LMFDB - Embedded newform 1045.6.a.c.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1045,6,Mod(1,1045)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1045, 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("1045.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 1045 = 5 \cdot 11 \cdot 19 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	1045.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:	$167.601091705$
Analytic rank:	$1$
Dimension:	$37$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	1045.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.08270 q^{2} +23.1648 q^{3} -30.8278 q^{4} -25.0000 q^{5} -25.0805 q^{6} -27.0095 q^{7} +68.0236 q^{8} +293.607 q^{9} +O(q^{10})$	\(q-1.08270 q^{2} +23.1648 q^{3} -30.8278 q^{4} -25.0000 q^{5} -25.0805 q^{6} -27.0095 q^{7} +68.0236 q^{8} +293.607 q^{9} +27.0675 q^{10} -121.000 q^{11} -714.119 q^{12} -478.552 q^{13} +29.2432 q^{14} -579.120 q^{15} +912.839 q^{16} +225.825 q^{17} -317.888 q^{18} -361.000 q^{19} +770.694 q^{20} -625.669 q^{21} +131.007 q^{22} +1479.30 q^{23} +1575.75 q^{24} +625.000 q^{25} +518.128 q^{26} +1172.31 q^{27} +832.642 q^{28} +4014.63 q^{29} +627.013 q^{30} +9421.44 q^{31} -3165.09 q^{32} -2802.94 q^{33} -244.500 q^{34} +675.237 q^{35} -9051.26 q^{36} +7996.87 q^{37} +390.854 q^{38} -11085.6 q^{39} -1700.59 q^{40} -4302.37 q^{41} +677.412 q^{42} +19500.0 q^{43} +3730.16 q^{44} -7340.18 q^{45} -1601.64 q^{46} -23155.0 q^{47} +21145.7 q^{48} -16077.5 q^{49} -676.687 q^{50} +5231.18 q^{51} +14752.7 q^{52} -38543.9 q^{53} -1269.26 q^{54} +3025.00 q^{55} -1837.28 q^{56} -8362.49 q^{57} -4346.64 q^{58} -6331.17 q^{59} +17853.0 q^{60} -13960.2 q^{61} -10200.6 q^{62} -7930.19 q^{63} -25784.0 q^{64} +11963.8 q^{65} +3034.74 q^{66} -134.408 q^{67} -6961.67 q^{68} +34267.7 q^{69} -731.079 q^{70} +42483.6 q^{71} +19972.2 q^{72} -21010.5 q^{73} -8658.20 q^{74} +14478.0 q^{75} +11128.8 q^{76} +3268.15 q^{77} +12002.3 q^{78} -11092.5 q^{79} -22821.0 q^{80} -44190.3 q^{81} +4658.17 q^{82} -5209.14 q^{83} +19288.0 q^{84} -5645.61 q^{85} -21112.6 q^{86} +92998.0 q^{87} -8230.85 q^{88} -39701.0 q^{89} +7947.21 q^{90} +12925.4 q^{91} -45603.5 q^{92} +218246. q^{93} +25069.9 q^{94} +9025.00 q^{95} -73318.5 q^{96} +160643. q^{97} +17407.1 q^{98} -35526.5 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9}+O(q^{10}) $ 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9} + 300 q^{10} - 4477 q^{11} - 568 q^{12} + 719 q^{13} + 687 q^{14} + 675 q^{15} + 11494 q^{16} + 999 q^{17} - 595 q^{18} - 13357 q^{19} - 14350 q^{20} - 1077 q^{21} + 1452 q^{22} + 5096 q^{23} - 3154 q^{24} + 23125 q^{25} - 10395 q^{26} - 7578 q^{27} + 19863 q^{28} - 7969 q^{29} + 1875 q^{30} + 603 q^{31} - 27809 q^{32} + 3267 q^{33} - 24081 q^{34} - 8425 q^{35} + 59869 q^{36} + 7963 q^{37} + 4332 q^{38} + 86 q^{39} + 17400 q^{40} + 1475 q^{41} - 46542 q^{42} + 38059 q^{43} - 69454 q^{44} - 78500 q^{45} - 3413 q^{46} - 37658 q^{47} - 51317 q^{48} + 39188 q^{49} - 7500 q^{50} - 40262 q^{51} + 25358 q^{52} - 52545 q^{53} + 64732 q^{54} + 111925 q^{55} - 54173 q^{56} + 9747 q^{57} + 105808 q^{58} - 34039 q^{59} + 14200 q^{60} + 30023 q^{61} - 100198 q^{62} + 30376 q^{63} + 160888 q^{64} - 17975 q^{65} + 9075 q^{66} - 45284 q^{67} + 125176 q^{68} + 109244 q^{69} - 17175 q^{70} - 84020 q^{71} - 291176 q^{72} + 24542 q^{73} + 38795 q^{74} - 16875 q^{75} - 207214 q^{76} - 40777 q^{77} + 1042 q^{78} + 49303 q^{79} - 287350 q^{80} + 344453 q^{81} - 286030 q^{82} - 402155 q^{83} - 203270 q^{84} - 24975 q^{85} - 276426 q^{86} + 116994 q^{87} + 84216 q^{88} - 442930 q^{89} + 14875 q^{90} - 93040 q^{91} + 402160 q^{92} - 241950 q^{93} - 170720 q^{94} + 333925 q^{95} - 234384 q^{96} - 87732 q^{97} - 712662 q^{98} - 379940 q^{99}+O(q^{100}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9 + 300 * q^10 - 4477 * q^11 - 568 * q^12 + 719 * q^13 + 687 * q^14 + 675 * q^15 + 11494 * q^16 + 999 * q^17 - 595 * q^18 - 13357 * q^19 - 14350 * q^20 - 1077 * q^21 + 1452 * q^22 + 5096 * q^23 - 3154 * q^24 + 23125 * q^25 - 10395 * q^26 - 7578 * q^27 + 19863 * q^28 - 7969 * q^29 + 1875 * q^30 + 603 * q^31 - 27809 * q^32 + 3267 * q^33 - 24081 * q^34 - 8425 * q^35 + 59869 * q^36 + 7963 * q^37 + 4332 * q^38 + 86 * q^39 + 17400 * q^40 + 1475 * q^41 - 46542 * q^42 + 38059 * q^43 - 69454 * q^44 - 78500 * q^45 - 3413 * q^46 - 37658 * q^47 - 51317 * q^48 + 39188 * q^49 - 7500 * q^50 - 40262 * q^51 + 25358 * q^52 - 52545 * q^53 + 64732 * q^54 + 111925 * q^55 - 54173 * q^56 + 9747 * q^57 + 105808 * q^58 - 34039 * q^59 + 14200 * q^60 + 30023 * q^61 - 100198 * q^62 + 30376 * q^63 + 160888 * q^64 - 17975 * q^65 + 9075 * q^66 - 45284 * q^67 + 125176 * q^68 + 109244 * q^69 - 17175 * q^70 - 84020 * q^71 - 291176 * q^72 + 24542 * q^73 + 38795 * q^74 - 16875 * q^75 - 207214 * q^76 - 40777 * q^77 + 1042 * q^78 + 49303 * q^79 - 287350 * q^80 + 344453 * q^81 - 286030 * q^82 - 402155 * q^83 - 203270 * q^84 - 24975 * q^85 - 276426 * q^86 + 116994 * q^87 + 84216 * q^88 - 442930 * q^89 + 14875 * q^90 - 93040 * q^91 + 402160 * q^92 - 241950 * q^93 - 170720 * q^94 + 333925 * q^95 - 234384 * q^96 - 87732 * q^97 - 712662 * q^98 - 379940 * 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 $

$2$	−1.08270	−0.191396	−0.0956980	−	0.995410i	$-0.530508\pi$
$2$	−1.08270	−0.191396	−0.0956980	+	0.995410i	$0.530508\pi$
$3$	23.1648	1.48602	0.743011	−	0.669279i	$-0.233397\pi$
$3$	23.1648	1.48602	0.743011	+	0.669279i	$0.233397\pi$
$4$	−30.8278	−0.963368
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	−25.0805	−0.284419
$7$	−27.0095	−0.208339	−0.104170	−	0.994560i	$-0.533219\pi$
$7$	−27.0095	−0.208339	−0.104170	+	0.994560i	$0.533219\pi$
$8$	68.0236	0.375781
$9$	293.607	1.20826
$10$	27.0675	0.0855949
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−714.119	−1.43159
$13$	−478.552	−0.785364	−0.392682	−	0.919674i	$-0.628453\pi$
$13$	−478.552	−0.785364	−0.392682	+	0.919674i	$0.628453\pi$
$14$	29.2432	0.0398753
$15$	−579.120	−0.664569
$16$	912.839	0.891445
$17$	225.825	0.189517	0.0947587	−	0.995500i	$-0.469792\pi$
$17$	225.825	0.189517	0.0947587	+	0.995500i	$0.469792\pi$
$18$	−317.888	−0.231256
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	770.694	0.430831
$21$	−625.669	−0.309597
$22$	131.007	0.0577081
$23$	1479.30	0.583092	0.291546	−	0.956557i	$-0.405830\pi$
$23$	1479.30	0.583092	0.291546	+	0.956557i	$0.405830\pi$
$24$	1575.75	0.558418
$25$	625.000	0.200000
$26$	518.128	0.150315
