LMFDB - Embedded newform 165.6.a.h.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:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 209x^{5} + 137x^{4} + 12724x^{3} - 1040x^{2} - 218208x - 8784 $ x^7 - x^6 - 209x^5 + 137x^4 + 12724x^3 - 1040x^2 - 218208*x - 8784
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$5.17374$ 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)

$f(q)$	$=$	$q+5.17374 q^{2} +9.00000 q^{3} -5.23241 q^{4} +25.0000 q^{5} +46.5637 q^{6} +24.5405 q^{7} -192.631 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+5.17374 q^{2} +9.00000 q^{3} -5.23241 q^{4} +25.0000 q^{5} +46.5637 q^{6} +24.5405 q^{7} -192.631 q^{8} +81.0000 q^{9} +129.343 q^{10} +121.000 q^{11} -47.0917 q^{12} +954.137 q^{13} +126.966 q^{14} +225.000 q^{15} -829.185 q^{16} +1130.25 q^{17} +419.073 q^{18} +2105.70 q^{19} -130.810 q^{20} +220.864 q^{21} +626.023 q^{22} -944.310 q^{23} -1733.68 q^{24} +625.000 q^{25} +4936.46 q^{26} +729.000 q^{27} -128.406 q^{28} -657.825 q^{29} +1164.09 q^{30} +477.750 q^{31} +1874.20 q^{32} +1089.00 q^{33} +5847.60 q^{34} +613.512 q^{35} -423.826 q^{36} -9315.20 q^{37} +10894.4 q^{38} +8587.23 q^{39} -4815.77 q^{40} +20254.2 q^{41} +1142.70 q^{42} +16803.1 q^{43} -633.122 q^{44} +2025.00 q^{45} -4885.61 q^{46} -16571.1 q^{47} -7462.66 q^{48} -16204.8 q^{49} +3233.59 q^{50} +10172.2 q^{51} -4992.44 q^{52} -593.161 q^{53} +3771.66 q^{54} +3025.00 q^{55} -4727.26 q^{56} +18951.3 q^{57} -3403.41 q^{58} -8929.71 q^{59} -1177.29 q^{60} -55398.1 q^{61} +2471.76 q^{62} +1987.78 q^{63} +36230.5 q^{64} +23853.4 q^{65} +5634.20 q^{66} +63430.4 q^{67} -5913.91 q^{68} -8498.79 q^{69} +3174.15 q^{70} -6287.83 q^{71} -15603.1 q^{72} +12474.3 q^{73} -48194.4 q^{74} +5625.00 q^{75} -11017.9 q^{76} +2969.40 q^{77} +44428.1 q^{78} -85339.3 q^{79} -20729.6 q^{80} +6561.00 q^{81} +104790. q^{82} +47988.8 q^{83} -1155.65 q^{84} +28256.1 q^{85} +86934.9 q^{86} -5920.42 q^{87} -23308.3 q^{88} +4127.92 q^{89} +10476.8 q^{90} +23415.0 q^{91} +4941.02 q^{92} +4299.75 q^{93} -85734.5 q^{94} +52642.6 q^{95} +16867.8 q^{96} -107861. q^{97} -83839.2 q^{98} +9801.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + q^{2} + 63 q^{3} + 195 q^{4} + 175 q^{5} + 9 q^{6} + 153 q^{8} + 567 q^{9}+O(q^{10}) $ 7 * q + q^2 + 63 * q^3 + 195 * q^4 + 175 * q^5 + 9 * q^6 + 153 * q^8 + 567 * q^9	\( 7 q + q^{2} + 63 q^{3} + 195 q^{4} + 175 q^{5} + 9 q^{6} + 153 q^{8} + 567 q^{9} + 25 q^{10} + 847 q^{11} + 1755 q^{12} + 1418 q^{13} + 2548 q^{14} + 1575 q^{15} + 3699 q^{16} + 630 q^{17} + 81 q^{18} + 2572 q^{19} + 4875 q^{20} + 121 q^{22} + 536 q^{23} + 1377 q^{24} + 4375 q^{25} - 7626 q^{26} + 5103 q^{27} - 11368 q^{28} - 1038 q^{29} + 225 q^{30} + 1872 q^{31} - 7523 q^{32} + 7623 q^{33} + 20790 q^{34} + 15795 q^{36} + 24298 q^{37} - 18952 q^{38} + 12762 q^{39} + 3825 q^{40} - 17658 q^{41} + 22932 q^{42} + 7244 q^{43} + 23595 q^{44} + 14175 q^{45} + 31016 q^{46} + 34560 q^{47} + 33291 q^{48} + 78735 q^{49} + 625 q^{50} + 5670 q^{51} + 110222 q^{52} - 10214 q^{53} + 729 q^{54} + 21175 q^{55} + 81124 q^{56} + 23148 q^{57} - 5718 q^{58} + 94676 q^{59} + 43875 q^{60} + 69538 q^{61} - 4208 q^{62} + 112339 q^{64} + 35450 q^{65} + 1089 q^{66} + 64908 q^{67} - 136010 q^{68} + 4824 q^{69} + 63700 q^{70} + 61816 q^{71} + 12393 q^{72} - 11890 q^{73} - 124050 q^{74} + 39375 q^{75} - 47216 q^{76} - 68634 q^{78} + 18928 q^{79} + 92475 q^{80} + 45927 q^{81} + 36398 q^{82} + 17492 q^{83} - 102312 q^{84} + 15750 q^{85} - 216688 q^{86} - 9342 q^{87} + 18513 q^{88} + 25302 q^{89} + 2025 q^{90} + 3392 q^{91} - 27408 q^{92} + 16848 q^{93} - 30800 q^{94} + 64300 q^{95} - 67707 q^{96} - 172546 q^{97} - 615271 q^{98} + 68607 q^{99}+O(q^{100}) \) 7 * q + q^2 + 63 * q^3 + 195 * q^4 + 175 * q^5 + 9 * q^6 + 153 * q^8 + 567 * q^9 + 25 * q^10 + 847 * q^11 + 1755 * q^12 + 1418 * q^13 + 2548 * q^14 + 1575 * q^15 + 3699 * q^16 + 630 * q^17 + 81 * q^18 + 2572 * q^19 + 4875 * q^20 + 121 * q^22 + 536 * q^23 + 1377 * q^24 + 4375 * q^25 - 7626 * q^26 + 5103 * q^27 - 11368 * q^28 - 1038 * q^29 + 225 * q^30 + 1872 * q^31 - 7523 * q^32 + 7623 * q^33 + 20790 * q^34 + 15795 * q^36 + 24298 * q^37 - 18952 * q^38 + 12762 * q^39 + 3825 * q^40 - 17658 * q^41 + 22932 * q^42 + 7244 * q^43 + 23595 * q^44 + 14175 * q^45 + 31016 * q^46 + 34560 * q^47 + 33291 * q^48 + 78735 * q^49 + 625 * q^50 + 5670 * q^51 + 110222 * q^52 - 10214 * q^53 + 729 * q^54 + 21175 * q^55 + 81124 * q^56 + 23148 * q^57 - 5718 * q^58 + 94676 * q^59 + 43875 * q^60 + 69538 * q^61 - 4208 * q^62 + 112339 * q^64 + 35450 * q^65 + 1089 * q^66 + 64908 * q^67 - 136010 * q^68 + 4824 * q^69 + 63700 * q^70 + 61816 * q^71 + 12393 * q^72 - 11890 * q^73 - 124050 * q^74 + 39375 * q^75 - 47216 * q^76 - 68634 * q^78 + 18928 * q^79 + 92475 * q^80 + 45927 * q^81 + 36398 * q^82 + 17492 * q^83 - 102312 * q^84 + 15750 * q^85 - 216688 * q^86 - 9342 * q^87 + 18513 * q^88 + 25302 * q^89 + 2025 * q^90 + 3392 * q^91 - 27408 * q^92 + 16848 * q^93 - 30800 * q^94 + 64300 * q^95 - 67707 * q^96 - 172546 * q^97 - 615271 * q^98 + 68607 * 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 $

$2$	5.17374	0.914597	0.457298	−	0.889313i	$-0.348817\pi$
$2$	5.17374	0.914597	0.457298	+	0.889313i	$0.348817\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	−5.23241	−0.163513
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	46.5637	0.528043
$7$	24.5405	0.189295	0.0946473	−	0.995511i	$-0.469828\pi$
$7$	24.5405	0.189295	0.0946473	+	0.995511i	$0.469828\pi$
$8$	−192.631	−1.06415
$9$	81.0000	0.333333
$10$	129.343	0.409020
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−47.0917	−0.0944043
$13$	954.137	1.56586	0.782929	−	0.622111i	$-0.213725\pi$
$13$	954.137	1.56586	0.782929	+	0.622111i	$0.213725\pi$
$14$	126.966	0.173128
$15$	225.000	0.258199
$16$	−829.185	−0.809751
$17$	1130.25	0.948529	0.474264	−	0.880383i	$-0.342714\pi$
$17$	1130.25	0.948529	0.474264	+	0.880383i	$0.342714\pi$
$18$	419.073	0.304866
$19$	2105.70	1.33818	0.669088	−	0.743184i	$-0.266685\pi$
$19$	2105.70	1.33818	0.669088	+	0.743184i	$0.266685\pi$
$20$	−130.810	−0.0731252
$21$	220.864	0.109289
$22$	626.023	0.275761
$23$	−944.310	−0.372216	−0.186108	−	0.982529i	$-0.559587\pi$
$23$	−944.310	−0.372216	−0.186108	+	0.982529i	$0.559587\pi$
$24$	−1733.68	−0.614384
$25$	625.000	0.200000
$26$	4936.46	1.43213
$27$	729.000	0.192450
$28$	−128.406	−0.0309521
$29$	−657.825	−0.145250	−0.0726248	−	0.997359i	$-0.523138\pi$
