707468\pi$
$593$	−1.03889e7	−1.21320	−0.606602	+	0.795006i	$0.707468\pi$
$594$	834696.	0.0970650
$595$	3.78588e6	0.438404
$596$	−3.14493e6	−0.362656
$597$	−5.72664e6	−0.657603
$598$	2.29853e7	2.62844
$599$	1.09690e7	1.24911	0.624553	−	0.780982i	$-0.285281\pi$
$599$	1.09690e7	1.24911	0.624553	+	0.780982i	$0.285281\pi$
$600$	−1.35959e6	−0.154181
$601$	1.37281e7	1.55033	0.775163	−	0.631761i	$-0.217667\pi$
$601$	1.37281e7	1.55033	0.775163	+	0.631761i	$0.217667\pi$
$602$	−5.38919e6	−0.606083
$603$	−1.10214e6	−0.123436
$604$	1.34433e7	1.49938
$605$	−366025.	−0.0406558
$606$	8.53039e6	0.943598
$607$	−7.84470e6	−0.864181	−0.432090	−	0.901830i	$-0.642224\pi$
$607$	−7.84470e6	−0.864181	−0.432090	+	0.901830i	$0.642224\pi$
$608$	1.00819e7	1.10607
$609$	5.91834e6	0.646631
$610$	−7.73595e6	−0.841762
$611$	7.20549e6	0.780837
$612$	6.28537e6	0.678347
$613$	5.47178e6	0.588135	0.294068	−	0.955785i	$-0.404991\pi$
$613$	5.47178e6	0.588135	0.294068	+	0.955785i	$0.404991\pi$
$614$	−2.21579e7	−2.37197
$615$	509823.	0.0543541
$616$	3.28432e6	0.348734
$617$	−4.23448e6	−0.447803	−0.223901	−	0.974612i	$-0.571879\pi$
$617$	−4.23448e6	−0.447803	−0.223901	+	0.974612i	$0.571879\pi$
$618$	946413.	0.0996803
$619$	−4.20082e6	−0.440664	−0.220332	−	0.975425i	$-0.570714\pi$
$619$	−4.20082e6	−0.440664	−0.220332	+	0.975425i	$0.570714\pi$
$620$	1.19382e7	1.24727
$621$	2.72933e6	0.284005
$622$	−1.03813e7	−1.07591
$623$	−3.99947e6	−0.412841
$624$	2.60319e6	0.267636
$625$	390625.	0.0400000
$626$	−1.84507e7	−1.88181
$627$	−3.12267e6	−0.317218
$628$	5.81107e6	0.587973
$629$	2.01192e7	2.02761
$630$	2.15186e6	0.216005
$631$	−9.69860e6	−0.969696	−0.484848	−	0.874598i	$-0.661125\pi$
$631$	−9.69860e6	−0.969696	−0.484848	+	0.874598i	$0.661125\pi$
$632$	1.32105e7	1.31560
$633$	6.34164e6	0.629060
$634$	−5.37935e6	−0.531504
$635$	−1.41603e6	−0.139360
$636$	1.20899e7	1.18517
$637$	2.72237e6	0.265827
$638$	−6.70478e6	−0.652128
$639$	3.49700e6	0.338800
$640$	8.43285e6	0.813813
$641$	6.27062e6	0.602789	0.301394	−	0.953500i	$-0.402548\pi$
$641$	6.27062e6	0.602789	0.301394	+	0.953500i	$0.402548\pi$
$642$	1.95122e7	1.86839
$643$	6.03514e6	0.575651	0.287826	−	0.957683i	$-0.407068\pi$
$643$	6.03514e6	0.575651	0.287826	+	0.957683i	$0.407068\pi$
$644$	2.41932e7	2.29868
$645$	1.14108e6	0.107998
$646$	−3.65905e7	−3.44974
$647$	8.55725e6	0.803662	0.401831	−	0.915714i	$-0.368374\pi$
$647$	8.55725e6	0.803662	0.401831	+	0.915714i	$0.368374\pi$
$648$	1.58583e6	0.148361
$649$	−3.30210e6	−0.307736
$650$	−3.83710e6	−0.356221
$651$	−8.38734e6	−0.775661
$652$	−1.18972e7	−1.09604
$653$	−4.99674e6	−0.458568	−0.229284	−	0.973360i	$-0.573638\pi$
$653$	−4.99674e6	−0.458568	−0.229284	+	0.973360i	$0.573638\pi$
$654$	−2.75047e6	−0.251456