$27$	1172.31	0.309480
$28$	832.642	0.200707
$29$	4014.63	0.886442	0.443221	−	0.896412i	$-0.353836\pi$
$29$	4014.63	0.886442	0.443221	+	0.896412i	$0.353836\pi$
$30$	627.013	0.127196
$31$	9421.44	1.76081	0.880406	−	0.474221i	$-0.157270\pi$
$31$	9421.44	1.76081	0.880406	+	0.474221i	$0.157270\pi$
$32$	−3165.09	−0.546400
$33$	−2802.94	−0.448052
$34$	−244.500	−0.0362729
$35$	675.237	0.0931722
$36$	−9051.26	−1.16400
$37$	7996.87	0.960319	0.480159	−	0.877181i	$-0.340579\pi$
$37$	7996.87	0.960319	0.480159	+	0.877181i	$0.340579\pi$
$38$	390.854	0.0439093
$39$	−11085.6	−1.16707
$40$	−1700.59	−0.168054
$41$	−4302.37	−0.399713	−0.199856	−	0.979825i	$-0.564048\pi$
$41$	−4302.37	−0.399713	−0.199856	+	0.979825i	$0.564048\pi$
$42$	677.412	0.0592556
$43$	19500.0	1.60828	0.804142	−	0.594437i	$-0.202625\pi$
$43$	19500.0	1.60828	0.804142	+	0.594437i	$0.202625\pi$
$44$	3730.16	0.290466
$45$	−7340.18	−0.540351
$46$	−1601.64	−0.111601
$47$	−23155.0	−1.52898	−0.764488	−	0.644638i	$-0.777008\pi$
$47$	−23155.0	−1.52898	−0.764488	+	0.644638i	$0.777008\pi$
$48$	21145.7	1.32471
$49$	−16077.5	−0.956595
$50$	−676.687	−0.0382792
$51$	5231.18	0.281627
$52$	14752.7	0.756594
$53$	−38543.9	−1.88480	−0.942400	−	0.334487i	$-0.891437\pi$
$53$	−38543.9	−1.88480	−0.942400	+	0.334487i	$0.891437\pi$
$54$	−1269.26	−0.0592332
$55$	3025.00	0.134840
$56$	−1837.28	−0.0782899
$57$	−8362.49	−0.340917
$58$	−4346.64	−0.169661
$59$	−6331.17	−0.236785	−0.118392	−	0.992967i	$-0.537774\pi$
$59$	−6331.17	−0.236785	−0.118392	+	0.992967i	$0.537774\pi$
$60$	17853.0	0.640224
$61$	−13960.2	−0.480360	−0.240180	−	0.970728i	$-0.577206\pi$
$61$	−13960.2	−0.480360	−0.240180	+	0.970728i	$0.577206\pi$
$62$	−10200.6	−0.337012
$63$	−7930.19	−0.251728
$64$	−25784.0	−0.786866
$65$	11963.8	0.351225
$66$	3034.74	0.0857554
$67$	−134.408	−0.00365795	−0.00182897	−	0.999998i	$-0.500582\pi$
$67$	−134.408	−0.00365795	−0.00182897	+	0.999998i	$0.500582\pi$
$68$	−6961.67	−0.182575
$69$	34267.7	0.866487
$70$	−731.079	−0.0178328
$71$	42483.6	1.00017	0.500087	−	0.865975i	$-0.333302\pi$
$71$	42483.6	1.00017	0.500087	+	0.865975i	$0.333302\pi$
$72$	19972.2	0.454041
$73$	−21010.5	−0.461454	−0.230727	−	0.973018i	$-0.574110\pi$
$73$	−21010.5	−0.461454	−0.230727	+	0.973018i	$0.574110\pi$
$74$	−8658.20	−0.183801
$75$	14478.0	0.297204
$76$	11128.8	0.221012
$77$	3268.15	0.0628167
$78$	12002.3	0.223372
$79$	−11092.5	−0.199969	−0.0999843	−	0.994989i	$-0.531879\pi$
$79$	−11092.5	−0.199969	−0.0999843	+	0.994989i	$0.531879\pi$
$80$	−22821.0	−0.398666
$81$	−44190.3	−0.748367
$82$	4658.17	0.0765034
$83$	−5209.14	−0.0829987	−0.0414993	−	0.999139i	$-0.513213\pi$
$83$	−5209.14	−0.0829987	−0.0414993	+	0.999139i	$0.513213\pi$
$84$	19288.0	0.298256
$85$	−5645.61	−0.0847547
$86$	−21112.6	−0.307819
$87$	92998.0	1.31727
$88$	−8230.85	−0.113302
$89$	−39701.0	−0.531283	−0.265642	−	0.964072i	$-0.585584\pi$
$89$	−39701.0	−0.531283	−0.265642	+	0.964072i	$0.585584\pi$
$90$	7947.21	0.103421
$91$	12925.4	0.163622
$92$	−45603.5	−0.561732
$93$	218246.	2.61660
$94$	25069.9	0.292640
$95$	9025.00	0.102598
$96$	−73318.5	−0.811962
$97$	160643.	1.73353	0.866766	−	0.498716i	$-0.166195\pi$
$97$	160643.	1.73353	0.866766	+	0.498716i	$0.166195\pi$
$98$	17407.1	0.183088
$99$	−35526.5	−0.364304
$100$	−19267.4	−0.192674
$101$	−181170.	−1.76719	−0.883595	−	0.468252i	$-0.844884\pi$
$101$	−181170.	−1.76719	−0.883595	+	0.468252i	$0.844884\pi$
$102$	−5663.79	−0.0539023
$103$	−66130.7	−0.614201	−0.307100	−	0.951677i	$-0.599359\pi$
$103$	−66130.7	−0.614201	−0.307100	+	0.951677i	$0.599359\pi$
$104$	−32552.8	−0.295125
$105$	15641.7	0.138456
$106$	41731.4	0.360743
$107$	15017.2	0.126803	0.0634015	−	0.997988i	$-0.479805\pi$
$107$	15017.2	0.126803	0.0634015	+	0.997988i	$0.479805\pi$
$108$	−36139.6	−0.298143
$109$	−199172.	−1.60569	−0.802844	−	0.596190i	$-0.796681\pi$
$109$	−199172.	−1.60569	−0.802844	+	0.596190i	$0.796681\pi$
$110$	−3275.17	−0.0258078
$111$	185246.	1.42705
$112$	−24655.3	−0.185723
$113$	41161.7	0.303247	0.151624	−	0.988438i	$-0.451550\pi$
$113$	41161.7	0.303247	0.151624	+	0.988438i	$0.451550\pi$
$114$	9054.06	0.0652501
$115$	−36982.5	−0.260767
$116$	−123762.	−0.853969
$117$	−140506.	−0.948924
$118$	6854.75	0.0453197
$119$	−6099.41	−0.0394839
$120$	−39393.8	−0.249732
$121$	14641.0	0.0909091
$122$	15114.7	0.0919390
$123$	−99663.5	−0.593982
$124$	−290442.	−1.69631
$125$	−15625.0	−0.0894427
$126$	8586.01	0.0481798
$127$	185734.	1.02184	0.510918	−	0.859630i	$-0.329306\pi$
$127$	185734.	1.02184	0.510918	+	0.859630i	$0.329306\pi$
$128$	129199.	0.697003
$129$	451713.	2.38995
$130$	−12953.2	−0.0672231
$131$	128764.	0.655568	0.327784	−	0.944753i	$-0.393698\pi$
$131$	128764.	0.655568	0.327784	+	0.944753i	$0.393698\pi$
$132$	86408.3	0.431639
$133$	9750.43	0.0477963
$134$	145.523	0.000700116 0
$135$	−29307.7	−0.138404
$136$	15361.4	0.0712169
$137$	−157783.	−0.718224	−0.359112	−	0.933294i	$-0.616920\pi$
$137$	−157783.	−0.718224	−0.359112	+	0.933294i	$0.616920\pi$
$138$	−37101.6	−0.165842
$139$	−331045.	−1.45328	−0.726640	−	0.687018i	$-0.758919\pi$
$139$	−331045.	−1.45328	−0.726640	+	0.687018i	$0.758919\pi$
$140$	−20816.1	−0.0897591
$141$	−536381.	−2.27209
$142$	−45996.9	−0.191429
$143$	57904.8	0.236796
$144$	268016.	1.07710
$145$	−100366.	−0.396429
$146$	22748.0	0.0883205
$147$	−372432.	−1.42152
$148$	−246525.	−0.925140
$149$	−400846.	−1.47915	−0.739574	−	0.673075i	$-0.764973\pi$
$149$	−400846.	−1.47915	−0.739574	+	0.673075i	$0.764973\pi$
$150$	−15675.3	−0.0568837
$151$	514346.	1.83575	0.917874	−	0.396872i	$-0.129904\pi$
$151$	514346.	1.83575	0.917874	+	0.396872i	$0.129904\pi$
$152$	−24556.5	−0.0862100
$153$	66303.7	0.228986
$154$	−3538.42	−0.0120229
$155$	−235536.	−0.787459
$156$	341743.	1.12431
$157$	−544710.	−1.76366	−0.881832	−	0.471564i	$-0.843690\pi$
$157$	−544710.	−1.76366	−0.881832	+	0.471564i	$0.843690\pi$
$158$	12009.8	0.0382732
$159$	−892860.	−2.80086
$160$	79127.1	0.244357
$161$	−39955.2	−0.121481
$162$	47844.8	0.143234
$163$	−634963.	−1.87189	−0.935943	−	0.352151i	$-0.885450\pi$
$163$	−634963.	−1.87189	−0.935943	+	0.352151i	$0.885450\pi$
$164$	132632.	0.385070
$165$	70073.5	0.200375
$166$	5639.94	0.0158856
$167$	471780.	1.30903	0.654513	−	0.756051i	$-0.272874\pi$
$167$	471780.	1.30903	0.654513	+	0.756051i	$0.272874\pi$
$168$	−42560.3	−0.116341
$169$	−142281.	−0.383204
$170$	6112.50	0.0162217
$171$	−105992.	−0.277194
$172$	−601140.	−1.54937
$173$	−457065.	−1.16108	−0.580541	−	0.814231i	$-0.697159\pi$