$29$	−657.825	−0.145250	−0.0726248	+	0.997359i	$0.523138\pi$
$30$	1164.09	0.236148
$31$	477.750	0.0892888	0.0446444	−	0.999003i	$-0.485785\pi$
$31$	477.750	0.0892888	0.0446444	+	0.999003i	$0.485785\pi$
$32$	1874.20	0.323550
$33$	1089.00	0.174078
$34$	5847.60	0.867521
$35$	613.512	0.0846551
$36$	−423.826	−0.0545043
$37$	−9315.20	−1.11863	−0.559317	−	0.828954i	$-0.688937\pi$
$37$	−9315.20	−1.11863	−0.559317	+	0.828954i	$0.688937\pi$
$38$	10894.4	1.22389
$39$	8587.23	0.904048
$40$	−4815.77	−0.475900
$41$	20254.2	1.88173	0.940863	−	0.338787i	$-0.110016\pi$
$41$	20254.2	1.88173	0.940863	+	0.338787i	$0.110016\pi$
$42$	1142.70	0.0999556
$43$	16803.1	1.38586	0.692928	−	0.721006i	$-0.256320\pi$
$43$	16803.1	1.38586	0.692928	+	0.721006i	$0.256320\pi$
$44$	−633.122	−0.0493010
$45$	2025.00	0.149071
$46$	−4885.61	−0.340427
$47$	−16571.1	−1.09422	−0.547112	−	0.837059i	$-0.684273\pi$
$47$	−16571.1	−1.09422	−0.547112	+	0.837059i	$0.684273\pi$
$48$	−7462.66	−0.467510
$49$	−16204.8	−0.964168
$50$	3233.59	0.182919
$51$	10172.2	0.547633
$52$	−4992.44	−0.256038
$53$	−593.161	−0.0290056	−0.0145028	−	0.999895i	$-0.504617\pi$
$53$	−593.161	−0.0290056	−0.0145028	+	0.999895i	$0.504617\pi$
$54$	3771.66	0.176014
$55$	3025.00	0.134840
$56$	−4727.26	−0.201437
$57$	18951.3	0.772596
$58$	−3403.41	−0.132845
$59$	−8929.71	−0.333970	−0.166985	−	0.985959i	$-0.553403\pi$
$59$	−8929.71	−0.333970	−0.166985	+	0.985959i	$0.553403\pi$
$60$	−1177.29	−0.0422189
$61$	−55398.1	−1.90621	−0.953103	−	0.302645i	$-0.902130\pi$
$61$	−55398.1	−1.90621	−0.953103	+	0.302645i	$0.902130\pi$
$62$	2471.76	0.0816632
$63$	1987.78	0.0630982
$64$	36230.5	1.10567
$65$	23853.4	0.700273
$66$	5634.20	0.159211
$67$	63430.4	1.72628	0.863138	−	0.504969i	$-0.168496\pi$
$67$	63430.4	1.72628	0.863138	+	0.504969i	$0.168496\pi$
$68$	−5913.91	−0.155097
$69$	−8498.79	−0.214899
$70$	3174.15	0.0774253
$71$	−6287.83	−0.148032	−0.0740159	−	0.997257i	$-0.523582\pi$
$71$	−6287.83	−0.148032	−0.0740159	+	0.997257i	$0.523582\pi$
$72$	−15603.1	−0.354715
$73$	12474.3	0.273974	0.136987	−	0.990573i	$-0.456258\pi$
$73$	12474.3	0.273974	0.136987	+	0.990573i	$0.456258\pi$
$74$	−48194.4	−1.02310
$75$	5625.00	0.115470
$76$	−11017.9	−0.218809
$77$	2969.40	0.0570745
$78$	44428.1	0.826839
$79$	−85339.3	−1.53844	−0.769222	−	0.638982i	$-0.779356\pi$
$79$	−85339.3	−1.53844	−0.769222	+	0.638982i	$0.779356\pi$
$80$	−20729.6	−0.362131
$81$	6561.00	0.111111
$82$	104790.	1.72102
$83$	47988.8	0.764618	0.382309	−	0.924034i	$-0.375129\pi$
$83$	47988.8	0.764618	0.382309	+	0.924034i	$0.375129\pi$
$84$	−1155.65	−0.0178702
$85$	28256.1	0.424195
$86$	86934.9	1.26750
$87$	−5920.42	−0.0838599
$88$	−23308.3	−0.320852
$89$	4127.92	0.0552403	0.0276201	−	0.999618i	$-0.491207\pi$
$89$	4127.92	0.0552403	0.0276201	+	0.999618i	$0.491207\pi$
$90$	10476.8	0.136340
$91$	23415.0	0.296408
$92$	4941.02	0.0608621
$93$	4299.75	0.0515509
$94$	−85734.5	−1.00077
$95$	52642.6	0.598450
$96$	16867.8	0.186802
$97$	−107861.	−1.16395	−0.581973	−	0.813208i	$-0.697719\pi$
$97$	−107861.	−1.16395	−0.581973	+	0.813208i	$0.697719\pi$
$98$	−83839.2	−0.881824
$99$	9801.00	0.100504
$100$	−3270.26	−0.0327026
$101$	−134275.	−1.30976	−0.654881	−	0.755732i	$-0.727281\pi$
$101$	−134275.	−1.30976	−0.654881	+	0.755732i	$0.727281\pi$
$102$	52628.4	0.500863
$103$	41259.1	0.383201	0.191601	−	0.981473i	$-0.438632\pi$
$103$	41259.1	0.383201	0.191601	+	0.981473i	$0.438632\pi$
$104$	−183796.	−1.66630
$105$	5521.61	0.0488757
$106$	−3068.86	−0.0265285
$107$	−101010.	−0.852913	−0.426457	−	0.904508i	$-0.640238\pi$
$107$	−101010.	−0.852913	−0.426457	+	0.904508i	$0.640238\pi$
$108$	−3814.43	−0.0314681
$109$	138978.	1.12041	0.560207	−	0.828352i	$-0.310721\pi$
$109$	138978.	1.12041	0.560207	+	0.828352i	$0.310721\pi$
$110$	15650.6	0.123324
$111$	−83836.8	−0.645844
$112$	−20348.6	−0.153281
$113$	−48675.2	−0.358601	−0.179301	−	0.983794i	$-0.557383\pi$
$113$	−48675.2	−0.358601	−0.179301	+	0.983794i	$0.557383\pi$
$114$	98049.2	0.706613
$115$	−23607.7	−0.166460
$116$	3442.01	0.0237502
$117$	77285.1	0.521952
$118$	−46200.0	−0.305448
$119$	27736.8	0.179551
$120$	−43341.9	−0.274761
$121$	14641.0	0.0909091
$122$	−286615.	−1.74341
$123$	182288.	1.08642
$124$	−2499.79	−0.0145999
$125$	15625.0	0.0894427
$126$	10284.3	0.0577094
$127$	−171864.	−0.945531	−0.472766	−	0.881188i	$-0.656744\pi$
$127$	−171864.	−0.945531	−0.472766	+	0.881188i	$0.656744\pi$
$128$	127473.	0.687691
$129$	151228.	0.800125
$130$	123411.	0.640467
$131$	−195688.	−0.996289	−0.498144	−	0.867094i	$-0.665985\pi$
$131$	−195688.	−0.996289	−0.498144	+	0.867094i	$0.665985\pi$
$132$	−5698.10	−0.0284640
$133$	51675.0	0.253309
$134$	328172.	1.57885
$135$	18225.0	0.0860663
$136$	−217720.	−1.00937
$137$	−66964.2	−0.304818	−0.152409	−	0.988317i	$-0.548703\pi$
$137$	−66964.2	−0.304818	−0.152409	+	0.988317i	$0.548703\pi$
$138$	−43970.5	−0.196546
$139$	−386365.	−1.69614	−0.848068	−	0.529888i	$-0.822234\pi$
$139$	−386365.	−1.69614	−0.848068	+	0.529888i	$0.822234\pi$
$140$	−3210.15	−0.0138422
$141$	−149140.	−0.631750
$142$	−32531.6	−0.135389
$143$	115451.	0.472124
$144$	−67163.9	−0.269917
$145$	−16445.6	−0.0649576
$146$	64538.8	0.250576
$147$	−145843.	−0.556662
$148$	48741.0	0.182911
$149$	−459593.	−1.69593	−0.847964	−	0.530054i	$-0.822172\pi$
$149$	−459593.	−1.69593	−0.847964	+	0.530054i	$0.822172\pi$
$150$	29102.3	0.105609
$151$	430109.	1.53510	0.767550	−	0.640989i	$-0.221476\pi$
$151$	430109.	1.53510	0.767550	+	0.640989i	$0.221476\pi$
$152$	−405623.	−1.42401
$153$	91549.9	0.316176
$154$	15362.9	0.0522001
$155$	11943.8	0.0399311
$156$	−44932.0	−0.147824
$157$	−166256.	−0.538304	−0.269152	−	0.963098i	$-0.586743\pi$
$157$	−166256.	−0.538304	−0.269152	+	0.963098i	$0.586743\pi$
$158$	−441524.	−1.40706
$159$	−5338.44	−0.0167464
$160$	46855.0	0.144696
$161$	−23173.8	−0.0704585
$162$	33944.9	0.101622
$163$	384902.	1.13470	0.567350	−	0.823476i	$-0.307968\pi$
$163$	384902.	1.13470	0.567350	+	0.823476i	$0.307968\pi$
$164$	−105979.	−0.307687
$165$	27225.0	0.0778499
$166$	248282.	0.699317
$167$	14767.3	0.0409741	0.0204870	−	0.999790i	$-0.493478\pi$
$167$	14767.3	0.0409741	0.0204870	+	0.999790i	$0.493478\pi$
$168$	−42545.3	−0.116300
$169$	539084.	1.45191
$170$	146190.	0.387967
$171$	170562.	0.446058
$172$	−87920.8	−0.226606
$173$	309864.	0.787146	0.393573	−	0.919293i	$-0.371239\pi$
$173$	309864.	0.787146	0.393573	+	0.919293i	$0.371239\pi$
$174$	−30630.7	−0.0766980
$175$	15337.8	0.0378589
$176$	−100331.	−0.244149
$177$	−80367.4	−0.192818