$655$	4.37983e6	0.398891
$656$	1.01017e6	0.0916503
$657$	−7.23291e6	−0.653732
$658$	1.18017e7	1.06263
$659$	−2.55152e6	−0.228868	−0.114434	−	0.993431i	$-0.536506\pi$
$659$	−2.55152e6	−0.228868	−0.114434	+	0.993431i	$0.536506\pi$
$660$	−1.56661e6	−0.139991
$661$	−1.71349e7	−1.52538	−0.762692	−	0.646762i	$-0.776123\pi$
$661$	−1.71349e7	−1.52538	−0.762692	+	0.646762i	$0.776123\pi$
$662$	1.37864e7	1.22266
$663$	7.87413e6	0.695695
$664$	2.91425e7	2.56512
$665$	−8.05031e6	−0.705925
$666$	1.14356e7	0.999015
$667$	−2.19236e7	−1.90808
$668$	−1.84345e7	−1.59842
$669$	3.54314e6	0.306072
$670$	3.21889e6	0.277025
$671$	−3.95679e6	−0.339263
$672$	−3.55352e6	−0.303554
$673$	−3.02957e6	−0.257835	−0.128918	−	0.991655i	$-0.541150\pi$
$673$	−3.02957e6	−0.257835	−0.128918	+	0.991655i	$0.541150\pi$
$674$	5.09241e6	0.431791
$675$	−455625.	−0.0384900
$676$	2.85648e6	0.240416
$677$	−1.18740e7	−0.995691	−0.497846	−	0.867266i	$-0.665875\pi$
$677$	−1.18740e7	−0.995691	−0.497846	+	0.867266i	$0.665875\pi$
$678$	−9.05535e6	−0.756539
$679$	1.85544e6	0.154445
$680$	−8.14855e6	−0.675784
$681$	1.29720e7	1.07186
$682$	9.50187e6	0.782255
$683$	−1.46423e7	−1.20104	−0.600518	−	0.799611i	$-0.705039\pi$
$683$	−1.46423e7	−1.20104	−0.600518	+	0.799611i	$0.705039\pi$
$684$	−1.33652e7	−1.09228
$685$	−278014.	−0.0226381
$686$	2.23189e7	1.81076
$687$	5.57220e6	0.450438
$688$	2.26095e6	0.182104
$689$	1.51459e7	1.21548
$690$	−7.97125e6	−0.637387
$691$	1.79851e6	0.143291	0.0716454	−	0.997430i	$-0.477175\pi$
$691$	1.79851e6	0.143291	0.0716454	+	0.997430i	$0.477175\pi$
$692$	52399.2	0.00415967
$693$	1.10064e6	0.0870585
$694$	−2.05999e6	−0.162356
$695$	3.44597e6	0.270613
$696$	−1.27383e7	−0.996758
$697$	3.05556e6	0.238237
$698$	1.35503e7	1.05271
$699$	5.27954e6	0.408699
$700$	−4.03874e6	−0.311531
$701$	−8.66684e6	−0.666141	−0.333070	−	0.942902i	$-0.608085\pi$
$701$	−8.66684e6	−0.666141	−0.333070	+	0.942902i	$0.608085\pi$
$702$	4.47559e6	0.342774
$703$	−4.27815e7	−3.26488
$704$	5.75192e6	0.437402
$705$	−2.49884e6	−0.189350
$706$	−2.08509e7	−1.57440
$707$	1.12482e7	0.846323
$708$	−1.41332e7	−1.05963
$709$	−1.40405e7	−1.04898	−0.524491	−	0.851416i	$-0.675744\pi$
$709$	−1.40405e7	−1.04898	−0.524491	+	0.851416i	$0.675744\pi$
$710$	−1.02133e7	−0.760361
$711$	4.42707e6	0.328430
$712$	8.60827e6	0.636379
$713$	3.10696e7	2.28882
$714$	1.28969e7	0.946760
$715$	−1.96260e6	−0.143571
$716$	−4.96229e6	−0.361742
$717$	−1.23112e7	−0.894340
$718$	2.27567e7	1.64740
$719$	−9.98192e6	−0.720098	−0.360049	−	0.932933i	$-0.617240\pi$
$719$	−9.98192e6	−0.720098	−0.360049	+	0.932933i	$0.617240\pi$
$720$	−902778.	−0.0649008
$721$	1.24795e6	0.0894043
$722$	5.43755e7	3.88204
$723$	2.71810e6	0.193383