$173$	−457065.	−1.16108	−0.580541	+	0.814231i	$0.697159\pi$
$174$	−100689.	−0.252121
$175$	−16880.9	−0.0416679
$176$	−110454.	−0.268781
$177$	−146660.	−0.351867
$178$	42984.2	0.101686
$179$	13954.5	0.0325524	0.0162762	−	0.999868i	$-0.494819\pi$
$179$	13954.5	0.0325524	0.0162762	+	0.999868i	$0.494819\pi$
$180$	226281.	0.520556
$181$	−110286.	−0.250221	−0.125111	−	0.992143i	$-0.539929\pi$
$181$	−110286.	−0.250221	−0.125111	+	0.992143i	$0.539929\pi$
$182$	−13994.4	−0.0313166
$183$	−323385.	−0.713825
$184$	100627.	0.219115
$185$	−199922.	−0.429468
$186$	−236294.	−0.500808
$187$	−27324.8	−0.0571416
$188$	713817.	1.47297
$189$	−31663.5	−0.0644769
$190$	−9771.36	−0.0196368
$191$	−159316.	−0.315992	−0.157996	−	0.987440i	$-0.550503\pi$
$191$	−159316.	−0.315992	−0.157996	+	0.987440i	$0.550503\pi$
$192$	−597281.	−1.16930
$193$	−529637.	−1.02349	−0.511747	−	0.859136i	$-0.671001\pi$
$193$	−529637.	−1.02349	−0.511747	+	0.859136i	$0.671001\pi$
$194$	−173928.	−0.331791
$195$	277139.	0.521928
$196$	495633.	0.921552
$197$	366574.	0.672971	0.336486	−	0.941689i	$-0.390762\pi$
$197$	366574.	0.672971	0.336486	+	0.941689i	$0.390762\pi$
$198$	38464.5	0.0697264
$199$	−499085.	−0.893392	−0.446696	−	0.894686i	$-0.647399\pi$
$199$	−499085.	−0.893392	−0.446696	+	0.894686i	$0.647399\pi$
$200$	42514.7	0.0751561
$201$	−3113.53	−0.00543579
$202$	196153.	0.338233
$203$	−108433.	−0.184681
$204$	−161266.	−0.271310
$205$	107559.	0.178757
$206$	71599.7	0.117556
$207$	434334.	0.704527
$208$	−436841.	−0.700108
$209$	43681.0	0.0691714
$210$	−16935.3	−0.0264999
$211$	−57957.0	−0.0896189	−0.0448095	−	0.998996i	$-0.514268\pi$
$211$	−57957.0	−0.0896189	−0.0448095	+	0.998996i	$0.514268\pi$
$212$	1.18822e6	1.81576
$213$	984123.	1.48628
$214$	−16259.1	−0.0242696
$215$	−487499.	−0.719247
$216$	79744.6	0.116297
$217$	−254468.	−0.366846
$218$	215643.	0.307322
$219$	−486703.	−0.685731
$220$	−93254.0	−0.129900
$221$	−108069.	−0.148840
$222$	−200565.	−0.273133
$223$	265446.	0.357449	0.178725	−	0.983899i	$-0.442803\pi$
$223$	265446.	0.357449	0.178725	+	0.983899i	$0.442803\pi$
$224$	85487.3	0.113837
$225$	183505.	0.241652
$226$	−44565.7	−0.0580403
$227$	483561.	0.622854	0.311427	−	0.950270i	$-0.399193\pi$
$227$	483561.	0.622854	0.311427	+	0.950270i	$0.399193\pi$
$228$	257797.	0.328428
$229$	1.19295e6	1.50326	0.751631	−	0.659584i	$-0.229268\pi$
$229$	1.19295e6	1.50326	0.751631	+	0.659584i	$0.229268\pi$
$230$	40041.0	0.0499097
$231$	75706.0	0.0933470
$232$	273089.	0.333108
$233$	1.47141e6	1.77559	0.887796	−	0.460236i	$-0.152235\pi$
$233$	1.47141e6	1.77559	0.887796	+	0.460236i	$0.152235\pi$
$234$	152126.	0.181620
$235$	578875.	0.683779
$236$	195176.	0.228111
$237$	−256956.	−0.297158
$238$	6603.82	0.00755706
$239$	245981.	0.278552	0.139276	−	0.990254i	$-0.455523\pi$
$239$	245981.	0.278552	0.139276	+	0.990254i	$0.455523\pi$
$240$	−528643.	−0.592427
$241$	−22414.5	−0.0248591	−0.0124296	−	0.999923i	$-0.503957\pi$
$241$	−22414.5	−0.0248591	−0.0124296	+	0.999923i	$0.503957\pi$
$242$	−15851.8	−0.0173996
$243$	−1.30853e6	−1.42157
$244$	430361.	0.462763
$245$	401937.	0.427802
$246$	107906.	0.113686
$247$	172757.	0.180175
$248$	640880.	0.661679
$249$	−120669.	−0.123338
$250$	16917.2	0.0171190
$251$	−188750.	−0.189105	−0.0945523	−	0.995520i	$-0.530142\pi$
$251$	−188750.	−0.189105	−0.0945523	+	0.995520i	$0.530142\pi$
$252$	244470.	0.242507
$253$	−178995.	−0.175809
$254$	−201094.	−0.195575
$255$	−130779.	−0.125947
$256$	685205.	0.653462
$257$	−1.75906e6	−1.66130	−0.830649	−	0.556796i	$-0.812030\pi$
$257$	−1.75906e6	−1.66130	−0.830649	+	0.556796i	$0.812030\pi$
$258$	−489069.	−0.457426
$259$	−215991.	−0.200072
$260$	−368817.	−0.338359
$261$	1.17872e6	1.07105
$262$	−139413.	−0.125473
$263$	−1.29407e6	−1.15364	−0.576818	−	0.816873i	$-0.695706\pi$
$263$	−1.29407e6	−1.15364	−0.576818	+	0.816873i	$0.695706\pi$
$264$	−190666.	−0.168369
$265$	963596.	0.842909
$266$	−10556.8	−0.00914803
$267$	−919665.	−0.789499
$268$	4143.49	0.00352395
$269$	−1.05941e6	−0.892655	−0.446327	−	0.894870i	$-0.647268\pi$
$269$	−1.05941e6	−0.892655	−0.446327	+	0.894870i	$0.647268\pi$
$270$	31731.4	0.0264899
$271$	1.67485e6	1.38533	0.692666	−	0.721259i	$-0.256436\pi$
$271$	1.67485e6	1.38533	0.692666	+	0.721259i	$0.256436\pi$
$272$	206142.	0.168944
$273$	299415.	0.243146
$274$	170832.	0.137465
$275$	−75625.0	−0.0603023
$276$	−1.05640e6	−0.834746
$277$	489566.	0.383364	0.191682	−	0.981457i	$-0.438606\pi$
$277$	489566.	0.383364	0.191682	+	0.981457i	$0.438606\pi$
$278$	358422.	0.278152
$279$	2.76620e6	2.12752
$280$	45932.1	0.0350123
$281$	130546.	0.0986276	0.0493138	−	0.998783i	$-0.484297\pi$
$281$	130546.	0.0986276	0.0493138	+	0.998783i	$0.484297\pi$
$282$	580739.	0.434869
$283$	870787.	0.646317	0.323159	−	0.946345i	$-0.395255\pi$
$283$	870787.	0.646317	0.323159	+	0.946345i	$0.395255\pi$
$284$	−1.30967e6	−0.963534
$285$	209062.	0.152463
$286$	−62693.5	−0.0453218
$287$	116205.	0.0832759
$288$	−929292.	−0.660193
$289$	−1.36886e6	−0.964083
$290$	108666.	0.0758749
$291$	3.72125e6	2.57607
$292$	647706.	0.444550
$293$	−219630.	−0.149459	−0.0747295	−	0.997204i	$-0.523809\pi$
$293$	−219630.	−0.149459	−0.0747295	+	0.997204i	$0.523809\pi$
$294$	403231.	0.272073
$295$	158279.	0.105893
$296$	543975.	0.360869
$297$	−141849.	−0.0933117
$298$	433996.	0.283103
$299$	−707922.	−0.457939
$300$	−446324.	−0.286317
$301$	−526684.	−0.335069
$302$	−556882.	−0.351355
$303$	−4.19677e6	−2.62608
$304$	−329535.	−0.204511
$305$	349005.	0.214823
$306$	−71787.0	−0.0438271
$307$	−2.97343e6	−1.80058	−0.900289	−	0.435293i	$-0.856645\pi$
$307$	−2.97343e6	−1.80058	−0.900289	+	0.435293i	$0.856645\pi$
$308$	−100750.	−0.0605156
$309$	−1.53190e6	−0.912716
$310$	255015.	0.150717
$311$	−1.71206e6	−1.00373	−0.501866	−	0.864945i	$-0.667353\pi$
$311$	−1.71206e6	−1.00373	−0.501866	+	0.864945i	$0.667353\pi$
$312$	−754079.	−0.438561
$313$	−1.14754e6	−0.662072	−0.331036	−	0.943618i	$-0.607398\pi$
$313$	−1.14754e6	−0.662072	−0.331036	+	0.943618i	$0.607398\pi$
$314$	589757.	0.337558
$315$	198255.	0.112576
$316$	341957.	0.192643
$317$	−1.33092e6	−0.743884	−0.371942	−	0.928256i	$-0.621308\pi$
$317$	−1.33092e6	−0.743884	−0.371942	+	0.928256i	$0.621308\pi$
$318$	966699.	0.536073
$319$	−485770.	−0.267272
$320$	644601.	0.351897
$321$	347870.	0.188432
$322$	43259.4	0.0232510
$323$	−81522.7	−0.0434783
$324$	1.36229e6	0.720952
$325$	−299095.	−0.157073
$326$	687474.	0.358272
$327$	−4.61377e6	−2.38609
$328$	−292663.	−0.150204
$329$	625405.	0.318546
$330$	−75868.5	−0.0383510
