LMFDB - Embedded newform 1045.6.a.b.1.4

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:	$36$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-9.55197 q^{2} -7.71824 q^{3} +59.2400 q^{4} +25.0000 q^{5} +73.7243 q^{6} +175.466 q^{7} -260.196 q^{8} -183.429 q^{9} +O(q^{10})$	\(q-9.55197 q^{2} -7.71824 q^{3} +59.2400 q^{4} +25.0000 q^{5} +73.7243 q^{6} +175.466 q^{7} -260.196 q^{8} -183.429 q^{9} -238.799 q^{10} -121.000 q^{11} -457.229 q^{12} -84.5196 q^{13} -1676.05 q^{14} -192.956 q^{15} +589.701 q^{16} -736.715 q^{17} +1752.11 q^{18} +361.000 q^{19} +1481.00 q^{20} -1354.29 q^{21} +1155.79 q^{22} +3310.98 q^{23} +2008.25 q^{24} +625.000 q^{25} +807.328 q^{26} +3291.28 q^{27} +10394.6 q^{28} -1615.12 q^{29} +1843.11 q^{30} +256.923 q^{31} +2693.46 q^{32} +933.907 q^{33} +7037.08 q^{34} +4386.65 q^{35} -10866.3 q^{36} -10444.7 q^{37} -3448.26 q^{38} +652.342 q^{39} -6504.90 q^{40} +16922.4 q^{41} +12936.1 q^{42} -7986.84 q^{43} -7168.05 q^{44} -4585.72 q^{45} -31626.4 q^{46} +5244.98 q^{47} -4551.45 q^{48} +13981.4 q^{49} -5969.98 q^{50} +5686.14 q^{51} -5006.94 q^{52} -7151.84 q^{53} -31438.2 q^{54} -3025.00 q^{55} -45655.6 q^{56} -2786.28 q^{57} +15427.6 q^{58} -17732.4 q^{59} -11430.7 q^{60} -50558.0 q^{61} -2454.12 q^{62} -32185.5 q^{63} -44598.3 q^{64} -2112.99 q^{65} -8920.64 q^{66} +40134.9 q^{67} -43643.0 q^{68} -25554.9 q^{69} -41901.2 q^{70} -47861.3 q^{71} +47727.4 q^{72} +11087.4 q^{73} +99767.3 q^{74} -4823.90 q^{75} +21385.7 q^{76} -21231.4 q^{77} -6231.15 q^{78} +77611.7 q^{79} +14742.5 q^{80} +19170.3 q^{81} -161642. q^{82} -84689.9 q^{83} -80228.1 q^{84} -18417.9 q^{85} +76290.0 q^{86} +12465.9 q^{87} +31483.7 q^{88} +23103.6 q^{89} +43802.6 q^{90} -14830.3 q^{91} +196143. q^{92} -1982.99 q^{93} -50099.9 q^{94} +9025.00 q^{95} -20788.8 q^{96} +155781. q^{97} -133549. q^{98} +22194.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) $ 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9} - 200 q^{10} - 4356 q^{11} - 2008 q^{12} - 43 q^{13} - 1937 q^{14} - 1575 q^{15} + 3612 q^{16} - 2431 q^{17} - 6225 q^{18} + 12996 q^{19} + 13000 q^{20} + 2863 q^{21} + 968 q^{22} - 11444 q^{23} - 6210 q^{24} + 22500 q^{25} - 6339 q^{26} - 12960 q^{27} - 1083 q^{28} - 873 q^{29} + 125 q^{30} - 1405 q^{31} - 14283 q^{32} + 7623 q^{33} + 19937 q^{34} - 12725 q^{35} - 1169 q^{36} - 22729 q^{37} - 2888 q^{38} + 3710 q^{39} - 17250 q^{40} - 17043 q^{41} - 39996 q^{42} - 42231 q^{43} - 62920 q^{44} + 48375 q^{45} + 50947 q^{46} - 72440 q^{47} + 42475 q^{48} + 54119 q^{49} - 5000 q^{50} - 114970 q^{51} + 16786 q^{52} - 67603 q^{53} - 26080 q^{54} - 108900 q^{55} - 216071 q^{56} - 22743 q^{57} - 115746 q^{58} - 247439 q^{59} - 50200 q^{60} - 66627 q^{61} - 262438 q^{62} - 226118 q^{63} + 1078 q^{64} - 1075 q^{65} - 605 q^{66} - 189550 q^{67} - 140936 q^{68} - 65684 q^{69} - 48425 q^{70} - 320146 q^{71} - 509978 q^{72} - 55266 q^{73} - 63309 q^{74} - 39375 q^{75} + 187720 q^{76} + 61589 q^{77} - 284264 q^{78} - 1033 q^{79} + 90300 q^{80} - 58588 q^{81} - 328242 q^{82} - 451983 q^{83} + 43932 q^{84} - 60775 q^{85} - 44142 q^{86} - 457510 q^{87} + 83490 q^{88} + 13940 q^{89} - 155625 q^{90} - 211732 q^{91} - 735304 q^{92} + 4486 q^{93} + 152164 q^{94} + 324900 q^{95} + 195996 q^{96} - 234346 q^{97} - 58328 q^{98} - 234135 q^{99}+O(q^{100}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9 - 200 * q^10 - 4356 * q^11 - 2008 * q^12 - 43 * q^13 - 1937 * q^14 - 1575 * q^15 + 3612 * q^16 - 2431 * q^17 - 6225 * q^18 + 12996 * q^19 + 13000 * q^20 + 2863 * q^21 + 968 * q^22 - 11444 * q^23 - 6210 * q^24 + 22500 * q^25 - 6339 * q^26 - 12960 * q^27 - 1083 * q^28 - 873 * q^29 + 125 * q^30 - 1405 * q^31 - 14283 * q^32 + 7623 * q^33 + 19937 * q^34 - 12725 * q^35 - 1169 * q^36 - 22729 * q^37 - 2888 * q^38 + 3710 * q^39 - 17250 * q^40 - 17043 * q^41 - 39996 * q^42 - 42231 * q^43 - 62920 * q^44 + 48375 * q^45 + 50947 * q^46 - 72440 * q^47 + 42475 * q^48 + 54119 * q^49 - 5000 * q^50 - 114970 * q^51 + 16786 * q^52 - 67603 * q^53 - 26080 * q^54 - 108900 * q^55 - 216071 * q^56 - 22743 * q^57 - 115746 * q^58 - 247439 * q^59 - 50200 * q^60 - 66627 * q^61 - 262438 * q^62 - 226118 * q^63 + 1078 * q^64 - 1075 * q^65 - 605 * q^66 - 189550 * q^67 - 140936 * q^68 - 65684 * q^69 - 48425 * q^70 - 320146 * q^71 - 509978 * q^72 - 55266 * q^73 - 63309 * q^74 - 39375 * q^75 + 187720 * q^76 + 61589 * q^77 - 284264 * q^78 - 1033 * q^79 + 90300 * q^80 - 58588 * q^81 - 328242 * q^82 - 451983 * q^83 + 43932 * q^84 - 60775 * q^85 - 44142 * q^86 - 457510 * q^87 + 83490 * q^88 + 13940 * q^89 - 155625 * q^90 - 211732 * q^91 - 735304 * q^92 + 4486 * q^93 + 152164 * q^94 + 324900 * q^95 + 195996 * q^96 - 234346 * q^97 - 58328 * q^98 - 234135 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−9.55197	−1.68856	−0.844282	−	0.535898i	$-0.819973\pi$
$2$	−9.55197	−1.68856	−0.844282	+	0.535898i	$0.819973\pi$
$3$	−7.71824	−0.495125	−0.247563	−	0.968872i	$-0.579630\pi$
$3$	−7.71824	−0.495125	−0.247563	+	0.968872i	$0.579630\pi$
$4$	59.2400	1.85125
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	73.7243	0.836051
$7$	175.466	1.35347	0.676734	−	0.736227i	$-0.263395\pi$
$7$	175.466	1.35347	0.676734	+	0.736227i	$0.263395\pi$
$8$	−260.196	−1.43739
$9$	−183.429	−0.754851
$10$	−238.799	−0.755149
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−457.229	−0.916601
$13$	−84.5196	−0.138707	−0.0693536	−	0.997592i	$-0.522094\pi$
$13$	−84.5196	−0.138707	−0.0693536	+	0.997592i	$0.522094\pi$
$14$	−1676.05	−2.28542
$15$	−192.956	−0.221427
$16$	589.701	0.575880
$17$	−736.715	−0.618269	−0.309134	−	0.951018i	$-0.600039\pi$
$17$	−736.715	−0.618269	−0.309134	+	0.951018i	$0.600039\pi$
$18$	1752.11	1.27462
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	1481.00	0.827905
$21$	−1354.29	−0.670136
$22$	1155.79	0.509121
$23$	3310.98	1.30508	0.652540	−	0.757754i	$-0.273703\pi$
$23$	3310.98	1.30508	0.652540	+	0.757754i	$0.273703\pi$
$24$	2008.25	0.711689
$25$	625.000	0.200000
$26$	807.328	0.234216
$27$	3291.28	0.868871
$28$	10394.6	2.50561
$29$	−1615.12	−0.356624	−0.178312	−	0.983974i	$-0.557064\pi$
$29$	−1615.12	−0.356624	−0.178312	+	0.983974i	$0.557064\pi$
$30$	1843.11	0.373893
$31$	256.923	0.0480174	0.0240087	−	0.999712i	$-0.492357\pi$
$31$	256.923	0.0480174	0.0240087	+	0.999712i	$0.492357\pi$
$32$	2693.46	0.464982
$33$	933.907	0.149286
$34$	7037.08	1.04399