$178$	21356.8	0.0505226
$179$	−856140.	−1.99716	−0.998579	−	0.0532965i	$-0.983027\pi$
$179$	−856140.	−1.99716	−0.998579	+	0.0532965i	$0.983027\pi$
$180$	−10595.6	−0.0243751
$181$	407609.	0.924799	0.462399	−	0.886672i	$-0.346989\pi$
$181$	407609.	0.924799	0.462399	+	0.886672i	$0.346989\pi$
$182$	121143.	0.271094
$183$	−498583.	−1.10055
$184$	181903.	0.396092
$185$	−232880.	−0.500268
$186$	22245.8	0.0471483
$187$	136760.	0.285992
$188$	86706.8	0.178920
$189$	17890.0	0.0364298
$190$	272359.	0.547340
$191$	−318673.	−0.632064	−0.316032	−	0.948748i	$-0.602351\pi$
$191$	−318673.	−0.632064	−0.316032	+	0.948748i	$0.602351\pi$
$192$	326075.	0.638358
$193$	240486.	0.464725	0.232362	−	0.972629i	$-0.425354\pi$
$193$	240486.	0.464725	0.232362	+	0.972629i	$0.425354\pi$
$194$	−558042.	−1.06454
$195$	214681.	0.404303
$196$	84790.0	0.157654
$197$	−535129.	−0.982411	−0.491205	−	0.871044i	$-0.663444\pi$
$197$	−535129.	−0.982411	−0.491205	+	0.871044i	$0.663444\pi$
$198$	50707.8	0.0919204
$199$	569525.	1.01948	0.509741	−	0.860328i	$-0.329741\pi$
$199$	569525.	1.01948	0.509741	+	0.860328i	$0.329741\pi$
$200$	−120394.	−0.212829
$201$	570873.	0.996666
$202$	−694705.	−1.19790
$203$	−16143.3	−0.0274950
$204$	−53225.2	−0.0895451
$205$	506356.	0.841534
$206$	213464.	0.350475
$207$	−76489.1	−0.124072
$208$	−791155.	−1.26795
$209$	254790.	0.403475
$210$	28567.4	0.0447015
$211$	1.23176e6	1.90467	0.952337	−	0.305049i	$-0.0986730\pi$
$211$	1.23176e6	1.90467	0.952337	+	0.305049i	$0.0986730\pi$
$212$	3103.66	0.00474280
$213$	−56590.5	−0.0854662
$214$	−522599.	−0.780071
$215$	420078.	0.619774
$216$	−140428.	−0.204795
$217$	11724.2	0.0169019
$218$	719034.	1.02473
$219$	112269.	0.158179
$220$	−15828.1	−0.0220481
$221$	1.07841e6	1.48526
$222$	−433750.	−0.590686
$223$	91200.4	0.122810	0.0614051	−	0.998113i	$-0.480442\pi$
$223$	91200.4	0.122810	0.0614051	+	0.998113i	$0.480442\pi$
$224$	45993.8	0.0612462
$225$	50625.0	0.0666667
$226$	−251833.	−0.327975
$227$	113644.	0.146380	0.0731899	−	0.997318i	$-0.476682\pi$
$227$	113644.	0.146380	0.0731899	+	0.997318i	$0.476682\pi$
$228$	−99161.2	−0.126329
$229$	497330.	0.626695	0.313348	−	0.949639i	$-0.398550\pi$
$229$	497330.	0.626695	0.313348	+	0.949639i	$0.398550\pi$
$230$	−122140.	−0.152244
$231$	26724.6	0.0329520
$232$	126717.	0.154567
$233$	635379.	0.766731	0.383365	−	0.923597i	$-0.374765\pi$
$233$	635379.	0.766731	0.383365	+	0.923597i	$0.374765\pi$
$234$	399853.	0.477376
$235$	−414277.	−0.489352
$236$	46723.9	0.0546084
$237$	−768054.	−0.888221
$238$	143503.	0.164217
$239$	951066.	1.07700	0.538500	−	0.842625i	$-0.318991\pi$
$239$	951066.	1.07700	0.538500	+	0.842625i	$0.318991\pi$
$240$	−186567.	−0.209077
$241$	895844.	0.993550	0.496775	−	0.867879i	$-0.334517\pi$
$241$	895844.	0.993550	0.496775	+	0.867879i	$0.334517\pi$
$242$	75748.7	0.0831452
$243$	59049.0	0.0641500
$244$	289866.	0.311689
$245$	−405119.	−0.431189
$246$	943112.	0.993632
$247$	2.00913e6	2.09539
$248$	−92029.4	−0.0950162
$249$	431899.	0.441453
$250$	80839.7	0.0818040
$251$	885541.	0.887206	0.443603	−	0.896223i	$-0.353700\pi$
$251$	885541.	0.887206	0.443603	+	0.896223i	$0.353700\pi$
$252$	−10400.9	−0.0103174
$253$	−114261.	−0.112227
$254$	−889180.	−0.864780
$255$	254305.	0.244909
$256$	−499865.	−0.476709
$257$	−1.32803e6	−1.25422	−0.627110	−	0.778931i	$-0.715762\pi$
$257$	−1.32803e6	−1.25422	−0.627110	+	0.778931i	$0.715762\pi$
$258$	782414.	0.731792
$259$	−228600.	−0.211751
$260$	−124811.	−0.114504
$261$	−53283.8	−0.0484166
$262$	−1.01244e6	−0.911203
$263$	885658.	0.789545	0.394772	−	0.918779i	$-0.370823\pi$
$263$	885658.	0.789545	0.394772	+	0.918779i	$0.370823\pi$
$264$	−209775.	−0.185244
$265$	−14829.0	−0.0129717
$266$	267353.	0.231676
$267$	37151.2	0.0318930
$268$	−331894.	−0.282268
$269$	507736.	0.427816	0.213908	−	0.976854i	$-0.431381\pi$
$269$	507736.	0.427816	0.213908	+	0.976854i	$0.431381\pi$
$270$	94291.4	0.0787159
$271$	−566288.	−0.468397	−0.234198	−	0.972189i	$-0.575247\pi$
$271$	−566288.	−0.468397	−0.234198	+	0.972189i	$0.575247\pi$
$272$	−937182.	−0.768072
$273$	210735.	0.171131
$274$	−346455.	−0.278786
$275$	75625.0	0.0603023
$276$	44469.2	0.0351388
$277$	−25605.7	−0.0200511	−0.0100255	−	0.999950i	$-0.503191\pi$
$277$	−25605.7	−0.0200511	−0.0100255	+	0.999950i	$0.503191\pi$
$278$	−1.99895e6	−1.55128
$279$	38697.8	0.0297629
$280$	−118181.	−0.0900853
$281$	1.37686e6	1.04022	0.520110	−	0.854099i	$-0.325891\pi$
$281$	1.37686e6	1.04022	0.520110	+	0.854099i	$0.325891\pi$
$282$	−771610.	−0.577797
$283$	−193069.	−0.143300	−0.0716500	−	0.997430i	$-0.522826\pi$
$283$	−193069.	−0.143300	−0.0716500	+	0.997430i	$0.522826\pi$
$284$	32900.5	0.0242051
$285$	473783.	0.345515
$286$	597311.	0.431803
$287$	497049.	0.356201
$288$	151810.	0.107850
$289$	−142403.	−0.100294
$290$	−85085.3	−0.0594100
$291$	−970745.	−0.672005
$292$	−65270.7	−0.0447983
$293$	−2.19083e6	−1.49087	−0.745436	−	0.666577i	$-0.767759\pi$
$293$	−2.19083e6	−1.49087	−0.745436	+	0.666577i	$0.767759\pi$
$294$	−754553.	−0.509122
$295$	−223243.	−0.149356
$296$	1.79440e6	1.19039
$297$	88209.0	0.0580259
$298$	−2.37781e6	−1.55109
$299$	−901001.	−0.582837
$300$	−29432.3	−0.0188809
$301$	412356.	0.262335
$302$	2.22527e6	1.40400
$303$	−1.20848e6	−0.756191
$304$	−1.74602e6	−1.08359
$305$	−1.38495e6	−0.852482
$306$	473655.	0.289174
$307$	−2.54210e6	−1.53938	−0.769691	−	0.638417i	$-0.779590\pi$
$307$	−2.54210e6	−1.53938	−0.769691	+	0.638417i	$0.779590\pi$
$308$	−15537.1	−0.00933241
$309$	371332.	0.221241
$310$	61793.9	0.0365209
$311$	−1.51867e6	−0.890353	−0.445176	−	0.895443i	$-0.646859\pi$
$311$	−1.51867e6	−0.890353	−0.445176	+	0.895443i	$0.646859\pi$
$312$	−1.65417e6	−0.962038
$313$	−2.24663e6	−1.29619	−0.648097	−	0.761558i	$-0.724435\pi$
$313$	−2.24663e6	−1.29619	−0.648097	+	0.761558i	$0.724435\pi$
$314$	−860164.	−0.492331
$315$	49694.5	0.0282184
$316$	446531.	0.251555
$317$	104379.	0.0583396	0.0291698	−	0.999574i	$-0.490714\pi$
$317$	104379.	0.0583396	0.0291698	+	0.999574i	$0.490714\pi$
$318$	−27619.7	−0.0153162
$319$	−79596.8	−0.0437944
$320$	905763.	0.494470
$321$	−909090.	−0.492430
$322$	−119895.	−0.0644411
$323$	2.37996e6	1.26930
$324$	−34329.9	−0.0181681
$325$	596335.	0.313171
$326$	1.99138e6	1.03779
$327$	1.25080e6	0.646872
$328$	−3.90159e6	−2.00243
$329$	−406662.	−0.207131
$330$	140855.	0.0712013
$331$	−129279.	−0.0648570	−0.0324285	−	0.999474i	$-0.510324\pi$
$331$	−129279.	−0.0648570	−0.0324285	+	0.999474i	$0.510324\pi$
