LMFDB - Embedded newform 1045.6.a.a.1.2

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:	$35$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
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)

$f(q)$	$=$	$q-10.0372 q^{2} -21.3301 q^{3} +68.7460 q^{4} -25.0000 q^{5} +214.096 q^{6} +45.5863 q^{7} -368.828 q^{8} +211.975 q^{9} +O(q^{10})$	\(q-10.0372 q^{2} -21.3301 q^{3} +68.7460 q^{4} -25.0000 q^{5} +214.096 q^{6} +45.5863 q^{7} -368.828 q^{8} +211.975 q^{9} +250.931 q^{10} +121.000 q^{11} -1466.36 q^{12} +590.564 q^{13} -457.560 q^{14} +533.254 q^{15} +1502.14 q^{16} +545.397 q^{17} -2127.64 q^{18} +361.000 q^{19} -1718.65 q^{20} -972.363 q^{21} -1214.50 q^{22} +253.238 q^{23} +7867.15 q^{24} +625.000 q^{25} -5927.62 q^{26} +661.762 q^{27} +3133.87 q^{28} +6044.62 q^{29} -5352.39 q^{30} -6500.02 q^{31} -3274.80 q^{32} -2580.95 q^{33} -5474.28 q^{34} -1139.66 q^{35} +14572.4 q^{36} +13571.0 q^{37} -3623.44 q^{38} -12596.8 q^{39} +9220.69 q^{40} -15169.1 q^{41} +9759.83 q^{42} -11437.9 q^{43} +8318.26 q^{44} -5299.38 q^{45} -2541.81 q^{46} -6287.49 q^{47} -32040.8 q^{48} -14728.9 q^{49} -6273.27 q^{50} -11633.4 q^{51} +40598.9 q^{52} +13921.0 q^{53} -6642.26 q^{54} -3025.00 q^{55} -16813.5 q^{56} -7700.18 q^{57} -60671.2 q^{58} -16958.1 q^{59} +36659.0 q^{60} +7640.48 q^{61} +65242.2 q^{62} +9663.17 q^{63} -15198.4 q^{64} -14764.1 q^{65} +25905.6 q^{66} -22736.3 q^{67} +37493.9 q^{68} -5401.61 q^{69} +11439.0 q^{70} -63586.6 q^{71} -78182.3 q^{72} +72895.7 q^{73} -136215. q^{74} -13331.3 q^{75} +24817.3 q^{76} +5515.94 q^{77} +126437. q^{78} -57519.5 q^{79} -37553.4 q^{80} -65625.5 q^{81} +152256. q^{82} -101694. q^{83} -66846.0 q^{84} -13634.9 q^{85} +114805. q^{86} -128933. q^{87} -44628.1 q^{88} -18016.6 q^{89} +53191.1 q^{90} +26921.6 q^{91} +17409.1 q^{92} +138646. q^{93} +63108.9 q^{94} -9025.00 q^{95} +69852.0 q^{96} -51497.8 q^{97} +147837. q^{98} +25649.0 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) $ 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9 + 100 * q^10 + 4235 * q^11 - 568 * q^12 - 717 * q^13 - 2585 * q^14 + 675 * q^15 + 3356 * q^16 - 3349 * q^17 - 5533 * q^18 + 12635 * q^19 - 13000 * q^20 + 289 * q^21 - 484 * q^22 - 820 * q^23 - 21748 * q^24 + 21875 * q^25 - 6267 * q^26 - 13650 * q^27 - 6487 * q^28 - 13357 * q^29 + 7275 * q^30 - 15341 * q^31 - 16405 * q^32 - 3267 * q^33 - 1255 * q^34 - 2925 * q^35 + 23487 * q^36 - 511 * q^37 - 1444 * q^38 - 33584 * q^39 + 12450 * q^40 - 36855 * q^41 + 16330 * q^42 + 10991 * q^43 + 62920 * q^44 - 51150 * q^45 - 20443 * q^46 - 33594 * q^47 + 36221 * q^48 + 23422 * q^49 - 2500 * q^50 - 53530 * q^51 + 89382 * q^52 + 13103 * q^53 + 65776 * q^54 - 105875 * q^55 + 130911 * q^56 - 9747 * q^57 + 127808 * q^58 - 161139 * q^59 + 14200 * q^60 - 91587 * q^61 + 131818 * q^62 + 16590 * q^63 - 23186 * q^64 + 17925 * q^65 - 35211 * q^66 + 39210 * q^67 + 26300 * q^68 - 23174 * q^69 + 64625 * q^70 - 167772 * q^71 + 135820 * q^72 - 5106 * q^73 - 256965 * q^74 - 16875 * q^75 + 187720 * q^76 + 14157 * q^77 + 492812 * q^78 - 156897 * q^79 - 83900 * q^80 + 31279 * q^81 + 46818 * q^82 - 185627 * q^83 + 165864 * q^84 + 83725 * q^85 - 159946 * q^86 - 112092 * q^87 - 60258 * q^88 - 144420 * q^89 + 138325 * q^90 - 442480 * q^91 - 205876 * q^92 + 125910 * q^93 - 110044 * q^94 - 315875 * q^95 - 554286 * q^96 + 41200 * q^97 + 41052 * q^98 + 247566 * 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 $

$2$	−10.0372	−1.77435	−0.887174	−	0.461435i	$-0.847335\pi$
$2$	−10.0372	−1.77435	−0.887174	+	0.461435i	$0.847335\pi$
$3$	−21.3301	−1.36833	−0.684165	−	0.729327i	$-0.739833\pi$
$3$	−21.3301	−1.36833	−0.684165	+	0.729327i	$0.739833\pi$
$4$	68.7460	2.14831
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	214.096	2.42789
$7$	45.5863	0.351633	0.175816	−	0.984423i	$-0.443744\pi$
$7$	45.5863	0.351633	0.175816	+	0.984423i	$0.443744\pi$
$8$	−368.828	−2.03750
$9$	211.975	0.872326
$10$	250.931	0.793513
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	−1466.36	−2.93960
$13$	590.564	0.969189	0.484594	−	0.874739i	$-0.338967\pi$
$13$	590.564	0.969189	0.484594	+	0.874739i	$0.338967\pi$
$14$	−457.560	−0.623919
$15$	533.254	0.611936
$16$	1502.14	1.46693
$17$	545.397	0.457710	0.228855	−	0.973460i	$-0.426502\pi$
$17$	545.397	0.457710	0.228855	+	0.973460i	$0.426502\pi$
$18$	−2127.64	−1.54781
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−1718.65	−0.960754
$21$	−972.363	−0.481149
$22$	−1214.50	−0.534986
$23$	253.238	0.0998182	0.0499091	−	0.998754i	$-0.484107\pi$
$23$	253.238	0.0998182	0.0499091	+	0.998754i	$0.484107\pi$
$24$	7867.15	2.78798
$25$	625.000	0.200000
$26$	−5927.62	−1.71968
$27$	661.762	0.174700
$28$	3133.87	0.755416
$29$	6044.62	1.33467	0.667335	−	0.744758i	$-0.267435\pi$
$29$	6044.62	1.33467	0.667335	+	0.744758i	$0.267435\pi$
$30$	−5352.39	−1.08579
$31$	−6500.02	−1.21482	−0.607408	−	0.794390i	$-0.707791\pi$
$31$	−6500.02	−1.21482	−0.607408	+	0.794390i	$0.707791\pi$
$32$	−3274.80	−0.565340
$33$	−2580.95	−0.412567
$34$	−5474.28	−0.812137
$35$	−1139.66	−0.157255
$36$	14572.4	1.87403
$37$	13571.0	1.62969	0.814847	−	0.579676i	$-0.196821\pi$
$37$	13571.0	1.62969	0.814847	+	0.579676i	$0.196821\pi$
$38$	−3623.44	−0.407063
$39$	−12596.8	−1.32617
$40$	9220.69	0.911199
$41$	−15169.1	−1.40929	−0.704646	−	0.709559i	$-0.748894\pi$
$41$	−15169.1	−1.40929	−0.704646	+	0.709559i	$0.748894\pi$
$42$	9759.83	0.853727
$43$	−11437.9	−0.943359	−0.471680	−	0.881770i	$-0.656352\pi$
$43$	−11437.9	−0.943359	−0.471680	+	0.881770i	$0.656352\pi$
$44$	8318.26	0.647740
$45$	−5299.38	−0.390116
$46$	−2541.81	−0.177112
$47$	−6287.49	−0.415176	−0.207588	−	0.978216i	$-0.566561\pi$
$47$	−6287.49	−0.415176	−0.207588	+	0.978216i	$0.566561\pi$
$48$	−32040.8	−2.00724
$49$	−14728.9	−0.876354
$50$	−6273.27	−0.354870
$51$	−11633.4	−0.626299
$52$	40598.9	2.08212
$53$	13921.0	0.680742	0.340371	−	0.940291i	$-0.389447\pi$
$53$	13921.0	0.680742	0.340371	+	0.940291i	$0.389447\pi$
$54$	−6642.26	−0.309978
$55$	−3025.00	−0.134840
$56$	−16813.5	−0.716453
$57$	−7700.18	−0.313916
$58$	−60671.2	−2.36817
$59$	−16958.1	−0.634231	−0.317116	−	0.948387i	$-0.602714\pi$
$59$	−16958.1	−0.634231	−0.317116	+	0.948387i	$0.602714\pi$
$60$	36659.0	1.31463