$35$	4386.65	0.605289
$36$	−10866.3	−1.39742
$37$	−10444.7	−1.25427	−0.627135	−	0.778910i	$-0.715773\pi$
$37$	−10444.7	−1.25427	−0.627135	+	0.778910i	$0.715773\pi$
$38$	−3448.26	−0.387383
$39$	652.342	0.0686774
$40$	−6504.90	−0.642822
$41$	16922.4	1.57218	0.786089	−	0.618113i	$-0.212103\pi$
$41$	16922.4	1.57218	0.786089	+	0.618113i	$0.212103\pi$
$42$	12936.1	1.13157
$43$	−7986.84	−0.658725	−0.329362	−	0.944204i	$-0.606834\pi$
$43$	−7986.84	−0.658725	−0.329362	+	0.944204i	$0.606834\pi$
$44$	−7168.05	−0.558173
$45$	−4585.72	−0.337580
$46$	−31626.4	−2.20371
$47$	5244.98	0.346338	0.173169	−	0.984892i	$-0.444599\pi$
$47$	5244.98	0.346338	0.173169	+	0.984892i	$0.444599\pi$
$48$	−4551.45	−0.285133
$49$	13981.4	0.831877
$50$	−5969.98	−0.337713
$51$	5686.14	0.306120
$52$	−5006.94	−0.256782
$53$	−7151.84	−0.349726	−0.174863	−	0.984593i	$-0.555948\pi$
$53$	−7151.84	−0.349726	−0.174863	+	0.984593i	$0.555948\pi$
$54$	−31438.2	−1.46714
$55$	−3025.00	−0.134840
$56$	−45655.6	−1.94547
$57$	−2786.28	−0.113589
$58$	15427.6	0.602183
$59$	−17732.4	−0.663188	−0.331594	−	0.943422i	$-0.607586\pi$
$59$	−17732.4	−0.663188	−0.331594	+	0.943422i	$0.607586\pi$
$60$	−11430.7	−0.409916
$61$	−50558.0	−1.73966	−0.869831	−	0.493350i	$-0.835772\pi$
$61$	−50558.0	−1.73966	−0.869831	+	0.493350i	$0.835772\pi$
$62$	−2454.12	−0.0810806
$63$	−32185.5	−1.02167
$64$	−44598.3	−1.36103
$65$	−2112.99	−0.0620317
$66$	−8920.64	−0.252079
$67$	40134.9	1.09228	0.546141	−	0.837693i	$-0.316096\pi$
$67$	40134.9	1.09228	0.546141	+	0.837693i	$0.316096\pi$
$68$	−43643.0	−1.14457
$69$	−25554.9	−0.646178
$70$	−41901.2	−1.02207
$71$	−47861.3	−1.12678	−0.563390	−	0.826191i	$-0.690503\pi$
$71$	−47861.3	−1.12678	−0.563390	+	0.826191i	$0.690503\pi$
$72$	47727.4	1.08502
$73$	11087.4	0.243512	0.121756	−	0.992560i	$-0.461147\pi$
$73$	11087.4	0.243512	0.121756	+	0.992560i	$0.461147\pi$
$74$	99767.3	2.11792
$75$	−4823.90	−0.0990250
$76$	21385.7	0.424706
$77$	−21231.4	−0.408086
$78$	−6231.15	−0.115966
$79$	77611.7	1.39913	0.699567	−	0.714567i	$-0.253376\pi$
$79$	77611.7	1.39913	0.699567	+	0.714567i	$0.253376\pi$
$80$	14742.5	0.257541
$81$	19170.3	0.324651
$82$	−161642.	−2.65472
$83$	−84689.9	−1.34939	−0.674694	−	0.738098i	$-0.735724\pi$
$83$	−84689.9	−1.34939	−0.674694	+	0.738098i	$0.735724\pi$
$84$	−80228.1	−1.24059
$85$	−18417.9	−0.276498
$86$	76290.0	1.11230
$87$	12465.9	0.176574
$88$	31483.7	0.433390
$89$	23103.6	0.309176	0.154588	−	0.987979i	$-0.450595\pi$
$89$	23103.6	0.309176	0.154588	+	0.987979i	$0.450595\pi$
$90$	43802.6	0.570025
$91$	−14830.3	−0.187736
$92$	196143.	2.41603
$93$	−1982.99	−0.0237746
$94$	−50099.9	−0.584813
$95$	9025.00	0.102598
$96$	−20788.8	−0.230224
$97$	155781.	1.68107	0.840534	−	0.541759i	$-0.182241\pi$
$97$	155781.	1.68107	0.840534	+	0.541759i	$0.182241\pi$
$98$	−133549.	−1.40468
$99$	22194.9	0.227596
$100$	37025.0	0.370250
$101$	−122806.	−1.19789	−0.598944	−	0.800791i	$-0.704413\pi$
$101$	−122806.	−1.19789	−0.598944	+	0.800791i	$0.704413\pi$
$102$	−54313.8	−0.516904
$103$	61907.0	0.574972	0.287486	−	0.957785i	$-0.407181\pi$
$103$	61907.0	0.574972	0.287486	+	0.957785i	$0.407181\pi$
$104$	21991.6	0.199377
$105$	−33857.2	−0.299694
$106$	68314.1	0.590535
$107$	−151914.	−1.28274	−0.641370	−	0.767232i	$-0.721633\pi$
$107$	−151914.	−1.28274	−0.641370	+	0.767232i	$0.721633\pi$
$108$	194975.	1.60850
$109$	−64594.4	−0.520750	−0.260375	−	0.965508i	$-0.583846\pi$
$109$	−64594.4	−0.520750	−0.260375	+	0.965508i	$0.583846\pi$
$110$	28894.7	0.227686
$111$	80614.6	0.621021
$112$	103473.	0.779436
$113$	−203713.	−1.50080	−0.750398	−	0.660986i	$-0.770138\pi$
$113$	−203713.	−1.50080	−0.750398	+	0.660986i	$0.770138\pi$
$114$	26614.5	0.191803
$115$	82774.6	0.583650
$116$	−95680.0	−0.660201
$117$	15503.3	0.104703
$118$	169379.	1.11984
$119$	−129269.	−0.836807
$120$	50206.3	0.318277
$121$	14641.0	0.0909091
$122$	482928.	2.93753
$123$	−130611.	−0.778425
$124$	15220.1	0.0888923
$125$	15625.0	0.0894427
$126$	307435.	1.72515
$127$	146272.	0.804735	0.402368	−	0.915478i	$-0.368187\pi$
$127$	146272.	0.804735	0.402368	+	0.915478i	$0.368187\pi$
$128$	339811.	1.83321
$129$	61644.3	0.326151
$130$	20183.2	0.104745
$131$	141645.	0.721144	0.360572	−	0.932731i	$-0.382581\pi$
$131$	141645.	0.721144	0.360572	+	0.932731i	$0.382581\pi$
$132$	55324.7	0.276366
$133$	63343.3	0.310507
$134$	−383367.	−1.84439
$135$	82282.0	0.388571
$136$	191690.	0.888695
$137$	−292251.	−1.33032	−0.665158	−	0.746703i	$-0.731636\pi$
$137$	−292251.	−1.33032	−0.665158	+	0.746703i	$0.731636\pi$
$138$	244100.	1.09111
$139$	73809.9	0.324024	0.162012	−	0.986789i	$-0.448202\pi$
$139$	73809.9	0.324024	0.162012	+	0.986789i	$0.448202\pi$
$140$	259865.	1.12054
$141$	−40482.0	−0.171480
$142$	457170.	1.90264
$143$	10226.9	0.0418218
$144$	−108168.	−0.434704
$145$	−40378.1	−0.159487
$146$	−105906.	−0.411186
$147$	−107911.	−0.411883
$148$	−618744.	−2.32197
$149$	69034.7	0.254743	0.127371	−	0.991855i	$-0.459346\pi$
$149$	69034.7	0.254743	0.127371	+	0.991855i	$0.459346\pi$
$150$	46077.7	0.167210
$151$	458501.	1.63643	0.818216	−	0.574911i	$-0.194963\pi$
$151$	458501.	1.63643	0.818216	+	0.574911i	$0.194963\pi$
$152$	−93930.7	−0.329761
$153$	135135.	0.466701
$154$	202802.	0.689080
$155$	6423.08	0.0214741
$156$	38644.8	0.127139
$157$	−236973.	−0.767271	−0.383636	−	0.923485i	$-0.625328\pi$
$157$	−236973.	−0.767271	−0.383636	+	0.923485i	$0.625328\pi$
$158$	−741344.	−2.36253
$159$	55199.6	0.173158
$160$	67336.6	0.207946
$161$	580965.	1.76639
$162$	−183114.	−0.548195
$163$	380603.	1.12203	0.561014	−	0.827807i	$-0.310412\pi$
$163$	380603.	1.12203	0.561014	+	0.827807i	$0.310412\pi$
$164$	1.00248e6	2.91050
$165$	23347.7	0.0667627
$166$	808955.	2.27853
$167$	−347137.	−0.963184	−0.481592	−	0.876396i	$-0.659941\pi$
$167$	−347137.	−0.963184	−0.481592	+	0.876396i	$0.659941\pi$
$168$	352380.	0.963249
$169$	−364149.	−0.980760
$170$	175927.	0.466885
$171$	−66217.8	−0.173175
$172$	−473141.	−1.21946
$173$	−415469.	−1.05541	−0.527707	−	0.849426i	$-0.676948\pi$
$173$	−415469.	−1.05541	−0.527707	+	0.849426i	$0.676948\pi$
$174$	−119074.	−0.298156
$175$	109666.	0.270694
$176$	−71353.9	−0.173634
$177$	136863.	0.328361
$178$	−220685.	−0.522063
$179$	502712.	1.17270	0.586350	−	0.810058i	$-0.300564\pi$
$179$	502712.	1.17270	0.586350	+	0.810058i	$0.300564\pi$
$180$	−271658.	−0.624945
$181$	608341.	1.38023	0.690114	−	0.723701i	$-0.257560\pi$