$332$	−251097.	−0.125025
$333$	−754532.	−0.372878
$334$	76402.0	0.0374747
$335$	1.58576e6	0.772014
$336$	−183137.	−0.0884971
$337$	−2.39588e6	−1.14918	−0.574592	−	0.818440i	$-0.694839\pi$
$337$	−2.39588e6	−1.14918	−0.574592	+	0.818440i	$0.694839\pi$
$338$	2.78908e6	1.32791
$339$	−438077.	−0.207038
$340$	−147848.	−0.0693614
$341$	57807.8	0.0269216
$342$	882443.	0.407963
$343$	−810125.	−0.371806
$344$	−3.23680e6	−1.47475
$345$	−212470.	−0.0961057
$346$	1.60315e6	0.719921
$347$	−2.37776e6	−1.06010	−0.530048	−	0.847968i	$-0.677826\pi$
$347$	−2.37776e6	−1.06010	−0.530048	+	0.847968i	$0.677826\pi$
$348$	30978.1	0.0137122
$349$	−676141.	−0.297149	−0.148574	−	0.988901i	$-0.547468\pi$
$349$	−676141.	−0.297149	−0.148574	+	0.988901i	$0.547468\pi$
$350$	79353.8	0.0346256
$351$	695566.	0.301349
$352$	226778.	0.0975540
$353$	2.58316e6	1.10335	0.551676	−	0.834059i	$-0.313989\pi$
$353$	2.58316e6	1.10335	0.551676	+	0.834059i	$0.313989\pi$
$354$	−415800.	−0.176350
$355$	−157196.	−0.0662018
$356$	−21599.0	−0.00903250
$357$	249631.	0.103664
$358$	−4.42945e6	−1.82659
$359$	−2.24916e6	−0.921052	−0.460526	−	0.887646i	$-0.652339\pi$
$359$	−2.24916e6	−0.921052	−0.460526	+	0.887646i	$0.652339\pi$
$360$	−390077.	−0.158633
$361$	1.95788e6	0.790713
$362$	2.10886e6	0.845818
$363$	131769.	0.0524864
$364$	−122517.	−0.0484666
$365$	311857.	0.122525
$366$	−2.57954e6	−1.00656
$367$	−574447.	−0.222631	−0.111315	−	0.993785i	$-0.535506\pi$
$367$	−574447.	−0.222631	−0.111315	+	0.993785i	$0.535506\pi$
$368$	783007.	0.301402
$369$	1.64059e6	0.627242
$370$	−1.20486e6	−0.457544
$371$	−14556.5	−0.00549061
$372$	−22498.1	−0.00842924
$373$	3.19211e6	1.18797	0.593986	−	0.804475i	$-0.297553\pi$
$373$	3.19211e6	1.18797	0.593986	+	0.804475i	$0.297553\pi$
$374$	707559.	0.261567
$375$	140625.	0.0516398
$376$	3.19210e6	1.16441
$377$	−627655.	−0.227440
$378$	92558.3	0.0333185
$379$	1.17249e6	0.419285	0.209643	−	0.977778i	$-0.432770\pi$
$379$	1.17249e6	0.419285	0.209643	+	0.977778i	$0.432770\pi$
$380$	−275448.	−0.0978543
$381$	−1.54678e6	−0.545903
$382$	−1.64873e6	−0.578084
$383$	−1.34408e6	−0.468198	−0.234099	−	0.972213i	$-0.575214\pi$
$383$	−1.34408e6	−0.468198	−0.234099	+	0.972213i	$0.575214\pi$
$384$	1.14726e6	0.397038
$385$	74235.0	0.0255245
$386$	1.24421e6	0.425036
$387$	1.36105e6	0.461952
$388$	564371.	0.190320
$389$	−866399.	−0.290298	−0.145149	−	0.989410i	$-0.546366\pi$
$389$	−866399.	−0.290298	−0.145149	+	0.989410i	$0.546366\pi$
$390$	1.11070e6	0.369774
$391$	−1.06730e6	−0.353057
$392$	3.12154e6	1.02601
$393$	−1.76119e6	−0.575208
$394$	−2.76862e6	−0.898510
$395$	−2.13348e6	−0.688013
$396$	−51282.9	−0.0164337
$397$	2.96049e6	0.942730	0.471365	−	0.881938i	$-0.343762\pi$
$397$	2.96049e6	0.942730	0.471365	+	0.881938i	$0.343762\pi$
$398$	2.94657e6	0.932415
$399$	465075.	0.146248
$400$	−518240.	−0.161950
$401$	4.44333e6	1.37990	0.689950	−	0.723857i	$-0.257633\pi$
$401$	4.44333e6	1.37990	0.689950	+	0.723857i	$0.257633\pi$
$402$	2.95355e6	0.911547
$403$	455839.	0.139813
$404$	702583.	0.214163
$405$	164025.	0.0496904
$406$	−83521.4	−0.0251468
$407$	−1.12714e6	−0.337281
$408$	−1.95948e6	−0.582761
$409$	4.40790e6	1.30294	0.651468	−	0.758676i	$-0.274154\pi$
$409$	4.40790e6	1.30294	0.651468	+	0.758676i	$0.274154\pi$
$410$	2.61976e6	0.769664
$411$	−602677.	−0.175987
$412$	−215885.	−0.0626584
$413$	−219139.	−0.0632187
$414$	−395735.	−0.113476
$415$	1.19972e6	0.341948
$416$	1.78824e6	0.506633
$417$	−3.47728e6	−0.979264
$418$	1.31822e6	0.369017
$419$	2.38585e6	0.663908	0.331954	−	0.943296i	$-0.392292\pi$
$419$	2.38585e6	0.663908	0.331954	+	0.943296i	$0.392292\pi$
$420$	−28891.4	−0.00799180
$421$	−2.16547e6	−0.595453	−0.297726	−	0.954651i	$-0.596228\pi$
$421$	−2.16547e6	−0.595453	−0.297726	+	0.954651i	$0.596228\pi$
$422$	6.37281e6	1.74201
$423$	−1.34226e6	−0.364741
$424$	114261.	0.0308662
$425$	706403.	0.189706
$426$	−292784.	−0.0781671
$427$	−1.35950e6	−0.360835
$428$	528526.	0.139462
$429$	1.03905e6	0.272581
$430$	2.17337e6	0.566843
$431$	5.20830e6	1.35053	0.675263	−	0.737577i	$-0.264030\pi$
$431$	5.20830e6	1.35053	0.675263	+	0.737577i	$0.264030\pi$
$432$	−604476.	−0.155837
$433$	−6.70176e6	−1.71779	−0.858893	−	0.512155i	$-0.828847\pi$
$433$	−6.70176e6	−1.71779	−0.858893	+	0.512155i	$0.828847\pi$
$434$	60658.1	0.0154584
$435$	−148011.	−0.0375033
$436$	−727189.	−0.183202
$437$	−1.98844e6	−0.498090
$438$	580849.	0.144670
$439$	3.00706e6	0.744699	0.372349	−	0.928093i	$-0.378552\pi$
$439$	3.00706e6	0.744699	0.372349	+	0.928093i	$0.378552\pi$
$440$	−582708.	−0.143489
$441$	−1.31259e6	−0.321389
$442$	5.57941e6	1.35841
$443$	−315911.	−0.0764812	−0.0382406	−	0.999269i	$-0.512175\pi$
$443$	−315911.	−0.0764812	−0.0382406	+	0.999269i	$0.512175\pi$
$444$	438669.	0.105604
$445$	103198.	0.0247042
$446$	471847.	0.112322
$447$	−4.13633e6	−0.979145
$448$	889115.	0.209297
$449$	−6.35788e6	−1.48832	−0.744161	−	0.668001i	$-0.767150\pi$
$449$	−6.35788e6	−1.48832	−0.744161	+	0.668001i	$0.767150\pi$
$450$	261921.	0.0609731
$451$	2.45076e6	0.567362
$452$	254689.	0.0586359
$453$	3.87098e6	0.886290
$454$	587964.	0.133879
$455$	585375.	0.132558
$456$	−3.65061e6	−0.822154
$457$	254178.	0.0569309	0.0284654	−	0.999595i	$-0.490938\pi$
$457$	254178.	0.0569309	0.0284654	+	0.999595i	$0.490938\pi$
$458$	2.57306e6	0.573173
$459$	823949.	0.182544
$460$	123526.	0.0272184
$461$	−6.43215e6	−1.40963	−0.704813	−	0.709393i	$-0.748969\pi$
$461$	−6.43215e6	−1.40963	−0.704813	+	0.709393i	$0.748969\pi$
$462$	138266.	0.0301377
$463$	−4.13026e6	−0.895417	−0.447709	−	0.894180i	$-0.647760\pi$
$463$	−4.13026e6	−0.895417	−0.447709	+	0.894180i	$0.647760\pi$
$464$	545458.	0.117616
$465$	107494.	0.0230543
$466$	3.28728e6	0.701249
$467$	−7.12335e6	−1.51144	−0.755722	−	0.654892i	$-0.772714\pi$
$467$	−7.12335e6	−1.51144	−0.755722	+	0.654892i	$0.772714\pi$
$468$	−404388.	−0.0853460
$469$	1.55661e6	0.326775
$470$	−2.14336e6	−0.447559
$471$	−1.49630e6	−0.310790
$472$	1.72014e6	0.355392
$473$	2.03318e6	0.417852
$474$	−3.97371e6	−0.812364
$475$	1.31606e6	0.267635
$476$	−145130.	−0.0293590
$477$	−48046.0	−0.00966855
$478$	4.92057e6	0.985021
$479$	−3.94991e6	−0.786589	−0.393295	−	0.919413i	$-0.628665\pi$
$479$	−3.94991e6	−0.786589	−0.393295	+	0.919413i	$0.628665\pi$
$480$	421695.	0.0835402
$481$	−8.88798e6	−1.75162
$482$	4.63486e6	0.908697
$483$	−208564.	−0.0406792
$484$	−76607.8	−0.0148648
$485$	−2.69651e6	−0.520533
$486$	305504.	0.0586714
$487$	4.99431e6	0.954230	0.477115	−	0.878841i	$-0.341683\pi$
