LMFDB - Embedded newform 1045.6.a.b.1.1

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			1.1
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)

$f(q)$	$=$	$q-10.8010 q^{2} -21.4786 q^{3} +84.6626 q^{4} +25.0000 q^{5} +231.991 q^{6} +40.5180 q^{7} -568.812 q^{8} +218.330 q^{9} +O(q^{10})$	\(q-10.8010 q^{2} -21.4786 q^{3} +84.6626 q^{4} +25.0000 q^{5} +231.991 q^{6} +40.5180 q^{7} -568.812 q^{8} +218.330 q^{9} -270.026 q^{10} -121.000 q^{11} -1818.43 q^{12} +266.356 q^{13} -437.637 q^{14} -536.965 q^{15} +3434.56 q^{16} -765.694 q^{17} -2358.19 q^{18} +361.000 q^{19} +2116.57 q^{20} -870.270 q^{21} +1306.93 q^{22} -2104.23 q^{23} +12217.3 q^{24} +625.000 q^{25} -2876.93 q^{26} +529.886 q^{27} +3430.36 q^{28} +4320.60 q^{29} +5799.78 q^{30} +9451.55 q^{31} -18894.9 q^{32} +2598.91 q^{33} +8270.29 q^{34} +1012.95 q^{35} +18484.4 q^{36} -1913.25 q^{37} -3899.18 q^{38} -5720.96 q^{39} -14220.3 q^{40} -10474.5 q^{41} +9399.83 q^{42} +8259.66 q^{43} -10244.2 q^{44} +5458.24 q^{45} +22727.9 q^{46} -20438.0 q^{47} -73769.5 q^{48} -15165.3 q^{49} -6750.66 q^{50} +16446.0 q^{51} +22550.4 q^{52} +1689.21 q^{53} -5723.32 q^{54} -3025.00 q^{55} -23047.1 q^{56} -7753.77 q^{57} -46667.0 q^{58} +19621.6 q^{59} -45460.8 q^{60} +20540.7 q^{61} -102087. q^{62} +8846.28 q^{63} +94178.4 q^{64} +6658.91 q^{65} -28070.9 q^{66} +28781.8 q^{67} -64825.7 q^{68} +45196.0 q^{69} -10940.9 q^{70} -74436.2 q^{71} -124188. q^{72} -79844.4 q^{73} +20665.1 q^{74} -13424.1 q^{75} +30563.2 q^{76} -4902.68 q^{77} +61792.3 q^{78} -7275.68 q^{79} +85864.0 q^{80} -64435.3 q^{81} +113135. q^{82} -70099.9 q^{83} -73679.4 q^{84} -19142.3 q^{85} -89213.0 q^{86} -92800.3 q^{87} +68826.2 q^{88} +47503.7 q^{89} -58954.7 q^{90} +10792.2 q^{91} -178150. q^{92} -203006. q^{93} +220751. q^{94} +9025.00 q^{95} +405835. q^{96} -91334.3 q^{97} +163801. q^{98} -26417.9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.8010	−1.90937	−0.954687	−	0.297612i	$-0.903810\pi$
$2$	−10.8010	−1.90937	−0.954687	+	0.297612i	$0.903810\pi$
$3$	−21.4786	−1.37785	−0.688926	−	0.724832i	$-0.741917\pi$
$3$	−21.4786	−1.37785	−0.688926	+	0.724832i	$0.741917\pi$
$4$	84.6626	2.64571
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	231.991	2.63083
$7$	40.5180	0.312538	0.156269	−	0.987715i	$-0.450053\pi$
$7$	40.5180	0.312538	0.156269	+	0.987715i	$0.450053\pi$
$8$	−568.812	−3.14227
$9$	218.330	0.898476
$10$	−270.026	−0.853898
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	−1818.43	−3.64539
$13$	266.356	0.437124	0.218562	−	0.975823i	$-0.429863\pi$
$13$	266.356	0.437124	0.218562	+	0.975823i	$0.429863\pi$
$14$	−437.637	−0.596752
$15$	−536.965	−0.616194
$16$	3434.56	3.35406
$17$	−765.694	−0.642588	−0.321294	−	0.946979i	$-0.604118\pi$
$17$	−765.694	−0.642588	−0.321294	+	0.946979i	$0.604118\pi$
$18$	−2358.19	−1.71553
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	2116.57	1.18320
$21$	−870.270	−0.430631
$22$	1306.93	0.575698
$23$	−2104.23	−0.829420	−0.414710	−	0.909954i	$-0.636117\pi$
$23$	−2104.23	−0.829420	−0.414710	+	0.909954i	$0.636117\pi$
$24$	12217.3	4.32958
$25$	625.000	0.200000
$26$	−2876.93	−0.834633
$27$	529.886	0.139885
$28$	3430.36	0.826885
$29$	4320.60	0.954001	0.477001	−	0.878903i	$-0.341724\pi$
$29$	4320.60	0.954001	0.477001	+	0.878903i	$0.341724\pi$
$30$	5799.78	1.17654
$31$	9451.55	1.76644	0.883220	−	0.468960i	$-0.155371\pi$
$31$	9451.55	1.76644	0.883220	+	0.468960i	$0.155371\pi$
$32$	−18894.9	−3.26189
$33$	2598.91	0.415438
$34$	8270.29	1.22694
$35$	1012.95	0.139771
$36$	18484.4	2.37710
$37$	−1913.25	−0.229756	−0.114878	−	0.993380i	$-0.536648\pi$
$37$	−1913.25	−0.229756	−0.114878	+	0.993380i	$0.536648\pi$
$38$	−3899.18	−0.438040
$39$	−5720.96	−0.602292
$40$	−14220.3	−1.40527
$41$	−10474.5	−0.973134	−0.486567	−	0.873643i	$-0.661751\pi$
$41$	−10474.5	−0.973134	−0.486567	+	0.873643i	$0.661751\pi$
$42$	9399.83	0.822236
$43$	8259.66	0.681226	0.340613	−	0.940204i	$-0.389365\pi$
$43$	8259.66	0.681226	0.340613	+	0.940204i	$0.389365\pi$
$44$	−10244.2	−0.797711
$45$	5458.24	0.401811
$46$	22727.9	1.58367
$47$	−20438.0	−1.34956	−0.674781	−	0.738018i	$-0.735762\pi$
$47$	−20438.0	−1.34956	−0.674781	+	0.738018i	$0.735762\pi$
$48$	−73769.5	−4.62140
$49$	−15165.3	−0.902320
$50$	−6750.66	−0.381875
$51$	16446.0	0.885391
$52$	22550.4	1.15650
$53$	1689.21	0.0826028	0.0413014	−	0.999147i	$-0.486850\pi$
$53$	1689.21	0.0826028	0.0413014	+	0.999147i	$0.486850\pi$
$54$	−5723.32	−0.267094
$55$	−3025.00	−0.134840
$56$	−23047.1	−0.982080
$57$	−7753.77	−0.316101
$58$	−46667.0	−1.82154
$59$	19621.6	0.733844	0.366922	−	0.930252i	$-0.380412\pi$
$59$	19621.6	0.733844	0.366922	+	0.930252i	$0.380412\pi$