$181$	608341.	1.38023	0.690114	+	0.723701i	$0.257560\pi$
$182$	141659.	0.317004
$183$	390218.	0.861350
$184$	−861504.	−1.87591
$185$	−261117.	−0.560927
$186$	18941.5	0.0401450
$187$	89142.5	0.186415
$188$	310713.	0.641158
$189$	577508.	1.17599
$190$	−86206.5	−0.173243
$191$	600671.	1.19139	0.595694	−	0.803212i	$-0.296877\pi$
$191$	600671.	1.19139	0.595694	+	0.803212i	$0.296877\pi$
$192$	344220.	0.673881
$193$	−147028.	−0.284124	−0.142062	−	0.989858i	$-0.545373\pi$
$193$	−147028.	−0.284124	−0.142062	+	0.989858i	$0.545373\pi$
$194$	−1.48801e6	−2.83859
$195$	16308.5	0.0307135
$196$	828256.	1.54001
$197$	−808652.	−1.48455	−0.742277	−	0.670093i	$-0.766254\pi$
$197$	−808652.	−1.48455	−0.742277	+	0.670093i	$0.766254\pi$
$198$	−212005.	−0.384311
$199$	−119036.	−0.213081	−0.106541	−	0.994308i	$-0.533977\pi$
$199$	−119036.	−0.213081	−0.106541	+	0.994308i	$0.533977\pi$
$200$	−162622.	−0.287479
$201$	−309770.	−0.540816
$202$	1.17304e6	2.02271
$203$	−283399.	−0.482679
$204$	336847.	0.566706
$205$	423059.	0.703099
$206$	−591333.	−0.970877
$207$	−607330.	−0.985142
$208$	−49841.3	−0.0798787
$209$	−43681.0	−0.0691714
$210$	323403.	0.506053
$211$	557307.	0.861763	0.430882	−	0.902408i	$-0.358203\pi$
$211$	557307.	0.861763	0.430882	+	0.902408i	$0.358203\pi$
$212$	−423675.	−0.647431
$213$	369405.	0.557897
$214$	1.45108e6	2.16599
$215$	−199671.	−0.294591
$216$	−856377.	−1.24891
$217$	45081.3	0.0649901
$218$	617004.	0.879319
$219$	−85574.8	−0.120569
$220$	−179201.	−0.249623
$221$	62266.8	0.0857583
$222$	−770028.	−1.04863
$223$	1.17494e6	1.58217	0.791087	−	0.611704i	$-0.209516\pi$
$223$	1.17494e6	1.58217	0.791087	+	0.611704i	$0.209516\pi$
$224$	472612.	0.629339
$225$	−114643.	−0.150970
$226$	1.94586e6	2.53419
$227$	−268565.	−0.345927	−0.172964	−	0.984928i	$-0.555334\pi$
$227$	−268565.	−0.345927	−0.172964	+	0.984928i	$0.555334\pi$
$228$	−165060.	−0.210283
$229$	−779486.	−0.982245	−0.491122	−	0.871091i	$-0.663413\pi$
$229$	−779486.	−0.982245	−0.491122	+	0.871091i	$0.663413\pi$
$230$	−790660.	−0.985530
$231$	163869.	0.202054
$232$	420248.	0.512609
$233$	−1.09043e6	−1.31586	−0.657929	−	0.753080i	$-0.728567\pi$
$233$	−1.09043e6	−1.31586	−0.657929	+	0.753080i	$0.728567\pi$
$234$	−148087.	−0.176798
$235$	131125.	0.154887
$236$	−1.05047e6	−1.22773
$237$	−599025.	−0.692746
$238$	1.23477e6	1.41300
$239$	1.64894e6	1.86728	0.933640	−	0.358212i	$-0.116613\pi$
$239$	1.64894e6	1.86728	0.933640	+	0.358212i	$0.116613\pi$
$240$	−113786.	−0.127515
$241$	−294701.	−0.326843	−0.163422	−	0.986556i	$-0.552253\pi$
$241$	−294701.	−0.326843	−0.163422	+	0.986556i	$0.552253\pi$
$242$	−139850.	−0.153506
$243$	−947742.	−1.02961
$244$	−2.99506e6	−3.22055
$245$	349534.	0.372027
$246$	1.24759e6	1.31442
$247$	−30511.6	−0.0318216
$248$	−66850.4	−0.0690199
$249$	653657.	0.668116
$250$	−149249.	−0.151030
$251$	−1.04110e6	−1.04306	−0.521531	−	0.853233i	$-0.674639\pi$
$251$	−1.04110e6	−1.04306	−0.521531	+	0.853233i	$0.674639\pi$
$252$	−1.90667e6	−1.89136
$253$	−400629.	−0.393497
$254$	−1.39719e6	−1.35885
$255$	142154.	0.136901
$256$	−1.81871e6	−1.73446
$257$	−316674.	−0.299075	−0.149537	−	0.988756i	$-0.547778\pi$
$257$	−316674.	−0.299075	−0.149537	+	0.988756i	$0.547778\pi$
$258$	−588824.	−0.550727
$259$	−1.83269e6	−1.69762
$260$	−125174.	−0.114836
$261$	296260.	0.269198
$262$	−1.35299e6	−1.21770
$263$	2.09824e6	1.87054	0.935268	−	0.353940i	$-0.115158\pi$
$263$	2.09824e6	1.87054	0.935268	+	0.353940i	$0.115158\pi$
$264$	−242999.	−0.214582
$265$	−178796.	−0.156402
$266$	−605053.	−0.524311
$267$	−178319.	−0.153081
$268$	2.37759e6	2.02209
$269$	235380.	0.198330	0.0991649	−	0.995071i	$-0.468383\pi$
$269$	235380.	0.198330	0.0991649	+	0.995071i	$0.468383\pi$
$270$	−785954.	−0.656127
$271$	162369.	0.134301	0.0671507	−	0.997743i	$-0.478609\pi$
$271$	162369.	0.134301	0.0671507	+	0.997743i	$0.478609\pi$
$272$	−434442.	−0.356049
$273$	114464.	0.0929527
$274$	2.79157e6	2.24632
$275$	−75625.0	−0.0603023
$276$	−1.51388e6	−1.19624
$277$	−849890.	−0.665523	−0.332762	−	0.943011i	$-0.607980\pi$
$277$	−849890.	−0.665523	−0.332762	+	0.943011i	$0.607980\pi$
$278$	−705030.	−0.547136
$279$	−47127.1	−0.0362460
$280$	−1.14139e6	−0.870039
$281$	1.17420e6	0.887105	0.443553	−	0.896248i	$-0.353718\pi$
$281$	1.17420e6	0.887105	0.443553	+	0.896248i	$0.353718\pi$
$282$	386683.	0.289556
$283$	−2.30733e6	−1.71255	−0.856275	−	0.516520i	$-0.827227\pi$
$283$	−2.30733e6	−1.71255	−0.856275	+	0.516520i	$0.827227\pi$
$284$	−2.83531e6	−2.08595
$285$	−69657.1	−0.0507988
$286$	−97686.7	−0.0706188
$287$	2.96930e6	2.12789
$288$	−494059.	−0.350992
$289$	−877108.	−0.617744
$290$	385690.	0.269304
$291$	−1.20235e6	−0.832339
$292$	656815.	0.450802
$293$	−1.68490e6	−1.14659	−0.573293	−	0.819351i	$-0.694334\pi$
$293$	−1.68490e6	−1.14659	−0.573293	+	0.819351i	$0.694334\pi$
$294$	1.03077e6	0.695491
$295$	−443309.	−0.296587
$296$	2.71767e6	1.80288
$297$	−398245.	−0.261974
$298$	−659417.	−0.430150
$299$	−279843.	−0.181024
$300$	−285768.	−0.183320
$301$	−1.40142e6	−0.891563
$302$	−4.37959e6	−2.76322
$303$	947846.	0.593104
$304$	212882.	0.132116
$305$	−1.26395e6	−0.778001
$306$	−1.29080e6	−0.788055
$307$	1.28041e6	0.775361	0.387680	−	0.921794i	$-0.373276\pi$
$307$	1.28041e6	0.775361	0.387680	+	0.921794i	$0.373276\pi$
$308$	−1.25775e6	−0.755470
$309$	−477813.	−0.284683
$310$	−61353.0	−0.0362603
$311$	460482.	0.269968	0.134984	−	0.990848i	$-0.456902\pi$
$311$	460482.	0.269968	0.134984	+	0.990848i	$0.456902\pi$
$312$	−169737.	−0.0987164
$313$	2.01941e6	1.16510	0.582550	−	0.812795i	$-0.302055\pi$
$313$	2.01941e6	1.16510	0.582550	+	0.812795i	$0.302055\pi$
$314$	2.26355e6	1.29559
$315$	−804639.	−0.456903
$316$	4.59772e6	2.59015
$317$	−2.91737e6	−1.63058	−0.815291	−	0.579051i	$-0.803423\pi$
$317$	−2.91737e6	−1.63058	−0.815291	+	0.579051i	$0.803423\pi$
$318$	−527265.	−0.292389
$319$	195430.	0.107526
$320$	−1.11496e6	−0.608672
$321$	1.17251e6	0.635116
$322$	−5.54936e6	−2.98266
$323$	−265954.	−0.141841
$324$	1.13565e6	0.601011
$325$	−52824.7	−0.0277414
$326$	−3.63551e6	−1.89462
$327$	498555.	0.257836
$328$	−4.40313e6	−2.25984
$329$	920317.	0.468757
$330$	−223016.	−0.112733
$331$	397598.	0.199468	0.0997342	−	0.995014i	$-0.468201\pi$
$331$	397598.	0.199468	0.0997342	+	0.995014i	$0.468201\pi$
$332$	−5.01704e6	−2.49806
$333$	1.91586e6	0.946787
$334$	3.31584e6	1.62640
$335$	1.00337e6	0.488483
$336$	−798626.	−0.385918