$724$	−1.34324e7	−0.952375
$725$	3.65985e6	0.258594
$726$	−1.24689e6	−0.0877986
$727$	1.32241e7	0.927964	0.463982	−	0.885845i	$-0.346420\pi$
$727$	1.32241e7	0.927964	0.463982	+	0.885845i	$0.346420\pi$
$728$	1.76103e7	1.23151
$729$	531441.	0.0370370
$730$	2.11244e7	1.46716
$731$	6.83892e6	0.473363
$732$	−1.69353e7	−1.16819
$733$	−1.58810e7	−1.09173	−0.545867	−	0.837872i	$-0.683800\pi$
$733$	−1.58810e7	−1.09173	−0.545867	+	0.837872i	$0.683800\pi$
$734$	−4.81880e7	−3.30140
$735$	−944111.	−0.0644621
$736$	1.31635e7	0.895727
$737$	1.64640e6	0.111652
$738$	1.73675e6	0.117381
$739$	−900405.	−0.0606495	−0.0303247	−	0.999540i	$-0.509654\pi$
$739$	−900405.	−0.0606495	−0.0303247	+	0.999540i	$0.509654\pi$
$740$	−2.14629e7	−1.44082
$741$	−1.67436e7	−1.12022
$742$	2.48072e7	1.65413
$743$	−6.73756e6	−0.447745	−0.223872	−	0.974618i	$-0.571870\pi$
$743$	−6.73756e6	−0.447745	−0.223872	+	0.974618i	$0.571870\pi$
$744$	1.80525e7	1.19565
$745$	1.36634e6	0.0901919
$746$	2.41839e7	1.59104
$747$	9.76620e6	0.640360
$748$	−9.38925e6	−0.613588
$749$	2.57289e7	1.67578
$750$	1.33069e6	0.0863824
$751$	2.72651e6	0.176403	0.0882016	−	0.996103i	$-0.471888\pi$
$751$	2.72651e6	0.176403	0.0882016	+	0.996103i	$0.471888\pi$
$752$	−4.95122e6	−0.319277
$753$	5.43029e6	0.349008
$754$	−3.59506e7	−2.30291
$755$	−5.84054e6	−0.372894
$756$	4.71079e6	0.299771
$757$	1.04686e7	0.663969	0.331984	−	0.943285i	$-0.392282\pi$
$757$	1.04686e7	0.663969	0.331984	+	0.943285i	$0.392282\pi$
$758$	1.72363e7	1.08961
$759$	−4.07714e6	−0.256893
$760$	1.73271e7	1.08816
$761$	2.55966e7	1.60221	0.801107	−	0.598521i	$-0.204245\pi$
$761$	2.55966e7	1.60221	0.801107	+	0.598521i	$0.204245\pi$
$762$	−4.82383e6	−0.300957
$763$	−3.62679e6	−0.225533
$764$	−4.54873e7	−2.81940
$765$	−2.73073e6	−0.168704
$766$	2.09226e6	0.128838
$767$	−1.77056e7	−1.08673
$768$	1.50366e7	0.919916
$769$	−1.93403e7	−1.17936	−0.589682	−	0.807635i	$-0.700747\pi$
$769$	−1.93403e7	−1.17936	−0.589682	+	0.807635i	$0.700747\pi$
$770$	−3.21451e6	−0.195384
$771$	2.10555e6	0.127565
$772$	3.07395e6	0.185632
$773$	−3.34724e6	−0.201483	−0.100741	−	0.994913i	$-0.532121\pi$
$773$	−3.34724e6	−0.201483	−0.100741	+	0.994913i	$0.532121\pi$
$774$	3.88718e6	0.233229
$775$	−5.18666e6	−0.310194
$776$	−3.99356e6	−0.238070
$777$	1.50790e7	0.896026
$778$	3.25426e7	1.92754
$779$	−6.49735e6	−0.383612
$780$	−8.40004e6	−0.494362
$781$	−5.22391e6	−0.306456
$782$	−4.77746e7	−2.79370
$783$	−4.26885e6	−0.248832
$784$	−1.87067e6	−0.108694
$785$	−2.52467e6	−0.146228
$786$	1.49202e7	0.861428
$787$	−1.87767e6	−0.108064	−0.0540321	−	0.998539i	$-0.517207\pi$
$787$	−1.87767e6	−0.108064	−0.0540321	+	0.998539i	$0.517207\pi$
$788$	−4.23145e7	−2.42758
$789$	−4.57197e6	−0.261463
$790$	−1.29297e7	−0.737088