$331$	448145.	0.224827	0.112414	−	0.993662i	$-0.464142\pi$
$331$	448145.	0.224827	0.112414	+	0.993662i	$0.464142\pi$
$332$	160586.	0.0799582
$333$	2.34794e6	1.16032
$334$	−510796.	−0.250542
$335$	3360.19	0.00163588
$336$	−571135.	−0.275988
$337$	−3.92206e6	−1.88122	−0.940609	−	0.339492i	$-0.889745\pi$
$337$	−3.92206e6	−1.88122	−0.940609	+	0.339492i	$0.889745\pi$
$338$	154047.	0.0733437
$339$	953502.	0.450632
$340$	174042.	0.0816499
$341$	−1.13999e6	−0.530905
$342$	114758.	0.0530538
$343$	888193.	0.407636
$344$	1.32646e6	0.604362
$345$	−856692.	−0.387505
$346$	494864.	0.222226
$347$	−3.09767e6	−1.38105	−0.690527	−	0.723306i	$-0.742621\pi$
$347$	−3.09767e6	−1.38105	−0.690527	+	0.723306i	$0.742621\pi$
$348$	−2.86692e6	−1.26902
$349$	2.00726e6	0.882144	0.441072	−	0.897472i	$-0.354598\pi$
$349$	2.00726e6	0.882144	0.441072	+	0.897472i	$0.354598\pi$
$350$	18277.0	0.00797506
$351$	−561011.	−0.243054
$352$	382975.	0.164746
$353$	521820.	0.222887	0.111443	−	0.993771i	$-0.464453\pi$
$353$	521820.	0.222887	0.111443	+	0.993771i	$0.464453\pi$
$354$	158789.	0.0673460
$355$	−1.06209e6	−0.447291
$356$	1.22389e6	0.511821
$357$	−141291.	−0.0586740
$358$	−15108.6	−0.00623039
$359$	−4.51303e6	−1.84813	−0.924063	−	0.382239i	$-0.875153\pi$
$359$	−4.51303e6	−1.84813	−0.924063	+	0.382239i	$0.875153\pi$
$360$	−499306.	−0.203053
$361$	130321.	0.0526316
$362$	119407.	0.0478913
$363$	339156.	0.135093
$364$	−398463.	−0.157628
$365$	525262.	0.206369
$366$	350129.	0.136623
$367$	−383844.	−0.148761	−0.0743805	−	0.997230i	$-0.523698\pi$
$367$	−383844.	−0.148761	−0.0743805	+	0.997230i	$0.523698\pi$
$368$	1.35036e6	0.519794
$369$	−1.26321e6	−0.482957
$370$	216455.	0.0821984
$371$	1.04105e6	0.392678
$372$	−6.72802e6	−2.52075
$373$	−1.99634e6	−0.742957	−0.371478	−	0.928442i	$-0.621149\pi$
$373$	−1.99634e6	−0.742957	−0.371478	+	0.928442i	$0.621149\pi$
$374$	29584.5	0.0109367
$375$	−361950.	−0.132914
$376$	−1.57509e6	−0.574559
$377$	−1.92121e6	−0.696179
$378$	34282.0	0.0123406
$379$	5.06892e6	1.81267	0.906333	−	0.422565i	$-0.138870\pi$
$379$	5.06892e6	1.81267	0.906333	+	0.422565i	$0.138870\pi$
$380$	−278221.	−0.0988394
$381$	4.30248e6	1.51847
$382$	172492.	0.0604797
$383$	813607.	0.283412	0.141706	−	0.989909i	$-0.454741\pi$
$383$	813607.	0.283412	0.141706	+	0.989909i	$0.454741\pi$
$384$	2.99287e6	1.03576
$385$	−81703.7	−0.0280925
$386$	573438.	0.195893
$387$	5.72533e6	1.94323
$388$	−4.95226e6	−1.67003
$389$	477509.	0.159995	0.0799977	−	0.996795i	$-0.474509\pi$
$389$	477509.	0.159995	0.0799977	+	0.996795i	$0.474509\pi$
$390$	−300058.	−0.0998950
$391$	334062.	0.110506
$392$	−1.09365e6	−0.359470
$393$	2.98280e6	0.974188
$394$	−396890.	−0.128804
$395$	277313.	0.0894287
$396$	1.09520e6	0.350959
$397$	−2.06137e6	−0.656417	−0.328209	−	0.944605i	$-0.606445\pi$
$397$	−2.06137e6	−0.656417	−0.328209	+	0.944605i	$0.606445\pi$
$398$	540359.	0.170992
$399$	225867.	0.0710264
$400$	570525.	0.178289
$401$	3.51672e6	1.09213	0.546067	−	0.837741i	$-0.316124\pi$
$401$	3.51672e6	1.09213	0.546067	+	0.837741i	$0.316124\pi$
$402$	3371.01	0.00104039
$403$	−4.50865e6	−1.38288
$404$	5.58507e6	1.70245
$405$	1.10476e6	0.334680
$406$	117400.	0.0353472
$407$	−967621.	−0.289547
$408$	355843.	0.105830
$409$	−4.77508e6	−1.41147	−0.705736	−	0.708475i	$-0.749383\pi$
$409$	−4.77508e6	−1.41147	−0.705736	+	0.708475i	$0.749383\pi$
$410$	−116454.	−0.0342134
$411$	−3.65502e6	−1.06730
$412$	2.03866e6	0.591701
$413$	171002.	0.0493316
$414$	−470253.	−0.134844
$415$	130229.	0.0371181
$416$	1.51466e6	0.429122
$417$	−7.66858e6	−2.15961
$418$	−47293.4	−0.0132391
$419$	3.96514e6	1.10338	0.551688	−	0.834051i	$-0.313984\pi$
$419$	3.96514e6	1.10338	0.551688	+	0.834051i	$0.313984\pi$
$420$	−482200.	−0.133384
$421$	−3.53055e6	−0.970816	−0.485408	−	0.874288i	$-0.661329\pi$
$421$	−3.53055e6	−0.970816	−0.485408	+	0.874288i	$0.661329\pi$
$422$	62750.0	0.0171527
$423$	−6.79848e6	−1.84740
$424$	−2.62189e6	−0.708272
$425$	141140.	0.0379035
$426$	−1.06551e6	−0.284468
$427$	377058.	0.100078
$428$	−462946.	−0.122158
$429$	1.34135e6	0.351884
$430$	527815.	0.137661
$431$	−5.50244e6	−1.42680	−0.713398	−	0.700759i	$-0.752845\pi$
$431$	−5.50244e6	−1.42680	−0.713398	+	0.700759i	$0.752845\pi$
$432$	1.07013e6	0.275884
$433$	1.14691e6	0.293974	0.146987	−	0.989138i	$-0.453043\pi$
$433$	1.14691e6	0.293974	0.146987	+	0.989138i	$0.453043\pi$
$434$	275513.	0.0702129
$435$	−2.32495e6	−0.589102
$436$	6.14001e6	1.54687
$437$	−534028.	−0.133770
$438$	526953.	0.131246
$439$	5.73925e6	1.42133	0.710663	−	0.703533i	$-0.248395\pi$
$439$	5.73925e6	1.42133	0.710663	+	0.703533i	$0.248395\pi$
$440$	205771.	0.0506703
$441$	−4.72047e6	−1.15582
$442$	117006.	0.0284874
$443$	6.80208e6	1.64677	0.823385	−	0.567484i	$-0.192083\pi$
$443$	6.80208e6	1.64677	0.823385	+	0.567484i	$0.192083\pi$
$444$	−5.71071e6	−1.37478
$445$	992525.	0.237597
$446$	−287398.	−0.0684143
$447$	−9.28551e6	−2.19805
$448$	696413.	0.163935
$449$	202897.	0.0474963	0.0237481	−	0.999718i	$-0.492440\pi$
$449$	202897.	0.0474963	0.0237481	+	0.999718i	$0.492440\pi$
$450$	−198680.	−0.0462513
$451$	520587.	0.120518
$452$	−1.26892e6	−0.292139
$453$	1.19147e7	2.72796
$454$	−523551.	−0.119212
$455$	−323136.	−0.0731741
$456$	−568846.	−0.128110
$457$	1.22358e6	0.274058	0.137029	−	0.990567i	$-0.456245\pi$
$457$	1.22358e6	0.274058	0.137029	+	0.990567i	$0.456245\pi$
$458$	−1.29161e6	−0.287718
$459$	264736.	0.0586518
$460$	1.14009e6	0.251214
$461$	−7.46856e6	−1.63676	−0.818379	−	0.574679i	$-0.805127\pi$
$461$	−7.46856e6	−1.63676	−0.818379	+	0.574679i	$0.805127\pi$
$462$	−81966.8	−0.0178662
$463$	2.22150e6	0.481609	0.240804	−	0.970574i	$-0.422589\pi$
$463$	2.22150e6	0.481609	0.240804	+	0.970574i	$0.422589\pi$
$464$	3.66471e6	0.790214
$465$	−5.45614e6	−1.17018
$466$	−1.59309e6	−0.339841
$467$	−2.60583e6	−0.552909	−0.276454	−	0.961027i	$-0.589159\pi$
$467$	−2.60583e6	−0.552909	−0.276454	+	0.961027i	$0.589159\pi$
$468$	4.33150e6	0.914163
$469$	3630.29	0.000762094 0
$470$	−626748.	−0.130872
$471$	−1.26181e7	−2.62084
$472$	−430669.	−0.0889791
$473$	−2.35950e6	−0.484916
$474$	278206.	0.0568748
$475$	−225625.	−0.0458831
$476$	188031.	0.0380375
$477$	−1.13168e7	−2.27733
$478$	−266323.	−0.0533137
$479$	−1.41683e6	−0.282149	−0.141074	−	0.989999i	$-0.545056\pi$
$479$	−1.41683e6	−0.282149	−0.141074	+	0.989999i	$0.545056\pi$
$480$	1.83296e6	0.363120
$481$	−3.82692e6	−0.754200
$482$	24268.1	0.00475793
$483$	−925553.	−0.180523
$484$	−451349.	−0.0875789
$485$	−4.01607e6	−0.775259