$60$	−45460.8	−1.63027
$61$	20540.7	0.706790	0.353395	−	0.935474i	$-0.385027\pi$
$61$	20540.7	0.706790	0.353395	+	0.935474i	$0.385027\pi$
$62$	−102087.	−3.37279
$63$	8846.28	0.280808
$64$	94178.4	2.87410
$65$	6658.91	0.195488
$66$	−28070.9	−0.793226
$67$	28781.8	0.783306	0.391653	−	0.920113i	$-0.371903\pi$
$67$	28781.8	0.783306	0.391653	+	0.920113i	$0.371903\pi$
$68$	−64825.7	−1.70010
$69$	45196.0	1.14282
$70$	−10940.9	−0.266876
$71$	−74436.2	−1.75242	−0.876211	−	0.481928i	$-0.839937\pi$
$71$	−74436.2	−1.75242	−0.876211	+	0.481928i	$0.839937\pi$
$72$	−124188.	−2.82325
$73$	−79844.4	−1.75363	−0.876814	−	0.480830i	$-0.840336\pi$
$73$	−79844.4	−1.75363	−0.876814	+	0.480830i	$0.840336\pi$
$74$	20665.1	0.438691
$75$	−13424.1	−0.275570
$76$	30563.2	0.606967
$77$	−4902.68	−0.0942338
$78$	61792.3	1.15000
$79$	−7275.68	−0.131161	−0.0655806	−	0.997847i	$-0.520890\pi$
$79$	−7275.68	−0.131161	−0.0655806	+	0.997847i	$0.520890\pi$
$80$	85864.0	1.49998
$81$	−64435.3	−1.09122
$82$	113135.	1.85808
$83$	−70099.9	−1.11692	−0.558460	−	0.829531i	$-0.688608\pi$
$83$	−70099.9	−1.11692	−0.558460	+	0.829531i	$0.688608\pi$
$84$	−73679.4	−1.13932
$85$	−19142.3	−0.287374
$86$	−89213.0	−1.30071
$87$	−92800.3	−1.31447
$88$	68826.2	0.947430
$89$	47503.7	0.635700	0.317850	−	0.948141i	$-0.397039\pi$
$89$	47503.7	0.635700	0.317850	+	0.948141i	$0.397039\pi$
$90$	−58954.7	−0.767206
$91$	10792.2	0.136618
$92$	−178150.	−2.19440
$93$	−203006.	−2.43389
$94$	220751.	2.57682
$95$	9025.00	0.102598
$96$	405835.	4.49440
$97$	−91334.3	−0.985609	−0.492804	−	0.870140i	$-0.664028\pi$
$97$	−91334.3	−0.985609	−0.492804	+	0.870140i	$0.664028\pi$
$98$	163801.	1.72287
$99$	−26417.9	−0.270901
$100$	52914.2	0.529142
$101$	39524.1	0.385530	0.192765	−	0.981245i	$-0.438254\pi$
$101$	39524.1	0.385530	0.192765	+	0.981245i	$0.438254\pi$
$102$	−177634.	−1.69054
$103$	−30451.9	−0.282827	−0.141413	−	0.989951i	$-0.545165\pi$
$103$	−30451.9	−0.282827	−0.141413	+	0.989951i	$0.545165\pi$
$104$	−151507.	−1.37356
$105$	−21756.7	−0.192584
$106$	−18245.3	−0.157720
$107$	62718.7	0.529588	0.264794	−	0.964305i	$-0.414696\pi$
$107$	62718.7	0.529588	0.264794	+	0.964305i	$0.414696\pi$
$108$	44861.5	0.370096
$109$	102461.	0.826024	0.413012	−	0.910726i	$-0.364477\pi$
$109$	102461.	0.826024	0.413012	+	0.910726i	$0.364477\pi$
$110$	32673.2	0.257460
$111$	41093.9	0.316570
$112$	139162.	1.04827
$113$	186314.	1.37261	0.686307	−	0.727312i	$-0.259231\pi$
$113$	186314.	1.37261	0.686307	+	0.727312i	$0.259231\pi$
$114$	83748.8	0.603555
$115$	−52605.8	−0.370928
$116$	365793.	2.52401
$117$	58153.5	0.392745
$118$	−211933.	−1.40118
$119$	−31024.4	−0.200833
$120$	305432.	1.93625
$121$	14641.0	0.0909091
$122$	−221861.	−1.34953
$123$	224977.	1.34083
$124$	800193.	4.67348
$125$	15625.0	0.0894427
$126$	−95549.1	−0.536167
$127$	−122306.	−0.672881	−0.336440	−	0.941705i	$-0.609223\pi$
$127$	−122306.	−0.672881	−0.336440	+	0.941705i	$0.609223\pi$
$128$	−412590.	−2.22584
$129$	−177406.	−0.938628
$130$	−71923.2	−0.373259
$131$	385181.	1.96104	0.980519	−	0.196423i	$-0.0629326\pi$
$131$	385181.	1.96104	0.980519	+	0.196423i	$0.0629326\pi$
$132$	220030.	1.09913
$133$	14627.0	0.0717012
$134$	−310874.	−1.49562
$135$	13247.1	0.0625587
$136$	435536.	2.01919
$137$	4972.43	0.0226343	0.0113172	−	0.999936i	$-0.496398\pi$
$137$	4972.43	0.0226343	0.0113172	+	0.999936i	$0.496398\pi$
$138$	−488164.	−2.18207
$139$	−19015.6	−0.0834783	−0.0417391	−	0.999129i	$-0.513290\pi$
$139$	−19015.6	−0.0834783	−0.0417391	+	0.999129i	$0.513290\pi$
$140$	85759.1	0.369794
$141$	438978.	1.85950
$142$	803989.	3.34603
$143$	−32229.1	−0.131798
$144$	749866.	3.01354
$145$	108015.	0.426642
$146$	862404.	3.34833
$147$	325729.	1.24326
$148$	−161981.	−0.607868
$149$	−148759.	−0.548931	−0.274465	−	0.961597i	$-0.588501\pi$
$149$	−148759.	−0.548931	−0.274465	+	0.961597i	$0.588501\pi$
$150$	144995.	0.526167
$151$	61360.4	0.219001	0.109500	−	0.993987i	$-0.465075\pi$
$151$	61360.4	0.219001	0.109500	+	0.993987i	$0.465075\pi$
$152$	−205341.	−0.720886
$153$	−167174.	−0.577350
$154$	52954.1	0.179928
$155$	236289.	0.789976
$156$	−484351.	−1.59349
$157$	268244.	0.868521	0.434261	−	0.900787i	$-0.357010\pi$
$157$	268244.	0.868521	0.434261	+	0.900787i	$0.357010\pi$
$158$	78584.9	0.250436
$159$	−36281.9	−0.113814
$160$	−472372.	−1.45876
$161$	−85259.4	−0.259225
$162$	695969.	2.08354
$163$	−40034.5	−0.118023	−0.0590113	−	0.998257i	$-0.518795\pi$
$163$	−40034.5	−0.118023	−0.0590113	+	0.998257i	$0.518795\pi$
$164$	−886797.	−2.57463
$165$	64972.7	0.185790
$166$	757152.	2.13262
$167$	136702.	0.379302	0.189651	−	0.981852i	$-0.439264\pi$
$167$	136702.	0.379302	0.189651	+	0.981852i	$0.439264\pi$