$487$	4.99431e6	0.954230	0.477115	+	0.878841i	$0.341683\pi$
$488$	1.06714e7	2.02848
$489$	3.46412e6	0.655120
$490$	−2.09598e6	−0.394364
$491$	−5.31105e6	−0.994207	−0.497103	−	0.867691i	$-0.665603\pi$
$491$	−5.31105e6	−0.994207	−0.497103	+	0.867691i	$0.665603\pi$
$492$	−953808.	−0.177643
$493$	−743503.	−0.137773
$494$	1.03947e7	1.91644
$495$	245025.	0.0449467
$496$	−396143.	−0.0723016
$497$	−154306.	−0.0280216
$498$	2.23453e6	0.403751
$499$	1.03269e7	1.85660	0.928300	−	0.371831i	$-0.121270\pi$
$499$	1.03269e7	1.85660	0.928300	+	0.371831i	$0.121270\pi$
$500$	−81756.5	−0.0146250
$501$	132905.	0.0236564
$502$	4.58156e6	0.811435
$503$	−5.18142e6	−0.913122	−0.456561	−	0.889692i	$-0.650919\pi$
$503$	−5.18142e6	−0.913122	−0.456561	+	0.889692i	$0.650919\pi$
$504$	−382908.	−0.0671456
$505$	−3.35688e6	−0.585743
$506$	−591159.	−0.102643
$507$	4.85176e6	0.838260
$508$	899264.	0.154607
$509$	−2.85947e6	−0.489206	−0.244603	−	0.969623i	$-0.578658\pi$
$509$	−2.85947e6	−0.489206	−0.244603	+	0.969623i	$0.578658\pi$
$510$	1.31571e6	0.223993
$511$	306125.	0.0518618
$512$	−6.66531e6	−1.12369
$513$	1.53506e6	0.257532
$514$	−6.87086e6	−1.14711
$515$	1.03148e6	0.171373
$516$	−791287.	−0.130831
$517$	−2.00510e6	−0.329921
$518$	−1.18272e6	−0.193667
$519$	2.78877e6	0.454459
$520$	−4.59490e6	−0.745192
$521$	−8.79205e6	−1.41904	−0.709522	−	0.704684i	$-0.751089\pi$
$521$	−8.79205e6	−1.41904	−0.709522	+	0.704684i	$0.751089\pi$
$522$	−275676.	−0.0442816
$523$	3.56687e6	0.570208	0.285104	−	0.958497i	$-0.407972\pi$
$523$	3.56687e6	0.570208	0.285104	+	0.958497i	$0.407972\pi$
$524$	1.02392e6	0.162906
$525$	138040.	0.0218579
$526$	4.58216e6	0.722115
$527$	539975.	0.0846929
$528$	−902982.	−0.140959
$529$	−5.54462e6	−0.861455
$530$	−76721.5	−0.0118639
$531$	−723306.	−0.111323
$532$	−270385.	−0.0414194
$533$	1.93253e7	2.94652
$534$	192211.	0.0291692
$535$	−2.52525e6	−0.381434
$536$	−1.22186e7	−1.83701
$537$	−7.70526e6	−1.15306
$538$	2.62690e6	0.391279
$539$	−1.96078e6	−0.290707
$540$	−95360.8	−0.0140730
$541$	−8.18416e6	−1.20221	−0.601106	−	0.799170i	$-0.705273\pi$
$541$	−8.18416e6	−1.20221	−0.601106	+	0.799170i	$0.705273\pi$
$542$	−2.92982e6	−0.428394
$543$	3.66848e6	0.533933
$544$	2.11831e6	0.306896
$545$	3.47444e6	0.501065
$546$	1.09029e6	0.156516
$547$	−8.18083e6	−1.16904	−0.584520	−	0.811380i	$-0.698717\pi$
$547$	−8.18083e6	−1.16904	−0.584520	+	0.811380i	$0.698717\pi$
$548$	350384.	0.0498417
$549$	−4.48724e6	−0.635402
$550$	391264.	0.0551523
$551$	−1.38518e6	−0.194369
$552$	1.63713e6	0.228684
$553$	−2.09427e6	−0.291219
$554$	−132477.	−0.0183387
$555$	−2.09592e6	−0.288830
$556$	2.02162e6	0.277340
$557$	−1.22255e7	−1.66966	−0.834829	−	0.550510i	$-0.814433\pi$
$557$	−1.22255e7	−1.66966	−0.834829	+	0.550510i	$0.814433\pi$
$558$	200212.	0.0272211
$559$	1.60325e7	2.17005
$560$	−508715.	−0.0685495
$561$	1.23084e6	0.165118
$562$	7.12353e6	0.951381
$563$	−7.14946e6	−0.950610	−0.475305	−	0.879821i	$-0.657662\pi$
$563$	−7.14946e6	−0.950610	−0.475305	+	0.879821i	$0.657662\pi$
$564$	780361.	0.103299
$565$	−1.21688e6	−0.160371
$566$	−998888.	−0.131062
$567$	161010.	0.0210327
$568$	1.21123e6	0.157527
$569$	1.33252e6	0.172542	0.0862710	−	0.996272i	$-0.472505\pi$
$569$	1.33252e6	0.172542	0.0862710	+	0.996272i	$0.472505\pi$
$570$	2.45123e6	0.316007
$571$	8.55769e6	1.09841	0.549207	−	0.835686i	$-0.314930\pi$
$571$	8.55769e6	1.09841	0.549207	+	0.835686i	$0.314930\pi$
$572$	−604085.	−0.0771984
$573$	−2.86805e6	−0.364923
$574$	2.57160e6	0.325780
$575$	−590194.	−0.0744432
$576$	2.93467e6	0.368556
$577$	5.88800e6	0.736256	0.368128	−	0.929775i	$-0.379999\pi$
$577$	5.88800e6	0.736256	0.368128	+	0.929775i	$0.379999\pi$
$578$	−736754.	−0.0917282
$579$	2.16437e6	0.268309
$580$	86050.3	0.0106214
$581$	1.17767e6	0.144738
$582$	−5.02238e6	−0.614614
$583$	−71772.4	−0.00874553
$584$	−2.40293e6	−0.291548
$585$	1.93213e6	0.233424
$586$	−1.13348e7	−1.36355
$587$	1.10533e7	1.32402	0.662012	−	0.749494i	$-0.269703\pi$
$587$	1.10533e7	1.32402	0.662012	+	0.749494i	$0.269703\pi$
$588$	763110.	0.0910215
$589$	1.00600e6	0.119484
$590$	−1.15500e6	−0.136600
$591$	−4.81616e6	−0.567195
$592$	7.72402e6	0.905815
$593$	3.84858e6	0.449431	0.224716	−	0.974424i	$-0.427855\pi$
$593$	3.84858e6	0.449431	0.224716	+	0.974424i	$0.427855\pi$
$594$	456370.	0.0530703
$595$	693419.	0.0802978
$596$	2.40478e6	0.277306
$597$	5.12572e6	0.588598
$598$	−4.66154e6	−0.533061
$599$	7.08379e6	0.806675	0.403337	−	0.915051i	$-0.367850\pi$
$599$	7.08379e6	0.806675	0.403337	+	0.915051i	$0.367850\pi$
$600$	−1.08355e6	−0.122877
$601$	1.39434e6	0.157465	0.0787323	−	0.996896i	$-0.474913\pi$
$601$	1.39434e6	0.157465	0.0787323	+	0.996896i	$0.474913\pi$
$602$	2.13343e6	0.239931
$603$	5.13786e6	0.575425
$604$	−2.25051e6	−0.251009
$605$	366025.	0.0406558
$606$	−6.25234e6	−0.691610
$607$	1.30713e7	1.43995	0.719976	−	0.693999i	$-0.244153\pi$
$607$	1.30713e7	1.43995	0.719976	+	0.693999i	$0.244153\pi$
$608$	3.94651e6	0.432966
$609$	−145290.	−0.0158742
$610$	−7.16538e6	−0.779677
$611$	−1.58111e7	−1.71340
$612$	−479027.	−0.0516989
$613$	−1.77204e7	−1.90468	−0.952339	−	0.305040i	$-0.901330\pi$
$613$	−1.77204e7	−1.90468	−0.952339	+	0.305040i	$0.901330\pi$
$614$	−1.31521e7	−1.40791
$615$	4.55721e6	0.485860
$616$	−571998.	−0.0607355
$617$	2.49941e6	0.264317	0.132158	−	0.991229i	$-0.457809\pi$
$617$	2.49941e6	0.264317	0.132158	+	0.991229i	$0.457809\pi$
$618$	1.92118e6	0.202347
$619$	329876.	0.0346039	0.0173019	−	0.999850i	$-0.494492\pi$
$619$	329876.	0.0346039	0.0173019	+	0.999850i	$0.494492\pi$
$620$	−62494.7	−0.00652926
$621$	−688402.	−0.0716330
$622$	−7.85720e6	−0.814314
$623$	101301.	0.0104567
$624$	−7.12040e6	−0.732054
$625$	390625.	0.0400000
$626$	−1.16235e7	−1.18550
$627$	2.29311e6	0.232946
$628$	869920.	0.0880197
$629$	−1.05285e7	−1.06106
$630$	257106.	0.0258084
$631$	4.46626e6	0.446551	0.223275	−	0.974755i	$-0.428325\pi$
$631$	4.46626e6	0.446551	0.223275	+	0.974755i	$0.428325\pi$
$632$	1.64390e7	1.63713
$633$	1.10859e7	1.09966
$634$	540028.	0.0533572
$635$	−4.29660e6	−0.422854
$636$	27933.0	0.00273826
$637$	−1.54616e7	−1.50975
$638$	−411813.	−0.0400542
$639$	−509314.	−0.0493439
$640$	3.18682e6	0.307545
$641$	−3.46308e6	−0.332903	−0.166451	−	0.986050i	$-0.553231\pi$
$641$	−3.46308e6	−0.332903	−0.166451	+	0.986050i	$0.553231\pi$
$642$	−4.70339e6	−0.450374
$643$	4.99873e6	0.476796	0.238398	−	0.971168i	$-0.423378\pi$
$643$	4.99873e6	0.476796	0.238398	+	0.971168i	$0.423378\pi$
$644$	121255.	0.0115209