$337$	−331753.	−0.159126	−0.0795629	−	0.996830i	$-0.525352\pi$
$337$	−331753.	−0.159126	−0.0795629	+	0.996830i	$0.525352\pi$
$338$	3.47834e6	1.65608
$339$	1.57230e6	0.743082
$340$	−1.09108e6	−0.511868
$341$	−31087.7	−0.0144778
$342$	632510.	0.292417
$343$	−495805.	−0.227549
$344$	2.07814e6	0.946846
$345$	−638874.	−0.288980
$346$	3.96854e6	1.78214
$347$	−978533.	−0.436267	−0.218133	−	0.975919i	$-0.569997\pi$
$347$	−978533.	−0.436267	−0.218133	+	0.975919i	$0.569997\pi$
$348$	738480.	0.326882
$349$	−436705.	−0.191922	−0.0959610	−	0.995385i	$-0.530592\pi$
$349$	−436705.	−0.191922	−0.0959610	+	0.995385i	$0.530592\pi$
$350$	−1.04753e6	−0.457084
$351$	−278177.	−0.120519
$352$	−325909.	−0.140197
$353$	511994.	0.218690	0.109345	−	0.994004i	$-0.465125\pi$
$353$	511994.	0.218690	0.109345	+	0.994004i	$0.465125\pi$
$354$	−1.30731e6	−0.554459
$355$	−1.19653e6	−0.503911
$356$	1.36866e6	0.572362
$357$	997725.	0.414324
$358$	−4.80189e6	−1.98018
$359$	3.65796e6	1.49797	0.748985	−	0.662587i	$-0.230541\pi$
$359$	3.65796e6	1.49797	0.748985	+	0.662587i	$0.230541\pi$
$360$	1.19319e6	0.485235
$361$	130321.	0.0526316
$362$	−5.81085e6	−2.33060
$363$	−113003.	−0.0450114
$364$	−878549.	−0.347546
$365$	277184.	0.108902
$366$	−3.72735e6	−1.45445
$367$	548457.	0.212558	0.106279	−	0.994336i	$-0.466106\pi$
$367$	548457.	0.212558	0.106279	+	0.994336i	$0.466106\pi$
$368$	1.95249e6	0.751570
$369$	−3.10405e6	−1.18676
$370$	2.49418e6	0.947161
$371$	−1.25491e6	−0.473343
$372$	−117473.	−0.0440128
$373$	−2.60080e6	−0.967908	−0.483954	−	0.875093i	$-0.660800\pi$
$373$	−2.60080e6	−0.967908	−0.483954	+	0.875093i	$0.660800\pi$
$374$	−851486.	−0.314774
$375$	−120597.	−0.0442853
$376$	−1.36472e6	−0.497823
$377$	136509.	0.0494663
$378$	−5.51633e6	−1.98573
$379$	−3.10049e6	−1.10875	−0.554373	−	0.832268i	$-0.687042\pi$
$379$	−3.10049e6	−1.10875	−0.554373	+	0.832268i	$0.687042\pi$
$380$	534641.	0.189934
$381$	−1.12897e6	−0.398445
$382$	−5.73759e6	−2.01174
$383$	−2.88012e6	−1.00326	−0.501630	−	0.865082i	$-0.667266\pi$
$383$	−2.88012e6	−1.00326	−0.501630	+	0.865082i	$0.667266\pi$
$384$	−2.62274e6	−0.907668
$385$	−530785.	−0.182502
$386$	1.40441e6	0.479762
$387$	1.46502e6	0.497239
$388$	9.22847e6	3.11208
$389$	−3.94360e6	−1.32135	−0.660677	−	0.750670i	$-0.729731\pi$
$389$	−3.94360e6	−1.32135	−0.660677	+	0.750670i	$0.729731\pi$
$390$	−155779.	−0.0518617
$391$	−2.43925e6	−0.806891
$392$	−3.63789e6	−1.19573
$393$	−1.09325e6	−0.357057
$394$	7.72422e6	2.50677
$395$	1.94029e6	0.625712
$396$	1.31483e6	0.421338
$397$	3.88827e6	1.23817	0.619084	−	0.785325i	$-0.287504\pi$
$397$	3.88827e6	1.23817	0.619084	+	0.785325i	$0.287504\pi$
$398$	1.13703e6	0.359802
$399$	−488898.	−0.153740
$400$	368563.	0.115176
$401$	47200.9	0.0146585	0.00732925	−	0.999973i	$-0.497667\pi$
$401$	47200.9	0.0146585	0.00732925	+	0.999973i	$0.497667\pi$
$402$	2.95892e6	0.913203
$403$	−21715.0	−0.00666036
$404$	−7.27503e6	−2.21759
$405$	479259.	0.145189
$406$	2.70702e6	0.815035
$407$	1.26381e6	0.378177
$408$	−1.47951e6	−0.440015
$409$	−549183.	−0.162334	−0.0811669	−	0.996701i	$-0.525865\pi$
$409$	−549183.	−0.162334	−0.0811669	+	0.996701i	$0.525865\pi$
$410$	−4.04105e6	−1.18723
$411$	2.25566e6	0.658672
$412$	3.66737e6	1.06442
$413$	−3.11143e6	−0.897604
$414$	5.80119e6	1.66348
$415$	−2.11725e6	−0.603464
$416$	−227650.	−0.0644963
$417$	−569682.	−0.160433
$418$	417239.	0.116800
$419$	4.98609e6	1.38748	0.693738	−	0.720227i	$-0.255963\pi$
$419$	4.98609e6	1.38748	0.693738	+	0.720227i	$0.255963\pi$
$420$	−2.00570e6	−0.554809
$421$	−1.12999e6	−0.310719	−0.155360	−	0.987858i	$-0.549654\pi$
$421$	−1.12999e6	−0.310719	−0.155360	+	0.987858i	$0.549654\pi$
$422$	−5.32337e6	−1.45514
$423$	−962081.	−0.261433
$424$	1.86088e6	0.502694
$425$	−460447.	−0.123654
$426$	−3.52854e6	−0.942045
$427$	−8.87121e6	−2.35458
$428$	−8.99939e6	−2.37467
$429$	−78933.4	−0.0207070
$430$	1.90725e6	0.497435
$431$	−6.75808e6	−1.75239	−0.876194	−	0.481959i	$-0.839925\pi$
$431$	−6.75808e6	−1.75239	−0.876194	+	0.481959i	$0.839925\pi$
$432$	1.94087e6	0.500365
$433$	−3.03003e6	−0.776653	−0.388327	−	0.921522i	$-0.626947\pi$
$433$	−3.03003e6	−0.776653	−0.388327	+	0.921522i	$0.626947\pi$
$434$	−430615.	−0.109740
$435$	311648.	0.0789661
$436$	−3.82658e6	−0.964038
$437$	1.19526e6	0.299406
$438$	817408.	0.203589
$439$	5.36726e6	1.32920	0.664602	−	0.747197i	$-0.268601\pi$
$439$	5.36726e6	1.32920	0.664602	+	0.747197i	$0.268601\pi$
$440$	787093.	0.193818
$441$	−2.56458e6	−0.627943
$442$	−594771.	−0.144808
$443$	−7.04621e6	−1.70587	−0.852936	−	0.522016i	$-0.825180\pi$
$443$	−7.04621e6	−1.70587	−0.852936	+	0.522016i	$0.825180\pi$
$444$	4.77561e6	1.14967
$445$	577591.	0.138268
$446$	−1.12230e7	−2.67160
$447$	−532826.	−0.126130
$448$	−7.82549e6	−1.84211
$449$	−6.17761e6	−1.44612	−0.723060	−	0.690785i	$-0.757265\pi$
$449$	−6.17761e6	−1.44612	−0.723060	+	0.690785i	$0.757265\pi$
$450$	1.09507e6	0.254923
$451$	−2.04761e6	−0.474030
$452$	−1.20679e7	−2.77835
$453$	−3.53882e6	−0.810239
$454$	2.56532e6	0.584121
$455$	−370758.	−0.0839580
$456$	724980.	0.163273
$457$	2.72500e6	0.610345	0.305172	−	0.952297i	$-0.401286\pi$
$457$	2.72500e6	0.610345	0.305172	+	0.952297i	$0.401286\pi$
$458$	7.44563e6	1.65858
$459$	−2.42473e6	−0.537196
$460$	4.90357e6	1.08048
$461$	701164.	0.153662	0.0768312	−	0.997044i	$-0.475520\pi$
$461$	701164.	0.153662	0.0768312	+	0.997044i	$0.475520\pi$
$462$	−1.56527e6	−0.341181
$463$	−5.19262e6	−1.12573	−0.562865	−	0.826549i	$-0.690301\pi$
$463$	−5.19262e6	−1.12573	−0.562865	+	0.826549i	$0.690301\pi$
$464$	−952440.	−0.205373
$465$	−49574.8	−0.0106323
$466$	1.04158e7	2.22191
$467$	−4.23009e6	−0.897548	−0.448774	−	0.893645i	$-0.648139\pi$
$467$	−4.23009e6	−0.897548	−0.448774	+	0.893645i	$0.648139\pi$
$468$	918418.	0.193832
$469$	7.04231e6	1.47837
$470$	−1.25250e6	−0.261536
$471$	1.82901e6	0.379895
$472$	4.61389e6	0.953262
$473$	966408.	0.198613
$474$	5.72187e6	1.16975
$475$	225625.	0.0458831
$476$	−7.65787e6	−1.54914
$477$	1.31185e6	0.263991
$478$	−1.57506e7	−3.15302
$479$	8.47153e6	1.68703	0.843516	−	0.537105i	$-0.180482\pi$
$479$	8.47153e6	1.68703	0.843516	+	0.537105i	$0.180482\pi$
$480$	−519720.	−0.102959
$481$	882780.	0.173976
$482$	2.81498e6	0.551896
$483$	−4.48403e6	−0.874582
$484$	867333.	0.168296
$485$	3.89453e6	0.751796
$486$	9.05280e6	1.73857
$487$	7.91048e6	1.51140	0.755702	−	0.654915i	$-0.227296\pi$
$487$	7.91048e6	1.51140	0.755702	+	0.654915i	$0.227296\pi$