$791$	−1.19405e7	−0.678547
$792$	−2.36896e6	−0.134197
$793$	−2.12161e7	−1.19807
$794$	3.43656e7	1.93452
$795$	−5.25257e6	−0.294750
$796$	3.66142e7	2.04817
$797$	−8.58000e6	−0.478455	−0.239228	−	0.970964i	$-0.576894\pi$
$797$	−8.58000e6	−0.478455	−0.239228	+	0.970964i	$0.576894\pi$
$798$	−2.74240e7	−1.52449
$799$	−1.49765e7	−0.829933
$800$	−2.19747e6	−0.121394
$801$	2.88479e6	0.158867
$802$	2.05731e7	1.12944
$803$	1.08047e7	0.591323
$804$	7.04668e6	0.384454
$805$	−1.05109e7	−0.571679
$806$	5.09484e7	2.76244
$807$	6.25734e6	0.338225
$808$	−2.42101e7	−1.30457
$809$	8.63327e6	0.463772	0.231886	−	0.972743i	$-0.425510\pi$
$809$	8.63327e6	0.463772	0.231886	+	0.972743i	$0.425510\pi$
$810$	−1.55212e6	−0.0831215
$811$	−6.04702e6	−0.322842	−0.161421	−	0.986886i	$-0.551608\pi$
$811$	−6.04702e6	−0.322842	−0.161421	+	0.986886i	$0.551608\pi$
$812$	−3.78399e7	−2.01400
$813$	−2.16514e7	−1.14884
$814$	−1.70827e7	−0.903643
$815$	5.16883e6	0.272583
$816$	−5.41068e6	−0.284464
$817$	−1.45423e7	−0.762215
$818$	2.86449e7	1.49680
$819$	5.90155e6	0.307437
$820$	−3.25964e6	−0.169291
$821$	773849.	0.0400680	0.0200340	−	0.999799i	$-0.493623\pi$
$821$	773849.	0.0400680	0.0200340	+	0.999799i	$0.493623\pi$
$822$	−947077.	−0.0488884
$823$	2.08816e7	1.07464	0.537322	−	0.843377i	$-0.319436\pi$
$823$	2.08816e7	1.07464	0.537322	+	0.843377i	$0.319436\pi$
$824$	−2.68602e6	−0.137813
$825$	680625.	0.0348155
$826$	−2.89998e7	−1.47892
$827$	−1.86507e7	−0.948266	−0.474133	−	0.880453i	$-0.657238\pi$
$827$	−1.86507e7	−0.948266	−0.474133	+	0.880453i	$0.657238\pi$
$828$	−1.74504e7	−0.884564
$829$	−1.23554e7	−0.624412	−0.312206	−	0.950014i	$-0.601068\pi$
$829$	−1.23554e7	−0.624412	−0.312206	+	0.950014i	$0.601068\pi$
$830$	−2.85231e7	−1.43715
$831$	−8.78313e6	−0.441211
$832$	3.08414e7	1.54464
$833$	−5.65840e6	−0.282541
$834$	1.17389e7	0.584405
$835$	8.00903e6	0.397524
$836$	1.99653e7	0.988008
$837$	6.04972e6	0.298485
$838$	−4.66376e7	−2.29417
$839$	−2.68045e6	−0.131463	−0.0657313	−	0.997837i	$-0.520938\pi$
$839$	−2.68045e6	−0.131463	−0.0657313	+	0.997837i	$0.520938\pi$
$840$	−6.10721e6	−0.298638
$841$	1.37788e7	0.671771
$842$	3.06255e7	1.48869
$843$	−5.45099e6	−0.264184
$844$	−4.05463e7	−1.95927
$845$	−1.24102e6	−0.0597911
$846$	−8.51250e6	−0.408913
$847$	−1.64416e6	−0.0787474
$848$	−1.04075e7	−0.496999
$849$	1.21030e7	0.576268
$850$	7.97534e6	0.378619
$851$	−5.58579e7	−2.64400
$852$	−2.23586e7	−1.05523
$853$	1.67043e7	0.786059	0.393030	−	0.919526i	$-0.371427\pi$
$853$	1.67043e7	0.786059	0.393030	+	0.919526i	$0.371427\pi$
$854$	−3.47494e7	−1.63043
$855$	5.80663e6	0.271649
$856$	−5.53776e7	−2.58315
$857$	−3.43482e7	−1.59754	−0.798770	−	0.601636i	$-0.794516\pi$