$168$	495020.	1.35316
$169$	−300347.	−0.808923
$170$	206757.	0.548705
$171$	78817.0	0.206124
$172$	699285.	1.80232
$173$	498964.	1.26752	0.633759	−	0.773530i	$-0.281511\pi$
$173$	498964.	1.26752	0.633759	+	0.773530i	$0.281511\pi$
$174$	1.00234e6	2.50982
$175$	25323.8	0.0625077
$176$	−415582.	−1.01129
$177$	−421443.	−1.01113
$178$	−513089.	−1.21379
$179$	−689538.	−1.60852	−0.804258	−	0.594280i	$-0.797437\pi$
$179$	−689538.	−1.60852	−0.804258	+	0.594280i	$0.797437\pi$
$180$	462109.	1.06307
$181$	553349.	1.25546	0.627730	−	0.778431i	$-0.283984\pi$
$181$	553349.	1.25546	0.627730	+	0.778431i	$0.283984\pi$
$182$	−116567.	−0.260855
$183$	−441185.	−0.973852
$184$	1.19691e6	2.60626
$185$	−47831.3	−0.102750
$186$	2.19268e6	4.64721
$187$	92648.9	0.193748
$188$	−1.73033e6	−3.57055
$189$	21469.9	0.0437196
$190$	−97479.5	−0.195898
$191$	−505159.	−1.00195	−0.500974	−	0.865463i	$-0.667025\pi$
$191$	−505159.	−1.00195	−0.500974	+	0.865463i	$0.667025\pi$
$192$	−2.02282e6	−3.96008
$193$	−827164.	−1.59845	−0.799223	−	0.601034i	$-0.794756\pi$
$193$	−827164.	−1.59845	−0.799223	+	0.601034i	$0.794756\pi$
$194$	986506.	1.88190
$195$	−143024.	−0.269353
$196$	−1.28393e6	−2.38727
$197$	−217703.	−0.399668	−0.199834	−	0.979830i	$-0.564040\pi$
$197$	−217703.	−0.399668	−0.199834	+	0.979830i	$0.564040\pi$
$198$	285341.	0.517250
$199$	84861.0	0.151906	0.0759531	−	0.997111i	$-0.475800\pi$
$199$	84861.0	0.151906	0.0759531	+	0.997111i	$0.475800\pi$
$200$	−355507.	−0.628454
$201$	−618193.	−1.07928
$202$	−426902.	−0.736121
$203$	175062.	0.298162
$204$	1.39236e6	2.34249
$205$	−261862.	−0.435199
$206$	328912.	0.540022
$207$	−459416.	−0.745213
$208$	914816.	1.46614
$209$	−43681.0	−0.0691714
$210$	234996.	0.367715
$211$	995569.	1.53945	0.769725	−	0.638376i	$-0.220393\pi$
$211$	995569.	1.53945	0.769725	+	0.638376i	$0.220393\pi$
$212$	143013.	0.218543
$213$	1.59879e6	2.41458
$214$	−677428.	−1.01118
$215$	206492.	0.304653
$216$	−301405.	−0.439558
$217$	382958.	0.552080
$218$	−1.10669e6	−1.57719
$219$	1.71495e6	2.41624
$220$	−256105.	−0.356747
$221$	−203947.	−0.280891
$222$	−443857.	−0.604451
$223$	310925.	0.418691	0.209345	−	0.977842i	$-0.432867\pi$
$223$	310925.	0.418691	0.209345	+	0.977842i	$0.432867\pi$
$224$	−765583.	−1.01946
$225$	136456.	0.179695
$226$	−2.01238e6	−2.62083
$227$	−1.51592e6	−1.95259	−0.976295	−	0.216442i	$-0.930555\pi$
$227$	−1.51592e6	−1.95259	−0.976295	+	0.216442i	$0.930555\pi$
$228$	−656455.	−0.836311
$229$	438466.	0.552518	0.276259	−	0.961083i	$-0.410905\pi$
$229$	438466.	0.552518	0.276259	+	0.961083i	$0.410905\pi$
$230$	568198.	0.708240
$231$	105303.	0.129840
$232$	−2.45761e6	−2.99773
$233$	558408.	0.673848	0.336924	−	0.941532i	$-0.390613\pi$
$233$	558408.	0.673848	0.336924	+	0.941532i	$0.390613\pi$
$234$	−628118.	−0.749897
$235$	−510949.	−0.603542
$236$	1.66121e6	1.94154
$237$	156271.	0.180721
$238$	335096.	0.383466
$239$	−78649.6	−0.0890639	−0.0445320	−	0.999008i	$-0.514180\pi$
$239$	−78649.6	−0.0890639	−0.0445320	+	0.999008i	$0.514180\pi$
$240$	−1.84424e6	−2.06675
$241$	1.55958e6	1.72967	0.864837	−	0.502053i	$-0.167422\pi$
$241$	1.55958e6	1.72967	0.864837	+	0.502053i	$0.167422\pi$
$242$	−158138.	−0.173579
$243$	1.25522e6	1.36365
$244$	1.73903e6	1.86996
$245$	−379132.	−0.403530
$246$	−2.42999e6	−2.56015
$247$	96154.6	0.100283
$248$	−5.37615e6	−5.55063
$249$	1.50565e6	1.53895
$250$	−168766.	−0.170780
$251$	988901.	0.990760	0.495380	−	0.868676i	$-0.335029\pi$
$251$	988901.	0.990760	0.495380	+	0.868676i	$0.335029\pi$
$252$	748950.	0.742936
$253$	254612.	0.250079
$254$	1.32103e6	1.28478
$255$	411150.	0.395959
$256$	1.44270e6	1.37586
$257$	672531.	0.635155	0.317578	−	0.948232i	$-0.397131\pi$
$257$	672531.	0.635155	0.317578	+	0.948232i	$0.397131\pi$
$258$	1.91617e6	1.79219
$259$	−77521.1	−0.0718077
$260$	563761.	0.517203
$261$	943314.	0.857147
$262$	−4.16035e6	−3.74436
$263$	237014.	0.211293	0.105646	−	0.994404i	$-0.466309\pi$
$263$	237014.	0.211293	0.105646	+	0.994404i	$0.466309\pi$
$264$	−1.47829e6	−1.30542
$265$	42230.4	0.0369411
$266$	−157987.	−0.136904
$267$	−1.02031e6	−0.875900
$268$	2.43675e6	2.07240
$269$	−701171.	−0.590804	−0.295402	−	0.955373i	$-0.595454\pi$
$269$	−701171.	−0.590804	−0.295402	+	0.955373i	$0.595454\pi$
$270$	−143083.	−0.119448
$271$	−1.10527e6	−0.914205	−0.457102	−	0.889414i	$-0.651113\pi$
$271$	−1.10527e6	−0.914205	−0.457102	+	0.889414i	$0.651113\pi$
$272$	−2.62982e6	−2.15528
$273$	−231802.	−0.188239
$274$	−53707.5	−0.0432174
$275$	−75625.0	−0.0603023
$276$	3.82641e6	3.02356
$277$	935127.	0.732270	0.366135	−	0.930562i	$-0.380681\pi$
$277$	935127.	0.732270	0.366135	+	0.930562i	$0.380681\pi$
$278$	205389.	0.159391