$486$	1.41674e6	0.272083
$487$	493020.	0.0941982	0.0470991	−	0.998890i	$-0.485002\pi$
$487$	493020.	0.0941982	0.0470991	+	0.998890i	$0.485002\pi$
$488$	−949622.	−0.180510
$489$	−1.47088e7	−2.78166
$490$	−435177.	−0.0818796
$491$	−6.63513e6	−1.24207	−0.621035	−	0.783783i	$-0.713287\pi$
$491$	−6.63513e6	−1.24207	−0.621035	+	0.783783i	$0.713287\pi$
$492$	3.07240e6	0.572223
$493$	906602.	0.167996
$494$	−187044.	−0.0344847
$495$	888162.	0.162922
$496$	8.60026e6	1.56967
$497$	−1.14746e6	−0.208375
$498$	130648.	0.0236064
$499$	−5.81251e6	−1.04499	−0.522495	−	0.852642i	$-0.674999\pi$
$499$	−5.81251e6	−1.04499	−0.522495	+	0.852642i	$0.674999\pi$
$500$	481684.	0.0861662
$501$	1.09287e7	1.94524
$502$	204359.	0.0361939
$503$	1.05170e7	1.85341	0.926705	−	0.375790i	$-0.122628\pi$
$503$	1.05170e7	1.85341	0.926705	+	0.375790i	$0.122628\pi$
$504$	−539440.	−0.0945946
$505$	4.52925e6	0.790311
$506$	193798.	0.0336491
$507$	−3.29591e6	−0.569449
$508$	−5.72575e6	−0.984403
$509$	3.30168e6	0.564859	0.282429	−	0.959288i	$-0.408860\pi$
$509$	3.30168e6	0.564859	0.282429	+	0.959288i	$0.408860\pi$
$510$	141595.	0.0241058
$511$	567482.	0.0961391
$512$	−4.87624e6	−0.822073
$513$	−423203.	−0.0709996
$514$	1.90453e6	0.317966
$515$	1.65327e6	0.274679
$516$	−1.39253e7	−2.30240
$517$	2.80176e6	0.461003
$518$	233854.	0.0382930
$519$	−1.05878e7	−1.72539
$520$	813821.	0.131984
$521$	1.07385e7	1.73320	0.866600	−	0.499004i	$-0.166301\pi$
$521$	1.07385e7	1.73320	0.866600	+	0.499004i	$0.166301\pi$
$522$	−1.27620e6	−0.204995
$523$	−2.79992e6	−0.447601	−0.223801	−	0.974635i	$-0.571846\pi$
$523$	−2.79992e6	−0.447601	−0.223801	+	0.974635i	$0.571846\pi$
$524$	−3.96952e6	−0.631553
$525$	−391043.	−0.0619194
$526$	1.40109e6	0.220801
$527$	2.12759e6	0.333704
$528$	−2.55863e6	−0.399414
$529$	−4.24801e6	−0.660004
$530$	−1.04329e6	−0.161329
$531$	−1.85888e6	−0.286098
$532$	−300584.	−0.0460454
$533$	2.05891e6	0.313920
$534$	995721.	0.151107
$535$	−375430.	−0.0567080
$536$	−9142.90	−0.00137459
$537$	323254.	0.0483735
$538$	1.14702e6	0.170851
$539$	1.94538e6	0.288424
$540$	903491.	0.133334
$541$	7.53086e6	1.10625	0.553123	−	0.833100i	$-0.313436\pi$
$541$	7.53086e6	1.10625	0.553123	+	0.833100i	$0.313436\pi$
$542$	−1.81336e6	−0.265147
$543$	−2.55475e6	−0.371834
$544$	−714754.	−0.103552
$545$	4.97929e6	0.718085
$546$	−324177.	−0.0465372
$547$	−1.08360e7	−1.54846	−0.774232	−	0.632901i	$-0.781864\pi$
$547$	−1.08360e7	−1.54846	−0.774232	+	0.632901i	$0.781864\pi$
$548$	4.86411e6	0.691914
$549$	−4.09881e6	−0.580400
$550$	81879.1	0.0115416
$551$	−1.44928e6	−0.203364
$552$	2.33101e6	0.325609
$553$	299603.	0.0416613
$554$	−530053.	−0.0733744
$555$	−4.63114e6	−0.638198
$556$	1.02054e7	1.40004
$557$	−2.30095e6	−0.314245	−0.157122	−	0.987579i	$-0.550222\pi$
$557$	−2.30095e6	−0.314245	−0.157122	+	0.987579i	$0.550222\pi$
$558$	−2.99497e6	−0.407199
$559$	−9.33175e6	−1.26309
$560$	616383.	0.0830579
$561$	−632973.	−0.0849137
$562$	−141342.	−0.0188769
$563$	−247593.	−0.0329206	−0.0164603	−	0.999865i	$-0.505240\pi$
$563$	−247593.	−0.0329206	−0.0164603	+	0.999865i	$0.505240\pi$
$564$	1.65354e7	2.18886
$565$	−1.02904e6	−0.135616
$566$	−942800.	−0.123703
$567$	1.19356e6	0.155914
$568$	2.88988e6	0.375846
$569$	9.87566e6	1.27875	0.639375	−	0.768895i	$-0.279193\pi$
$569$	9.87566e6	1.27875	0.639375	+	0.768895i	$0.279193\pi$
$570$	−226352.	−0.0291807
$571$	2.68559e6	0.344707	0.172353	−	0.985035i	$-0.444863\pi$
$571$	2.68559e6	0.344707	0.172353	+	0.985035i	$0.444863\pi$
$572$	−1.78508e6	−0.228122
$573$	−3.69053e6	−0.469572
$574$	−125815.	−0.0159387
$575$	924563.	0.116618
$576$	−7.57038e6	−0.950739
$577$	−1.11266e7	−1.39131	−0.695653	−	0.718378i	$-0.744885\pi$
$577$	−1.11266e7	−1.39131	−0.695653	+	0.718378i	$0.744885\pi$
$578$	1.48206e6	0.184522
$579$	−1.22689e7	−1.52093
$580$	3.09405e6	0.381907
$581$	140696.	0.0172919
$582$	−4.02900e6	−0.493049
$583$	4.66381e6	0.568289
$584$	−1.42921e6	−0.173406
$585$	3.51266e6	0.424372
$586$	237793.	0.0286058
$587$	7.40614e6	0.887149	0.443575	−	0.896237i	$-0.353710\pi$
$587$	7.40614e6	0.887149	0.443575	+	0.896237i	$0.353710\pi$
$588$	1.14812e7	1.36945
$589$	−3.40114e6	−0.403958
$590$	−171369.	−0.0202676
$591$	8.49161e6	1.00005
$592$	7.29985e6	0.856071
$593$	−1.16239e7	−1.35743	−0.678714	−	0.734403i	$-0.737462\pi$
$593$	−1.16239e7	−1.35743	−0.678714	+	0.734403i	$0.737462\pi$
$594$	153580.	0.0178595
$595$	152485.	0.0176577
$596$	1.23572e7	1.42496
$597$	−1.15612e7	−1.32760
$598$	766467.	0.0876477
$599$	8.76692e6	0.998343	0.499172	−	0.866503i	$-0.333638\pi$
$599$	8.76692e6	0.998343	0.499172	+	0.866503i	$0.333638\pi$
$600$	984845.	0.111684
$601$	1.47418e7	1.66481	0.832406	−	0.554167i	$-0.186963\pi$
$601$	1.47418e7	1.66481	0.832406	+	0.554167i	$0.186963\pi$
$602$	570241.	0.0641309
$603$	−39463.1	−0.00441975
$604$	−1.58561e7	−1.76850
$605$	−366025.	−0.0406558
$606$	4.54384e6	0.502622
$607$	5.09830e6	0.561634	0.280817	−	0.959761i	$-0.409395\pi$
$607$	5.09830e6	0.561634	0.280817	+	0.959761i	$0.409395\pi$
$608$	1.14260e6	0.125353
$609$	−2.51183e6	−0.274440
$610$	−377867.	−0.0411164
$611$	1.10809e7	1.20080
$612$	−2.04400e6	−0.220598
$613$	−1.82479e6	−0.196138	−0.0980689	−	0.995180i	$-0.531267\pi$
$613$	−1.82479e6	−0.196138	−0.0980689	+	0.995180i	$0.531267\pi$
$614$	3.21933e6	0.344623
$615$	2.49159e6	0.265637
$616$	222311.	0.0236053
$617$	−1.30957e7	−1.38489	−0.692446	−	0.721469i	$-0.743467\pi$
$617$	−1.30957e7	−1.38489	−0.692446	+	0.721469i	$0.743467\pi$
$618$	1.65859e6	0.174690
$619$	−4.18198e6	−0.438688	−0.219344	−	0.975648i	$-0.570392\pi$
$619$	−4.18198e6	−0.438688	−0.219344	+	0.975648i	$0.570392\pi$
$620$	7.26105e6	0.758612
$621$	1.73420e6	0.180455
$622$	1.85364e6	0.192110
$623$	1.07230e6	0.110687
$624$	−1.01193e7	−1.04038
$625$	390625.	0.0400000
$626$	1.24244e6	0.126718
$627$	1.01186e6	0.102790
$628$	1.67922e7	1.69906
$629$	1.80589e6	0.181997
$630$	−214650.	−0.0215467
$631$	−9.04125e6	−0.903972	−0.451986	−	0.892025i	$-0.649284\pi$
$631$	−9.04125e6	−0.903972	−0.451986	+	0.892025i	$0.649284\pi$
$632$	−754552.	−0.0751444
$633$	−1.34256e6	−0.133176
$634$	1.44099e6	0.142376
$635$	−4.64334e6	−0.456979
$636$	2.75249e7	2.69825
$637$	7.69391e6	0.751275
$638$	525943.	0.0511549
$639$	1.24735e7	1.20847
$640$	−3.22998e6	−0.311709
$641$	1.29780e7	1.24756	0.623782	−	0.781599i	$-0.285595\pi$
$641$	1.29780e7	1.24756	0.623782	+	0.781599i	$0.285595\pi$
$642$	−376639.	−0.0360651
$643$	−1.54273e7	−1.47151	−0.735756	−	0.677247i	$-0.763173\pi$