$488$	1.31550e7	2.50058
$489$	−2.93759e6	−0.555544
$490$	−3.33874e6	−0.628191
$491$	−7.26504e6	−1.35999	−0.679993	−	0.733219i	$-0.738017\pi$
$491$	−7.26504e6	−1.35999	−0.679993	+	0.733219i	$0.738017\pi$
$492$	−7.73740e6	−1.44106
$493$	1.18989e6	0.220490
$494$	291445.	0.0537328
$495$	554872.	0.101784
$496$	151508.	0.0276523
$497$	−8.39804e6	−1.52506
$498$	−6.24371e6	−1.12816
$499$	−1.97987e6	−0.355948	−0.177974	−	0.984035i	$-0.556954\pi$
$499$	−1.97987e6	−0.355948	−0.177974	+	0.984035i	$0.556954\pi$
$500$	925626.	0.165581
$501$	2.67928e6	0.476897
$502$	9.94459e6	1.76128
$503$	−5.73048e6	−1.00988	−0.504941	−	0.863154i	$-0.668486\pi$
$503$	−5.73048e6	−1.00988	−0.504941	+	0.863154i	$0.668486\pi$
$504$	8.37455e6	1.46854
$505$	−3.07015e6	−0.535712
$506$	3.82679e6	0.664444
$507$	2.81059e6	0.485599
$508$	8.66518e6	1.48977
$509$	9.38637e6	1.60584	0.802921	−	0.596085i	$-0.203278\pi$
$509$	9.38637e6	1.60584	0.802921	+	0.596085i	$0.203278\pi$
$510$	−1.35785e6	−0.231167
$511$	1.94545e6	0.329586
$512$	6.49835e6	1.09554
$513$	1.18815e6	0.199333
$514$	3.02486e6	0.505007
$515$	1.54767e6	0.257135
$516$	3.65181e6	0.603788
$517$	−634643.	−0.104425
$518$	1.75058e7	2.86653
$519$	3.20669e6	0.522562
$520$	549791.	0.0891640
$521$	−3.72531e6	−0.601269	−0.300634	−	0.953739i	$-0.597198\pi$
$521$	−3.72531e6	−0.601269	−0.300634	+	0.953739i	$0.597198\pi$
$522$	−2.82987e6	−0.454558
$523$	−4.34263e6	−0.694222	−0.347111	−	0.937824i	$-0.612837\pi$
$523$	−4.34263e6	−0.694222	−0.347111	+	0.937824i	$0.612837\pi$
$524$	8.39104e6	1.33502
$525$	−846431.	−0.134027
$526$	−2.00423e7	−3.15852
$527$	−189279.	−0.0296877
$528$	550726.	0.0859707
$529$	4.52626e6	0.703235
$530$	1.70785e6	0.264095
$531$	3.25263e6	0.500608
$532$	3.75246e6	0.574826
$533$	−1.43027e6	−0.218072
$534$	1.70330e6	0.258487
$535$	−3.79785e6	−0.573658
$536$	−1.04429e7	−1.57004
$537$	−3.88005e6	−0.580633
$538$	−2.24834e6	−0.334893
$539$	−1.69174e6	−0.250820
$540$	4.87439e6	0.719342
$541$	3.43732e6	0.504924	0.252462	−	0.967607i	$-0.418760\pi$
$541$	3.43732e6	0.504924	0.252462	+	0.967607i	$0.418760\pi$
$542$	−1.55094e6	−0.226777
$543$	−4.69532e6	−0.683385
$544$	−1.98432e6	−0.287484
$545$	−1.61486e6	−0.232886
$546$	−1.09336e6	−0.156957
$547$	5.11703e6	0.731222	0.365611	−	0.930768i	$-0.380860\pi$
$547$	5.11703e6	0.731222	0.365611	+	0.930768i	$0.380860\pi$
$548$	−1.73130e7	−2.46275
$549$	9.27379e6	1.31319
$550$	722367.	0.101824
$551$	−583059.	−0.0818152
$552$	6.64929e6	0.928812
$553$	1.36182e7	1.89368
$554$	8.11812e6	1.12378
$555$	2.01536e6	0.277729
$556$	4.37250e6	0.599851
$557$	7.29503e6	0.996297	0.498149	−	0.867092i	$-0.334013\pi$
$557$	7.29503e6	0.996297	0.498149	+	0.867092i	$0.334013\pi$
$558$	450157.	0.0612038
$559$	675044.	0.0913698
$560$	2.58681e6	0.348574
$561$	−688023.	−0.0922988
$562$	−1.12159e7	−1.49794
$563$	6.96402e6	0.925954	0.462977	−	0.886370i	$-0.346781\pi$
$563$	6.96402e6	0.925954	0.462977	+	0.886370i	$0.346781\pi$
$564$	−2.39816e6	−0.317453
$565$	−5.09281e6	−0.671176
$566$	2.20395e7	2.89175
$567$	3.36375e6	0.439405
$568$	1.24533e7	1.61962
$569$	−3.71762e6	−0.481376	−0.240688	−	0.970603i	$-0.577373\pi$
$569$	−3.71762e6	−0.481376	−0.240688	+	0.970603i	$0.577373\pi$
$570$	665362.	0.0857770
$571$	2.58386e6	0.331649	0.165825	−	0.986155i	$-0.446971\pi$
$571$	2.58386e6	0.331649	0.165825	+	0.986155i	$0.446971\pi$
$572$	605840.	0.0774226
$573$	−4.63612e6	−0.589886
$574$	−2.83627e7	−3.59309
$575$	2.06936e6	0.261016
$576$	8.18062e6	1.02738
$577$	−9.71924e6	−1.21533	−0.607663	−	0.794195i	$-0.707893\pi$
$577$	−9.71924e6	−1.21533	−0.607663	+	0.794195i	$0.707893\pi$
$578$	8.37810e6	1.04310
$579$	1.13480e6	0.140677
$580$	−2.39200e6	−0.295251
$581$	−1.48602e7	−1.82635
$582$	1.14849e7	1.40546
$583$	865373.	0.105446
$584$	−2.88488e6	−0.350023
$585$	387583.	0.0468247
$586$	1.60942e7	1.93608
$587$	−1.65591e6	−0.198354	−0.0991770	−	0.995070i	$-0.531621\pi$
$587$	−1.65591e6	−0.198354	−0.0991770	+	0.995070i	$0.531621\pi$
$588$	−6.39268e6	−0.762499
$589$	92749.3	0.0110160
$590$	4.23447e6	0.500806
$591$	6.24137e6	0.735040
$592$	−6.15925e6	−0.722309
$593$	−3.50275e6	−0.409046	−0.204523	−	0.978862i	$-0.565564\pi$
$593$	−3.50275e6	−0.409046	−0.204523	+	0.978862i	$0.565564\pi$
$594$	3.80402e6	0.442361
$595$	−3.23171e6	−0.374232
$596$	4.08962e6	0.471593
$597$	918748.	0.105502
$598$	2.67305e6	0.305671
$599$	−521011.	−0.0593308	−0.0296654	−	0.999560i	$-0.509444\pi$
$599$	−521011.	−0.0593308	−0.0296654	+	0.999560i	$0.509444\pi$
$600$	1.25516e6	0.142338
$601$	1.10790e7	1.25116	0.625582	−	0.780159i	$-0.284862\pi$
$601$	1.10790e7	1.25116	0.625582	+	0.780159i	$0.284862\pi$
$602$	1.33863e7	1.50546
$603$	−7.36189e6	−0.824510
$604$	2.71616e7	3.02945
$605$	366025.	0.0406558
$606$	−9.05379e6	−1.00150
$607$	−926069.	−0.102017	−0.0510084	−	0.998698i	$-0.516244\pi$
$607$	−926069.	−0.102017	−0.0510084	+	0.998698i	$0.516244\pi$
$608$	972340.	0.106674
$609$	2.18734e6	0.238987
$610$	1.20732e7	1.31370
$611$	−443304.	−0.0480395
$612$	8.00539e6	0.863981
$613$	436756.	0.0469448	0.0234724	−	0.999724i	$-0.492528\pi$
$613$	436756.	0.0469448	0.0234724	+	0.999724i	$0.492528\pi$
$614$	−1.22304e7	−1.30925
$615$	−3.26527e6	−0.348122
$616$	5.52432e6	0.586580
$617$	1.61308e7	1.70586	0.852929	−	0.522026i	$-0.174824\pi$
$617$	1.61308e7	1.70586	0.852929	+	0.522026i	$0.174824\pi$
$618$	4.56405e6	0.480706
$619$	−8.96379e6	−0.940297	−0.470148	−	0.882587i	$-0.655800\pi$
$619$	−8.96379e6	−0.940297	−0.470148	+	0.882587i	$0.655800\pi$
$620$	380503.	0.0397539
$621$	1.08974e7	1.13395
$622$	−4.39851e6	−0.455858
$623$	4.05390e6	0.418459
$624$	384687.	0.0395499
$625$	390625.	0.0400000
$626$	−1.92893e7	−1.96735
$627$	337140.	0.0342485
$628$	−1.40383e7	−1.42041
$629$	7.69476e6	0.775476
$630$	7.68588e6	0.771511
$631$	−6.07119e6	−0.607017	−0.303508	−	0.952829i	$-0.598158\pi$
$631$	−6.07119e6	−0.607017	−0.303508	+	0.952829i	$0.598158\pi$
$632$	−2.01942e7	−2.01111
$633$	−4.30142e6	−0.426681
$634$	2.78666e7	2.75334
$635$	3.65681e6	0.359889
$636$	3.27003e6	0.320559
$637$	−1.18170e6	−0.115387
$638$	−1.86674e6	−0.181565
$639$	8.77915e6	0.850551
$640$	8.49527e6	0.819836
$641$	−8.85683e6	−0.851400	−0.425700	−	0.904864i	$-0.639972\pi$
$641$	−8.85683e6	−0.851400	−0.425700	+	0.904864i	$0.639972\pi$
$642$	−1.11998e7	−1.07244
$643$	1.15918e7	1.10566	0.552832	−	0.833293i	$-0.313547\pi$
$643$	1.15918e7	1.10566	0.552832	+	0.833293i	$0.313547\pi$