$61$	7640.48	0.262903	0.131452	−	0.991323i	$-0.458036\pi$
$61$	7640.48	0.262903	0.131452	+	0.991323i	$0.458036\pi$
$62$	65242.2	2.15551
$63$	9663.17	0.306738
$64$	−15198.4	−0.463820
$65$	−14764.1	−0.433434
$66$	25905.6	0.732037
$67$	−22736.3	−0.618776	−0.309388	−	0.950936i	$-0.600124\pi$
$67$	−22736.3	−0.618776	−0.309388	+	0.950936i	$0.600124\pi$
$68$	37493.9	0.983304
$69$	−5401.61	−0.136584
$70$	11439.0	0.279025
$71$	−63586.6	−1.49699	−0.748496	−	0.663139i	$-0.769224\pi$
$71$	−63586.6	−1.49699	−0.748496	+	0.663139i	$0.769224\pi$
$72$	−78182.3	−1.77737
$73$	72895.7	1.60101	0.800506	−	0.599324i	$-0.204564\pi$
$73$	72895.7	1.60101	0.800506	+	0.599324i	$0.204564\pi$
$74$	−136215.	−2.89164
$75$	−13331.3	−0.273666
$76$	24817.3	0.492856
$77$	5515.94	0.106021
$78$	126437.	2.35309
$79$	−57519.5	−1.03693	−0.518463	−	0.855100i	$-0.673496\pi$
$79$	−57519.5	−1.03693	−0.518463	+	0.855100i	$0.673496\pi$
$80$	−37553.4	−0.656031
$81$	−65625.5	−1.11137
$82$	152256.	2.50057
$83$	−101694.	−1.62032	−0.810159	−	0.586211i	$-0.800619\pi$
$83$	−101694.	−1.62032	−0.810159	+	0.586211i	$0.800619\pi$
$84$	−66846.0	−1.03366
$85$	−13634.9	−0.204694
$86$	114805.	1.67385
$87$	−128933.	−1.82627
$88$	−44628.1	−0.614330
$89$	−18016.6	−0.241100	−0.120550	−	0.992707i	$-0.538466\pi$
$89$	−18016.6	−0.241100	−0.120550	+	0.992707i	$0.538466\pi$
$90$	53191.1	0.692202
$91$	26921.6	0.340798
$92$	17409.1	0.214441
$93$	138646.	1.66227
$94$	63108.9	0.736667
$95$	−9025.00	−0.102598
$96$	69852.0	0.773571
$97$	−51497.8	−0.555724	−0.277862	−	0.960621i	$-0.589626\pi$
$97$	−51497.8	−0.555724	−0.277862	+	0.960621i	$0.589626\pi$
$98$	147837.	1.55496
$99$	25649.0	0.263016
$100$	42966.2	0.429662
$101$	52377.3	0.510904	0.255452	−	0.966822i	$-0.417776\pi$
$101$	52377.3	0.510904	0.255452	+	0.966822i	$0.417776\pi$
$102$	116767.	1.11127
$103$	33807.9	0.313997	0.156999	−	0.987599i	$-0.449818\pi$
$103$	33807.9	0.313997	0.156999	+	0.987599i	$0.449818\pi$
$104$	−217816.	−1.97473
$105$	24309.1	0.215177
$106$	−139729.	−1.20787
$107$	58041.7	0.490095	0.245048	−	0.969511i	$-0.421196\pi$
$107$	58041.7	0.490095	0.245048	+	0.969511i	$0.421196\pi$
$108$	45493.5	0.375309
$109$	166191.	1.33981	0.669904	−	0.742448i	$-0.266335\pi$
$109$	166191.	1.33981	0.669904	+	0.742448i	$0.266335\pi$
$110$	30362.6	0.239253
$111$	−289471.	−2.22996
$112$	68476.8	0.515820
$113$	−189618.	−1.39696	−0.698480	−	0.715630i	$-0.746140\pi$
$113$	−189618.	−1.39696	−0.698480	+	0.715630i	$0.746140\pi$
$114$	77288.5	0.556997
$115$	−6330.96	−0.0446401
$116$	415543.	2.86729
$117$	125185.	0.845449
$118$	170212.	1.12535
$119$	24862.6	0.160946
$120$	−196679.	−1.24682
$121$	14641.0	0.0909091
$122$	−76689.3	−0.466482
$123$	323560.	1.92838
$124$	−446850.	−2.60980
$125$	−15625.0	−0.0894427
$126$	−96991.4	−0.544261
$127$	281147.	1.54676	0.773381	−	0.633941i	$-0.218564\pi$
$127$	281147.	1.54676	0.773381	+	0.633941i	$0.218564\pi$
$128$	257344.	1.38832
$129$	243973.	1.29083
$130$	148191.	0.769063
$131$	−362543.	−1.84578	−0.922892	−	0.385058i	$-0.874181\pi$
$131$	−362543.	−1.84578	−0.922892	+	0.385058i	$0.874181\pi$
$132$	−177430.	−0.886322
$133$	16456.7	0.0806701
$134$	228210.	1.09792
$135$	−16544.0	−0.0781281
$136$	−201158.	−0.932586
$137$	188089.	0.856174	0.428087	−	0.903738i	$-0.359188\pi$
$137$	188089.	0.856174	0.428087	+	0.903738i	$0.359188\pi$
$138$	54217.2	0.242348
$139$	356004.	1.56285	0.781427	−	0.623997i	$-0.214492\pi$
$139$	356004.	1.56285	0.781427	+	0.623997i	$0.214492\pi$
$140$	−78346.8	−0.337832
$141$	134113.	0.568098
$142$	638233.	2.65619
$143$	71458.2	0.292221
$144$	318416.	1.27964
$145$	−151115.	−0.596883
$146$	−731671.	−2.84075
$147$	314169.	1.19914
$148$	932948.	3.50109
$149$	283119.	1.04473	0.522364	−	0.852723i	$-0.325050\pi$
$149$	283119.	1.04473	0.522364	+	0.852723i	$0.325050\pi$
$150$	133810.	0.485579
$151$	523212.	1.86739	0.933695	−	0.358069i	$-0.116565\pi$
$151$	523212.	1.86739	0.933695	+	0.358069i	$0.116565\pi$
$152$	−133147.	−0.467435
$153$	115611.	0.399273
$154$	−55364.8	−0.188119
$155$	162500.	0.543282
$156$	−865980.	−2.84902
$157$	−434996.	−1.40843	−0.704216	−	0.709985i	$-0.748701\pi$
$157$	−434996.	−1.40843	−0.704216	+	0.709985i	$0.748701\pi$
$158$	577337.	1.83987
$159$	−296938.	−0.931479
$160$	81870.0	0.252828
$161$	11544.2	0.0350994
$162$	658698.	1.97196
$163$	360460.	1.06264	0.531322	−	0.847170i	$-0.321695\pi$
$163$	360460.	1.06264	0.531322	+	0.847170i	$0.321695\pi$
$164$	−1.04282e6	−3.02760
$165$	64523.7	0.184506
$166$	1.02073e6	2.87501
$167$	−67930.4	−0.188483	−0.0942416	−	0.995549i	$-0.530043\pi$
$167$	−67930.4	−0.188483	−0.0942416	+	0.995549i	$0.530043\pi$
$168$	358634.	0.980344
$169$	−22527.6	−0.0606735
$170$	136857.	0.363199
$171$	76523.1	0.200125
$172$	−786313.	−2.02663
$173$	−176616.	−0.448659	−0.224329	−	0.974513i	$-0.572019\pi$
$173$	−176616.	−0.448659	−0.224329	+	0.974513i	$0.572019\pi$
$174$	1.29413e6	3.24044
$175$	28491.4	0.0703265
$176$	181758.	0.442296
$177$	361719.	0.867837
$178$	180837.	0.427796
$179$	236326.	0.551287	0.275644	−	0.961260i	$-0.411109\pi$
$179$	236326.	0.551287	0.275644	+	0.961260i	$0.411109\pi$
$180$	−364311.	−0.838091
$181$	481024.	1.09137	0.545683	−	0.837992i	$-0.316270\pi$
$181$	481024.	1.09137	0.545683	+	0.837992i	$0.316270\pi$
$182$	−270218.	−0.604695
$183$	−162973.	−0.359738
$184$	−93401.3	−0.203380
$185$	−339274.	−0.728821
$186$	−1.39163e6	−2.94944
$187$	65993.1	0.138005
$188$	−432239.	−0.891927
$189$	30167.3	0.0614302
$190$	90586.0	0.182044
$191$	−565416.	−1.12146	−0.560731	−	0.827998i	$-0.689480\pi$
$191$	−565416.	−1.12146	−0.560731	+	0.827998i	$0.689480\pi$
$192$	324185.	0.634658
$193$	425197.	0.821670	0.410835	−	0.911710i	$-0.365237\pi$
$193$	425197.	0.821670	0.410835	+	0.911710i	$0.365237\pi$
$194$	516895.	0.986048
$195$	314920.	0.593081
$196$	−1.01255e6	−1.88268
$197$	−620404.	−1.13896	−0.569481	−	0.822005i	$-0.692856\pi$
$197$	−620404.	−1.13896	−0.569481	+	0.822005i	$0.692856\pi$
$198$	−257445.	−0.466682
$199$	−946338.	−1.69400	−0.847000	−	0.531593i	$-0.821594\pi$
$199$	−946338.	−1.69400	−0.847000	+	0.531593i	$0.821594\pi$
$200$	−230517.	−0.407501
$201$	484969.	0.846689
$202$	−525723.	−0.906522
$203$	275552.	0.469314
$204$	−799750.	−1.34548
$205$	379228.	0.630255
$206$	−339338.	−0.557140
$207$	53680.3	0.0870741