$643$	−1.54273e7	−1.47151	−0.735756	+	0.677247i	$0.763173\pi$
$644$	1.23173e6	0.117031
$645$	−1.12928e7	−1.06882
$646$	88264.5	0.00832156
$647$	8.67413e6	0.814639	0.407319	−	0.913286i	$-0.366464\pi$
$647$	8.67413e6	0.814639	0.407319	+	0.913286i	$0.366464\pi$
$648$	−3.00598e6	−0.281222
$649$	766071.	0.0713933
$650$	323830.	0.0300631
$651$	−5.89470e6	−0.545142
$652$	1.95745e7	1.80331
$653$	1.76775e7	1.62232	0.811162	−	0.584822i	$-0.198835\pi$
$653$	1.76775e7	1.62232	0.811162	+	0.584822i	$0.198835\pi$
$654$	4.99532e6	0.456687
$655$	−3.21911e6	−0.293179
$656$	−3.92737e6	−0.356322
$657$	−6.16883e6	−0.557557
$658$	−677126.	−0.0609684
$659$	4.70096e6	0.421671	0.210835	−	0.977522i	$-0.432382\pi$
$659$	4.70096e6	0.421671	0.210835	+	0.977522i	$0.432382\pi$
$660$	−2.16021e6	−0.193035
$661$	−3.87912e6	−0.345326	−0.172663	−	0.984981i	$-0.555237\pi$
$661$	−3.87912e6	−0.345326	−0.172663	+	0.984981i	$0.555237\pi$
$662$	−485206.	−0.0430310
$663$	−2.50339e6	−0.221179
$664$	−354345.	−0.0311893
$665$	−243761.	−0.0213752
$666$	−2.54211e6	−0.222080
$667$	5.93884e6	0.516877
$668$	−1.45439e7	−1.26107
$669$	6.14900e6	0.531177
$670$	−3638.08	−0.000313102 0
$671$	1.68918e6	0.144834
$672$	1.98030e6	0.169164
$673$	6.89339e6	0.586672	0.293336	−	0.956009i	$-0.405235\pi$
$673$	6.89339e6	0.586672	0.293336	+	0.956009i	$0.405235\pi$
$674$	4.24641e6	0.360058
$675$	732693.	0.0618960
$676$	4.38620e6	0.369166
$677$	−1.65983e7	−1.39185	−0.695925	−	0.718115i	$-0.745005\pi$
$677$	−1.65983e7	−1.39185	−0.695925	+	0.718115i	$0.745005\pi$
$678$	−1.03236e6	−0.0862492
$679$	−4.33888e6	−0.361163
$680$	−384035.	−0.0318492
$681$	1.12016e7	0.925575
$682$	1.23427e6	0.101613
$683$	−2.11823e7	−1.73749	−0.868743	−	0.495264i	$-0.835071\pi$
$683$	−2.11823e7	−1.73749	−0.868743	+	0.495264i	$0.835071\pi$
$684$	3.26750e6	0.267040
$685$	3.94459e6	0.321200
$686$	−961646.	−0.0780198
$687$	2.76345e7	2.23388
$688$	1.78003e7	1.43370
$689$	1.84452e7	1.48025
$690$	927540.	0.0741669
$691$	−9.14147e6	−0.728317	−0.364159	−	0.931337i	$-0.618643\pi$
$691$	−9.14147e6	−0.728317	−0.364159	+	0.931337i	$0.618643\pi$
$692$	1.40903e7	1.11855
$693$	959552.	0.0758989
$694$	3.35384e6	0.264328
$695$	8.27612e6	0.649927
$696$	6.32606e6	0.495005
$697$	−971581.	−0.0757525
$698$	−2.17326e6	−0.168839
$699$	3.40849e7	2.63857
$700$	520401.	0.0401415
$701$	3.24074e6	0.249086	0.124543	−	0.992214i	$-0.460254\pi$
$701$	3.24074e6	0.249086	0.124543	+	0.992214i	$0.460254\pi$
$702$	607406.	0.0465196
$703$	−2.88687e6	−0.220312
$704$	3.11987e6	0.237249
$705$	1.34095e7	1.01611
$706$	−564974.	−0.0426596
$707$	4.89331e6	0.368175
$708$	4.52120e6	0.338978
$709$	1.82802e6	0.136573	0.0682865	−	0.997666i	$-0.478247\pi$
$709$	1.82802e6	0.136573	0.0682865	+	0.997666i	$0.478247\pi$
$710$	1.14992e6	0.0856097
$711$	−3.25684e6	−0.241614
$712$	−2.70060e6	−0.199646
$713$	1.39371e7	1.02671
$714$	152976.	0.0112300
$715$	−1.44762e6	−0.105898
$716$	−430187.	−0.0313599
$717$	5.69809e6	0.413934
$718$	4.88625e6	0.353724
$719$	−2.13675e7	−1.54146	−0.770729	−	0.637163i	$-0.780108\pi$
$719$	−2.13675e7	−1.54146	−0.770729	+	0.637163i	$0.780108\pi$
$720$	−6.70041e6	−0.481693
$721$	1.78616e6	0.127962
$722$	−141098.	−0.0100735
$723$	−519226.	−0.0369412
$724$	3.39987e6	0.241055
$725$	2.50914e6	0.177288
$726$	−367204.	−0.0258562
$727$	1.30297e7	0.914320	0.457160	−	0.889384i	$-0.348867\pi$
$727$	1.30297e7	0.914320	0.457160	+	0.889384i	$0.348867\pi$
$728$	879235.	0.0614861
$729$	−1.95736e7	−1.36412
$730$	−568701.	−0.0394981
$731$	4.40357e6	0.304798
$732$	9.96923e6	0.687676
$733$	1.03859e7	0.713980	0.356990	−	0.934108i	$-0.383803\pi$
$733$	1.03859e7	0.713980	0.356990	+	0.934108i	$0.383803\pi$
$734$	415587.	0.0284723
$735$	9.31079e6	0.635723
$736$	−4.68211e6	−0.318601
$737$	16263.3	0.00110291
$738$	1.36767e6	0.0924361
$739$	8.25246e6	0.555869	0.277935	−	0.960600i	$-0.410350\pi$
$739$	8.25246e6	0.555869	0.277935	+	0.960600i	$0.410350\pi$
$740$	6.16314e6	0.413735
$741$	4.00189e6	0.267744
$742$	−1.12714e6	−0.0751570
$743$	1.46255e7	0.971939	0.485969	−	0.873976i	$-0.338467\pi$
$743$	1.46255e7	0.971939	0.485969	+	0.873976i	$0.338467\pi$
$744$	1.48458e7	0.983270
$745$	1.00211e7	0.661495
$746$	2.16144e6	0.142199
$747$	−1.52944e6	−0.100284
$748$	842362.	0.0550484
$749$	−405607.	−0.0264180
$750$	391883.	0.0254392
$751$	1.23640e7	0.799945	0.399972	−	0.916527i	$-0.369020\pi$
$751$	1.23640e7	0.799945	0.399972	+	0.916527i	$0.369020\pi$
$752$	−2.11368e7	−1.36300
$753$	−4.37235e6	−0.281014
$754$	2.08009e6	0.133246
$755$	−1.28586e7	−0.820971
$756$	976114.	0.0621149
$757$	−1.05146e7	−0.666889	−0.333444	−	0.942770i	$-0.608211\pi$
$757$	−1.05146e7	−0.666889	−0.333444	+	0.942770i	$0.608211\pi$
$758$	−5.48812e6	−0.346937
$759$	−4.14639e6	−0.261256
$760$	613913.	0.0385543
$761$	2.84459e7	1.78057	0.890284	−	0.455405i	$-0.150506\pi$
$761$	2.84459e7	1.78057	0.890284	+	0.455405i	$0.150506\pi$
$762$	−4.65829e6	−0.290629
$763$	5.37952e6	0.334528
$764$	4.91136e6	0.304417
$765$	−1.65759e6	−0.102406
$766$	−880892.	−0.0542438
$767$	3.02979e6	0.185962
$768$	1.58726e7	0.971059
$769$	−2.74153e7	−1.67177	−0.835885	−	0.548905i	$-0.815045\pi$
$769$	−2.74153e7	−1.67177	−0.835885	+	0.548905i	$0.815045\pi$
$770$	88460.6	0.00537679
$771$	−4.07482e7	−2.46872
$772$	1.63275e7	0.986000
$773$	1.91213e7	1.15098	0.575491	−	0.817808i	$-0.304811\pi$
$773$	1.91213e7	1.15098	0.575491	+	0.817808i	$0.304811\pi$
$774$	−6.19882e6	−0.371926
$775$	5.88840e6	0.352162
$776$	1.09275e7	0.651428
$777$	−5.00339e6	−0.297312
$778$	−516998.	−0.0306225
$779$	1.55316e6	0.0917004
$780$	−8.54357e6	−0.502809
$781$	−5.14051e6	−0.301564
$782$	−361689.	−0.0211504
$783$	4.70638e6	0.274336
$784$	−1.46762e7	−0.852751
$785$	1.36177e7	0.788735
$786$	−3.22948e6	−0.186456
$787$	2.90975e7	1.67463	0.837316	−	0.546720i	$-0.184124\pi$
$787$	2.90975e7	1.67463	0.837316	+	0.546720i	$0.184124\pi$
$788$	−1.13007e7	−0.648319
$789$	−2.99769e7	−1.71433
$790$	−300246.	−0.0171163
$791$	−1.11176e6	−0.0631784
$792$	−2.41664e6	−0.136899
$793$	6.68068e6	0.377257
$794$	2.23185e6	0.125636
$795$	2.23215e7	1.25258
$796$	1.53857e7	0.860665
$797$	−3.57458e7	−1.99333	−0.996665	−	0.0815987i	$-0.973997\pi$
$797$	−3.57458e7	−1.99333	−0.996665	+	0.0815987i	$0.973997\pi$
$798$	−244546.	−0.0135942
$799$	−5.22897e6	−0.289767
$800$	−1.97818e6	−0.109280
$801$	−1.16565e7	−0.641929
$802$	−3.80755e6	−0.209030
$803$	2.54227e6	0.139134
$804$	95983.1	0.00523666
$805$	998879.	0.0543279
$806$	4.88151e6	0.264677
$807$	−2.45410e7	−1.32650
$808$	−1.23238e7	−0.664076