$644$	3.44164e7	3.27002
$645$	1.54111e6	0.145859
$646$	2.54039e6	0.239507
$647$	−1.19582e7	−1.12307	−0.561535	−	0.827453i	$-0.689789\pi$
$647$	−1.19582e7	−1.12307	−0.561535	+	0.827453i	$0.689789\pi$
$648$	−4.98805e6	−0.466652
$649$	2.14562e6	0.199959
$650$	504580.	0.0468432
$651$	−347948.	−0.0321782
$652$	2.25469e7	2.07715
$653$	−7.36520e6	−0.675929	−0.337965	−	0.941159i	$-0.609738\pi$
$653$	−7.36520e6	−0.675929	−0.337965	+	0.941159i	$0.609738\pi$
$654$	−4.76218e6	−0.435373
$655$	3.54112e6	0.322505
$656$	9.97915e6	0.905386
$657$	−2.03374e6	−0.183815
$658$	−8.79084e6	−0.791526
$659$	3.39691e6	0.304699	0.152350	−	0.988327i	$-0.451316\pi$
$659$	3.39691e6	0.304699	0.152350	+	0.988327i	$0.451316\pi$
$660$	1.38312e6	0.123594
$661$	−1.70729e7	−1.51986	−0.759928	−	0.650007i	$-0.774766\pi$
$661$	−1.70729e7	−1.51986	−0.759928	+	0.650007i	$0.774766\pi$
$662$	−3.79784e6	−0.336815
$663$	−480590.	−0.0424611
$664$	2.20360e7	1.93960
$665$	1.58358e6	0.138863
$666$	−1.83002e7	−1.59871
$667$	−5.34764e6	−0.465423
$668$	−2.05644e7	−1.78310
$669$	−9.06847e6	−0.783374
$670$	−9.58417e6	−0.824836
$671$	6.11751e6	0.524528
$672$	−3.64773e6	−0.311601
$673$	1.34767e7	1.14696	0.573478	−	0.819221i	$-0.305594\pi$
$673$	1.34767e7	1.14696	0.573478	+	0.819221i	$0.305594\pi$
$674$	3.16890e6	0.268694
$675$	2.05705e6	0.173774
$676$	−2.15722e7	−1.81563
$677$	2.51310e6	0.210736	0.105368	−	0.994433i	$-0.466398\pi$
$677$	2.51310e6	0.210736	0.105368	+	0.994433i	$0.466398\pi$
$678$	−1.50186e7	−1.25474
$679$	2.73343e7	2.27527
$680$	4.79226e6	0.397437
$681$	2.07285e6	0.171277
$682$	296949.	0.0244467
$683$	−1.41870e7	−1.16370	−0.581849	−	0.813297i	$-0.697670\pi$
$683$	−1.41870e7	−1.16370	−0.581849	+	0.813297i	$0.697670\pi$
$684$	−3.92275e6	−0.320590
$685$	−7.30627e6	−0.594935
$686$	4.73591e6	0.384232
$687$	6.01626e6	0.486334
$688$	−4.70985e6	−0.379346
$689$	604470.	0.0485095
$690$	6.10250e6	0.487961
$691$	−9.16769e6	−0.730407	−0.365204	−	0.930928i	$-0.619001\pi$
$691$	−9.16769e6	−0.730407	−0.365204	+	0.930928i	$0.619001\pi$
$692$	−2.46124e7	−1.95384
$693$	3.89445e6	0.308044
$694$	9.34692e6	0.736664
$695$	1.84525e6	0.144908
$696$	−3.24358e6	−0.253806
$697$	−1.24670e7	−0.972029
$698$	4.17139e6	0.324073
$699$	8.41621e6	0.651514
$700$	6.49664e6	0.501122
$701$	−1.70990e7	−1.31425	−0.657123	−	0.753784i	$-0.728227\pi$
$701$	−1.70990e7	−1.31425	−0.657123	+	0.753784i	$0.728227\pi$
$702$	2.65714e6	0.203503
$703$	−3.77053e6	−0.287749
$704$	5.39640e6	0.410367
$705$	−1.01205e6	−0.0766884
$706$	−4.89055e6	−0.369272
$707$	−2.15483e7	−1.62130
$708$	8.10774e6	0.607879
$709$	−2.25661e7	−1.68593	−0.842967	−	0.537965i	$-0.819193\pi$
$709$	−2.25661e7	−1.68593	−0.842967	+	0.537965i	$0.819193\pi$
$710$	1.14292e7	0.850886
$711$	−1.42362e7	−1.05614
$712$	−6.01147e6	−0.444407
$713$	850668.	0.0626666
$714$	−9.53024e6	−0.699613
$715$	255672.	0.0187033
$716$	2.97807e7	2.17096
$717$	−1.27269e7	−0.924537
$718$	−3.49407e7	−2.52942
$719$	7.93465e6	0.572408	0.286204	−	0.958169i	$-0.407607\pi$
$719$	7.93465e6	0.572408	0.286204	+	0.958169i	$0.407607\pi$
$720$	−2.70421e6	−0.194405
$721$	1.08626e7	0.778206
$722$	−1.24482e6	−0.0888718
$723$	2.27458e6	0.161828
$724$	3.60382e7	2.55515
$725$	−1.00945e6	−0.0713248
$726$	1.07940e6	0.0760046
$727$	−2.27203e7	−1.59433	−0.797164	−	0.603763i	$-0.793667\pi$
$727$	−2.27203e7	−1.59433	−0.797164	+	0.603763i	$0.793667\pi$
$728$	3.85879e6	0.269850
$729$	2.65650e6	0.185136
$730$	−2.64765e6	−0.183888
$731$	5.88403e6	0.407269
$732$	2.31165e7	1.59458
$733$	1.86530e7	1.28230	0.641148	−	0.767417i	$-0.278459\pi$
$733$	1.86530e7	1.28230	0.641148	+	0.767417i	$0.278459\pi$
$734$	−5.23884e6	−0.358918
$735$	−2.69778e6	−0.184200
$736$	8.91801e6	0.606839
$737$	−4.85632e6	−0.329335
$738$	2.96498e7	2.00392
$739$	1.62961e7	1.09767	0.548835	−	0.835930i	$-0.315071\pi$
$739$	1.62961e7	1.09767	0.548835	+	0.835930i	$0.315071\pi$
$740$	−1.54686e7	−1.03842
$741$	235495.	0.0157557
$742$	1.19868e7	0.799271
$743$	−3.48714e6	−0.231738	−0.115869	−	0.993265i	$-0.536965\pi$
$743$	−3.48714e6	−0.231738	−0.115869	+	0.993265i	$0.536965\pi$
$744$	515967.	0.0341735
$745$	1.72587e6	0.113924
$746$	2.48427e7	1.63438
$747$	1.55346e7	1.01859
$748$	5.28081e6	0.345101
$749$	−2.66558e7	−1.73615
$750$	1.15194e6	0.0747787
$751$	565994.	0.0366195	0.0183097	−	0.999832i	$-0.494172\pi$
$751$	565994.	0.0366195	0.0183097	+	0.999832i	$0.494172\pi$
$752$	3.09297e6	0.199449
$753$	8.03549e6	0.516446
$754$	−1.30393e6	−0.0835271
$755$	1.14625e7	0.731835
$756$	3.42116e7	2.17705
$757$	−2.07589e7	−1.31663	−0.658315	−	0.752742i	$-0.728731\pi$
$757$	−2.07589e7	−1.31663	−0.658315	+	0.752742i	$0.728731\pi$
$758$	2.96158e7	1.87219
$759$	3.09215e6	0.194830
$760$	−2.34827e6	−0.147473
$761$	−1.10197e7	−0.689779	−0.344889	−	0.938643i	$-0.612084\pi$
$761$	−1.10197e7	−0.689779	−0.344889	+	0.938643i	$0.612084\pi$
$762$	1.07838e7	0.672800
$763$	−1.13341e7	−0.704818
$764$	3.55838e7	2.20556
$765$	3.37837e6	0.208715
$766$	2.75108e7	1.69407
$767$	1.49873e6	0.0919889
$768$	1.40373e7	0.858775
$769$	−1.27157e7	−0.775397	−0.387699	−	0.921786i	$-0.626730\pi$
$769$	−1.27157e7	−0.775397	−0.387699	+	0.921786i	$0.626730\pi$
$770$	5.07004e6	0.308166
$771$	2.44417e6	0.148079
$772$	−8.70997e6	−0.525985
$773$	−2.65522e7	−1.59828	−0.799138	−	0.601147i	$-0.794710\pi$
$773$	−2.65522e7	−1.59828	−0.799138	+	0.601147i	$0.794710\pi$
$774$	−1.39938e7	−0.839620
$775$	160577.	0.00960349
$776$	−4.05336e7	−2.41636
$777$	1.41451e7	0.840532
$778$	3.76692e7	2.23119
$779$	6.10898e6	0.360682
$780$	966119.	0.0568583
$781$	5.79122e6	0.339737
$782$	2.32996e7	1.36249
$783$	−5.31582e6	−0.309860
$784$	8.24482e6	0.479061
$785$	−5.92431e6	−0.343134
$786$	1.04427e7	0.602913
$787$	8.94998e6	0.515093	0.257546	−	0.966266i	$-0.417086\pi$
$787$	8.94998e6	0.515093	0.257546	+	0.966266i	$0.417086\pi$
$788$	−4.79046e7	−2.74828
$789$	−1.61947e7	−0.926149
$790$	−1.85336e7	−1.05655
$791$	−3.57447e7	−2.03128
$792$	−5.77502e6	−0.327145
$793$	4.27314e6	0.241304
$794$	−3.71406e7	−2.09073
$795$	1.37999e6	0.0774387
$796$	−7.05170e6	−0.394467
$797$	−3.05773e6	−0.170512	−0.0852558	−	0.996359i	$-0.527171\pi$
$797$	−3.05773e6	−0.170512	−0.0852558	+	0.996359i	$0.527171\pi$
$798$	4.66994e6	0.259600
$799$	−3.86406e6	−0.214130
$800$	1.68341e6	0.0929964
$801$	−4.23787e6	−0.233382
$802$	−450861.	−0.0247518
$803$	−1.34157e6	−0.0734217
$804$	−1.83508e7	−1.00119
$805$	1.45241e7	0.789952