$208$	887107.	1.42173
$209$	43681.0	0.0691714
$210$	−243996.	−0.381798
$211$	171167.	0.264676	0.132338	−	0.991205i	$-0.457752\pi$
$211$	171167.	0.264676	0.132338	+	0.991205i	$0.457752\pi$
$212$	957016.	1.46244
$213$	1.35631e6	2.04838
$214$	−582577.	−0.869599
$215$	285949.	0.421883
$216$	−244076.	−0.355951
$217$	−296312.	−0.427169
$218$	−1.66810e6	−2.37728
$219$	−1.55488e6	−2.19071
$220$	−207957.	−0.289678
$221$	322092.	0.443608
$222$	2.90548e6	3.95672
$223$	484865.	0.652918	0.326459	−	0.945211i	$-0.394144\pi$
$223$	484865.	0.652918	0.326459	+	0.945211i	$0.394144\pi$
$224$	−149286.	−0.198792
$225$	132485.	0.174465
$226$	1.90324e6	2.47869
$227$	−451755.	−0.581887	−0.290943	−	0.956740i	$-0.593969\pi$
$227$	−451755.	−0.581887	−0.290943	+	0.956740i	$0.593969\pi$
$228$	−529357.	−0.674390
$229$	77974.4	0.0982570	0.0491285	−	0.998792i	$-0.484356\pi$
$229$	77974.4	0.0982570	0.0491285	+	0.998792i	$0.484356\pi$
$230$	63545.3	0.0792070
$231$	−117656.	−0.145072
$232$	−2.22942e6	−2.71939
$233$	−1.11386e6	−1.34413	−0.672063	−	0.740494i	$-0.734592\pi$
$233$	−1.11386e6	−1.34413	−0.672063	+	0.740494i	$0.734592\pi$
$234$	−1.25651e6	−1.50012
$235$	157187.	0.185672
$236$	−1.16580e6	−1.36253
$237$	1.22690e6	1.41886
$238$	−249552.	−0.285574
$239$	1.24063e6	1.40490	0.702452	−	0.711731i	$-0.252089\pi$
$239$	1.24063e6	1.40490	0.702452	+	0.711731i	$0.252089\pi$
$240$	801020.	0.897666
$241$	−163443.	−0.181269	−0.0906344	−	0.995884i	$-0.528889\pi$
$241$	−163443.	−0.181269	−0.0906344	+	0.995884i	$0.528889\pi$
$242$	−146955.	−0.161304
$243$	1.23899e6	1.34603
$244$	525252.	0.564798
$245$	368222.	0.391918
$246$	−3.24764e6	−3.42161
$247$	213193.	0.222347
$248$	2.39739e6	2.47519
$249$	2.16915e6	2.21713
$250$	156832.	0.158703
$251$	894322.	0.896004	0.448002	−	0.894033i	$-0.352136\pi$
$251$	894322.	0.896004	0.448002	+	0.894033i	$0.352136\pi$
$252$	664304.	0.658970
$253$	30641.8	0.0300963
$254$	−2.82193e6	−2.74449
$255$	290835.	0.280089
$256$	−2.09667e6	−1.99954
$257$	1.40041e6	1.32258	0.661291	−	0.750129i	$-0.270009\pi$
$257$	1.40041e6	1.32258	0.661291	+	0.750129i	$0.270009\pi$
$258$	−2.44881e6	−2.29038
$259$	618650.	0.573054
$260$	−1.01497e6	−0.931152
$261$	1.28131e6	1.16427
$262$	3.63892e6	3.27506
$263$	26892.4	0.0239740	0.0119870	−	0.999928i	$-0.496184\pi$
$263$	26892.4	0.0239740	0.0119870	+	0.999928i	$0.496184\pi$
$264$	951925.	0.840607
$265$	−348026.	−0.304437
$266$	−165179.	−0.143137
$267$	384297.	0.329905
$268$	−1.56303e6	−1.32932
$269$	−750989.	−0.632780	−0.316390	−	0.948629i	$-0.602471\pi$
$269$	−750989.	−0.632780	−0.316390	+	0.948629i	$0.602471\pi$
$270$	166056.	0.138626
$271$	−794375.	−0.657056	−0.328528	−	0.944494i	$-0.606552\pi$
$271$	−794375.	−0.657056	−0.328528	+	0.944494i	$0.606552\pi$
$272$	819261.	0.671429
$273$	−574242.	−0.466325
$274$	−1.88789e6	−1.51915
$275$	75625.0	0.0603023
$276$	−371339.	−0.293425
$277$	1.14572e6	0.897177	0.448588	−	0.893738i	$-0.351927\pi$
$277$	1.14572e6	0.897177	0.448588	+	0.893738i	$0.351927\pi$
$278$	−3.57330e6	−2.77305
$279$	−1.37784e6	−1.05972
$280$	420337.	0.320407
$281$	−2.26321e6	−1.70986	−0.854928	−	0.518747i	$-0.826399\pi$
$281$	−2.26321e6	−1.70986	−0.854928	+	0.518747i	$0.826399\pi$
$282$	−1.34612e6	−1.00800
$283$	−1.90850e6	−1.41653	−0.708267	−	0.705944i	$-0.750523\pi$
$283$	−1.90850e6	−1.41653	−0.708267	+	0.705944i	$0.750523\pi$
$284$	−4.37132e6	−3.21601
$285$	192505.	0.140388
$286$	−717242.	−0.518502
$287$	−691504.	−0.495553
$288$	−694176.	−0.493161
$289$	−1.12240e6	−0.790501
$290$	1.51678e6	1.05908
$291$	1.09846e6	0.760414
$292$	5.01129e6	3.43947
$293$	−633883.	−0.431360	−0.215680	−	0.976464i	$-0.569197\pi$
$293$	−633883.	−0.431360	−0.215680	+	0.976464i	$0.569197\pi$
$294$	−3.15339e6	−2.12770
$295$	423953.	0.283637
$296$	−5.00534e6	−3.32051
$297$	80073.2	0.0526740
$298$	−2.84173e6	−1.85371
$299$	149553.	0.0967427
$300$	−916476.	−0.587920
$301$	−521414.	−0.331716
$302$	−5.25160e6	−3.31340
$303$	−1.11722e6	−0.699085
$304$	542271.	0.336537
$305$	−191012.	−0.117574
$306$	−1.16041e6	−0.708449
$307$	2.02564e6	1.22664	0.613318	−	0.789836i	$-0.289835\pi$
$307$	2.02564e6	1.22664	0.613318	+	0.789836i	$0.289835\pi$
$308$	379199.	0.227767
$309$	−721129.	−0.429652
$310$	−1.63105e6	−0.963971
$311$	−1.57896e6	−0.925700	−0.462850	−	0.886437i	$-0.653173\pi$
$311$	−1.57896e6	−0.925700	−0.462850	+	0.886437i	$0.653173\pi$
$312$	4.64605e6	2.70208
$313$	24442.2	0.0141020	0.00705098	−	0.999975i	$-0.497756\pi$
$313$	24442.2	0.0141020	0.00705098	+	0.999975i	$0.497756\pi$
$314$	4.36615e6	2.49905
$315$	−241579.	−0.137178
$316$	−3.95423e6	−2.22764
$317$	−2.40458e6	−1.34398	−0.671988	−	0.740562i	$-0.734559\pi$
$317$	−2.40458e6	−1.34398	−0.671988	+	0.740562i	$0.734559\pi$
$318$	2.98043e6	1.65277
$319$	731399.	0.402418
$320$	379961.	0.207426
$321$	−1.23804e6	−0.670612
$322$	−115872.	−0.0622785
$323$	196888.	0.105006
$324$	−4.51149e6	−2.38758
$325$	369102.	0.193838
$326$	−3.61802e6	−1.88550
$327$	−3.54489e6	−1.83330
$328$	5.59479e6	2.87144
$329$	−286623.	−0.145989
$330$	−647639.	−0.327377
$331$	548401.	0.275124	0.137562	−	0.990493i	$-0.456073\pi$
$331$	548401.	0.275124	0.137562	+	0.990493i	$0.456073\pi$
$332$	−6.99105e6	−3.48095
$333$	2.87671e6	1.42162
$334$	681833.	0.334435
$335$	568408.	0.276725
$336$	−1.46062e6	−0.705812
$337$	3.75593e6	1.80154	0.900768	−	0.434301i	$-0.143005\pi$
$337$	3.75593e6	1.80154	0.900768	+	0.434301i	$0.143005\pi$
$338$	226115.	0.107656
$339$	4.04458e6	1.91150
$340$	−937346.	−0.439747
$341$	−786502.	−0.366281
$342$	−768080.	−0.355092
$343$	−1.43760e6	−0.659788
$344$	4.21863e6	1.92210
$345$	135040.	0.0610823
$346$	1.77274e6	0.796076
$347$	3.78299e6	1.68660	0.843299	−	0.537445i	$-0.180611\pi$
$347$	3.78299e6	1.68660	0.843299	+	0.537445i	$0.180611\pi$
$348$	−8.86360e6	−3.92339
$349$	−3.33353e6	−1.46501	−0.732506	−	0.680760i	$-0.761650\pi$
$349$	−3.33353e6	−1.46501	−0.732506	+	0.680760i	$0.761650\pi$
$350$	−285975.	−0.124784
$351$	390812.	0.169317
$352$	−396251.	−0.170456
$353$	−2.81059e6	−1.20049	−0.600247	−	0.799815i	$-0.704931\pi$
$353$	−2.81059e6	−1.20049	−0.600247	+	0.799815i	$0.704931\pi$
$354$	−3.63066e6	−1.53985
$355$	1.58966e6	0.669476
$356$	−1.23857e6	−0.517958
$357$	−530324.	−0.220227
$358$	−2.37205e6	−0.978176