$279$	2.06355e6	1.58710
$280$	−576178.	−0.439199
$281$	−902052.	−0.681500	−0.340750	−	0.940154i	$-0.610681\pi$
$281$	−902052.	−0.681500	−0.340750	+	0.940154i	$0.610681\pi$
$282$	−4.74143e6	−3.55047
$283$	−172108.	−0.127742	−0.0638712	−	0.997958i	$-0.520345\pi$
$283$	−172108.	−0.127742	−0.0638712	+	0.997958i	$0.520345\pi$
$284$	−6.30197e6	−4.63640
$285$	−193844.	−0.141365
$286$	348108.	0.251651
$287$	−424405.	−0.304142
$288$	−4.12531e6	−2.93073
$289$	−833570.	−0.587080
$290$	−1.16667e6	−0.814619
$291$	1.96173e6	1.35802
$292$	−6.75984e6	−4.63959
$293$	760544.	0.517554	0.258777	−	0.965937i	$-0.416681\pi$
$293$	760544.	0.517554	0.258777	+	0.965937i	$0.416681\pi$
$294$	−3.51821e6	−2.37385
$295$	490539.	0.328185
$296$	1.08828e6	0.721957
$297$	−64116.2	−0.0421771
$298$	1.60675e6	1.04811
$299$	−560476.	−0.362559
$300$	−1.13652e6	−0.729079
$301$	334665.	0.212909
$302$	−662756.	−0.418154
$303$	−848921.	−0.531203
$304$	1.23988e6	0.769475
$305$	513517.	0.316086
$306$	1.80565e6	1.10238
$307$	−2.26313e6	−1.37045	−0.685225	−	0.728332i	$-0.740296\pi$
$307$	−2.26313e6	−1.37045	−0.685225	+	0.728332i	$0.740296\pi$
$308$	−415074.	−0.249315
$309$	654063.	0.389694
$310$	−2.55217e6	−1.50836
$311$	−57066.9	−0.0334567	−0.0167284	−	0.999860i	$-0.505325\pi$
$311$	−57066.9	−0.0334567	−0.0167284	+	0.999860i	$0.505325\pi$
$312$	3.25415e6	1.89256
$313$	−186837.	−0.107796	−0.0538980	−	0.998546i	$-0.517165\pi$
$313$	−186837.	−0.107796	−0.0538980	+	0.998546i	$0.517165\pi$
$314$	−2.89731e6	−1.65833
$315$	221157.	0.125581
$316$	−615978.	−0.347014
$317$	−372462.	−0.208177	−0.104089	−	0.994568i	$-0.533193\pi$
$317$	−372462.	−0.208177	−0.104089	+	0.994568i	$0.533193\pi$
$318$	391883.	0.217314
$319$	−522792.	−0.287642
$320$	2.35446e6	1.28534
$321$	−1.34711e6	−0.729693
$322$	920891.	0.494958
$323$	−276415.	−0.147420
$324$	−5.45526e6	−2.88704
$325$	166473.	0.0874248
$326$	432415.	0.225349
$327$	−2.20072e6	−1.13814
$328$	5.95801e6	3.05785
$329$	−828105.	−0.421790
$330$	−701773.	−0.354742
$331$	−152183.	−0.0763476	−0.0381738	−	0.999271i	$-0.512154\pi$
$331$	−152183.	−0.0763476	−0.0381738	+	0.999271i	$0.512154\pi$
$332$	−5.93484e6	−2.95504
$333$	−417719.	−0.206431
$334$	−1.47653e6	−0.724228
$335$	719546.	0.350305
$336$	−2.98899e6	−1.44436
$337$	2.51718e6	1.20737	0.603683	−	0.797224i	$-0.293699\pi$
$337$	2.51718e6	1.20737	0.603683	+	0.797224i	$0.293699\pi$
$338$	3.24407e6	1.54454
$339$	−4.00175e6	−1.89126
$340$	−1.62064e6	−0.760308
$341$	−1.14364e6	−0.532601
$342$	−851306.	−0.393569
$343$	−1.29545e6	−0.594548
$344$	−4.69819e6	−2.14060
$345$	1.12990e6	0.511083
$346$	−5.38934e6	−2.42017
$347$	2.26947e6	1.01181	0.505906	−	0.862589i	$-0.331158\pi$
$347$	2.26947e6	1.01181	0.505906	+	0.862589i	$0.331158\pi$
$348$	−7.85672e6	−3.47771
$349$	2.23772e6	0.983429	0.491715	−	0.870756i	$-0.336370\pi$
$349$	2.23772e6	0.983429	0.491715	+	0.870756i	$0.336370\pi$
$350$	−273523.	−0.119350
$351$	141138.	0.0611473
$352$	2.28628e6	0.983496
$353$	−2.69978e6	−1.15317	−0.576583	−	0.817038i	$-0.695614\pi$
$353$	−2.69978e6	−1.15317	−0.576583	+	0.817038i	$0.695614\pi$
$354$	4.55203e6	1.93062
$355$	−1.86091e6	−0.783707
$356$	4.02179e6	1.68188
$357$	666360.	0.276719
$358$	7.44773e6	3.07126
$359$	1.10704e6	0.453343	0.226671	−	0.973971i	$-0.427216\pi$
$359$	1.10704e6	0.453343	0.226671	+	0.973971i	$0.427216\pi$
$360$	−3.10471e6	−1.26260
$361$	130321.	0.0526316
$362$	−5.97675e6	−2.39714
$363$	−314468.	−0.125259
$364$	913699.	0.361451
$365$	−1.99611e6	−0.784246
$366$	4.76526e6	1.85945
$367$	−84879.7	−0.0328957	−0.0164478	−	0.999865i	$-0.505236\pi$
$367$	−84879.7	−0.0328957	−0.0164478	+	0.999865i	$0.505236\pi$
$368$	−7.22711e6	−2.78192
$369$	−2.28689e6	−0.874337
$370$	516628.	0.196188
$371$	68443.6	0.0258165
$372$	−1.71870e7	−6.43937
$373$	3.10486e6	1.15550	0.577749	−	0.816214i	$-0.303931\pi$
$373$	3.10486e6	1.15550	0.577749	+	0.816214i	$0.303931\pi$
$374$	−1.00071e6	−0.369937
$375$	−335603.	−0.123239
$376$	1.16253e7	4.24069
$377$	1.15082e6	0.417017
$378$	−231898.	−0.0834770
$379$	3.64825e6	1.30463	0.652314	−	0.757949i	$-0.273798\pi$
$379$	3.64825e6	1.30463	0.652314	+	0.757949i	$0.273798\pi$
$380$	764080.	0.271444
$381$	2.62696e6	0.927130
$382$	5.45625e6	1.91309
$383$	−730812.	−0.254571	−0.127285	−	0.991866i	$-0.540626\pi$
$383$	−730812.	−0.254571	−0.127285	+	0.991866i	$0.540626\pi$
$384$	8.86186e6	3.06688
$385$	−122567.	−0.0421426
$386$	8.93424e6	3.05203
$387$	1.80333e6	0.612065
$388$	−7.73260e6	−2.60763
$389$	4.01332e6	1.34471	0.672356	−	0.740228i	$-0.265282\pi$
$389$	4.01332e6	1.34471	0.672356	+	0.740228i	$0.265282\pi$
$390$	1.54481e6	0.514296
$391$	1.61120e6	0.532975
$392$	8.62620e6	2.83533
$393$	−8.27313e6	−2.70202