$857$	−3.43482e7	−1.59754	−0.798770	+	0.601636i	$0.794516\pi$
$858$	−6.68576e6	−0.310050
$859$	2.49284e7	1.15269	0.576344	−	0.817207i	$-0.304479\pi$
$859$	2.49284e7	1.15269	0.576344	+	0.817207i	$0.304479\pi$
$860$	−7.29568e6	−0.336372
$861$	2.29010e6	0.105280
$862$	−4.24610e7	−1.94636
$863$	5.92328e6	0.270729	0.135365	−	0.990796i	$-0.456779\pi$
$863$	5.92328e6	0.270729	0.135365	+	0.990796i	$0.456779\pi$
$864$	2.56312e6	0.116811
$865$	−22765.2	−0.00103450
$866$	4.69407e7	2.12694
$867$	−3.58755e6	−0.162088
$868$	5.36258e7	2.41588
$869$	−6.61327e6	−0.297076
$870$	1.24676e7	0.558449
$871$	8.82789e6	0.394286
$872$	7.80611e6	0.347651
$873$	−1.33831e6	−0.0594323
$874$	1.01588e8	4.49846
$875$	1.75466e6	0.0774772
$876$	4.62448e7	2.03611
$877$	8.25691e6	0.362509	0.181254	−	0.983436i	$-0.441984\pi$
$877$	8.25691e6	0.362509	0.181254	+	0.983436i	$0.441984\pi$
$878$	2.37416e7	1.03938
$879$	1.52463e7	0.665568
$880$	1.34859e6	0.0587050
$881$	9.97157e6	0.432836	0.216418	−	0.976301i	$-0.430563\pi$
$881$	9.97157e6	0.432836	0.216418	+	0.976301i	$0.430563\pi$
$882$	−3.21619e6	−0.139210
$883$	−2.99656e7	−1.29336	−0.646682	−	0.762760i	$-0.723844\pi$
$883$	−2.99656e7	−1.29336	−0.646682	+	0.762760i	$0.723844\pi$
$884$	−5.03445e7	−2.16681
$885$	6.14027e6	0.263529
$886$	5.01653e7	2.14694
$887$	2.33812e7	0.997834	0.498917	−	0.866650i	$-0.333731\pi$
$887$	2.33812e7	0.997834	0.498917	+	0.866650i	$0.333731\pi$
$888$	−3.24553e7	−1.38119
$889$	−6.36074e6	−0.269931
$890$	−8.42529e6	−0.356541
$891$	−793881.	−0.0335013
$892$	−2.26536e7	−0.953292
$893$	3.18460e7	1.33637
$894$	4.65454e6	0.194775
$895$	2.15591e6	0.0899647
$896$	3.78799e7	1.57630
$897$	−2.18614e7	−0.907186
$898$	−3.75602e7	−1.55431
$899$	−4.85950e7	−2.00536
$900$	2.91311e6	0.119881
$901$	−3.14806e7	−1.29190
$902$	−2.59441e6	−0.106175
$903$	5.12567e6	0.209185
$904$	2.57000e7	1.04595
$905$	5.83582e6	0.236854
$906$	−1.98963e7	−0.805287
$907$	−7434.06	−0.000300060 0	−0.000150030	−	1.00000i	$-0.500048\pi$
$907$	−7434.06	−0.000300060 0	−0.000150030		1.00000i	$0.500048\pi$
$908$	−8.29387e7	−3.33843
$909$	−8.11326e6	−0.325676
$910$	−1.72360e7	−0.689975
$911$	−1.84874e7	−0.738038	−0.369019	−	0.929422i	$-0.620306\pi$
$911$	−1.84874e7	−0.738038	−0.369019	+	0.929422i	$0.620306\pi$
$912$	1.15053e7	0.458047
$913$	−1.45890e7	−0.579227
$914$	1.71456e7	0.678870
$915$	7.35767e6	0.290528
$916$	−3.56268e7	−1.40294
$917$	1.96739e7	0.772623
$918$	−9.30244e6	−0.364326
$919$	1.66211e7	0.649187	0.324593	−	0.945854i	$-0.394773\pi$
$919$	1.66211e7	0.649187	0.324593	+	0.945854i	$0.394773\pi$
$920$	2.26232e7	0.881222
$921$	2.10744e7	0.818667
$922$	2.15743e7	0.835815
$923$	−2.80103e7	−1.08221
$924$	−7.03710e6	−0.271153
$925$	9.32474e6	0.358329
$926$	5.06976e7	1.94294