$809$	−1.45180e7	−0.779895	−0.389947	−	0.920837i	$-0.627507\pi$
$809$	−1.45180e7	−0.779895	−0.389947	+	0.920837i	$0.627507\pi$
$810$	−1.19612e6	−0.0640564
$811$	3.87598e6	0.206933	0.103466	−	0.994633i	$-0.467007\pi$
$811$	3.87598e6	0.206933	0.103466	+	0.994633i	$0.467007\pi$
$812$	3.34275e6	0.177915
$813$	3.87976e7	2.05863
$814$	1.04764e6	0.0554182
$815$	1.58741e7	0.837133
$816$	4.77522e6	0.251055
$817$	−7.03949e6	−0.368966
$818$	5.16997e6	0.270150
$819$	3.79501e6	0.197698
$820$	−3.31581e6	−0.172209
$821$	−2.61246e7	−1.35267	−0.676335	−	0.736594i	$-0.736433\pi$
$821$	−2.61246e7	−1.35267	−0.676335	+	0.736594i	$0.736433\pi$
$822$	3.95729e6	0.204276
$823$	2.95337e7	1.51991	0.759956	−	0.649975i	$-0.225220\pi$
$823$	2.95337e7	1.51991	0.759956	+	0.649975i	$0.225220\pi$
$824$	−4.49845e6	−0.230805
$825$	−1.75184e6	−0.0896105
$826$	−185143.	−0.00944187
$827$	2.95054e7	1.50016	0.750080	−	0.661348i	$-0.230015\pi$
$827$	2.95054e7	1.50016	0.750080	+	0.661348i	$0.230015\pi$
$828$	−1.33895e7	−0.678718
$829$	1.19193e7	0.602372	0.301186	−	0.953565i	$-0.402618\pi$
$829$	1.19193e7	0.602372	0.301186	+	0.953565i	$0.402618\pi$
$830$	−140998.	−0.00710426
$831$	1.13407e7	0.569688
$832$	1.23390e7	0.617976
$833$	−3.63069e6	−0.181291
$834$	8.30276e6	0.413340
$835$	−1.17945e7	−0.585414
$836$	−1.34659e6	−0.0666375
$837$	1.10448e7	0.544936
$838$	−4.29305e6	−0.211182
$839$	−2.49898e7	−1.22563	−0.612814	−	0.790228i	$-0.709962\pi$
$839$	−2.49898e7	−1.22563	−0.612814	+	0.790228i	$0.709962\pi$
$840$	1.06401e6	0.0520291
$841$	−4.39391e6	−0.214221
$842$	3.82252e6	0.185810
$843$	3.02408e6	0.146563
$844$	1.78668e6	0.0863360
$845$	3.55702e6	0.171374
$846$	7.36071e6	0.353585
$847$	−395446.	−0.0189399
$848$	−3.51843e7	−1.68020
$849$	2.01716e7	0.960442
$850$	−152813.	−0.00725457
$851$	1.18298e7	0.559954
$852$	−3.03383e7	−1.43183
$853$	−1.60748e6	−0.0756437	−0.0378219	−	0.999284i	$-0.512042\pi$
$853$	−1.60748e6	−0.0756437	−0.0378219	+	0.999284i	$0.512042\pi$
$854$	−408240.	−0.0191545
$855$	2.64981e6	0.123965
$856$	1.02152e6	0.0476501
$857$	2.90277e7	1.35008	0.675042	−	0.737780i	$-0.264126\pi$
$857$	2.90277e7	1.35008	0.675042	+	0.737780i	$0.264126\pi$
$858$	−1.45228e6	−0.0673492
$859$	−2.30629e7	−1.06643	−0.533213	−	0.845981i	$-0.679015\pi$
$859$	−2.30629e7	−1.06643	−0.533213	+	0.845981i	$0.679015\pi$
$860$	1.50285e7	0.692899
$861$	2.69186e6	0.123750
$862$	5.95748e6	0.273083
$863$	−1.33534e7	−0.610332	−0.305166	−	0.952299i	$-0.598712\pi$
$863$	−1.33534e7	−0.610332	−0.305166	+	0.952299i	$0.598712\pi$
$864$	−3.71046e6	−0.169100
$865$	1.14266e7	0.519251
$866$	−1.24175e6	−0.0562654
$867$	−3.17094e7	−1.43265
$868$	7.84469e6	0.353408
$869$	1.34219e6	0.0602928
$870$	2.51722e6	0.112752
$871$	64321.1	0.00287282
$872$	−1.35484e7	−0.603386
$873$	4.71659e7	2.09456
$874$	578191.	0.0256031
$875$	422023.	0.0186344
$876$	1.50040e7	0.660611
$877$	2.86871e7	1.25947	0.629734	−	0.776810i	$-0.283164\pi$
$877$	2.86871e7	1.25947	0.629734	+	0.776810i	$0.283164\pi$
$878$	−6.21388e6	−0.272036
$879$	−5.08767e6	−0.222099
$880$	2.76134e6	0.120202
$881$	−2.67154e7	−1.15963	−0.579817	−	0.814747i	$-0.696876\pi$
$881$	−2.67154e7	−1.15963	−0.579817	+	0.814747i	$0.696876\pi$
$882$	5.11085e6	0.221219
$883$	3.46426e7	1.49523	0.747617	−	0.664131i	$-0.231198\pi$
$883$	3.46426e7	1.49523	0.747617	+	0.664131i	$0.231198\pi$
$884$	3.33152e6	0.143388
$885$	3.66650e6	0.157360
$886$	−7.36461e6	−0.315185
$887$	2.39231e7	1.02096	0.510480	−	0.859890i	$-0.329468\pi$
$887$	2.39231e7	1.02096	0.510480	+	0.859890i	$0.329468\pi$
$888$	1.26011e7	0.536260
$889$	−5.01657e6	−0.212889
$890$	−1.07461e6	−0.0454752
$891$	5.34703e6	0.225641
$892$	−8.18311e6	−0.344355
$893$	8.35896e6	0.350771
$894$	1.00534e7	0.420698
$895$	−348863.	−0.0145579
$896$	−3.48960e6	−0.145213
$897$	−1.63989e7	−0.680507
$898$	−219676.	−0.00909060
$899$	3.78236e7	1.56086
$900$	−5.65704e6	−0.232800
$901$	−8.70415e6	−0.357202
$902$	−563639.	−0.0230667
$903$	−1.22005e7	−0.497920
$904$	2.79997e6	0.113955
$905$	2.75715e6	0.111902
$906$	−1.29001e7	−0.522121
$907$	−1.81475e7	−0.732487	−0.366243	−	0.930519i	$-0.619356\pi$
$907$	−1.81475e7	−0.732487	−0.366243	+	0.930519i	$0.619356\pi$
$908$	−1.49071e7	−0.600037
$909$	−5.31929e7	−2.13523
$910$	349859.	0.0140052
$911$	2.84310e7	1.13500	0.567501	−	0.823373i	$-0.307910\pi$
$911$	2.84310e7	1.13500	0.567501	+	0.823373i	$0.307910\pi$
$912$	−7.63361e6	−0.303908
$913$	630306.	0.0250250
$914$	−1.32477e6	−0.0524536
$915$	8.08462e6	0.319232
$916$	−3.67761e7	−1.44819
$917$	−3.47786e6	−0.136581
$918$	−286630.	−0.0112257
$919$	5.92137e6	0.231278	0.115639	−	0.993291i	$-0.463108\pi$
$919$	5.92137e6	0.231278	0.115639	+	0.993291i	$0.463108\pi$
$920$	−2.51568e6	−0.0979911
$921$	−6.88789e7	−2.67570
$922$	8.08620e6	0.313269
$923$	−2.03306e7	−0.785500
$924$	−2.33385e6	−0.0899274
$925$	4.99804e6	0.192064
$926$	−2.40522e6	−0.0921780
$927$	−1.94165e7	−0.742115
$928$	−1.27066e7	−0.484352
$929$	−3.01827e7	−1.14741	−0.573706	−	0.819062i	$-0.694495\pi$
$929$	−3.01827e7	−1.14741	−0.573706	+	0.819062i	$0.694495\pi$
$930$	5.90736e6	0.223968
$931$	5.80397e6	0.219458
$932$	−4.53602e7	−1.71055
$933$	−3.96595e7	−1.49157
$934$	2.82133e6	0.105824
$935$	683119.	0.0255545
$936$	−9.55775e6	−0.356587
$937$	6.76409e6	0.251687	0.125843	−	0.992050i	$-0.459836\pi$
$937$	6.76409e6	0.251687	0.125843	+	0.992050i	$0.459836\pi$
$938$	−3930.51	−0.000145862 0
$939$	−2.65824e7	−0.983854
$940$	−1.78454e7	−0.658730
$941$	−5.10861e6	−0.188074	−0.0940370	−	0.995569i	$-0.529977\pi$
$941$	−5.10861e6	−0.188074	−0.0940370	+	0.995569i	$0.529977\pi$
$942$	1.36616e7	0.501619
$943$	−6.36450e6	−0.233069
$944$	−5.77934e6	−0.211080
$945$	791586.	0.0288349
$946$	2.55462e6	0.0928110
$947$	5.07774e7	1.83990	0.919952	−	0.392031i	$-0.128227\pi$
$947$	5.07774e7	1.83990	0.919952	+	0.392031i	$0.128227\pi$
$948$	7.92136e6	0.286272
$949$	1.00546e7	0.362410
$950$	244284.	0.00878185
$951$	−3.08306e7	−1.10543
$952$	−414903.	−0.0148373
$953$	−4.91559e7	−1.75325	−0.876624	−	0.481175i	$-0.840210\pi$
$953$	−4.91559e7	−1.75325	−0.876624	+	0.481175i	$0.840210\pi$
$954$	1.22526e7	0.435872
$955$	3.98291e6	0.141316
$956$	−7.58303e6	−0.268348
$957$	−1.12528e7	−0.397172
$958$	1.53400e6	0.0540021
$959$	4.26165e6	0.149634
$960$	1.49320e7	0.522927
$961$	6.01343e7	2.10046
$962$	4.14340e6	0.144351
$963$	4.40916e6	0.153211
$964$	690987.	0.0239485
$965$	1.32409e7	0.457720
$966$	1.00210e6	0.0345515
$967$	−3.10381e7	−1.06740	−0.533702	−	0.845673i	$-0.679199\pi$