$394$	2.35142e6	0.763115
$395$	−181892.	−0.0586571
$396$	−2.23661e6	−0.716724
$397$	−227090.	−0.0723140	−0.0361570	−	0.999346i	$-0.511512\pi$
$397$	−227090.	−0.0723140	−0.0361570	+	0.999346i	$0.511512\pi$
$398$	−916588.	−0.290046
$399$	−314167.	−0.0987936
$400$	2.14660e6	0.670812
$401$	5.17440e6	1.60694	0.803468	−	0.595348i	$-0.202986\pi$
$401$	5.17440e6	1.60694	0.803468	+	0.595348i	$0.202986\pi$
$402$	6.67713e6	2.06075
$403$	2.51748e6	0.772153
$404$	3.34621e6	1.02000
$405$	−1.61088e6	−0.488007
$406$	−1.89085e6	−0.569302
$407$	231503.	0.0692742
$408$	−9.35469e6	−2.78214
$409$	6.64167e6	1.96322	0.981610	−	0.190897i	$-0.0611396\pi$
$409$	6.64167e6	1.96322	0.981610	+	0.190897i	$0.0611396\pi$
$410$	2.82838e6	0.830957
$411$	−106801.	−0.0311867
$412$	−2.57814e6	−0.748277
$413$	795027.	0.229354
$414$	4.96218e6	1.42289
$415$	−1.75250e6	−0.499502
$416$	−5.03277e6	−1.42585
$417$	408429.	0.115021
$418$	471801.	0.132074
$419$	−2.11483e6	−0.588493	−0.294246	−	0.955730i	$-0.595069\pi$
$419$	−2.11483e6	−0.588493	−0.294246	+	0.955730i	$0.595069\pi$
$420$	−1.84198e6	−0.509522
$421$	−3.85718e6	−1.06063	−0.530316	−	0.847800i	$-0.677927\pi$
$421$	−3.85718e6	−1.06063	−0.530316	+	0.847800i	$0.677927\pi$
$422$	−1.07532e7	−2.93938
$423$	−4.46221e6	−1.21255
$424$	−960845.	−0.259561
$425$	−478559.	−0.128518
$426$	−1.72686e7	−4.61033
$427$	832268.	0.220899
$428$	5.30993e6	1.40113
$429$	692236.	0.181598
$430$	−2.23033e6	−0.581697
$431$	−3.48777e6	−0.904387	−0.452194	−	0.891920i	$-0.649358\pi$
$431$	−3.48777e6	−0.904387	−0.452194	+	0.891920i	$0.649358\pi$
$432$	1.81992e6	0.469185
$433$	−1.14432e6	−0.293311	−0.146656	−	0.989188i	$-0.546851\pi$
$433$	−1.14432e6	−0.293311	−0.146656	+	0.989188i	$0.546851\pi$
$434$	−4.13635e6	−1.05413
$435$	−2.32001e6	−0.587850
$436$	8.67462e6	2.18542
$437$	−759628.	−0.190282
$438$	−1.85232e7	−4.61350
$439$	−6.72987e6	−1.66665	−0.833326	−	0.552781i	$-0.813566\pi$
$439$	−6.72987e6	−1.66665	−0.833326	+	0.552781i	$0.813566\pi$
$440$	1.72066e6	0.423704
$441$	−3.31103e6	−0.810712
$442$	2.20284e6	0.536325
$443$	4.93465e6	1.19467	0.597334	−	0.801993i	$-0.296227\pi$
$443$	4.93465e6	1.19467	0.597334	+	0.801993i	$0.296227\pi$
$444$	3.47912e6	0.837552
$445$	1.18759e6	0.284294
$446$	−3.35831e6	−0.799437
$447$	3.19513e6	0.756345
$448$	3.81592e6	0.898266
$449$	−7.86985e6	−1.84226	−0.921129	−	0.389257i	$-0.872732\pi$
$449$	−7.86985e6	−1.84226	−0.921129	+	0.389257i	$0.872732\pi$
$450$	−1.47387e6	−0.343105
$451$	1.26741e6	0.293411
$452$	1.57738e7	3.63154
$453$	−1.31793e6	−0.301751
$454$	1.63735e7	3.72823
$455$	269806.	0.0610974
$456$	4.41044e6	0.993275
$457$	4.45086e6	0.996905	0.498453	−	0.866917i	$-0.333902\pi$
$457$	4.45086e6	0.996905	0.498453	+	0.866917i	$0.333902\pi$
$458$	−4.73589e6	−1.05496
$459$	−405730.	−0.0898888
$460$	−4.45375e6	−0.981366
$461$	7.34925e6	1.61061	0.805306	−	0.592860i	$-0.202001\pi$
$461$	7.34925e6	1.61061	0.805306	+	0.592860i	$0.202001\pi$
$462$	−1.13738e6	−0.247914
$463$	−906242.	−0.196468	−0.0982340	−	0.995163i	$-0.531319\pi$
$463$	−906242.	−0.196468	−0.0982340	+	0.995163i	$0.531319\pi$
$464$	1.48394e7	3.19978
$465$	−5.07515e6	−1.08847
$466$	−6.03139e6	−1.28663
$467$	−4.47048e6	−0.948553	−0.474276	−	0.880376i	$-0.657290\pi$
$467$	−4.47048e6	−0.948553	−0.474276	+	0.880376i	$0.657290\pi$
$468$	4.92343e6	1.03909
$469$	1.16618e6	0.244813
$470$	5.51878e6	1.15239
$471$	−5.76150e6	−1.19669
$472$	−1.11610e7	−2.30594
$473$	−999419.	−0.205397
$474$	−1.68789e6	−0.345063
$475$	225625.	0.0458831
$476$	−2.62661e6	−0.531346
$477$	368805.	0.0742166
$478$	849498.	0.170056
$479$	−3.66011e6	−0.728878	−0.364439	−	0.931227i	$-0.618739\pi$
$479$	−3.66011e6	−0.728878	−0.364439	+	0.931227i	$0.618739\pi$
$480$	1.01459e7	2.00996
$481$	−509606.	−0.100432
$482$	−1.68451e7	−3.30259
$483$	1.83125e6	0.357174
$484$	1.23955e6	0.240519
$485$	−2.28336e6	−0.440778
$486$	−1.35577e7	−2.60372
$487$	1.44677e6	0.276424	0.138212	−	0.990403i	$-0.455864\pi$
$487$	1.44677e6	0.276424	0.138212	+	0.990403i	$0.455864\pi$
$488$	−1.16838e7	−2.22093
$489$	859885.	0.162618
$490$	4.09503e6	0.770489
$491$	−4.34087e6	−0.812593	−0.406297	−	0.913741i	$-0.633180\pi$
$491$	−4.34087e6	−0.812593	−0.406297	+	0.913741i	$0.633180\pi$
$492$	1.90471e7	3.54746
$493$	−3.30825e6	−0.613030
$494$	−1.03857e6	−0.191478
$495$	−660447.	−0.121150
$496$	3.24619e7	5.92475
$497$	−3.01601e6	−0.547699
$498$	−1.62626e7	−2.93843
$499$	−251435.	−0.0452038	−0.0226019	−	0.999745i	$-0.507195\pi$
$499$	−251435.	−0.0452038	−0.0226019	+	0.999745i	$0.507195\pi$
$500$	1.32285e6	0.236639
$501$	−2.93617e6	−0.522621
$502$	−1.06812e7	−1.89173
$503$	−784360.	−0.138228	−0.0691140	−	0.997609i	$-0.522017\pi$