$927$	−900135.	−0.0344039
$928$	−2.05885e7	−0.784794
$929$	4.30541e7	1.63672	0.818362	−	0.574704i	$-0.194883\pi$
$929$	4.30541e7	1.63672	0.818362	+	0.574704i	$0.194883\pi$
$930$	−1.76688e7	−0.669883
$931$	1.20320e7	0.454951
$932$	−3.37556e7	−1.27293
$933$	9.87364e6	0.371341
$934$	4.18413e7	1.56941
$935$	4.07924e6	0.152598
$936$	−1.27022e7	−0.473902
$937$	4.98798e7	1.85599	0.927996	−	0.372591i	$-0.121531\pi$
$937$	4.98798e7	1.85599	0.927996	+	0.372591i	$0.121531\pi$
$938$	1.44591e7	0.536578
$939$	1.75485e7	0.649494
$940$	1.59768e7	0.589751
$941$	−7.31964e6	−0.269473	−0.134737	−	0.990881i	$-0.543019\pi$
$941$	−7.31964e6	−0.269473	−0.134737	+	0.990881i	$0.543019\pi$
$942$	−8.60048e6	−0.315788
$943$	−8.48331e6	−0.310660
$944$	1.21664e7	0.444356
$945$	−2.04664e6	−0.0745525
$946$	−5.80678e6	−0.210963
$947$	1.96212e7	0.710970	0.355485	−	0.934682i	$-0.384316\pi$
$947$	1.96212e7	0.710970	0.355485	+	0.934682i	$0.384316\pi$
$948$	−2.83052e7	−1.02293
$949$	5.79342e7	2.08819
$950$	−1.69588e7	−0.609657
$951$	5.11631e6	0.183445
$952$	−3.66028e7	−1.30895
$953$	−2.23896e7	−0.798573	−0.399286	−	0.916826i	$-0.630742\pi$
$953$	−2.23896e7	−0.798573	−0.399286	+	0.916826i	$0.630742\pi$
$954$	−1.78933e7	−0.636530
$955$	1.97623e7	0.701180
$956$	7.87137e7	2.78551
$957$	6.37693e6	0.225077
$958$	2.91388e7	1.02579
$959$	−1.24882e6	−0.0438485
$960$	−1.06957e7	−0.374569
$961$	4.02386e7	1.40551
$962$	−9.15966e7	−3.19111
$963$	−1.85580e7	−0.644861
$964$	−1.73786e7	−0.602312
$965$	−1.33550e6	−0.0461664
$966$	−3.58064e7	−1.23457
$967$	4.14912e7	1.42689	0.713443	−	0.700713i	$-0.247135\pi$
$967$	4.14912e7	1.42689	0.713443	+	0.700713i	$0.247135\pi$
$968$	3.53881e6	0.121386
$969$	3.48013e7	1.19065
$970$	3.90867e6	0.133383
$971$	−3.22766e7	−1.09860	−0.549300	−	0.835625i	$-0.685106\pi$
$971$	−3.22766e7	−1.09860	−0.549300	+	0.835625i	$0.685106\pi$
$972$	−3.39785e6	−0.115356
$973$	1.54791e7	0.524159
$974$	3.22082e7	1.08785
$975$	3.64947e6	0.122947
$976$	1.45785e7	0.489880
$977$	−9.88356e6	−0.331266	−0.165633	−	0.986187i	$-0.552967\pi$
$977$	−9.88356e6	−0.331266	−0.165633	+	0.986187i	$0.552967\pi$
$978$	1.76080e7	0.588659
$979$	−4.30938e6	−0.143700
$980$	6.03632e6	0.200774
$981$	2.61597e6	0.0867882
$982$	1.11429e7	0.368740
$983$	−1.20720e7	−0.398469	−0.199234	−	0.979952i	$-0.563846\pi$
$983$	−1.20720e7	−0.398469	−0.199234	+	0.979952i	$0.563846\pi$
$984$	−4.92909e6	−0.162285
$985$	1.83839e7	0.603735
$986$	7.47227e7	2.44771
$987$	−1.12247e7	−0.366758
$988$	1.07053e8	3.48904
$989$	−1.89872e7	−0.617264
$990$	2.31860e6	0.0751862
$991$	−4.77674e7	−1.54507	−0.772533	−	0.634975i	$-0.781011\pi$
$991$	−4.77674e7	−1.54507	−0.772533	+	0.634975i	$0.781011\pi$
$992$	2.91776e7	0.941393