$806$	207421.	0.0112465
$807$	−1.81672e6	−0.0981981
$808$	3.19536e7	1.72184
$809$	−2.64704e7	−1.42197	−0.710983	−	0.703209i	$-0.751750\pi$
$809$	−2.64704e7	−1.42197	−0.710983	+	0.703209i	$0.751750\pi$
$810$	−4.57786e6	−0.245160
$811$	1.18355e7	0.631881	0.315941	−	0.948779i	$-0.397680\pi$
$811$	1.18355e7	0.631881	0.315941	+	0.948779i	$0.397680\pi$
$812$	−1.67886e7	−0.893561
$813$	−1.25320e6	−0.0664960
$814$	−1.20718e7	−0.638576
$815$	9.51508e6	0.501786
$816$	3.35313e6	0.176289
$817$	−2.88325e6	−0.151122
$818$	5.24578e6	0.274111
$819$	2.72031e6	0.141713
$820$	2.50621e7	1.30161
$821$	2.99430e6	0.155038	0.0775190	−	0.996991i	$-0.475300\pi$
$821$	2.99430e6	0.155038	0.0775190	+	0.996991i	$0.475300\pi$
$822$	−2.15460e7	−1.11221
$823$	−7.08431e6	−0.364584	−0.182292	−	0.983244i	$-0.558352\pi$
$823$	−7.08431e6	−0.364584	−0.182292	+	0.983244i	$0.558352\pi$
$824$	−1.61079e7	−0.826460
$825$	583692.	0.0298572
$826$	2.97203e7	1.51566
$827$	−1.27908e7	−0.650330	−0.325165	−	0.945657i	$-0.605420\pi$
$827$	−1.27908e7	−0.650330	−0.325165	+	0.945657i	$0.605420\pi$
$828$	−3.59782e7	−1.82374
$829$	−1.41945e7	−0.717356	−0.358678	−	0.933461i	$-0.616772\pi$
$829$	−1.41945e7	−0.717356	−0.358678	+	0.933461i	$0.616772\pi$
$830$	2.02239e7	1.01899
$831$	6.55965e6	0.329517
$832$	3.76943e6	0.188785
$833$	−1.03003e7	−0.514323
$834$	5.44159e6	0.270901
$835$	−8.67842e6	−0.430749
$836$	−2.58766e6	−0.128054
$837$	845606.	0.0417210
$838$	−4.76270e7	−2.34284
$839$	−5.99576e6	−0.294063	−0.147031	−	0.989132i	$-0.546972\pi$
$839$	−5.99576e6	−0.294063	−0.147031	+	0.989132i	$0.546972\pi$
$840$	8.80951e6	0.430778
$841$	−1.79025e7	−0.872819
$842$	1.07936e7	0.524669
$843$	−9.06273e6	−0.439228
$844$	3.30149e7	1.59534
$845$	−9.10374e6	−0.438609
$846$	9.18977e6	0.441447
$847$	2.56900e6	0.123043
$848$	−4.21745e6	−0.201400
$849$	1.78085e7	0.847927
$850$	4.39817e6	0.208797
$851$	−3.45822e7	−1.63692
$852$	2.18836e7	1.03281
$853$	2.27846e6	0.107218	0.0536092	−	0.998562i	$-0.482927\pi$
$853$	2.27846e6	0.107218	0.0536092	+	0.998562i	$0.482927\pi$
$854$	8.47375e7	3.97586
$855$	−1.65545e6	−0.0774461
$856$	3.95274e7	1.84380
$857$	1.47012e7	0.683757	0.341879	−	0.939744i	$-0.388937\pi$
$857$	1.47012e7	0.683757	0.341879	+	0.939744i	$0.388937\pi$
$858$	753969.	0.0349651
$859$	−3.48563e7	−1.61175	−0.805876	−	0.592085i	$-0.798305\pi$
$859$	−3.48563e7	−1.61175	−0.805876	+	0.592085i	$0.798305\pi$
$860$	−1.18285e7	−0.545361
$861$	−2.29178e7	−1.05357
$862$	6.45530e7	2.95902
$863$	−2.58906e7	−1.18336	−0.591678	−	0.806175i	$-0.701534\pi$
$863$	−2.58906e7	−1.18336	−0.591678	+	0.806175i	$0.701534\pi$
$864$	8.86494e6	0.404009
$865$	−1.03867e7	−0.471996
$866$	2.89427e7	1.31143
$867$	6.76972e6	0.305860
$868$	2.67062e6	0.120313
$869$	−9.39101e6	−0.421855
$870$	−2.97685e6	−0.133339
$871$	−3.39218e6	−0.151507
$872$	1.68072e7	0.748522
$873$	−2.85747e7	−1.26896
$874$	−1.14171e7	−0.505566
$875$	2.74166e6	0.121058
$876$	−5.06945e6	−0.223203
$877$	3.36202e7	1.47605	0.738025	−	0.674774i	$-0.235759\pi$
$877$	3.36202e7	1.47605	0.738025	+	0.674774i	$0.235759\pi$
$878$	−5.12679e7	−2.24445
$879$	1.30045e7	0.567703
$880$	−1.78385e6	−0.0776517
$881$	−4.26488e7	−1.85126	−0.925628	−	0.378434i	$-0.876463\pi$
$881$	−4.26488e7	−1.85126	−0.925628	+	0.378434i	$0.876463\pi$
$882$	2.44968e7	1.06032
$883$	−3.56278e7	−1.53775	−0.768877	−	0.639396i	$-0.779184\pi$
$883$	−3.56278e7	−1.53775	−0.768877	+	0.639396i	$0.779184\pi$
$884$	3.68869e6	0.158760
$885$	3.42156e6	0.146847
$886$	6.73052e7	2.88047
$887$	−1.36960e7	−0.584498	−0.292249	−	0.956342i	$-0.594404\pi$
$887$	−1.36960e7	−0.584498	−0.292249	+	0.956342i	$0.594404\pi$
$888$	−2.09756e7	−0.892651
$889$	2.56659e7	1.08918
$890$	−5.51713e6	−0.233474
$891$	−2.31961e6	−0.0978861
$892$	6.96036e7	2.92900
$893$	1.89344e6	0.0794553
$894$	5.08954e6	0.212978
$895$	1.25678e7	0.524447
$896$	5.96253e7	2.48119
$897$	2.15989e6	0.0896295
$898$	5.90083e7	2.44187
$899$	−414962.	−0.0171242
$900$	−6.79146e6	−0.279484
$901$	5.26887e6	0.216225
$902$	1.95587e7	0.800430
$903$	1.08165e7	0.441435
$904$	5.30052e7	2.15723
$905$	1.52085e7	0.617257
$906$	3.38027e7	1.36814
$907$	3.50795e7	1.41591	0.707955	−	0.706258i	$-0.249618\pi$
$907$	3.50795e7	1.41591	0.707955	+	0.706258i	$0.249618\pi$
$908$	−1.59098e7	−0.640398
$909$	2.25262e7	0.904227
$910$	3.54147e6	0.141768
$911$	−2.15930e7	−0.862021	−0.431011	−	0.902347i	$-0.641843\pi$
$911$	−2.15930e7	−0.862021	−0.431011	+	0.902347i	$0.641843\pi$
$912$	−1.64307e6	−0.0654139
$913$	1.02475e7	0.406856
$914$	−2.60291e7	−1.03061
$915$	9.75546e6	0.385208
$916$	−4.61768e7	−1.81838
$917$	2.48538e7	0.976046
$918$	2.31610e7	0.907090
$919$	−2.13695e7	−0.834653	−0.417327	−	0.908757i	$-0.637033\pi$
$919$	−2.13695e7	−0.834653	−0.417327	+	0.908757i	$0.637033\pi$
$920$	−2.15376e7	−0.838934
$921$	−9.88252e6	−0.383900
$922$	−6.69750e6	−0.259469
$923$	4.04522e6	0.156292
$924$	9.70760e6	0.374052
$925$	−6.52793e6	−0.250854
$926$	4.95997e7	1.90087
$927$	−1.13555e7	−0.434018
$928$	−4.35028e6	−0.165824
$929$	−4.13699e7	−1.57270	−0.786349	−	0.617782i	$-0.788031\pi$
$929$	−4.13699e7	−1.57270	−0.786349	+	0.617782i	$0.788031\pi$
$930$	473537.	0.0179534
$931$	5.04727e6	0.190846
$932$	−6.45973e7	−2.43598
$933$	−3.55411e6	−0.133668
$934$	4.04057e7	1.51557
$935$	2.22856e6	0.0833673
$936$	−4.03390e6	−0.150500
$937$	−1.96284e7	−0.730359	−0.365179	−	0.930937i	$-0.618992\pi$
$937$	−1.96284e7	−0.730359	−0.365179	+	0.930937i	$0.618992\pi$
$938$	−6.72679e7	−2.49632
$939$	−1.55863e7	−0.576870
$940$	7.76783e6	0.286734
$941$	−3.87252e7	−1.42567	−0.712836	−	0.701331i	$-0.752590\pi$
$941$	−3.87252e7	−1.42567	−0.712836	+	0.701331i	$0.752590\pi$
$942$	−1.74706e7	−0.641478
$943$	5.60297e7	2.05182
$944$	−1.04568e7	−0.381917
$945$	1.44377e7	0.525918
$946$	−9.23109e6	−0.335371
$947$	4.69657e7	1.70179	0.850895	−	0.525336i	$-0.176060\pi$
$947$	4.69657e7	1.70179	0.850895	+	0.525336i	$0.176060\pi$
$948$	−3.54863e7	−1.28245
$949$	−937098.	−0.0337769
$950$	−2.15516e6	−0.0774767
$951$	2.25169e7	0.807342
$952$	3.36352e7	1.20282
$953$	2.92175e7	1.04210	0.521051	−	0.853525i	$-0.325540\pi$
$953$	2.92175e7	1.04210	0.521051	+	0.853525i	$0.325540\pi$
$954$	−1.25308e7	−0.445766
$955$	1.50168e7	0.532805
$956$	9.76832e7	3.45681
$957$	−1.50837e6	−0.0532389
$958$	−8.09198e7	−2.84866
$959$	−5.12801e7	−1.80054
$960$	8.60551e6	0.301369
$961$	−2.85631e7	−0.997694
$962$	−8.43229e6	−0.293770
$963$	2.78654e7	0.968277