$503$	−784360.	−0.138228	−0.0691140	+	0.997609i	$0.522017\pi$
$504$	−5.03187e6	−0.882375
$505$	988102.	0.172414
$506$	−2.75008e6	−0.477495
$507$	6.45104e6	1.11458
$508$	−1.03547e7	−1.78025
$509$	−6.00192e6	−1.02682	−0.513412	−	0.858142i	$-0.671619\pi$
$509$	−6.00192e6	−1.02682	−0.513412	+	0.858142i	$0.671619\pi$
$510$	−4.44086e6	−0.756034
$511$	−3.23514e6	−0.548076
$512$	−2.37976e6	−0.401197
$513$	191289.	0.0320919
$514$	−7.26404e6	−1.21275
$515$	−761297.	−0.126484
$516$	−1.50196e7	−2.48334
$517$	2.47299e6	0.406908
$518$	837310.	0.137108
$519$	−1.07171e7	−1.74645
$520$	−3.78766e6	−0.614275
$521$	−6.97624e6	−1.12597	−0.562985	−	0.826467i	$-0.690347\pi$
$521$	−6.97624e6	−1.12597	−0.562985	+	0.826467i	$0.690347\pi$
$522$	−1.01888e7	−1.63661
$523$	−6.40310e6	−1.02361	−0.511807	−	0.859101i	$-0.671024\pi$
$523$	−6.40310e6	−1.02361	−0.511807	+	0.859101i	$0.671024\pi$
$524$	3.26104e7	5.18833
$525$	−543919.	−0.0861263
$526$	−2.56000e6	−0.403436
$527$	−7.23699e6	−1.13509
$528$	8.92611e6	1.39340
$529$	−2.00855e6	−0.312063
$530$	−456132.	−0.0705344
$531$	4.28397e6	0.659341
$532$	1.23836e6	0.189700
$533$	−2.78994e6	−0.425380
$534$	1.10204e7	1.67242
$535$	1.56797e6	0.236839
$536$	−1.63714e7	−2.46136
$537$	1.48103e7	2.21630
$538$	7.57338e6	1.12806
$539$	1.83500e6	0.272060
$540$	1.12154e6	0.165512
$541$	−3.40932e6	−0.500813	−0.250406	−	0.968141i	$-0.580564\pi$
$541$	−3.40932e6	−0.500813	−0.250406	+	0.968141i	$0.580564\pi$
$542$	1.19380e7	1.74556
$543$	−1.18852e7	−1.72984
$544$	1.44677e7	2.09605
$545$	2.56153e6	0.369409
$546$	2.50370e6	0.359419
$547$	1.22715e6	0.175359	0.0876795	−	0.996149i	$-0.472055\pi$
$547$	1.22715e6	0.175359	0.0876795	+	0.996149i	$0.472055\pi$
$548$	420979.	0.0598838
$549$	4.48464e6	0.635034
$550$	816829.	0.115140
$551$	1.55974e6	0.218863
$552$	−2.57080e7	−3.59104
$553$	−294796.	−0.0409929
$554$	−1.01003e7	−1.39818
$555$	1.02735e6	0.141575
$556$	−1.60991e6	−0.220859
$557$	25545.4	0.00348879	0.00174440	−	0.999998i	$-0.499445\pi$
$557$	25545.4	0.00348879	0.00174440	+	0.999998i	$0.499445\pi$
$558$	−2.22885e7	−3.03037
$559$	2.20001e6	0.297780
$560$	3.47904e6	0.468802
$561$	−1.98997e6	−0.266956
$562$	9.74311e6	1.30124
$563$	1.19801e7	1.59290	0.796451	−	0.604703i	$-0.206708\pi$
$563$	1.19801e7	1.59290	0.796451	+	0.604703i	$0.206708\pi$
$564$	3.71651e7	4.91968
$565$	4.65784e6	0.613852
$566$	1.85895e6	0.243908
$567$	−2.61079e6	−0.341047
$568$	4.23402e7	5.50658
$569$	−9.72342e6	−1.25904	−0.629518	−	0.776986i	$-0.716748\pi$
$569$	−9.72342e6	−1.25904	−0.629518	+	0.776986i	$0.716748\pi$
$570$	2.09372e6	0.269918
$571$	−1.17465e7	−1.50772	−0.753858	−	0.657037i	$-0.771809\pi$
$571$	−1.17465e7	−1.50772	−0.753858	+	0.657037i	$0.771809\pi$
$572$	−2.72860e6	−0.348698
$573$	1.08501e7	1.38053
$574$	4.58402e6	0.580720
$575$	−1.31515e6	−0.165884
$576$	2.05619e7	2.58231
$577$	−483248.	−0.0604269	−0.0302135	−	0.999543i	$-0.509619\pi$
$577$	−483248.	−0.0604269	−0.0302135	+	0.999543i	$0.509619\pi$
$578$	9.00343e6	1.12096
$579$	1.77663e7	2.20242
$580$	9.14483e6	1.12877
$581$	−2.84031e6	−0.349080
$582$	−2.11888e7	−2.59297
$583$	−204395.	−0.0249057
$584$	4.54165e7	5.51037
$585$	1.45384e6	0.175641
$586$	−8.21468e6	−0.988204
$587$	824949.	0.0988171	0.0494085	−	0.998779i	$-0.484266\pi$
$587$	824949.	0.0988171	0.0494085	+	0.998779i	$0.484266\pi$
$588$	2.75771e7	3.28931
$589$	3.41201e6	0.405249
$590$	−5.29834e6	−0.626627
$591$	4.67595e6	0.550683
$592$	−6.57117e6	−0.770617
$593$	9.38968e6	1.09651	0.548257	−	0.836310i	$-0.315292\pi$
$593$	9.38968e6	1.09651	0.548257	+	0.836310i	$0.315292\pi$
$594$	692522.	0.0805318
$595$	−775610.	−0.0898154
$596$	−1.25943e7	−1.45231
$597$	−1.82269e6	−0.209304
$598$	6.05373e6	0.692261
$599$	1.35721e7	1.54554	0.772772	−	0.634684i	$-0.218870\pi$
$599$	1.35721e7	1.54554	0.772772	+	0.634684i	$0.218870\pi$
$600$	7.63580e6	0.865917
$601$	−7.24943e6	−0.818687	−0.409343	−	0.912380i	$-0.634242\pi$
$601$	−7.24943e6	−0.818687	−0.409343	+	0.912380i	$0.634242\pi$
$602$	−3.61474e6	−0.406523
$603$	6.28392e6	0.703781
$604$	5.19493e6	0.579412
$605$	366025.	0.0406558
$606$	9.16924e6	1.01427
$607$	4.15564e6	0.457790	0.228895	−	0.973451i	$-0.426489\pi$
$607$	4.15564e6	0.457790	0.228895	+	0.973451i	$0.426489\pi$
$608$	−6.82105e6	−0.748328
$609$	−3.76009e6	−0.410823
$610$	−5.54653e6	−0.603527
$611$	−5.44378e6	−0.589926
$612$	−1.41534e7	−1.52750
$613$	3.51912e6	0.378253	0.189126	−	0.981953i	$-0.439434\pi$
$613$	3.51912e6	0.378253	0.189126	+	0.981953i	$0.439434\pi$
$614$	2.44442e7	2.61670
$615$	5.62442e6	0.599640
$616$	2.78870e6	0.296108
$617$	415848.	0.0439766	0.0219883	−	0.999758i	$-0.493000\pi$
$617$	415848.	0.0439766	0.0219883	+	0.999758i	$0.493000\pi$