$359$	−1.77609e6	−0.727324	−0.363662	−	0.931531i	$-0.618474\pi$
$359$	−1.77609e6	−0.727324	−0.363662	+	0.931531i	$0.618474\pi$
$360$	1.95456e6	0.794863
$361$	130321.	0.0526316
$362$	−4.82815e6	−1.93646
$363$	−312295.	−0.124394
$364$	1.85075e6	0.732141
$365$	−1.82239e6	−0.715995
$366$	1.63579e6	0.638301
$367$	−4.59659e6	−1.78144	−0.890720	−	0.454553i	$-0.849799\pi$
$367$	−4.59659e6	−1.78144	−0.890720	+	0.454553i	$0.849799\pi$
$368$	380398.	0.146426
$369$	−3.21548e6	−1.22936
$370$	3.40537e6	1.29318
$371$	634609.	0.239371
$372$	9.53138e6	3.57107
$373$	2.34753e6	0.873653	0.436827	−	0.899546i	$-0.356102\pi$
$373$	2.34753e6	0.873653	0.436827	+	0.899546i	$0.356102\pi$
$374$	−662387.	−0.244869
$375$	333284.	0.122387
$376$	2.31900e6	0.845923
$377$	3.56973e6	1.29355
$378$	−302796.	−0.108998
$379$	107669.	0.0385029	0.0192515	−	0.999815i	$-0.493872\pi$
$379$	107669.	0.0385029	0.0192515	+	0.999815i	$0.493872\pi$
$380$	−620432.	−0.220412
$381$	−5.99690e6	−2.11648
$382$	5.67521e6	1.98986
$383$	3.60665e6	1.25634	0.628170	−	0.778076i	$-0.283804\pi$
$383$	3.60665e6	1.25634	0.628170	+	0.778076i	$0.283804\pi$
$384$	−5.48918e6	−1.89968
$385$	−137899.	−0.0474141
$386$	−4.26780e6	−1.45793
$387$	−2.42456e6	−0.822917
$388$	−3.54027e6	−1.19387
$389$	2.46669e6	0.826497	0.413248	−	0.910618i	$-0.364394\pi$
$389$	2.46669e6	0.826497	0.413248	+	0.910618i	$0.364394\pi$
$390$	−3.16093e6	−1.05233
$391$	138115.	0.0456878
$392$	5.43242e6	1.78558
$393$	7.73309e6	2.52564
$394$	6.22714e6	2.02091
$395$	1.43799e6	0.463727
$396$	1.76327e6	0.565041
$397$	346619.	0.110376	0.0551882	−	0.998476i	$-0.482424\pi$
$397$	346619.	0.110376	0.0551882	+	0.998476i	$0.482424\pi$
$398$	9.49861e6	3.00575
$399$	−351023.	−0.110383
$400$	938835.	0.293386
$401$	−3.29568e6	−1.02349	−0.511746	−	0.859137i	$-0.671001\pi$
$401$	−3.29568e6	−1.02349	−0.511746	+	0.859137i	$0.671001\pi$
$402$	−4.86775e6	−1.50232
$403$	−3.83867e6	−1.17739
$404$	3.60073e6	1.09758
$405$	1.64064e6	0.497021
$406$	−2.76578e6	−0.832726
$407$	1.64209e6	0.491371
$408$	4.29072e6	1.27609
$409$	2.54411e6	0.752017	0.376008	−	0.926616i	$-0.377296\pi$
$409$	2.54411e6	0.752017	0.376008	+	0.926616i	$0.377296\pi$
$410$	−3.80640e6	−1.11829
$411$	−4.01197e6	−1.17153
$412$	2.32416e6	0.674564
$413$	−773058.	−0.223016
$414$	−538801.	−0.154500
$415$	2.54235e6	0.724628
$416$	−1.93398e6	−0.547921
$417$	−7.59363e6	−2.13850
$418$	−438436.	−0.122734
$419$	−330591.	−0.0919933	−0.0459966	−	0.998942i	$-0.514646\pi$
$419$	−330591.	−0.0919933	−0.0459966	+	0.998942i	$0.514646\pi$
$420$	1.67115e6	0.462266
$421$	−2.41740e6	−0.664726	−0.332363	−	0.943152i	$-0.607846\pi$
$421$	−2.41740e6	−0.664726	−0.332363	+	0.943152i	$0.607846\pi$
$422$	−1.71804e6	−0.469627
$423$	−1.33279e6	−0.362169
$424$	−5.13447e6	−1.38701
$425$	340873.	0.0915420
$426$	−1.36136e7	−3.63454
$427$	348301.	0.0924454
$428$	3.99013e6	1.05288
$429$	−1.52421e6	−0.399855
$430$	−2.87013e6	−0.748567
$431$	−3.07852e6	−0.798267	−0.399134	−	0.916893i	$-0.630689\pi$
$431$	−3.07852e6	−0.798267	−0.399134	+	0.916893i	$0.630689\pi$
$432$	994056.	0.256272
$433$	4.19886e6	1.07625	0.538123	−	0.842866i	$-0.319133\pi$
$433$	4.19886e6	1.07625	0.538123	+	0.842866i	$0.319133\pi$
$434$	2.97415e6	0.757946
$435$	3.22332e6	0.816732
$436$	1.14250e7	2.87832
$437$	91419.0	0.0228999
$438$	1.56066e7	3.88709
$439$	3.40182e6	0.842461	0.421230	−	0.906954i	$-0.361598\pi$
$439$	3.40182e6	0.842461	0.421230	+	0.906954i	$0.361598\pi$
$440$	1.11570e6	0.274737
$441$	−3.12216e6	−0.764467
$442$	−3.23291e6	−0.787114
$443$	−1.04038e6	−0.251874	−0.125937	−	0.992038i	$-0.540194\pi$
$443$	−1.04038e6	−0.251874	−0.125937	+	0.992038i	$0.540194\pi$
$444$	−1.98999e7	−4.79065
$445$	450415.	0.107823
$446$	−4.86670e6	−1.15850
$447$	−6.03896e6	−1.42953
$448$	−692841.	−0.163094
$449$	5.72758e6	1.34077	0.670387	−	0.742012i	$-0.266128\pi$
$449$	5.72758e6	1.34077	0.670387	+	0.742012i	$0.266128\pi$
$450$	−1.32978e6	−0.309562
$451$	−1.83546e6	−0.424918
$452$	−1.30355e7	−3.00110
$453$	−1.11602e7	−2.55521
$454$	4.53437e6	1.03247
$455$	−673040.	−0.152410
$456$	2.84004e6	0.639606
$457$	−7.20308e6	−1.61335	−0.806673	−	0.590998i	$-0.798734\pi$
$457$	−7.20308e6	−1.61335	−0.806673	+	0.590998i	$0.798734\pi$
$458$	−782647.	−0.174342
$459$	360923.	0.0799619
$460$	−435228.	−0.0959008
$461$	757304.	0.165966	0.0829828	−	0.996551i	$-0.473555\pi$
$461$	757304.	0.165966	0.0829828	+	0.996551i	$0.473555\pi$
$462$	1.18094e6	0.257408
$463$	−6.04775e6	−1.31112	−0.655559	−	0.755144i	$-0.727567\pi$
$463$	−6.04775e6	−1.31112	−0.655559	+	0.755144i	$0.727567\pi$
$464$	9.07984e6	1.95787
$465$	−3.46616e6	−0.743389
$466$	1.11800e7	2.38495
$467$	2.77561e6	0.588934	0.294467	−	0.955662i	$-0.404858\pi$
$467$	2.77561e6	0.588934	0.294467	+	0.955662i	$0.404858\pi$
$468$	8.60595e6	1.81629
$469$	−1.03646e6	−0.217582
$470$	−1.57772e6	−0.329447
$471$	9.27853e6	1.92720
$472$	6.25462e6	1.29225
$473$	−1.38399e6	−0.284433
$474$	−1.23147e7	−2.51754
$475$	225625.	0.0458831
$476$	1.70921e6	0.345762
$477$	2.95092e6	0.593829
$478$	−1.24525e7	−2.49279
$479$	−9.05636e6	−1.80350	−0.901748	−	0.432263i	$-0.857715\pi$
$479$	−9.05636e6	−1.80350	−0.901748	+	0.432263i	$0.857715\pi$
$480$	−1.74630e6	−0.345952
$481$	8.01451e6	1.57948
$482$	1.64051e6	0.321634
$483$	−246239.	−0.0480275
$484$	1.00651e6	0.195301
$485$	1.28745e6	0.248527
$486$	−1.24361e7	−2.38832
$487$	−918773.	−0.175544	−0.0877720	−	0.996141i	$-0.527975\pi$
$487$	−918773.	−0.175544	−0.0877720	+	0.996141i	$0.527975\pi$
$488$	−2.81802e6	−0.535667
$489$	−7.68867e6	−1.45405
$490$	−3.69593e6	−0.695398
$491$	−2.99635e6	−0.560905	−0.280452	−	0.959868i	$-0.590485\pi$
$491$	−2.99635e6	−0.560905	−0.280452	+	0.959868i	$0.590485\pi$
$492$	2.22434e7	4.14275
$493$	3.29672e6	0.610892
$494$	−2.13987e6	−0.394521
$495$	−641225.	−0.117624
$496$	−9.76391e6	−1.78205
$497$	−2.89868e6	−0.526392
$498$	−2.17722e7	−3.93396
$499$	350713.	0.0630523	0.0315262	−	0.999503i	$-0.489963\pi$
$499$	350713.	0.0630523	0.0315262	+	0.999503i	$0.489963\pi$
$500$	−1.07416e6	−0.192151
$501$	1.44896e6	0.257907
$502$	−8.97652e6	−1.58982
$503$	9.61222e6	1.69396	0.846981	−	0.531623i	$-0.178418\pi$
$503$	9.61222e6	1.69396	0.846981	+	0.531623i	$0.178418\pi$
$504$	−3.56404e6	−0.624981
$505$	−1.30943e6	−0.228483
$506$	−307559.	−0.0534014