$645$	3.78070e6	0.357827
$646$	1.23133e7	1.16090
$647$	9.25338e6	0.869040	0.434520	−	0.900662i	$-0.356918\pi$
$647$	9.25338e6	0.869040	0.434520	+	0.900662i	$0.356918\pi$
$648$	−1.26385e6	−0.118238
$649$	−1.08049e6	−0.100696
$650$	3.08528e6	0.286426
$651$	105518.	0.00975830
$652$	−2.01397e6	−0.185538
$653$	−1.44388e7	−1.32510	−0.662549	−	0.749019i	$-0.730525\pi$
$653$	−1.44388e7	−1.32510	−0.662549	+	0.749019i	$0.730525\pi$
$654$	6.47131e6	0.591627
$655$	−4.89219e6	−0.445554
$656$	−1.67945e7	−1.52373
$657$	1.01042e6	0.0913246
$658$	−2.10397e6	−0.189441
$659$	1.06958e7	0.959397	0.479699	−	0.877433i	$-0.340746\pi$
$659$	1.06958e7	0.959397	0.479699	+	0.877433i	$0.340746\pi$
$660$	−142452.	−0.0127295
$661$	1.41860e6	0.126286	0.0631432	−	0.998004i	$-0.479888\pi$
$661$	1.41860e6	0.126286	0.0631432	+	0.998004i	$0.479888\pi$
$662$	−668854.	−0.0593180
$663$	9.70568e6	0.857516
$664$	−9.24412e6	−0.813665
$665$	1.29187e6	0.113283
$666$	−3.90375e6	−0.341033
$667$	621190.	0.0540642
$668$	−77268.5	−0.00669979
$669$	820803.	0.0709045
$670$	8.20430e6	0.706081
$671$	−6.70317e6	−0.574743
$672$	413944.	0.0353605
$673$	−888726.	−0.0756363	−0.0378182	−	0.999285i	$-0.512041\pi$
$673$	−888726.	−0.0756363	−0.0378182	+	0.999285i	$0.512041\pi$
$674$	−1.23956e7	−1.05104
$675$	455625.	0.0384900
$676$	−2.82071e6	−0.237406
$677$	−1.67805e7	−1.40713	−0.703565	−	0.710631i	$-0.748410\pi$
$677$	−1.67805e7	−1.40713	−0.703565	+	0.710631i	$0.748410\pi$
$678$	−2.26650e6	−0.189357
$679$	−2.64695e6	−0.220329
$680$	−5.44300e6	−0.451405
$681$	1.02279e6	0.0845125
$682$	299082.	0.0246224
$683$	4.42656e6	0.363090	0.181545	−	0.983383i	$-0.441890\pi$
$683$	4.42656e6	0.363090	0.181545	+	0.983383i	$0.441890\pi$
$684$	−892450.	−0.0729363
$685$	−1.67410e6	−0.136319
$686$	−4.19138e6	−0.340053
$687$	4.47597e6	0.361823
$688$	−1.39329e7	−1.12220
$689$	−565956.	−0.0454187
$690$	−1.09926e6	−0.0878980
$691$	−1.22943e7	−0.979507	−0.489754	−	0.871861i	$-0.662913\pi$
$691$	−1.22943e7	−0.979507	−0.489754	+	0.871861i	$0.662913\pi$
$692$	−1.62133e6	−0.128709
$693$	240521.	0.0190248
$694$	−1.23019e7	−0.969560
$695$	−9.65912e6	−0.758535
$696$	1.14046e6	0.0892391
$697$	2.28923e7	1.78487
$698$	−3.49818e6	−0.271771
$699$	5.71841e6	0.442672
$700$	−80253.8	−0.00619042
$701$	−1.70682e7	−1.31188	−0.655938	−	0.754815i	$-0.727727\pi$
$701$	−1.70682e7	−1.31188	−0.655938	+	0.754815i	$0.727727\pi$
$702$	3.59868e6	0.275613
$703$	−1.96150e7	−1.49693
$704$	4.38389e6	0.333372
$705$	−3.72849e6	−0.282527
$706$	1.33646e7	1.00912
$707$	−3.29518e6	−0.247931
$708$	420515.	0.0315282
$709$	1.29170e7	0.965039	0.482519	−	0.875885i	$-0.339722\pi$
$709$	1.29170e7	0.965039	0.482519	+	0.875885i	$0.339722\pi$
$710$	−813290.	−0.0605480
$711$	−6.91249e6	−0.512815
$712$	−795164.	−0.0587837
$713$	−451144.	−0.0332347
$714$	1.29153e6	0.0948107
$715$	2.88626e6	0.211140
$716$	4.47968e6	0.326561
$717$	8.55959e6	0.621806
$718$	−1.16366e7	−0.842391
$719$	1.30692e7	0.942819	0.471409	−	0.881914i	$-0.343745\pi$
$719$	1.30692e7	0.942819	0.471409	+	0.881914i	$0.343745\pi$
$720$	−1.67910e6	−0.120710
$721$	1.01252e6	0.0725379
$722$	1.01296e7	0.723183
$723$	8.06259e6	0.573626
$724$	−2.13278e6	−0.151217
$725$	−411140.	−0.0290499
$726$	681739.	0.0480039
$727$	−2.15158e7	−1.50981	−0.754905	−	0.655834i	$-0.772317\pi$
$727$	−2.15158e7	−1.50981	−0.754905	+	0.655834i	$0.772317\pi$
$728$	−4.51045e6	−0.315421
$729$	531441.	0.0370370
$730$	1.61347e6	0.112061
$731$	1.89916e7	1.31452
$732$	2.60879e6	0.179954
$733$	1.18814e7	0.816785	0.408392	−	0.912807i	$-0.366090\pi$
$733$	1.18814e7	0.816785	0.408392	+	0.912807i	$0.366090\pi$
$734$	−2.97204e6	−0.203617
$735$	−3.64607e6	−0.248947
$736$	−1.76983e6	−0.120430
$737$	7.67507e6	0.520492
$738$	8.48801e6	0.573674
$739$	1.70435e7	1.14801	0.574007	−	0.818851i	$-0.305388\pi$
$739$	1.70435e7	1.14801	0.574007	+	0.818851i	$0.305388\pi$
$740$	1.21853e6	0.0818004
$741$	1.80822e7	1.20977
$742$	−75311.3	−0.00502170
$743$	1.83497e7	1.21943	0.609714	−	0.792621i	$-0.291284\pi$
$743$	1.83497e7	1.21943	0.609714	+	0.792621i	$0.291284\pi$
$744$	−828265.	−0.0548576
$745$	−1.14898e7	−0.758442
$746$	1.65152e7	1.08652
$747$	3.88709e6	0.254873
$748$	−715583.	−0.0467634
$749$	−2.47883e6	−0.161452
$750$	727557.	0.0472296
$751$	2.80166e7	1.81266	0.906330	−	0.422571i	$-0.138872\pi$
$751$	2.80166e7	1.81266	0.906330	+	0.422571i	$0.138872\pi$
$752$	1.37405e7	0.886048
$753$	7.96987e6	0.512228
$754$	−3.24732e6	−0.208016
$755$	1.07527e7	0.686517
$756$	−93608.0	−0.00595674
$757$	1.79519e7	1.13860	0.569299	−	0.822131i	$-0.307215\pi$
$757$	1.79519e7	1.13860	0.569299	+	0.822131i	$0.307215\pi$
$758$	6.06613e6	0.383477
$759$	−1.02835e6	−0.0647945
$760$	−1.01406e7	−0.636838
$761$	−2.55099e7	−1.59679	−0.798394	−	0.602136i	$-0.794316\pi$
$761$	−2.55099e7	−1.59679	−0.798394	+	0.602136i	$0.794316\pi$
$762$	−8.00262e6	−0.499281
$763$	3.41058e6	0.212088
$764$	1.66743e6	0.103351
$765$	2.28875e6	0.141398
$766$	−6.95394e6	−0.428212
$767$	−8.52016e6	−0.522949
$768$	−4.49879e6	−0.275228
$769$	1.84130e6	0.112281	0.0561407	−	0.998423i	$-0.482120\pi$
$769$	1.84130e6	0.112281	0.0561407	+	0.998423i	$0.482120\pi$
$770$	384073.	0.0233446
$771$	−1.19522e7	−0.724124
$772$	−1.25832e6	−0.0759885
$773$	−2.77942e7	−1.67303	−0.836517	−	0.547941i	$-0.815412\pi$
$773$	−2.77942e7	−1.67303	−0.836517	+	0.547941i	$0.815412\pi$
$774$	7.04173e6	0.422500
$775$	298594.	0.0178578
$776$	2.07773e7	1.23861
$777$	−2.05740e6	−0.122255
$778$	−4.48253e6	−0.265506
$779$	4.26494e7	2.51808
$780$	−1.12330e6	−0.0661087
$781$	−760827.	−0.0446333
$782$	−5.52194e6	−0.322905
$783$	−479554.	−0.0279533
$784$	1.34367e7	0.780735
$785$	−4.15640e6	−0.240737
$786$	−9.11194e6	−0.526083
$787$	−2.55266e6	−0.146912	−0.0734558	−	0.997298i	$-0.523403\pi$
$787$	−2.55266e6	−0.146912	−0.0734558	+	0.997298i	$0.523403\pi$
$788$	2.80002e6	0.160637
$789$	7.97092e6	0.455844
$790$	−1.10381e7	−0.629254
$791$	−1.19451e6	−0.0678813
$792$	−1.88797e6	−0.106951
$793$	−5.28573e7	−2.98485
$794$	1.53168e7	0.862217
$795$	−133461.	−0.00748923
$796$	−2.97999e6	−0.166699
$797$	−1.91036e7	−1.06529	−0.532647	−	0.846338i	$-0.678803\pi$
$797$	−1.91036e7	−1.06529	−0.532647	+	0.846338i	$0.678803\pi$
$798$	2.40618e6	0.133758
$799$	−1.87294e7	−1.03790
$800$	1.17138e6	0.0647100
$801$	334361.	0.0184134
$802$	2.29886e7	1.26205
$803$	1.50939e6	0.0826062
$804$	−2.98705e6	−0.162968
$805$	−579346.	−0.0315100
$806$	2.35839e6	0.127873
$807$	4.56963e6	0.247000
$808$	2.58655e7	1.39378