$618$	−7.06456e6	−0.744071
$619$	−2.20566e6	−0.231372	−0.115686	−	0.993286i	$-0.536907\pi$
$619$	−2.20566e6	−0.231372	−0.115686	+	0.993286i	$0.536907\pi$
$620$	2.00048e7	2.09004
$621$	−1.11500e6	−0.116024
$622$	616383.	0.0638814
$623$	1.92475e6	0.198681
$624$	−1.96490e7	−2.02012
$625$	390625.	0.0400000
$626$	2.01804e6	0.205823
$627$	938206.	0.0953080
$628$	2.27102e7	2.29785
$629$	1.46496e6	0.147639
$630$	−2.38873e6	−0.239781
$631$	−1.95187e7	−1.95154	−0.975769	−	0.218805i	$-0.929784\pi$
$631$	−1.95187e7	−1.95154	−0.975769	+	0.218805i	$0.929784\pi$
$632$	4.13849e6	0.412144
$633$	−2.13834e7	−2.12113
$634$	4.02298e6	0.397489
$635$	−3.05765e6	−0.300922
$636$	−3.07172e6	−0.301120
$637$	−4.03937e6	−0.394426
$638$	5.64671e6	0.549216
$639$	−1.62516e7	−1.57451
$640$	−1.03148e7	−0.995426
$641$	8.87373e6	0.853024	0.426512	−	0.904482i	$-0.359742\pi$
$641$	8.87373e6	0.853024	0.426512	+	0.904482i	$0.359742\pi$
$642$	1.45502e7	1.39326
$643$	−1.55594e7	−1.48411	−0.742055	−	0.670339i	$-0.766149\pi$
$643$	−1.55594e7	−1.48411	−0.742055	+	0.670339i	$0.766149\pi$
$644$	−7.21829e6	−0.685835
$645$	−4.43515e6	−0.419767
$646$	2.98558e6	0.281480
$647$	−1.08177e7	−1.01596	−0.507979	−	0.861369i	$-0.669607\pi$
$647$	−1.08177e7	−1.01596	−0.507979	+	0.861369i	$0.669607\pi$
$648$	3.66516e7	3.42890
$649$	−2.37421e6	−0.221262
$650$	−1.79808e6	−0.166927
$651$	−8.22540e6	−0.760684
$652$	−3.38943e6	−0.312254
$653$	−8.49278e6	−0.779412	−0.389706	−	0.920939i	$-0.627423\pi$
$653$	−8.49278e6	−0.779412	−0.389706	+	0.920939i	$0.627423\pi$
$654$	2.37701e7	2.17313
$655$	9.62951e6	0.877003
$656$	−3.59752e7	−3.26395
$657$	−1.74324e7	−1.57559
$658$	8.94441e6	0.805354
$659$	−1.43251e7	−1.28494	−0.642472	−	0.766309i	$-0.722091\pi$
$659$	−1.43251e7	−1.28494	−0.642472	+	0.766309i	$0.722091\pi$
$660$	5.50076e6	0.491545
$661$	6.50410e6	0.579007	0.289503	−	0.957177i	$-0.406510\pi$
$661$	6.50410e6	0.579007	0.289503	+	0.957177i	$0.406510\pi$
$662$	1.64373e6	0.145776
$663$	4.38050e6	0.387026
$664$	3.98737e7	3.50967
$665$	365675.	0.0320657
$666$	4.51181e6	0.394153
$667$	−9.09155e6	−0.791267
$668$	1.15736e7	1.00352
$669$	−6.67823e6	−0.576894
$670$	−7.77185e6	−0.668863
$671$	−2.48542e6	−0.213105
$672$	1.64436e7	1.40467
$673$	1.64296e7	1.39827	0.699133	−	0.714991i	$-0.253569\pi$
$673$	1.64296e7	1.39827	0.699133	+	0.714991i	$0.253569\pi$
$674$	−2.71882e7	−2.30531
$675$	331178.	0.0279771
$676$	−2.54282e7	−2.14017
$677$	−3.08078e6	−0.258339	−0.129169	−	0.991623i	$-0.541231\pi$
$677$	−3.08078e6	−0.258339	−0.129169	+	0.991623i	$0.541231\pi$
$678$	4.32231e7	3.61112
$679$	−3.70069e6	−0.308040
$680$	1.08884e7	0.903008
$681$	3.25598e7	2.69038
$682$	1.23525e7	1.01694
$683$	−4.11296e6	−0.337367	−0.168684	−	0.985670i	$-0.553952\pi$
$683$	−4.11296e6	−0.337367	−0.168684	+	0.985670i	$0.553952\pi$
$684$	6.67285e6	0.545345
$685$	124311.	0.0101224
$686$	1.39923e7	1.13521
$687$	−9.41762e6	−0.761288
$688$	2.83683e7	2.28487
$689$	449933.	0.0361077
$690$	−1.22041e7	−0.975849
$691$	−1.41427e7	−1.12678	−0.563388	−	0.826193i	$-0.690502\pi$
$691$	−1.41427e7	−1.12678	−0.563388	+	0.826193i	$0.690502\pi$
$692$	4.22437e7	3.35348
$693$	−1.07040e6	−0.0846668
$694$	−2.45126e7	−1.93193
$695$	−475390.	−0.0373326
$696$	5.27859e7	4.13043
$697$	8.02024e6	0.625325
$698$	−2.41698e7	−1.87773
$699$	−1.19938e7	−0.928463
$700$	2.14398e6	0.165377
$701$	3.93479e6	0.302431	0.151216	−	0.988501i	$-0.451681\pi$
$701$	3.93479e6	0.302431	0.151216	+	0.988501i	$0.451681\pi$
$702$	−1.52444e6	−0.116753
$703$	−690684.	−0.0527097
$704$	−1.13956e7	−0.866573
$705$	1.09745e7	0.831592
$706$	2.91605e7	2.20183
$707$	1.60144e6	0.120493
$708$	−3.56805e7	−2.67515
$709$	9.20143e6	0.687448	0.343724	−	0.939071i	$-0.388312\pi$
$709$	9.20143e6	0.687448	0.343724	+	0.939071i	$0.388312\pi$
$710$	2.00997e7	1.49639
$711$	−1.58850e6	−0.117845
$712$	−2.70206e7	−1.99754
$713$	−1.98883e7	−1.46512
$714$	−7.19739e6	−0.528359
$715$	−805728.	−0.0589418
$716$	−5.83781e7	−4.25567
$717$	1.68928e6	0.122717
$718$	−1.19572e7	−0.865601
$719$	−2.42500e7	−1.74940	−0.874702	−	0.484661i	$-0.838943\pi$
$719$	−2.42500e7	−1.74940	−0.874702	+	0.484661i	$0.838943\pi$
$720$	1.87466e7	1.34770
$721$	−1.23385e6	−0.0883942
$722$	−1.40760e6	−0.100493
$723$	−3.34975e7	−2.38323
$724$	4.68480e7	3.32158
$725$	2.70037e6	0.190800
$726$	3.39658e6	0.239167
$727$	2.56599e7	1.80061	0.900304	−	0.435262i	$-0.143344\pi$
$727$	2.56599e7	1.80061	0.900304	+	0.435262i	$0.143344\pi$
$728$	−6.13875e6	−0.429291
$729$	−1.13025e7	−0.787691
$730$	2.15601e7	1.49742
$731$	−6.32437e6	−0.437748
$732$	−3.73519e7	−2.57653
$733$	−1.60459e7	−1.10307	−0.551537	−	0.834151i	$-0.685958\pi$