$507$	480518.	0.0830213
$508$	1.93277e7	3.32293
$509$	1.28850e6	0.220440	0.110220	−	0.993907i	$-0.464844\pi$
$509$	1.28850e6	0.220440	0.110220	+	0.993907i	$0.464844\pi$
$510$	−2.91918e6	−0.496976
$511$	3.32305e6	0.562968
$512$	1.28097e7	2.15956
$513$	238896.	0.0400789
$514$	−1.40562e7	−2.34672
$515$	−845199.	−0.140424
$516$	1.67722e7	2.77310
$517$	−760786.	−0.125180
$518$	−6.20953e6	−1.01680
$519$	3.76726e6	0.613913
$520$	5.44540e6	0.883124
$521$	8.39869e6	1.35556	0.677778	−	0.735267i	$-0.262943\pi$
$521$	8.39869e6	1.35556	0.677778	+	0.735267i	$0.262943\pi$
$522$	−1.28608e7	−2.06582
$523$	−1.61748e6	−0.258573	−0.129287	−	0.991607i	$-0.541269\pi$
$523$	−1.61748e6	−0.258573	−0.129287	+	0.991607i	$0.541269\pi$
$524$	−2.49234e7	−3.96532
$525$	−607727.	−0.0962299
$526$	−269925.	−0.0425382
$527$	−3.54509e6	−0.556033
$528$	−3.87693e6	−0.605207
$529$	−6.37221e6	−0.990036
$530$	3.49322e6	0.540177
$531$	−3.59470e6	−0.553256
$532$	1.13133e6	0.173304
$533$	−8.95833e6	−1.36587
$534$	−3.85727e6	−0.585366
$535$	−1.45104e6	−0.219177
$536$	8.38578e6	1.26076
$537$	−5.04086e6	−0.754343
$538$	7.53785e6	1.12277
$539$	−1.78220e6	−0.264231
$540$	−1.13734e6	−0.167844
$541$	6.19660e6	0.910250	0.455125	−	0.890428i	$-0.349595\pi$
$541$	6.19660e6	0.910250	0.455125	+	0.890428i	$0.349595\pi$
$542$	7.97332e6	1.16585
$543$	−1.02603e7	−1.49335
$544$	−1.78607e6	−0.258762
$545$	−4.15479e6	−0.599180
$546$	5.76380e6	0.827422
$547$	1.46936e6	0.209971	0.104985	−	0.994474i	$-0.466520\pi$
$547$	1.46936e6	0.209971	0.104985	+	0.994474i	$0.466520\pi$
$548$	1.29304e7	1.83933
$549$	1.61959e6	0.229337
$550$	−759065.	−0.106997
$551$	2.18211e6	0.306194
$552$	1.99226e6	0.278291
$553$	−2.62210e6	−0.364617
$554$	−1.14998e7	−1.59190
$555$	7.23676e6	0.997268
$556$	2.44739e7	3.35750
$557$	−1.79425e6	−0.245044	−0.122522	−	0.992466i	$-0.539098\pi$
$557$	−1.79425e6	−0.245044	−0.122522	+	0.992466i	$0.539098\pi$
$558$	1.38297e7	1.88030
$559$	−6.75484e6	−0.914293
$560$	−1.71192e6	−0.230682
$561$	−1.40764e6	−0.188836
$562$	2.27164e7	3.03388
$563$	−1.48352e7	−1.97253	−0.986264	−	0.165177i	$-0.947180\pi$
$563$	−1.48352e7	−1.97253	−0.986264	+	0.165177i	$0.947180\pi$
$564$	9.21973e6	1.22045
$565$	4.74045e6	0.624739
$566$	1.91561e7	2.51343
$567$	−2.99162e6	−0.390795
$568$	2.34525e7	3.05013
$569$	9.29345e6	1.20336	0.601681	−	0.798736i	$-0.294498\pi$
$569$	9.29345e6	1.20336	0.601681	+	0.798736i	$0.294498\pi$
$570$	−1.93221e6	−0.249097
$571$	4.53135e6	0.581618	0.290809	−	0.956781i	$-0.406076\pi$
$571$	4.53135e6	0.581618	0.290809	+	0.956781i	$0.406076\pi$
$572$	4.91246e6	0.627782
$573$	1.20604e7	1.53453
$574$	6.94079e6	0.879284
$575$	158274.	0.0199636
$576$	−3.22169e6	−0.404602
$577$	7.13723e6	0.892463	0.446231	−	0.894918i	$-0.352766\pi$
$577$	7.13723e6	0.892463	0.446231	+	0.894918i	$0.352766\pi$
$578$	1.12658e7	1.40262
$579$	−9.06952e6	−1.12432
$580$	−1.03886e7	−1.28229
$581$	−4.63585e6	−0.569756
$582$	−1.10255e7	−1.34924
$583$	1.68445e6	0.205251
$584$	−2.68859e7	−3.26207
$585$	−3.12962e6	−0.378096
$586$	6.36242e6	0.765383
$587$	8.27785e6	0.991567	0.495784	−	0.868446i	$-0.334881\pi$
$587$	8.27785e6	0.991567	0.495784	+	0.868446i	$0.334881\pi$
$588$	2.15979e7	2.57613
$589$	−2.34651e6	−0.278698
$590$	−4.25531e6	−0.503270
$591$	1.32333e7	1.55848
$592$	2.03854e7	2.39065
$593$	348773.	0.0407292	0.0203646	−	0.999793i	$-0.493517\pi$
$593$	348773.	0.0407292	0.0203646	+	0.999793i	$0.493517\pi$
$594$	−803713.	−0.0934619
$595$	−621566.	−0.0719772
$596$	1.94633e7	2.24440
$597$	2.01855e7	2.31795
$598$	−1.50110e6	−0.171655
$599$	−1.17454e7	−1.33753	−0.668763	−	0.743476i	$-0.733176\pi$
$599$	−1.17454e7	−1.33753	−0.668763	+	0.743476i	$0.733176\pi$
$600$	4.91697e6	0.557595
$601$	−883129.	−0.0997328	−0.0498664	−	0.998756i	$-0.515880\pi$
$601$	−883129.	−0.0997328	−0.0498664	+	0.998756i	$0.515880\pi$
$602$	5.23355e6	0.588579
$603$	−4.81954e6	−0.539774
$604$	3.59687e7	4.01174
$605$	−366025.	−0.0406558
$606$	1.12137e7	1.24042
$607$	−8.44501e6	−0.930312	−0.465156	−	0.885229i	$-0.654002\pi$
$607$	−8.44501e6	−0.930312	−0.465156	+	0.885229i	$0.654002\pi$
$608$	−1.18220e6	−0.129698
$609$	−5.87756e6	−0.642176
$610$	1.91723e6	0.208617
$611$	−3.71316e6	−0.402384
$612$	7.94777e6	0.857762
$613$	8.48065e6	0.911545	0.455773	−	0.890096i	$-0.349363\pi$
$613$	8.48065e6	0.911545	0.455773	+	0.890096i	$0.349363\pi$
$614$	−2.03318e7	−2.17648
$615$	−8.08899e6	−0.862396
$616$	−2.03443e6	−0.216019
$617$	−7.16224e6	−0.757418	−0.378709	−	0.925516i	$-0.623632\pi$
$617$	−7.16224e6	−0.757418	−0.378709	+	0.925516i	$0.623632\pi$
$618$	7.23813e6	0.762352
$619$	4.60337e6	0.482891	0.241445	−	0.970414i	$-0.422379\pi$
$619$	4.60337e6	0.482891	0.241445	+	0.970414i	$0.422379\pi$
$620$	1.11712e7	1.16714
$621$	167583.	0.0174382
$622$	1.58484e7	1.64251
$623$	−821310.	−0.0847787
$624$	−1.89221e7	−1.94540
$625$	390625.	0.0400000
$626$	−245332.	−0.0250218
$627$	−931722.	−0.0946493
$628$	−2.99042e7	−3.02575
$629$	7.40156e6	0.745928
$630$	2.42479e6	0.243401
$631$	−3.82415e6	−0.382351	−0.191175	−	0.981556i	$-0.561230\pi$
$631$	−3.82415e6	−0.382351	−0.191175	+	0.981556i	$0.561230\pi$
$632$	2.12148e7	2.11274
$633$	−3.65102e6	−0.362164
$634$	2.41353e7	2.38468
$635$	−7.02867e6	−0.691733
$636$	−2.04133e7	−2.00111
$637$	−8.69835e6	−0.849353
$638$	−7.34122e6	−0.714030
$639$	−1.34788e7	−1.30587
$640$	−6.43359e6	−0.620874
$641$	768138.	0.0738404	0.0369202	−	0.999318i	$-0.488245\pi$
$641$	768138.	0.0738404	0.0369202	+	0.999318i	$0.488245\pi$
$642$	1.24265e7	1.18990
$643$	−1.09863e7	−1.04791	−0.523955	−	0.851746i	$-0.675544\pi$
$643$	−1.09863e7	−1.04791	−0.523955	+	0.851746i	$0.675544\pi$
$644$	793617.	0.0754043
$645$	−6.09933e6	−0.577275
$646$	−1.97621e6	−0.186317
$647$	−2.16555e6	−0.203380	−0.101690	−	0.994816i	$-0.532425\pi$
$647$	−2.16555e6	−0.203380	−0.101690	+	0.994816i	$0.532425\pi$
$648$	2.42045e7	2.26443
$649$	−2.05193e6	−0.191228
$650$	−3.70476e6	−0.343936
$651$	6.32037e6	0.584508
$652$	2.47802e7	2.28289
$653$	1.26384e7	1.15987	0.579936	−	0.814662i	$-0.303078\pi$
$653$	1.26384e7	1.15987	0.579936	+	0.814662i	$0.303078\pi$
$654$	3.55808e7	3.25291
$655$	9.06357e6	0.825460
$656$	−2.27861e7	−2.06733
$657$	1.54521e7	1.39661
$658$	2.87690e6	0.259036
$659$	−4.36646e6	−0.391666	−0.195833	−	0.980637i	$-0.562741\pi$