$809$	−9.30740e6	−0.499985	−0.249992	−	0.968248i	$-0.580428\pi$
$809$	−9.30740e6	−0.499985	−0.249992	+	0.968248i	$0.580428\pi$
$810$	848623.	0.0454467
$811$	3.25689e7	1.73881	0.869403	−	0.494103i	$-0.164503\pi$
$811$	3.25689e7	1.73881	0.869403	+	0.494103i	$0.164503\pi$
$812$	84468.6	0.00449578
$813$	−5.09659e6	−0.270429
$814$	−5.83153e6	−0.308476
$815$	9.62256e6	0.507454
$816$	−8.43464e6	−0.443446
$817$	3.53823e7	1.85452
$818$	2.28053e7	1.19166
$819$	1.89661e6	0.0988028
$820$	−2.64947e6	−0.137602
$821$	4.45814e6	0.230832	0.115416	−	0.993317i	$-0.463180\pi$
$821$	4.45814e6	0.230832	0.115416	+	0.993317i	$0.463180\pi$
$822$	−3.11810e6	−0.160957
$823$	−1.07715e6	−0.0554339	−0.0277169	−	0.999616i	$-0.508824\pi$
$823$	−1.07715e6	−0.0554339	−0.0277169	+	0.999616i	$0.508824\pi$
$824$	−7.94778e6	−0.407782
$825$	680625.	0.0348155
$826$	−1.13377e6	−0.0578196
$827$	−9.24580e6	−0.470090	−0.235045	−	0.971985i	$-0.575524\pi$
$827$	−9.24580e6	−0.470090	−0.235045	+	0.971985i	$0.575524\pi$
$828$	400223.	0.0202874
$829$	−6.57252e6	−0.332159	−0.166079	−	0.986112i	$-0.553111\pi$
$829$	−6.57252e6	−0.332159	−0.166079	+	0.986112i	$0.553111\pi$
$830$	6.20704e6	0.312744
$831$	−230452.	−0.0115765
$832$	3.45689e7	1.73132
$833$	−1.83154e7	−0.914540
$834$	−1.79906e7	−0.895632
$835$	369182.	0.0183242
$836$	−1.33317e6	−0.0659734
$837$	348280.	0.0171836
$838$	1.23438e7	0.607208
$839$	4.37670e6	0.214655	0.107328	−	0.994224i	$-0.465771\pi$
$839$	4.37670e6	0.214655	0.107328	+	0.994224i	$0.465771\pi$
$840$	−1.06363e6	−0.0520108
$841$	−2.00784e7	−0.978903
$842$	−1.12036e7	−0.544599
$843$	1.23918e7	0.600571
$844$	−6.44509e6	−0.311439
$845$	1.34771e7	0.649314
$846$	−6.94449e6	−0.333591
$847$	359297.	0.0172086
$848$	491840.	0.0234873
$849$	−1.73762e6	−0.0827342
$850$	3.65475e6	0.173504
$851$	8.79644e6	0.416373
$852$	296105.	0.0139748
$853$	−6.14596e6	−0.289212	−0.144606	−	0.989489i	$-0.546192\pi$
$853$	−6.14596e6	−0.289212	−0.144606	+	0.989489i	$0.546192\pi$
$854$	−7.03368e6	−0.330018
$855$	4.26405e6	0.199483
$856$	1.94576e7	0.907623
$857$	3.47028e7	1.61404	0.807018	−	0.590527i	$-0.201080\pi$
$857$	3.47028e7	1.61404	0.807018	+	0.590527i	$0.201080\pi$
$858$	5.37580e6	0.249301
$859$	7.95808e6	0.367981	0.183990	−	0.982928i	$-0.441098\pi$
$859$	7.95808e6	0.367981	0.183990	+	0.982928i	$0.441098\pi$
$860$	−2.19802e6	−0.101341
$861$	4.47344e6	0.205653
$862$	2.69464e7	1.23519
$863$	−2.71064e6	−0.123892	−0.0619462	−	0.998079i	$-0.519731\pi$
$863$	−2.71064e6	−0.123892	−0.0619462	+	0.998079i	$0.519731\pi$
$864$	1.36629e6	0.0622672
$865$	7.74659e6	0.352022
$866$	−3.46731e7	−1.57108
$867$	−1.28162e6	−0.0579045
$868$	−61346.0	−0.00276368
$869$	−1.03261e7	−0.463858
$870$	−765768.	−0.0343004
$871$	6.05212e7	2.70310
$872$	−2.67714e7	−1.19228
$873$	−8.73670e6	−0.387982
$874$	−1.02876e7	−0.455552
$875$	383445.	0.0169310
$876$	−587436.	−0.0258643
$877$	1.26063e7	0.553464	0.276732	−	0.960947i	$-0.410749\pi$
$877$	1.26063e7	0.553464	0.276732	+	0.960947i	$0.410749\pi$
$878$	1.55577e7	0.681099
$879$	−1.97175e7	−0.860756
$880$	−2.50828e6	−0.109187
$881$	1.01937e7	0.442478	0.221239	−	0.975220i	$-0.428990\pi$
$881$	1.01937e7	0.442478	0.221239	+	0.975220i	$0.428990\pi$
$882$	−6.79098e6	−0.293941
$883$	−5.60501e6	−0.241921	−0.120961	−	0.992657i	$-0.538598\pi$
$883$	−5.60501e6	−0.241921	−0.120961	+	0.992657i	$0.538598\pi$
$884$	−5.64268e6	−0.242859
$885$	−2.00918e6	−0.0862306
$886$	−1.63444e6	−0.0699495
$887$	1.36403e7	0.582122	0.291061	−	0.956704i	$-0.405992\pi$
$887$	1.36403e7	0.582122	0.291061	+	0.956704i	$0.405992\pi$
$888$	1.61496e7	0.687271
$889$	−4.21763e6	−0.178984
$890$	533919.	0.0225944
$891$	793881.	0.0335013
$892$	−477198.	−0.0200811
$893$	−3.48938e7	−1.46426
$894$	−2.14003e7	−0.895522
$895$	−2.14035e7	−0.893156
$896$	3.12825e6	0.130176
$897$	−8.10901e6	−0.336501
$898$	−3.28940e7	−1.36121
$899$	−314276.	−0.0129692
$900$	−264891.	−0.0109009
$901$	−670417.	−0.0275127
$902$	1.26796e7	0.518907
$903$	3.71121e6	0.151459
$904$	9.37634e6	0.381604
$905$	1.01902e7	0.413583
$906$	2.00275e7	0.810598
$907$	−3.82149e6	−0.154246	−0.0771230	−	0.997022i	$-0.524573\pi$
$907$	−3.82149e6	−0.154246	−0.0771230	+	0.997022i	$0.524573\pi$
$908$	−594632.	−0.0239350
$909$	−1.08763e7	−0.436587
$910$	3.02858e6	0.121237
$911$	3.07694e7	1.22835	0.614177	−	0.789168i	$-0.289488\pi$
$911$	3.07694e7	1.22835	0.614177	+	0.789168i	$0.289488\pi$
$912$	−1.57141e7	−0.625610
$913$	5.80665e6	0.230541
$914$	1.31505e6	0.0520688
$915$	−1.24646e7	−0.492180
$916$	−2.60224e6	−0.102473
$917$	−4.80227e6	−0.188592
$918$	4.26290e6	0.166954
$919$	2.58662e7	1.01028	0.505142	−	0.863036i	$-0.331440\pi$
$919$	2.58662e7	1.01028	0.505142	+	0.863036i	$0.331440\pi$
$920$	4.54758e6	0.177138
$921$	−2.28789e7	−0.888762
$922$	−3.32783e7	−1.28924
$923$	−5.99945e6	−0.231797
$924$	−139834.	−0.00538807
$925$	−5.82200e6	−0.223727
$926$	−2.13689e7	−0.818945
$927$	3.34199e6	0.127734
$928$	−1.23290e6	−0.0469955
$929$	4.53888e7	1.72548	0.862738	−	0.505651i	$-0.168747\pi$
$929$	4.53888e7	1.72548	0.862738	+	0.505651i	$0.168747\pi$
$930$	556145.	0.0210853
$931$	−3.41224e7	−1.29023
$932$	−3.32456e6	−0.125370
$933$	−1.36680e7	−0.514045
$934$	−3.68544e7	−1.38236
$935$	3.41899e6	0.127900
$936$	−1.48875e7	−0.555433
$937$	−789247.	−0.0293673	−0.0146837	−	0.999892i	$-0.504674\pi$
$937$	−789247.	−0.0293673	−0.0146837	+	0.999892i	$0.504674\pi$
$938$	8.05351e6	0.298867
$939$	−2.02196e7	−0.748358
$940$	2.16767e6	0.0800154
$941$	7.18444e6	0.264496	0.132248	−	0.991217i	$-0.457781\pi$
$941$	7.18444e6	0.264496	0.132248	+	0.991217i	$0.457781\pi$
$942$	−7.74148e6	−0.284248
$943$	−1.91263e7	−0.700409
$944$	7.40437e6	0.270432
$945$	447250.	0.0162919
$946$	1.05191e7	0.382166
$947$	2.34025e7	0.847985	0.423992	−	0.905666i	$-0.360628\pi$
$947$	2.34025e7	0.847985	0.423992	+	0.905666i	$0.360628\pi$
$948$	4.01878e6	0.145236
$949$	1.19022e7	0.429004
$950$	6.80897e6	0.244778
$951$	939408.	0.0336824
$952$	−5.34296e6	−0.191069
$953$	−1.11980e7	−0.399399	−0.199699	−	0.979857i	$-0.563997\pi$
$953$	−1.11980e7	−0.399399	−0.199699	+	0.979857i	$0.563997\pi$
$954$	−248578.	−0.00884282
$955$	−7.96682e6	−0.282668
$956$	−4.97637e6	−0.176103
$957$	−716371.	−0.0252847
$958$	−2.04358e7	−0.719412
$959$	−1.64333e6	−0.0577005
$960$	8.15187e6	0.285482
$961$	−2.84009e7	−0.992028
$962$	−4.59841e7	−1.60203
$963$	−8.18181e6	−0.284304
$964$	−4.68743e6	−0.162458
$965$	6.01214e6	0.207831
$966$	−1.07906e6	−0.0372051
$967$	−3.96686e7	−1.36421	−0.682104	−	0.731255i	$-0.738935\pi$