$964$	−1.74581e7	−0.605069
$965$	−3.67571e6	−0.127064
$966$	4.28313e7	1.47679
$967$	3.27232e6	0.112536	0.0562678	−	0.998416i	$-0.482080\pi$
$967$	3.27232e6	0.112536	0.0562678	+	0.998416i	$0.482080\pi$
$968$	−3.80953e6	−0.130672
$969$	2.05270e6	0.0702288
$970$	−3.72004e7	−1.26946
$971$	1.04659e7	0.356228	0.178114	−	0.984010i	$-0.443000\pi$
$971$	1.04659e7	0.356228	0.178114	+	0.984010i	$0.443000\pi$
$972$	−5.61443e7	−1.90607
$973$	1.29511e7	0.438557
$974$	−7.55607e7	−2.55210
$975$	407714.	0.0137355
$976$	−2.98141e7	−1.00184
$977$	5.90288e7	1.97846	0.989231	−	0.146361i	$-0.0467561\pi$
$977$	5.90288e7	1.97846	0.989231	+	0.146361i	$0.0467561\pi$
$978$	2.80597e7	0.938072
$979$	−2.79554e6	−0.0932199
$980$	2.07064e7	0.688715
$981$	1.18485e7	0.393088
$982$	6.93954e7	2.29642
$983$	1.75162e7	0.578169	0.289085	−	0.957304i	$-0.406649\pi$
$983$	1.75162e7	0.578169	0.289085	+	0.957304i	$0.406649\pi$
$984$	3.39844e7	1.11890
$985$	−2.02163e7	−0.663913
$986$	−1.13657e7	−0.372311
$987$	−7.10322e6	−0.232093
$988$	−1.80751e6	−0.0589098
$989$	−2.64443e7	−0.859689
$990$	−5.30012e6	−0.171869
$991$	−2.76193e7	−0.893364	−0.446682	−	0.894693i	$-0.647394\pi$
$991$	−2.76193e7	−0.893364	−0.446682	+	0.894693i	$0.647394\pi$
$992$	692013.	0.0223272
$993$	−3.06876e6	−0.0987619
$994$	8.02178e7	2.57516
$995$	−2.97590e6	−0.0952929
$996$	3.87227e7	1.23685
$997$	−1.10517e7	−0.352121	−0.176061	−	0.984379i	$-0.556336\pi$
$997$	−1.10517e7	−0.352121	−0.176061	+	0.984379i	$0.556336\pi$
$998$	1.89117e7	0.601041
$999$	−3.43764e7	−1.08980

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.b.1.4	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.b.1.4	✓	36	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)

\(f(q)\)	\(=\)	\(q-9.55197 q^{2} -7.71824 q^{3} +59.2400 q^{4} +25.0000 q^{5} +73.7243 q^{6} +175.466 q^{7} -260.196 q^{8} -183.429 q^{9} +O(q^{10})\)	\(q-9.55197 q^{2} -7.71824 q^{3} +59.2400 q^{4} +25.0000 q^{5} +73.7243 q^{6} +175.466 q^{7} -260.196 q^{8} -183.429 q^{9} -238.799 q^{10} -121.000 q^{11} -457.229 q^{12} -84.5196 q^{13} -1676.05 q^{14} -192.956 q^{15} +589.701 q^{16} -736.715 q^{17} +1752.11 q^{18} +361.000 q^{19} +1481.00 q^{20} -1354.29 q^{21} +1155.79 q^{22} +3310.98 q^{23} +2008.25 q^{24} +625.000 q^{25} +807.328 q^{26} +3291.28 q^{27} +10394.6 q^{28} -1615.12 q^{29} +1843.11 q^{30} +256.923 q^{31} +2693.46 q^{32} +933.907 q^{33} +7037.08 q^{34} +4386.65 q^{35} -10866.3 q^{36} -10444.7 q^{37} -3448.26 q^{38} +652.342 q^{39} -6504.90 q^{40} +16922.4 q^{41} +12936.1 q^{42} -7986.84 q^{43} -7168.05 q^{44} -4585.72 q^{45} -31626.4 q^{46} +5244.98 q^{47} -4551.45 q^{48} +13981.4 q^{49} -5969.98 q^{50} +5686.14 q^{51} -5006.94 q^{52} -7151.84 q^{53} -31438.2 q^{54} -3025.00 q^{55} -45655.6 q^{56} -2786.28 q^{57} +15427.6 q^{58} -17732.4 q^{59} -11430.7 q^{60} -50558.0 q^{61} -2454.12 q^{62} -32185.5 q^{63} -44598.3 q^{64} -2112.99 q^{65} -8920.64 q^{66} +40134.9 q^{67} -43643.0 q^{68} -25554.9 q^{69} -41901.2 q^{70} -47861.3 q^{71} +47727.4 q^{72} +11087.4 q^{73} +99767.3 q^{74} -4823.90 q^{75} +21385.7 q^{76} -21231.4 q^{77} -6231.15 q^{78} +77611.7 q^{79} +14742.5 q^{80} +19170.3 q^{81} -161642. q^{82} -84689.9 q^{83} -80228.1 q^{84} -18417.9 q^{85} +76290.0 q^{86} +12465.9 q^{87} +31483.7 q^{88} +23103.6 q^{89} +43802.6 q^{90} -14830.3 q^{91} +196143. q^{92} -1982.99 q^{93} -50099.9 q^{94} +9025.00 q^{95} -20788.8 q^{96} +155781. q^{97} -133549. q^{98} +22194.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9} - 200 q^{10} - 4356 q^{11} - 2008 q^{12} - 43 q^{13} - 1937 q^{14} - 1575 q^{15} + 3612 q^{16} - 2431 q^{17} - 6225 q^{18} + 12996 q^{19} + 13000 q^{20} + 2863 q^{21} + 968 q^{22} - 11444 q^{23} - 6210 q^{24} + 22500 q^{25} - 6339 q^{26} - 12960 q^{27} - 1083 q^{28} - 873 q^{29} + 125 q^{30} - 1405 q^{31} - 14283 q^{32} + 7623 q^{33} + 19937 q^{34} - 12725 q^{35} - 1169 q^{36} - 22729 q^{37} - 2888 q^{38} + 3710 q^{39} - 17250 q^{40} - 17043 q^{41} - 39996 q^{42} - 42231 q^{43} - 62920 q^{44} + 48375 q^{45} + 50947 q^{46} - 72440 q^{47} + 42475 q^{48} + 54119 q^{49} - 5000 q^{50} - 114970 q^{51} + 16786 q^{52} - 67603 q^{53} - 26080 q^{54} - 108900 q^{55} - 216071 q^{56} - 22743 q^{57} - 115746 q^{58} - 247439 q^{59} - 50200 q^{60} - 66627 q^{61} - 262438 q^{62} - 226118 q^{63} + 1078 q^{64} - 1075 q^{65} - 605 q^{66} - 189550 q^{67} - 140936 q^{68} - 65684 q^{69} - 48425 q^{70} - 320146 q^{71} - 509978 q^{72} - 55266 q^{73} - 63309 q^{74} - 39375 q^{75} + 187720 q^{76} + 61589 q^{77} - 284264 q^{78} - 1033 q^{79} + 90300 q^{80} - 58588 q^{81} - 328242 q^{82} - 451983 q^{83} + 43932 q^{84} - 60775 q^{85} - 44142 q^{86} - 457510 q^{87} + 83490 q^{88} + 13940 q^{89} - 155625 q^{90} - 211732 q^{91} - 735304 q^{92} + 4486 q^{93} + 152164 q^{94} + 324900 q^{95} + 195996 q^{96} - 234346 q^{97} - 58328 q^{98} - 234135 q^{99}+O(q^{100}) \) 36 * q - 8 * q^2 - 63 * q^3 + 520 * q^4 + 900 * q^5 + 5 * q^6 - 509 * q^7 - 690 * q^8 + 1935 * q^9 - 200 * q^10 - 4356 * q^11 - 2008 * q^12 - 43 * q^13 - 1937 * q^14 - 1575 * q^15 + 3612 * q^16 - 2431 * q^17 - 6225 * q^18 + 12996 * q^19 + 13000 * q^20 + 2863 * q^21 + 968 * q^22 - 11444 * q^23 - 6210 * q^24 + 22500 * q^25 - 6339 * q^26 - 12960 * q^27 - 1083 * q^28 - 873 * q^29 + 125 * q^30 - 1405 * q^31 - 14283 * q^32 + 7623 * q^33 + 19937 * q^34 - 12725 * q^35 - 1169 * q^36 - 22729 * q^37 - 2888 * q^38 + 3710 * q^39 - 17250 * q^40 - 17043 * q^41 - 39996 * q^42 - 42231 * q^43 - 62920 * q^44 + 48375 * q^45 + 50947 * q^46 - 72440 * q^47 + 42475 * q^48 + 54119 * q^49 - 5000 * q^50 - 114970 * q^51 + 16786 * q^52 - 67603 * q^53 - 26080 * q^54 - 108900 * q^55 - 216071 * q^56 - 22743 * q^57 - 115746 * q^58 - 247439 * q^59 - 50200 * q^60 - 66627 * q^61 - 262438 * q^62 - 226118 * q^63 + 1078 * q^64 - 1075 * q^65 - 605 * q^66 - 189550 * q^67 - 140936 * q^68 - 65684 * q^69 - 48425 * q^70 - 320146 * q^71 - 509978 * q^72 - 55266 * q^73 - 63309 * q^74 - 39375 * q^75 + 187720 * q^76 + 61589 * q^77 - 284264 * q^78 - 1033 * q^79 + 90300 * q^80 - 58588 * q^81 - 328242 * q^82 - 451983 * q^83 + 43932 * q^84 - 60775 * q^85 - 44142 * q^86 - 457510 * q^87 + 83490 * q^88 + 13940 * q^89 - 155625 * q^90 - 211732 * q^91 - 735304 * q^92 + 4486 * q^93 + 152164 * q^94 + 324900 * q^95 + 195996 * q^96 - 234346 * q^97 - 58328 * q^98 - 234135 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more