$659$	−4.36646e6	−0.391666	−0.195833	+	0.980637i	$0.562741\pi$
$660$	4.43574e6	0.396375
$661$	−1.45290e7	−1.29340	−0.646698	−	0.762746i	$-0.723850\pi$
$661$	−1.45290e7	−1.29340	−0.646698	+	0.762746i	$0.723850\pi$
$662$	−5.50443e6	−0.488166
$663$	−6.87027e6	−0.607001
$664$	3.75075e7	3.30140
$665$	−411416.	−0.0360768
$666$	−2.88742e7	−2.52246
$667$	1.53073e6	0.133224
$668$	−4.66994e6	−0.404921
$669$	−1.03422e7	−0.893408
$670$	−5.70524e6	−0.491006
$671$	924498.	0.0792683
$672$	3.18429e6	0.272013
$673$	1.80978e7	1.54024	0.770120	−	0.637900i	$-0.220197\pi$
$673$	1.80978e7	1.54024	0.770120	+	0.637900i	$0.220197\pi$
$674$	−3.76991e7	−3.19655
$675$	413601.	0.0349400
$676$	−1.54868e6	−0.130346
$677$	1.02308e7	0.857904	0.428952	−	0.903327i	$-0.358883\pi$
$677$	1.02308e7	0.857904	0.428952	+	0.903327i	$0.358883\pi$
$678$	−4.05964e7	−3.39167
$679$	−2.34759e6	−0.195411
$680$	5.02894e6	0.417065
$681$	9.63600e6	0.796213
$682$	7.89430e6	0.649909
$683$	1.88068e7	1.54263	0.771317	−	0.636451i	$-0.219598\pi$
$683$	1.88068e7	1.54263	0.771317	+	0.636451i	$0.219598\pi$
$684$	5.26065e6	0.429932
$685$	−4.70223e6	−0.382893
$686$	1.44296e7	1.17069
$687$	−1.66321e6	−0.134448
$688$	−1.71814e7	−1.38384
$689$	8.22126e6	0.659767
$690$	−1.35543e6	−0.108381
$691$	8.82043e6	0.702740	0.351370	−	0.936237i	$-0.385716\pi$
$691$	8.82043e6	0.702740	0.351370	+	0.936237i	$0.385716\pi$
$692$	−1.21417e7	−0.963858
$693$	1.16924e6	0.0924851
$694$	−3.79707e7	−2.99261
$695$	−8.90011e6	−0.698930
$696$	4.75539e7	3.72103
$697$	−8.27320e6	−0.645047
$698$	3.34594e7	2.59944
$699$	2.37588e7	1.83921
$700$	1.95867e6	0.151083
$701$	1.53235e7	1.17778	0.588888	−	0.808214i	$-0.299566\pi$
$701$	1.53235e7	1.17778	0.588888	+	0.808214i	$0.299566\pi$
$702$	−3.92267e6	−0.300427
$703$	4.89911e6	0.373877
$704$	−1.83901e6	−0.139847
$705$	−3.35283e6	−0.254061
$706$	2.82105e7	2.13009
$707$	2.38769e6	0.179651
$708$	2.48667e7	1.86438
$709$	8.01222e6	0.598601	0.299300	−	0.954159i	$-0.403247\pi$
$709$	8.01222e6	0.598601	0.299300	+	0.954159i	$0.403247\pi$
$710$	−1.59558e7	−1.18788
$711$	−1.21927e7	−0.904537
$712$	6.64501e6	0.491243
$713$	−1.64605e6	−0.121261
$714$	5.32298e6	0.390759
$715$	−1.78645e6	−0.130685
$716$	1.62464e7	1.18434
$717$	−2.64628e7	−1.92237
$718$	1.78270e7	1.29053
$719$	2.83978e6	0.204863	0.102431	−	0.994740i	$-0.467338\pi$
$719$	2.83978e6	0.204863	0.102431	+	0.994740i	$0.467338\pi$
$720$	−7.96039e6	−0.572273
$721$	1.54118e6	0.110412
$722$	−1.30806e6	−0.0933867
$723$	3.48626e6	0.248035
$724$	3.30684e7	2.34459
$725$	3.77789e6	0.266934
$726$	3.13457e6	0.220718
$727$	−5.14911e6	−0.361323	−0.180662	−	0.983545i	$-0.557824\pi$
$727$	−5.14911e6	−0.361323	−0.180662	+	0.983545i	$0.557824\pi$
$728$	−9.92943e6	−0.694378
$729$	−1.04809e7	−0.730433
$730$	1.82918e7	1.27042
$731$	−6.23823e6	−0.431785
$732$	−1.12037e7	−0.772830
$733$	−6.56744e6	−0.451477	−0.225739	−	0.974188i	$-0.572480\pi$
$733$	−6.56744e6	−0.451477	−0.225739	+	0.974188i	$0.572480\pi$
$734$	4.61371e7	3.16089
$735$	−7.85424e6	−0.536273
$736$	−829305.	−0.0564312
$737$	−2.75109e6	−0.186568
$738$	3.22745e7	2.18132
$739$	−1.85326e7	−1.24832	−0.624159	−	0.781297i	$-0.714558\pi$
$739$	−1.85326e7	−1.24832	−0.624159	+	0.781297i	$0.714558\pi$
$740$	−2.33237e7	−1.56574
$741$	−4.54745e6	−0.304244
$742$	−6.36972e6	−0.424727
$743$	−2.11163e7	−1.40329	−0.701643	−	0.712529i	$-0.747550\pi$
$743$	−2.11163e7	−1.40329	−0.701643	+	0.712529i	$0.747550\pi$
$744$	−5.11366e7	−3.38688
$745$	−7.07797e6	−0.467216
$746$	−2.35627e7	−1.55017
$747$	−2.15566e7	−1.41345
$748$	4.53676e6	0.296477
$749$	2.64590e6	0.172333
$750$	−3.34524e6	−0.217157
$751$	−1.42227e7	−0.920199	−0.460100	−	0.887867i	$-0.652186\pi$
$751$	−1.42227e7	−0.920199	−0.460100	+	0.887867i	$0.652186\pi$
$752$	−9.44466e6	−0.609034
$753$	−1.90760e7	−1.22603
$754$	−3.58302e7	−2.29520
$755$	−1.30803e7	−0.835122
$756$	2.07388e6	0.131971
$757$	−2.88203e7	−1.82792	−0.913962	−	0.405800i	$-0.866993\pi$
$757$	−2.88203e7	−1.82792	−0.913962	+	0.405800i	$0.866993\pi$
$758$	−1.08070e6	−0.0683176
$759$	−653595.	−0.0411817
$760$	3.32867e6	0.209043
$761$	−1.53179e6	−0.0958823	−0.0479412	−	0.998850i	$-0.515266\pi$
$761$	−1.53179e6	−0.0958823	−0.0479412	+	0.998850i	$0.515266\pi$
$762$	6.01922e7	3.75537
$763$	7.57605e6	0.471120
$764$	−3.88700e7	−2.40925
$765$	−2.89027e6	−0.178560
$766$	−3.62008e7	−2.22918
$767$	−1.00148e7	−0.614690
$768$	4.47222e7	2.73603
$769$	−1.87825e7	−1.14535	−0.572675	−	0.819782i	$-0.694094\pi$
$769$	−1.87825e7	−1.14535	−0.572675	+	0.819782i	$0.694094\pi$
$770$	1.38412e6	0.0841292
$771$	−2.98710e7	−1.80973
$772$	2.92306e7	1.76520
$773$	−9.97295e6	−0.600309	−0.300155	−	0.953891i	$-0.597038\pi$
$773$	−9.97295e6	−0.600309	−0.300155	+	0.953891i	$0.597038\pi$
$774$	2.43359e7	1.46014
$775$	−4.06251e6	−0.242963
$776$	1.89938e7	1.13229
$777$	−1.31959e7	−0.784126
$778$	−2.47588e7	−1.46649
$779$	−5.47606e6	−0.323314
$780$	2.16495e7	1.27412
$781$	−7.69398e6	−0.451360
$782$	−1.38630e6	−0.0810661
$783$	4.00010e6	0.233167
$784$	−2.21248e7	−1.28555
$785$	1.08749e7	0.629870
$786$	−7.76188e7	−4.48137
$787$	−2.21631e7	−1.27554	−0.637770	−	0.770227i	$-0.720143\pi$
$787$	−2.21631e7	−1.27554	−0.637770	+	0.770227i	$0.720143\pi$
$788$	−4.26503e7	−2.44684
$789$	−573619.	−0.0328043
$790$	−1.44334e7	−0.822813
$791$	−8.64399e6	−0.491217
$792$	−9.46006e6	−0.535897
$793$	4.51219e6	0.254803
$794$	−3.47910e6	−0.195846
$795$	7.42345e6	0.416570
$796$	−6.50569e7	−3.63924
$797$	−2.27378e7	−1.26795	−0.633976	−	0.773353i	$-0.718578\pi$
$797$	−2.27378e7	−1.26795	−0.633976	+	0.773353i	$0.718578\pi$
$798$	3.52330e6	0.195858
$799$	−3.42918e6	−0.190030
$800$	−2.04675e6	−0.113068
$801$	−3.81907e6	−0.210318
$802$	3.30795e7	1.81603
$803$	8.82038e6	0.482724
$804$	3.33397e7	1.81895
$805$	−288605.	−0.0156969
$806$	3.85296e7	2.08909
$807$	1.60187e7	0.865852
$808$	−1.93182e7	−1.04097
$809$	−1.89079e7	−1.01571	−0.507857	−	0.861441i	$-0.669562\pi$
$809$	−1.89079e7	−1.01571	−0.507857	+	0.861441i	$0.669562\pi$
$810$	−1.64674e7	−0.881889
$811$	2.13760e7	1.14123	0.570617	−	0.821216i	$-0.306704\pi$
$811$	2.13760e7	1.14123	0.570617	+	0.821216i	$0.306704\pi$
$812$	1.89431e7	1.00823
$813$	1.69441e7	0.899069
$814$	−1.64820e7	−0.871864
$815$	−9.01150e6	−0.475229