$967$	−3.96686e7	−1.36421	−0.682104	+	0.731255i	$0.738935\pi$
$968$	−2.82031e6	−0.0967405
$969$	2.14196e7	0.732829
$970$	−1.39511e7	−0.476078
$971$	1.30783e7	0.445148	0.222574	−	0.974916i	$-0.428554\pi$
$971$	1.30783e7	0.445148	0.222574	+	0.974916i	$0.428554\pi$
$972$	−308969.	−0.0104894
$973$	−9.48158e6	−0.321069
$974$	2.58392e7	0.872735
$975$	5.36702e6	0.180810
$976$	4.59352e7	1.54355
$977$	−5.68578e7	−1.90570	−0.952848	−	0.303447i	$-0.901863\pi$
$977$	−5.68578e7	−1.90570	−0.952848	+	0.303447i	$0.901863\pi$
$978$	1.79225e7	0.599170
$979$	499478.	0.0166556
$980$	2.11975e6	0.0705050
$981$	1.12572e7	0.373471
$982$	−2.74780e7	−0.909298
$983$	−3.78900e7	−1.25066	−0.625332	−	0.780359i	$-0.715036\pi$
$983$	−3.78900e7	−1.25066	−0.625332	+	0.780359i	$0.715036\pi$
$984$	−3.51143e7	−1.15610
$985$	−1.33782e7	−0.439347
$986$	−3.84669e6	−0.126007
$987$	−3.65996e6	−0.119587
$988$	−1.05126e7	−0.342624
$989$	−1.58673e7	−0.515838
$990$	1.26770e6	0.0411081
$991$	4.98308e7	1.61181	0.805905	−	0.592045i	$-0.201679\pi$
$991$	4.98308e7	1.61181	0.805905	+	0.592045i	$0.201679\pi$
$992$	895400.	0.0288894
$993$	−1.16351e6	−0.0374452
$994$	−798341.	−0.0256285
$995$	1.42381e7	0.455926
$996$	−2.25988e6	−0.0721832
$997$	2.01809e7	0.642989	0.321494	−	0.946911i	$-0.395815\pi$
$997$	2.01809e7	0.642989	0.321494	+	0.946911i	$0.395815\pi$
$998$	5.34287e7	1.69804
$999$	−6.79078e6	−0.215281

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	165.6.a.h.1.5	✓	7
3.2	odd	2		495.6.a.n.1.3		7
5.4	even	2		825.6.a.n.1.3		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.6.a.h.1.5	✓	7	1.1	even	1	trivial
495.6.a.n.1.3		7	3.2	odd	2
825.6.a.n.1.3		7	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)

\(f(q)\)	\(=\)	\(q+5.17374 q^{2} +9.00000 q^{3} -5.23241 q^{4} +25.0000 q^{5} +46.5637 q^{6} +24.5405 q^{7} -192.631 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+5.17374 q^{2} +9.00000 q^{3} -5.23241 q^{4} +25.0000 q^{5} +46.5637 q^{6} +24.5405 q^{7} -192.631 q^{8} +81.0000 q^{9} +129.343 q^{10} +121.000 q^{11} -47.0917 q^{12} +954.137 q^{13} +126.966 q^{14} +225.000 q^{15} -829.185 q^{16} +1130.25 q^{17} +419.073 q^{18} +2105.70 q^{19} -130.810 q^{20} +220.864 q^{21} +626.023 q^{22} -944.310 q^{23} -1733.68 q^{24} +625.000 q^{25} +4936.46 q^{26} +729.000 q^{27} -128.406 q^{28} -657.825 q^{29} +1164.09 q^{30} +477.750 q^{31} +1874.20 q^{32} +1089.00 q^{33} +5847.60 q^{34} +613.512 q^{35} -423.826 q^{36} -9315.20 q^{37} +10894.4 q^{38} +8587.23 q^{39} -4815.77 q^{40} +20254.2 q^{41} +1142.70 q^{42} +16803.1 q^{43} -633.122 q^{44} +2025.00 q^{45} -4885.61 q^{46} -16571.1 q^{47} -7462.66 q^{48} -16204.8 q^{49} +3233.59 q^{50} +10172.2 q^{51} -4992.44 q^{52} -593.161 q^{53} +3771.66 q^{54} +3025.00 q^{55} -4727.26 q^{56} +18951.3 q^{57} -3403.41 q^{58} -8929.71 q^{59} -1177.29 q^{60} -55398.1 q^{61} +2471.76 q^{62} +1987.78 q^{63} +36230.5 q^{64} +23853.4 q^{65} +5634.20 q^{66} +63430.4 q^{67} -5913.91 q^{68} -8498.79 q^{69} +3174.15 q^{70} -6287.83 q^{71} -15603.1 q^{72} +12474.3 q^{73} -48194.4 q^{74} +5625.00 q^{75} -11017.9 q^{76} +2969.40 q^{77} +44428.1 q^{78} -85339.3 q^{79} -20729.6 q^{80} +6561.00 q^{81} +104790. q^{82} +47988.8 q^{83} -1155.65 q^{84} +28256.1 q^{85} +86934.9 q^{86} -5920.42 q^{87} -23308.3 q^{88} +4127.92 q^{89} +10476.8 q^{90} +23415.0 q^{91} +4941.02 q^{92} +4299.75 q^{93} -85734.5 q^{94} +52642.6 q^{95} +16867.8 q^{96} -107861. q^{97} -83839.2 q^{98} +9801.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + q^{2} + 63 q^{3} + 195 q^{4} + 175 q^{5} + 9 q^{6} + 153 q^{8} + 567 q^{9}+O(q^{10}) \) 7 * q + q^2 + 63 * q^3 + 195 * q^4 + 175 * q^5 + 9 * q^6 + 153 * q^8 + 567 * q^9	\( 7 q + q^{2} + 63 q^{3} + 195 q^{4} + 175 q^{5} + 9 q^{6} + 153 q^{8} + 567 q^{9} + 25 q^{10} + 847 q^{11} + 1755 q^{12} + 1418 q^{13} + 2548 q^{14} + 1575 q^{15} + 3699 q^{16} + 630 q^{17} + 81 q^{18} + 2572 q^{19} + 4875 q^{20} + 121 q^{22} + 536 q^{23} + 1377 q^{24} + 4375 q^{25} - 7626 q^{26} + 5103 q^{27} - 11368 q^{28} - 1038 q^{29} + 225 q^{30} + 1872 q^{31} - 7523 q^{32} + 7623 q^{33} + 20790 q^{34} + 15795 q^{36} + 24298 q^{37} - 18952 q^{38} + 12762 q^{39} + 3825 q^{40} - 17658 q^{41} + 22932 q^{42} + 7244 q^{43} + 23595 q^{44} + 14175 q^{45} + 31016 q^{46} + 34560 q^{47} + 33291 q^{48} + 78735 q^{49} + 625 q^{50} + 5670 q^{51} + 110222 q^{52} - 10214 q^{53} + 729 q^{54} + 21175 q^{55} + 81124 q^{56} + 23148 q^{57} - 5718 q^{58} + 94676 q^{59} + 43875 q^{60} + 69538 q^{61} - 4208 q^{62} + 112339 q^{64} + 35450 q^{65} + 1089 q^{66} + 64908 q^{67} - 136010 q^{68} + 4824 q^{69} + 63700 q^{70} + 61816 q^{71} + 12393 q^{72} - 11890 q^{73} - 124050 q^{74} + 39375 q^{75} - 47216 q^{76} - 68634 q^{78} + 18928 q^{79} + 92475 q^{80} + 45927 q^{81} + 36398 q^{82} + 17492 q^{83} - 102312 q^{84} + 15750 q^{85} - 216688 q^{86} - 9342 q^{87} + 18513 q^{88} + 25302 q^{89} + 2025 q^{90} + 3392 q^{91} - 27408 q^{92} + 16848 q^{93} - 30800 q^{94} + 64300 q^{95} - 67707 q^{96} - 172546 q^{97} - 615271 q^{98} + 68607 q^{99}+O(q^{100}) \) 7 * q + q^2 + 63 * q^3 + 195 * q^4 + 175 * q^5 + 9 * q^6 + 153 * q^8 + 567 * q^9 + 25 * q^10 + 847 * q^11 + 1755 * q^12 + 1418 * q^13 + 2548 * q^14 + 1575 * q^15 + 3699 * q^16 + 630 * q^17 + 81 * q^18 + 2572 * q^19 + 4875 * q^20 + 121 * q^22 + 536 * q^23 + 1377 * q^24 + 4375 * q^25 - 7626 * q^26 + 5103 * q^27 - 11368 * q^28 - 1038 * q^29 + 225 * q^30 + 1872 * q^31 - 7523 * q^32 + 7623 * q^33 + 20790 * q^34 + 15795 * q^36 + 24298 * q^37 - 18952 * q^38 + 12762 * q^39 + 3825 * q^40 - 17658 * q^41 + 22932 * q^42 + 7244 * q^43 + 23595 * q^44 + 14175 * q^45 + 31016 * q^46 + 34560 * q^47 + 33291 * q^48 + 78735 * q^49 + 625 * q^50 + 5670 * q^51 + 110222 * q^52 - 10214 * q^53 + 729 * q^54 + 21175 * q^55 + 81124 * q^56 + 23148 * q^57 - 5718 * q^58 + 94676 * q^59 + 43875 * q^60 + 69538 * q^61 - 4208 * q^62 + 112339 * q^64 + 35450 * q^65 + 1089 * q^66 + 64908 * q^67 - 136010 * q^68 + 4824 * q^69 + 63700 * q^70 + 61816 * q^71 + 12393 * q^72 - 11890 * q^73 - 124050 * q^74 + 39375 * q^75 - 47216 * q^76 - 68634 * q^78 + 18928 * q^79 + 92475 * q^80 + 45927 * q^81 + 36398 * q^82 + 17492 * q^83 - 102312 * q^84 + 15750 * q^85 - 216688 * q^86 - 9342 * q^87 + 18513 * q^88 + 25302 * q^89 + 2025 * q^90 + 3392 * q^91 - 27408 * q^92 + 16848 * q^93 - 30800 * q^94 + 64300 * q^95 - 67707 * q^96 - 172546 * q^97 - 615271 * q^98 + 68607 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more