$967$	−3.10381e7	−1.06740	−0.533702	+	0.845673i	$0.679199\pi$
$968$	995933.	0.0341619
$969$	−1.88846e6	−0.0646096
$970$	4.34819e6	0.148381
$971$	4.61311e7	1.57017	0.785084	−	0.619390i	$-0.212620\pi$
$971$	4.61311e7	1.57017	0.785084	+	0.619390i	$0.212620\pi$
$972$	4.03391e7	1.36949
$973$	8.94135e6	0.302776
$974$	−533793.	−0.0180292
$975$	−6.92847e6	−0.233413
$976$	−1.27434e7	−0.428214
$977$	6.70081e6	0.224590	0.112295	−	0.993675i	$-0.464180\pi$
$977$	6.70081e6	0.224590	0.112295	+	0.993675i	$0.464180\pi$
$978$	1.59252e7	0.532399
$979$	4.80382e6	0.160188
$980$	−1.23908e7	−0.412131
$981$	−5.84782e7	−1.94009
$982$	7.18386e6	0.237727
$983$	4.15188e6	0.137044	0.0685221	−	0.997650i	$-0.478172\pi$
$983$	4.15188e6	0.137044	0.0685221	+	0.997650i	$0.478172\pi$
$984$	−6.77947e6	−0.223207
$985$	−9.16436e6	−0.300962
$986$	−981577.	−0.0321538
$987$	1.44874e7	0.473366
$988$	−5.32572e6	−0.173575
$989$	2.88463e7	0.937777
$990$	−961613.	−0.0311826
$991$	−552308.	−0.0178647	−0.00893237	−	0.999960i	$-0.502843\pi$
$991$	−552308.	−0.0178647	−0.00893237	+	0.999960i	$0.502843\pi$
$992$	−2.98197e7	−0.962107
$993$	1.03812e7	0.334098
$994$	1.24235e6	0.0398822
$995$	1.24771e7	0.399537
$996$	3.71995e6	0.118820
$997$	−8.05615e6	−0.256679	−0.128339	−	0.991730i	$-0.540965\pi$
$997$	−8.05615e6	−0.256679	−0.128339	+	0.991730i	$0.540965\pi$
$998$	6.29320e6	0.200007
$999$	9.37479e6	0.297199

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.c.1.17	✓	37

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.c.1.17	✓	37	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1045 = 5 \cdot 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	1045.a (trivial)

\(f(q)\)	\(=\)	\(q-1.08270 q^{2} +23.1648 q^{3} -30.8278 q^{4} -25.0000 q^{5} -25.0805 q^{6} -27.0095 q^{7} +68.0236 q^{8} +293.607 q^{9} +O(q^{10})\)	\(q-1.08270 q^{2} +23.1648 q^{3} -30.8278 q^{4} -25.0000 q^{5} -25.0805 q^{6} -27.0095 q^{7} +68.0236 q^{8} +293.607 q^{9} +27.0675 q^{10} -121.000 q^{11} -714.119 q^{12} -478.552 q^{13} +29.2432 q^{14} -579.120 q^{15} +912.839 q^{16} +225.825 q^{17} -317.888 q^{18} -361.000 q^{19} +770.694 q^{20} -625.669 q^{21} +131.007 q^{22} +1479.30 q^{23} +1575.75 q^{24} +625.000 q^{25} +518.128 q^{26} +1172.31 q^{27} +832.642 q^{28} +4014.63 q^{29} +627.013 q^{30} +9421.44 q^{31} -3165.09 q^{32} -2802.94 q^{33} -244.500 q^{34} +675.237 q^{35} -9051.26 q^{36} +7996.87 q^{37} +390.854 q^{38} -11085.6 q^{39} -1700.59 q^{40} -4302.37 q^{41} +677.412 q^{42} +19500.0 q^{43} +3730.16 q^{44} -7340.18 q^{45} -1601.64 q^{46} -23155.0 q^{47} +21145.7 q^{48} -16077.5 q^{49} -676.687 q^{50} +5231.18 q^{51} +14752.7 q^{52} -38543.9 q^{53} -1269.26 q^{54} +3025.00 q^{55} -1837.28 q^{56} -8362.49 q^{57} -4346.64 q^{58} -6331.17 q^{59} +17853.0 q^{60} -13960.2 q^{61} -10200.6 q^{62} -7930.19 q^{63} -25784.0 q^{64} +11963.8 q^{65} +3034.74 q^{66} -134.408 q^{67} -6961.67 q^{68} +34267.7 q^{69} -731.079 q^{70} +42483.6 q^{71} +19972.2 q^{72} -21010.5 q^{73} -8658.20 q^{74} +14478.0 q^{75} +11128.8 q^{76} +3268.15 q^{77} +12002.3 q^{78} -11092.5 q^{79} -22821.0 q^{80} -44190.3 q^{81} +4658.17 q^{82} -5209.14 q^{83} +19288.0 q^{84} -5645.61 q^{85} -21112.6 q^{86} +92998.0 q^{87} -8230.85 q^{88} -39701.0 q^{89} +7947.21 q^{90} +12925.4 q^{91} -45603.5 q^{92} +218246. q^{93} +25069.9 q^{94} +9025.00 q^{95} -73318.5 q^{96} +160643. q^{97} +17407.1 q^{98} -35526.5 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9}+O(q^{10}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9	\( 37 q - 12 q^{2} - 27 q^{3} + 574 q^{4} - 925 q^{5} - 75 q^{6} + 337 q^{7} - 696 q^{8} + 3140 q^{9} + 300 q^{10} - 4477 q^{11} - 568 q^{12} + 719 q^{13} + 687 q^{14} + 675 q^{15} + 11494 q^{16} + 999 q^{17} - 595 q^{18} - 13357 q^{19} - 14350 q^{20} - 1077 q^{21} + 1452 q^{22} + 5096 q^{23} - 3154 q^{24} + 23125 q^{25} - 10395 q^{26} - 7578 q^{27} + 19863 q^{28} - 7969 q^{29} + 1875 q^{30} + 603 q^{31} - 27809 q^{32} + 3267 q^{33} - 24081 q^{34} - 8425 q^{35} + 59869 q^{36} + 7963 q^{37} + 4332 q^{38} + 86 q^{39} + 17400 q^{40} + 1475 q^{41} - 46542 q^{42} + 38059 q^{43} - 69454 q^{44} - 78500 q^{45} - 3413 q^{46} - 37658 q^{47} - 51317 q^{48} + 39188 q^{49} - 7500 q^{50} - 40262 q^{51} + 25358 q^{52} - 52545 q^{53} + 64732 q^{54} + 111925 q^{55} - 54173 q^{56} + 9747 q^{57} + 105808 q^{58} - 34039 q^{59} + 14200 q^{60} + 30023 q^{61} - 100198 q^{62} + 30376 q^{63} + 160888 q^{64} - 17975 q^{65} + 9075 q^{66} - 45284 q^{67} + 125176 q^{68} + 109244 q^{69} - 17175 q^{70} - 84020 q^{71} - 291176 q^{72} + 24542 q^{73} + 38795 q^{74} - 16875 q^{75} - 207214 q^{76} - 40777 q^{77} + 1042 q^{78} + 49303 q^{79} - 287350 q^{80} + 344453 q^{81} - 286030 q^{82} - 402155 q^{83} - 203270 q^{84} - 24975 q^{85} - 276426 q^{86} + 116994 q^{87} + 84216 q^{88} - 442930 q^{89} + 14875 q^{90} - 93040 q^{91} + 402160 q^{92} - 241950 q^{93} - 170720 q^{94} + 333925 q^{95} - 234384 q^{96} - 87732 q^{97} - 712662 q^{98} - 379940 q^{99}+O(q^{100}) \) 37 * q - 12 * q^2 - 27 * q^3 + 574 * q^4 - 925 * q^5 - 75 * q^6 + 337 * q^7 - 696 * q^8 + 3140 * q^9 + 300 * q^10 - 4477 * q^11 - 568 * q^12 + 719 * q^13 + 687 * q^14 + 675 * q^15 + 11494 * q^16 + 999 * q^17 - 595 * q^18 - 13357 * q^19 - 14350 * q^20 - 1077 * q^21 + 1452 * q^22 + 5096 * q^23 - 3154 * q^24 + 23125 * q^25 - 10395 * q^26 - 7578 * q^27 + 19863 * q^28 - 7969 * q^29 + 1875 * q^30 + 603 * q^31 - 27809 * q^32 + 3267 * q^33 - 24081 * q^34 - 8425 * q^35 + 59869 * q^36 + 7963 * q^37 + 4332 * q^38 + 86 * q^39 + 17400 * q^40 + 1475 * q^41 - 46542 * q^42 + 38059 * q^43 - 69454 * q^44 - 78500 * q^45 - 3413 * q^46 - 37658 * q^47 - 51317 * q^48 + 39188 * q^49 - 7500 * q^50 - 40262 * q^51 + 25358 * q^52 - 52545 * q^53 + 64732 * q^54 + 111925 * q^55 - 54173 * q^56 + 9747 * q^57 + 105808 * q^58 - 34039 * q^59 + 14200 * q^60 + 30023 * q^61 - 100198 * q^62 + 30376 * q^63 + 160888 * q^64 - 17975 * q^65 + 9075 * q^66 - 45284 * q^67 + 125176 * q^68 + 109244 * q^69 - 17175 * q^70 - 84020 * q^71 - 291176 * q^72 + 24542 * q^73 + 38795 * q^74 - 16875 * q^75 - 207214 * q^76 - 40777 * q^77 + 1042 * q^78 + 49303 * q^79 - 287350 * q^80 + 344453 * q^81 - 286030 * q^82 - 402155 * q^83 - 203270 * q^84 - 24975 * q^85 - 276426 * q^86 + 116994 * q^87 + 84216 * q^88 - 442930 * q^89 + 14875 * q^90 - 93040 * q^91 + 402160 * q^92 - 241950 * q^93 - 170720 * q^94 + 333925 * q^95 - 234384 * q^96 - 87732 * q^97 - 712662 * q^98 - 379940 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more