$816$	−1.74750e7	−0.918736
$817$	−4.12910e6	−0.216421
$818$	−2.55358e7	−1.33434
$819$	5.70672e6	0.297287
$820$	2.60704e7	1.35398
$821$	−3.59719e6	−0.186254	−0.0931269	−	0.995654i	$-0.529686\pi$
$821$	−3.59719e6	−0.186254	−0.0931269	+	0.995654i	$0.529686\pi$
$822$	4.02690e7	2.07870
$823$	1.79216e7	0.922308	0.461154	−	0.887320i	$-0.347436\pi$
$823$	1.79216e7	0.922308	0.461154	+	0.887320i	$0.347436\pi$
$824$	−1.24693e7	−0.639770
$825$	−1.61309e6	−0.0825134
$826$	7.75936e6	0.395709
$827$	−9.95628e6	−0.506213	−0.253106	−	0.967438i	$-0.581452\pi$
$827$	−9.95628e6	−0.506213	−0.253106	+	0.967438i	$0.581452\pi$
$828$	3.69030e6	0.187062
$829$	−1.70509e7	−0.861711	−0.430855	−	0.902421i	$-0.641788\pi$
$829$	−1.70509e7	−0.861711	−0.430855	+	0.902421i	$0.641788\pi$
$830$	−2.55181e7	−1.28574
$831$	−2.44383e7	−1.22763
$832$	−8.97565e6	−0.449529
$833$	−8.03310e6	−0.401116
$834$	7.62190e7	3.79444
$835$	1.69826e6	0.0842923
$836$	3.00289e6	0.148602
$837$	−4.30146e6	−0.212228
$838$	3.31822e6	0.163228
$839$	833322.	0.0408703	0.0204352	−	0.999791i	$-0.493495\pi$
$839$	833322.	0.0408703	0.0204352	+	0.999791i	$0.493495\pi$
$840$	−8.96585e6	−0.438423
$841$	1.60263e7	0.781344
$842$	2.42640e7	1.17946
$843$	4.82746e7	2.33965
$844$	1.17670e7	0.568606
$845$	563191.	0.0271340
$846$	1.33775e7	0.642614
$847$	667429.	0.0319666
$848$	2.09113e7	0.998600
$849$	4.07087e7	1.93829
$850$	−3.42142e6	−0.162427
$851$	3.43669e6	0.162673
$852$	9.32409e7	4.40056
$853$	3.98036e7	1.87305	0.936525	−	0.350600i	$-0.114022\pi$
$853$	3.98036e7	1.87305	0.936525	+	0.350600i	$0.114022\pi$
$854$	−3.49598e6	−0.164030
$855$	−1.91308e6	−0.0894988
$856$	−2.14074e7	−0.998570
$857$	−2.44196e7	−1.13576	−0.567880	−	0.823111i	$-0.692236\pi$
$857$	−2.44196e7	−1.13576	−0.567880	+	0.823111i	$0.692236\pi$
$858$	1.52989e7	0.709482
$859$	1.05741e7	0.488946	0.244473	−	0.969656i	$-0.421385\pi$
$859$	1.05741e7	0.488946	0.244473	+	0.969656i	$0.421385\pi$
$860$	1.96578e7	0.906336
$861$	1.47499e7	0.678080
$862$	3.08998e7	1.41640
$863$	−1.89897e7	−0.867941	−0.433971	−	0.900927i	$-0.642888\pi$
$863$	−1.89897e7	−0.867941	−0.433971	+	0.900927i	$0.642888\pi$
$864$	−2.16714e6	−0.0987648
$865$	4.41541e6	0.200646
$866$	−4.21449e7	−1.90964
$867$	2.39409e7	1.08167
$868$	−2.03702e7	−0.917691
$869$	−6.95986e6	−0.312645
$870$	−3.23532e7	−1.44917
$871$	−1.34272e7	−0.599710
$872$	−6.12960e7	−2.72986
$873$	−1.09163e7	−0.484773
$874$	−917594.	−0.0406323
$875$	−712286.	−0.0314510
$876$	−1.06891e8	−4.70633
$877$	−5.23888e6	−0.230006	−0.115003	−	0.993365i	$-0.536688\pi$
$877$	−5.23888e6	−0.230006	−0.115003	+	0.993365i	$0.536688\pi$
$878$	−3.41448e7	−1.49482
$879$	1.35208e7	0.590243
$880$	−4.54396e6	−0.197801
$881$	3.24651e7	1.40922	0.704608	−	0.709597i	$-0.251123\pi$
$881$	3.24651e7	1.40922	0.704608	+	0.709597i	$0.251123\pi$
$882$	3.13378e7	1.35643
$883$	1.58932e7	0.685979	0.342990	−	0.939339i	$-0.388560\pi$
$883$	1.58932e7	0.685979	0.342990	+	0.939339i	$0.388560\pi$
$884$	2.21425e7	0.953007
$885$	−9.04298e6	−0.388109
$886$	1.04425e7	0.446911
$887$	−3.41180e7	−1.45604	−0.728022	−	0.685553i	$-0.759560\pi$
$887$	−3.41180e7	−1.45604	−0.728022	+	0.685553i	$0.759560\pi$
$888$	1.06765e8	4.54355
$889$	1.28164e7	0.543892
$890$	−4.52092e6	−0.191316
$891$	−7.94068e6	−0.335092
$892$	3.33325e7	1.40267
$893$	−2.26978e6	−0.0952479
$894$	6.06145e7	2.53649
$895$	−5.90814e6	−0.246543
$896$	1.17314e7	0.488178
$897$	−3.19000e6	−0.132376
$898$	−5.74890e7	−2.37900
$899$	−3.92901e7	−1.62138
$900$	9.10778e6	0.374806
$901$	7.59250e6	0.311582
$902$	1.84230e7	0.753952
$903$	1.11218e7	0.453897
$904$	6.99364e7	2.84631
$905$	−1.20256e7	−0.488073
$906$	1.12017e8	4.53382
$907$	3.87957e7	1.56590	0.782952	−	0.622082i	$-0.213713\pi$
$907$	3.87957e7	1.56590	0.782952	+	0.622082i	$0.213713\pi$
$908$	−3.10563e7	−1.25007
$909$	1.11027e7	0.445675
$910$	6.75546e6	0.270428
$911$	−1.64385e7	−0.656244	−0.328122	−	0.944635i	$-0.606416\pi$
$911$	−1.64385e7	−0.656244	−0.328122	+	0.944635i	$0.606416\pi$
$912$	−1.15667e7	−0.460493
$913$	−1.23050e7	−0.488544
$914$	7.22989e7	2.86264
$915$	4.07432e6	0.160880
$916$	5.36043e6	0.211087
$917$	−1.65270e7	−0.649038
$918$	−3.62267e6	−0.141880
$919$	4.37235e7	1.70776	0.853879	−	0.520472i	$-0.174244\pi$
$919$	4.37235e7	1.70776	0.853879	+	0.520472i	$0.174244\pi$
$920$	2.33503e6	0.0909543
$921$	−4.32071e7	−1.67844
$922$	−7.60123e6	−0.294481
$923$	−3.75519e7	−1.45087
$924$	−8.08837e6	−0.311660
$925$	8.48185e6	0.325939
$926$	6.07027e7	2.32638
$927$	7.16645e6	0.273908
$928$	−1.97949e7	−0.754542
$929$	1.15292e6	0.0438288	0.0219144	−	0.999760i	$-0.493024\pi$
$929$	1.15292e6	0.0438288	0.0219144	+	0.999760i	$0.493024\pi$
$930$	3.47906e7	1.31903
$931$	−5.31713e6	−0.201050
$932$	−7.65733e7	−2.88760
$933$	3.36794e7	1.26666
$934$	−2.78595e7	−1.04497
$935$	−1.64983e6	−0.0617176
$936$	−4.61716e7	−1.72260
$937$	−3.33100e7	−1.23944	−0.619719	−	0.784823i	$-0.712754\pi$
$937$	−3.33100e7	−1.23944	−0.619719	+	0.784823i	$0.712754\pi$
$938$	1.04032e7	0.386066
$939$	−521356.	−0.0192961
$940$	1.08060e7	0.398882
$941$	−1.53770e7	−0.566107	−0.283053	−	0.959104i	$-0.591347\pi$
$941$	−1.53770e7	−0.566107	−0.283053	+	0.959104i	$0.591347\pi$
$942$	−9.31307e7	−3.41952
$943$	−3.84140e6	−0.140673
$944$	−2.54734e7	−0.930372
$945$	−754182.	−0.0274724
$946$	1.38914e7	0.504684
$947$	−1.30035e7	−0.471177	−0.235589	−	0.971853i	$-0.575702\pi$
$947$	−1.30035e7	−0.471177	−0.235589	+	0.971853i	$0.575702\pi$
$948$	8.43444e7	3.04814
$949$	4.30496e7	1.55168
$950$	−2.26465e6	−0.0814127
$951$	5.12901e7	1.83900
$952$	−9.17003e6	−0.327928
$953$	1.56383e7	0.557772	0.278886	−	0.960324i	$-0.410035\pi$
$953$	1.56383e7	0.557772	0.278886	+	0.960324i	$0.410035\pi$
$954$	−2.96190e7	−1.05366
$955$	1.41354e7	0.501533
$956$	8.52881e7	3.01817
$957$	−1.56008e7	−0.550641
$958$	9.09008e7	3.20003
$959$	8.57428e6	0.301059
$960$	−8.10463e6	−0.283828
$961$	1.36211e7	0.475776
$962$	−8.04435e7	−2.80255
$963$	1.23034e7	0.427523
$964$	−1.12360e7	−0.389422
$965$	−1.06299e7	−0.367462
$966$	2.47156e6	0.0852175
$967$	3.26283e7	1.12209	0.561046	−	0.827785i	$-0.310399\pi$
$967$	3.26283e7	1.12209	0.561046	+	0.827785i	$0.310399\pi$
$968$	−5.40000e6	−0.185228
$969$	−4.19966e6	−0.143683
$970$	−1.29224e7	−0.440974