$993$	−1.31122e7	−0.421992
$994$	−4.58775e7	−1.47277
$995$	−1.59073e7	−0.509377
$996$	−6.24418e7	−1.99447
$997$	1.18753e7	0.378363	0.189181	−	0.981942i	$-0.439417\pi$
$997$	1.18753e7	0.378363	0.189181	+	0.981942i	$0.439417\pi$
$998$	9.33729e7	2.96753
$999$	−1.08764e7	−0.344803

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.a.g.1.5	✓	5
3.2	odd	2		495.6.a.i.1.1		5
5.4	even	2		825.6.a.k.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.g.1.5	✓	5	1.1	even	1	trivial
495.6.a.i.1.1		5	3.2	odd	2
825.6.a.k.1.1		5	5.4	even	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:	\( N \)	\(=\)	\( 165 = 3 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	165.a (trivial)

\(f(q)\)	\(=\)	\(q+9.46271 q^{2} -9.00000 q^{3} +57.5429 q^{4} -25.0000 q^{5} -85.1644 q^{6} -112.299 q^{7} +241.706 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+9.46271 q^{2} -9.00000 q^{3} +57.5429 q^{4} -25.0000 q^{5} -85.1644 q^{6} -112.299 q^{7} +241.706 q^{8} +81.0000 q^{9} -236.568 q^{10} -121.000 q^{11} -517.887 q^{12} -648.794 q^{13} -1062.65 q^{14} +225.000 q^{15} +445.816 q^{16} +1348.51 q^{17} +766.480 q^{18} -2867.47 q^{19} -1438.57 q^{20} +1010.69 q^{21} -1144.99 q^{22} -3743.93 q^{23} -2175.35 q^{24} +625.000 q^{25} -6139.35 q^{26} -729.000 q^{27} -6461.99 q^{28} +5855.76 q^{29} +2129.11 q^{30} -8298.66 q^{31} -3515.95 q^{32} +1089.00 q^{33} +12760.5 q^{34} +2807.46 q^{35} +4660.98 q^{36} +14919.6 q^{37} -27134.0 q^{38} +5839.15 q^{39} -6042.64 q^{40} +2265.88 q^{41} +9563.84 q^{42} +5071.47 q^{43} -6962.70 q^{44} -2025.00 q^{45} -35427.8 q^{46} -11106.0 q^{47} -4012.35 q^{48} -4196.05 q^{49} +5914.20 q^{50} -12136.6 q^{51} -37333.5 q^{52} -23344.7 q^{53} -6898.32 q^{54} +3025.00 q^{55} -27143.2 q^{56} +25807.2 q^{57} +55411.4 q^{58} +27290.1 q^{59} +12947.2 q^{60} +32700.8 q^{61} -78527.8 q^{62} -9096.18 q^{63} -47536.5 q^{64} +16219.9 q^{65} +10304.9 q^{66} -13606.6 q^{67} +77597.1 q^{68} +33695.4 q^{69} +26566.2 q^{70} +43172.8 q^{71} +19578.2 q^{72} -89295.2 q^{73} +141180. q^{74} -5625.00 q^{75} -165003. q^{76} +13588.1 q^{77} +55254.2 q^{78} +54655.2 q^{79} -11145.4 q^{80} +6561.00 q^{81} +21441.4 q^{82} +120570. q^{83} +58157.9 q^{84} -33712.7 q^{85} +47989.9 q^{86} -52701.9 q^{87} -29246.4 q^{88} +35614.7 q^{89} -19162.0 q^{90} +72858.6 q^{91} -215437. q^{92} +74687.9 q^{93} -105093. q^{94} +71686.8 q^{95} +31643.5 q^{96} -16522.4 q^{97} -39706.0 q^{98} -9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9}+O(q^{10}) \) 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9	\( 5 q - q^{2} - 45 q^{3} + 127 q^{4} - 125 q^{5} + 9 q^{6} + 116 q^{7} - 153 q^{8} + 405 q^{9} + 25 q^{10} - 605 q^{11} - 1143 q^{12} - 926 q^{13} + 368 q^{14} + 1125 q^{15} + 