$971$	2.99551e7	1.01958	0.509792	−	0.860298i	$-0.329722\pi$
$971$	2.99551e7	1.01958	0.509792	+	0.860298i	$0.329722\pi$
$972$	8.51758e7	2.89168
$973$	1.62289e7	0.549551
$974$	9.22194e6	0.311476
$975$	−7.87301e6	−0.265234
$976$	1.14770e7	0.385661
$977$	2.68540e7	0.900063	0.450031	−	0.893013i	$-0.351413\pi$
$977$	2.68540e7	0.900063	0.450031	+	0.893013i	$0.351413\pi$
$978$	7.71729e7	2.57999
$979$	−2.18001e6	−0.0726944
$980$	2.53138e7	0.841961
$981$	3.52285e7	1.16875
$982$	3.00751e7	0.995241
$983$	4.78145e6	0.157825	0.0789125	−	0.996882i	$-0.474855\pi$
$983$	4.78145e6	0.157825	0.0789125	+	0.996882i	$0.474855\pi$
$984$	−1.19338e8	−3.92907
$985$	1.55101e7	0.509359
$986$	−3.30899e7	−1.08394
$987$	6.11372e6	0.199762
$988$	1.46562e7	0.477671
$989$	−2.89653e6	−0.0941644
$990$	6.43612e6	0.208707
$991$	−5.75490e7	−1.86146	−0.930730	−	0.365706i	$-0.880827\pi$
$991$	−5.75490e7	−1.86146	−0.930730	+	0.365706i	$0.880827\pi$
$992$	2.12863e7	0.686784
$993$	−1.16975e7	−0.376460
$994$	2.90947e7	0.934002
$995$	2.36584e7	0.757580
$996$	1.49120e8	4.76308
$997$	−1.55769e7	−0.496298	−0.248149	−	0.968722i	$-0.579822\pi$
$997$	−1.55769e7	−0.496298	−0.248149	+	0.968722i	$0.579822\pi$
$998$	−3.52019e6	−0.111877
$999$	8.98074e6	0.284707

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.a.1.2	✓	35

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.a.1.2	✓	35	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)

\(f(q)\)	\(=\)	\(q-10.0372 q^{2} -21.3301 q^{3} +68.7460 q^{4} -25.0000 q^{5} +214.096 q^{6} +45.5863 q^{7} -368.828 q^{8} +211.975 q^{9} +O(q^{10})\)	\(q-10.0372 q^{2} -21.3301 q^{3} +68.7460 q^{4} -25.0000 q^{5} +214.096 q^{6} +45.5863 q^{7} -368.828 q^{8} +211.975 q^{9} +250.931 q^{10} +121.000 q^{11} -1466.36 q^{12} +590.564 q^{13} -457.560 q^{14} +533.254 q^{15} +1502.14 q^{16} +545.397 q^{17} -2127.64 q^{18} +361.000 q^{19} -1718.65 q^{20} -972.363 q^{21} -1214.50 q^{22} +253.238 q^{23} +7867.15 q^{24} +625.000 q^{25} -5927.62 q^{26} +661.762 q^{27} +3133.87 q^{28} +6044.62 q^{29} -5352.39 q^{30} -6500.02 q^{31} -3274.80 q^{32} -2580.95 q^{33} -5474.28 q^{34} -1139.66 q^{35} +14572.4 q^{36} +13571.0 q^{37} -3623.44 q^{38} -12596.8 q^{39} +9220.69 q^{40} -15169.1 q^{41} +9759.83 q^{42} -11437.9 q^{43} +8318.26 q^{44} -5299.38 q^{45} -2541.81 q^{46} -6287.49 q^{47} -32040.8 q^{48} -14728.9 q^{49} -6273.27 q^{50} -11633.4 q^{51} +40598.9 q^{52} +13921.0 q^{53} -6642.26 q^{54} -3025.00 q^{55} -16813.5 q^{56} -7700.18 q^{57} -60671.2 q^{58} -16958.1 q^{59} +36659.0 q^{60} +7640.48 q^{61} +65242.2 q^{62} +9663.17 q^{63} -15198.4 q^{64} -14764.1 q^{65} +25905.6 q^{66} -22736.3 q^{67} +37493.9 q^{68} -5401.61 q^{69} +11439.0 q^{70} -63586.6 q^{71} -78182.3 q^{72} +72895.7 q^{73} -136215. q^{74} -13331.3 q^{75} +24817.3 q^{76} +5515.94 q^{77} +126437. q^{78} -57519.5 q^{79} -37553.4 q^{80} -65625.5 q^{81} +152256. q^{82} -101694. q^{83} -66846.0 q^{84} -13634.9 q^{85} +114805. q^{86} -128933. q^{87} -44628.1 q^{88} -18016.6 q^{89} +53191.1 q^{90} +26921.6 q^{91} +17409.1 q^{92} +138646. q^{93} +63108.9 q^{94} -9025.00 q^{95} +69852.0 q^{96} -51497.8 q^{97} +147837. q^{98} +25649.0 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9}+O(q^{10}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9	\( 35 q - 4 q^{2} - 27 q^{3} + 520 q^{4} - 875 q^{5} - 291 q^{6} + 117 q^{7} - 498 q^{8} + 2046 q^{9} + 100 q^{10} + 4235 q^{11} - 568 q^{12} - 717 q^{13} - 2585 q^{14} + 675 q^{15} + 3356 q^{16} - 3349 q^{17} - 5533 q^{18} + 12635 q^{19} - 13000 q^{20} + 289 q^{21} - 484 q^{22} - 820 q^{23} - 21748 q^{24} + 21875 q^{25} - 6267 q^{26} - 13650 q^{27} - 6487 q^{28} - 13357 q^{29} + 7275 q^{30} - 15341 q^{31} - 16405 q^{32} - 3267 q^{33} - 1255 q^{34} - 2925 q^{35} + 23487 q^{36} - 511 q^{37} - 1444 q^{38} - 33584 q^{39} + 12450 q^{40} - 36855 q^{41} + 16330 q^{42} + 10991 q^{43} + 62920 q^{44} - 51150 q^{45} - 20443 q^{46} - 33594 q^{47} + 36221 q^{48} + 23422 q^{49} - 2500 q^{50} - 53530 q^{51} + 89382 q^{52} + 13103 q^{53} + 65776 q^{54} - 105875 q^{55} + 130911 q^{56} - 9747 q^{57} + 127808 q^{58} - 161139 q^{59} + 14200 q^{60} - 91587 q^{61} + 131818 q^{62} + 16590 q^{63} - 23186 q^{64} + 17925 q^{65} - 35211 q^{66} + 39210 q^{67} + 26300 q^{68} - 23174 q^{69} + 64625 q^{70} - 167772 q^{71} + 135820 q^{72} - 5106 q^{73} - 256965 q^{74} - 16875 q^{75} + 187720 q^{76} + 14157 q^{77} + 492812 q^{78} - 156897 q^{79} - 83900 q^{80} + 31279 q^{81} + 46818 q^{82} - 185627 q^{83} + 165864 q^{84} + 83725 q^{85} - 159946 q^{86} - 112092 q^{87} - 60258 q^{88} - 144420 q^{89} + 138325 q^{90} - 442480 q^{91} - 205876 q^{92} + 125910 q^{93} - 110044 q^{94} - 315875 q^{95} - 554286 q^{96} + 41200 q^{97} + 41052 q^{98} + 247566 q^{99}+O(q^{100}) \) 35 * q - 4 * q^2 - 27 * q^3 + 520 * q^4 - 875 * q^5 - 291 * q^6 + 117 * q^7 - 498 * q^8 + 2046 * q^9 + 100 * q^10 + 4235 * q^11 - 568 * q^12 - 717 * q^13 - 2585 * q^14 + 675 * q^15 + 3356 * q^16 - 3349 * q^17 - 5533 * q^18 + 12635 * q^19 - 13000 * q^20 + 289 * q^21 - 484 * q^22 - 820 * q^23 - 21748 * q^24 + 21875 * q^25 - 6267 * q^26 - 13650 * q^27 - 6487 * q^28 - 13357 * q^29 + 7275 * q^30 - 15341 * q^31 - 16405 * q^32 - 3267 * q^33 - 1255 * q^34 - 2925 * q^35 + 23487 * q^36 - 511 * q^37 - 1444 * q^38 - 33584 * q^39 + 12450 * q^40 - 36855 * q^41 + 16330 * q^42 + 10991 * q^43 + 62920 * q^44 - 51150 * q^45 - 20443 * q^46 - 33594 * q^47 + 36221 * q^48 + 23422 * q^49 - 2500 * q^50 - 53530 * q^51 + 89382 * q^52 + 13103 * q^53 + 65776 * q^54 - 105875 * q^55 + 130911 * q^56 - 9747 * q^57 + 127808 * q^58 - 161139 * q^59 + 14200 * q^60 - 91587 * q^61 + 131818 * q^62 + 16590 * q^63 - 23186 * q^64 + 17925 * q^65 - 35211 * q^66 + 39210 * q^67 + 26300 * q^68 - 23174 * q^69 + 64625 * q^70 - 167772 * q^71 + 135820 * q^72 - 5106 * q^73 - 256965 * q^74 - 16875 * q^75 + 187720 * q^76 + 14157 * q^77 + 492812 * q^78 - 156897 * q^79 - 83900 * q^80 + 31279 * q^81 + 46818 * q^82 - 185627 * q^83 + 165864 * q^84 + 83725 * q^85 - 159946 * q^86 - 112092 * q^87 - 60258 * q^88 - 144420 * q^89 + 138325 * q^90 - 442480 * q^91 - 205876 * q^92 + 125910 * q^93 - 110044 * q^94 - 315875 * q^95 - 554286 * q^96 + 41200 * q^97 + 41052 * q^98 + 247566 * q^99

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