1891 q^{16} - 246 q^{17} - 81 q^{18} + 3420 q^{19} - 3175 q^{20} - 1044 q^{21} + 121 q^{22} - 4244 q^{23} + 1377 q^{24} + 3125 q^{25} - 8862 q^{26} - 3645 q^{27} - 4904 q^{28} - 2922 q^{29} - 225 q^{30} - 6112 q^{31} - 24757 q^{32} + 5445 q^{33} + 10866 q^{34} - 2900 q^{35} + 10287 q^{36} + 6654 q^{37} - 45692 q^{38} + 8334 q^{39} + 3825 q^{40} - 14934 q^{41} - 3312 q^{42} + 10804 q^{43} - 15367 q^{44} - 10125 q^{45} - 101500 q^{46} - 41460 q^{47} - 17019 q^{48} - 12099 q^{49} - 625 q^{50} + 2214 q^{51} - 97742 q^{52} - 62398 q^{53} + 729 q^{54} + 15125 q^{55} - 74368 q^{56} - 30780 q^{57} - 27822 q^{58} + 8524 q^{59} + 28575 q^{60} + 59010 q^{61} - 142624 q^{62} + 9396 q^{63} + 13799 q^{64} + 23150 q^{65} - 1089 q^{66} - 15772 q^{67} - 83686 q^{68} + 38196 q^{69} - 9200 q^{70} + 88124 q^{71} - 12393 q^{72} - 118358 q^{73} + 67194 q^{74} - 28125 q^{75} + 100668 q^{76} - 14036 q^{77} + 79758 q^{78} + 57324 q^{79} - 47275 q^{80} + 32805 q^{81} + 29102 q^{82} - 7268 q^{83} + 44136 q^{84} + 6150 q^{85} - 35288 q^{86} + 26298 q^{87} + 18513 q^{88} + 72978 q^{89} + 2025 q^{90} - 1464 q^{91} + 62148 q^{92} + 55008 q^{93} + 344836 q^{94} - 85500 q^{95} + 222813 q^{96} - 59174 q^{97} + 272767 q^{98} - 49005 q^{99}+O(q^{100}) \) 5 * q - q^2 - 45 * q^3 + 127 * q^4 - 125 * q^5 + 9 * q^6 + 116 * q^7 - 153 * q^8 + 405 * q^9 + 25 * q^10 - 605 * q^11 - 1143 * q^12 - 926 * q^13 + 368 * q^14 + 1125 * q^15 + 1891 * q^16 - 246 * q^17 - 81 * q^18 + 3420 * q^19 - 3175 * q^20 - 1044 * q^21 + 121 * q^22 - 4244 * q^23 + 1377 * q^24 + 3125 * q^25 - 8862 * q^26 - 3645 * q^27 - 4904 * q^28 - 2922 * q^29 - 225 * q^30 - 6112 * q^31 - 24757 * q^32 + 5445 * q^33 + 10866 * q^34 - 2900 * q^35 + 10287 * q^36 + 6654 * q^37 - 45692 * q^38 + 8334 * q^39 + 3825 * q^40 - 14934 * q^41 - 3312 * q^42 + 10804 * q^43 - 15367 * q^44 - 10125 * q^45 - 101500 * q^46 - 41460 * q^47 - 17019 * q^48 - 12099 * q^49 - 625 * q^50 + 2214 * q^51 - 97742 * q^52 - 62398 * q^53 + 729 * q^54 + 15125 * q^55 - 74368 * q^56 - 30780 * q^57 - 27822 * q^58 + 8524 * q^59 + 28575 * q^60 + 59010 * q^61 - 142624 * q^62 + 9396 * q^63 + 13799 * q^64 + 23150 * q^65 - 1089 * q^66 - 15772 * q^67 - 83686 * q^68 + 38196 * q^69 - 9200 * q^70 + 88124 * q^71 - 12393 * q^72 - 118358 * q^73 + 67194 * q^74 - 28125 * q^75 + 100668 * q^76 - 14036 * q^77 + 79758 * q^78 + 57324 * q^79 - 47275 * q^80 + 32805 * q^81 + 29102 * q^82 - 7268 * q^83 + 44136 * q^84 + 6150 * q^85 - 35288 * q^86 + 26298 * q^87 + 18513 * q^88 + 72978 * q^89 + 2025 * q^90 - 1464 * q^91 + 62148 * q^92 + 55008 * q^93 + 344836 * q^94 - 85500 * q^95 + 222813 * q^96 - 59174 * q^97 + 272767 * q^98 - 49005 * q^99

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