$733$	−1.60459e7	−1.10307	−0.551537	+	0.834151i	$0.685958\pi$
$734$	916789.	0.0628101
$735$	8.14322e6	0.556004
$736$	3.97592e7	2.70547
$737$	−3.48260e6	−0.236176
$738$	2.47008e7	1.66944
$739$	1.65143e7	1.11237	0.556184	−	0.831059i	$-0.312265\pi$
$739$	1.65143e7	1.11237	0.556184	+	0.831059i	$0.312265\pi$
$740$	−4.04952e6	−0.271847
$741$	−2.06526e6	−0.138175
$742$	−739263.	−0.0492934
$743$	8.65599e6	0.575234	0.287617	−	0.957745i	$-0.407137\pi$
$743$	8.65599e6	0.575234	0.287617	+	0.957745i	$0.407137\pi$
$744$	1.15472e8	7.64795
$745$	−3.71897e6	−0.245489
$746$	−3.35357e7	−2.20628
$747$	−1.53049e7	−1.00353
$748$	7.84390e6	0.512600
$749$	2.54124e6	0.165516
$750$	3.62486e6	0.235309
$751$	−9.67299e6	−0.625837	−0.312918	−	0.949780i	$-0.601307\pi$
$751$	−9.67299e6	−0.625837	−0.312918	+	0.949780i	$0.601307\pi$
$752$	−7.01954e7	−4.52651
$753$	−2.12402e7	−1.36512
$754$	−1.24300e7	−0.796241
$755$	1.53401e6	0.0979401
$756$	1.81770e6	0.115669
$757$	1.21088e7	0.768003	0.384002	−	0.923332i	$-0.374546\pi$
$757$	1.21088e7	0.768003	0.384002	+	0.923332i	$0.374546\pi$
$758$	−3.94050e7	−2.49102
$759$	−5.46871e6	−0.344572
$760$	−5.13353e6	−0.322390
$761$	−285178.	−0.0178507	−0.00892533	−	0.999960i	$-0.502841\pi$
$761$	−285178.	−0.0178507	−0.00892533	+	0.999960i	$0.502841\pi$
$762$	−2.83739e7	−1.77024
$763$	4.15152e6	0.258164
$764$	−4.27681e7	−2.65086
$765$	−4.17934e6	−0.258199
$766$	7.89354e6	0.486071
$767$	5.22632e6	0.320781
$768$	−3.09871e7	−1.89574
$769$	9.15921e6	0.558524	0.279262	−	0.960215i	$-0.409910\pi$
$769$	9.15921e6	0.558524	0.279262	+	0.960215i	$0.409910\pi$
$770$	1.32385e6	0.0804661
$771$	−1.44450e7	−0.875150
$772$	−7.00299e7	−4.22902
$773$	−3.10582e7	−1.86951	−0.934756	−	0.355291i	$-0.884382\pi$
$773$	−3.10582e7	−1.86951	−0.934756	+	0.355291i	$0.884382\pi$
$774$	−1.94778e7	−1.16866
$775$	5.90722e6	0.353288
$776$	5.19520e7	3.09705
$777$	1.66504e6	0.0989403
$778$	−4.33480e7	−2.56756
$779$	−3.78129e6	−0.223252
$780$	−1.21088e7	−0.712630
$781$	9.00679e6	0.528375
$782$	−1.74026e7	−1.01765
$783$	2.28942e6	0.133451
$784$	−5.20861e7	−3.02644
$785$	6.70609e6	0.388415
$786$	8.93585e7	5.15917
$787$	4.80900e6	0.276769	0.138385	−	0.990379i	$-0.455809\pi$
$787$	4.80900e6	0.276769	0.138385	+	0.990379i	$0.455809\pi$
$788$	−1.84313e7	−1.05740
$789$	−5.09072e6	−0.291130
$790$	1.96462e6	0.111998
$791$	7.54906e6	0.428995
$792$	1.50268e7	0.851243
$793$	5.47114e6	0.308955
$794$	2.45281e6	0.138074
$795$	−907048.	−0.0508994
$796$	7.18456e6	0.401899
$797$	1.33255e7	0.743082	0.371541	−	0.928416i	$-0.378829\pi$
$797$	1.33255e7	0.743082	0.371541	+	0.928416i	$0.378829\pi$
$798$	3.39334e6	0.188634
$799$	1.56492e7	0.867212
$800$	−1.18093e7	−0.652377
$801$	1.03715e7	0.571161
$802$	−5.58889e7	−3.06824
$803$	9.66118e6	0.528739
$804$	−5.23378e7	−2.85546
$805$	−2.13148e6	−0.115929
$806$	−2.71914e7	−1.47433
$807$	1.50602e7	0.814040
$808$	−2.24818e7	−1.21144
$809$	−2.57838e7	−1.38508	−0.692542	−	0.721377i	$-0.743509\pi$
$809$	−2.57838e7	−1.38508	−0.692542	+	0.721377i	$0.743509\pi$
$810$	1.73992e7	0.931788
$811$	−2.41103e7	−1.28721	−0.643606	−	0.765357i	$-0.722563\pi$
$811$	−2.41103e7	−1.28721	−0.643606	+	0.765357i	$0.722563\pi$
$812$	1.48212e7	0.788849
$813$	2.37395e7	1.25964
$814$	−2.50048e6	−0.132270
$815$	−1.00086e6	−0.0527814
$816$	5.64848e7	2.96966
$817$	2.98174e6	0.156284
$818$	−7.17370e7	−3.74852
$819$	2.35626e6	0.122748
$820$	−2.21699e7	−1.15141
$821$	−2.71873e7	−1.40770	−0.703848	−	0.710351i	$-0.748536\pi$
$821$	−2.71873e7	−1.40770	−0.703848	+	0.710351i	$0.748536\pi$
$822$	1.15356e6	0.0595471
$823$	9.94097e6	0.511598	0.255799	−	0.966730i	$-0.417661\pi$
$823$	9.94097e6	0.511598	0.255799	+	0.966730i	$0.417661\pi$
$824$	1.73214e7	0.888719
$825$	1.62432e6	0.0830876
$826$	−8.58712e6	−0.437923
$827$	−1.31310e7	−0.667626	−0.333813	−	0.942639i	$-0.608335\pi$
$827$	−1.31310e7	−0.667626	−0.333813	+	0.942639i	$0.608335\pi$
$828$	−3.88954e7	−1.97162
$829$	−7.33251e6	−0.370567	−0.185283	−	0.982685i	$-0.559320\pi$
$829$	−7.33251e6	−0.370567	−0.185283	+	0.982685i	$0.559320\pi$
$830$	1.89288e7	0.953736
$831$	−2.00852e7	−1.00896
$832$	2.50850e7	1.25634
$833$	1.16120e7	0.579820
$834$	−4.41146e6	−0.219617
$835$	3.41756e6	0.169629
$836$	−3.69815e6	−0.183007
$837$	5.00824e6	0.247099
$838$	2.28424e7	1.12365
$839$	−1.34041e7	−0.657405	−0.328703	−	0.944433i	$-0.606611\pi$
$839$	−1.34041e7	−0.657405	−0.328703	+	0.944433i	$0.606611\pi$
$840$	1.23755e7	0.605152
$841$	−1.84358e6	−0.0898819
$842$	4.16616e7	2.02514
$843$	1.93748e7	0.939006
$844$	8.42875e7	4.07293
$845$	−7.50868e6	−0.361761
$846$	4.81965e7	2.31521
$847$	593224.	0.0284126
$848$	5.80171e6	0.277055
$849$	3.69664e6	0.176010
$850$	5.16893e6	0.245388
$851$	4.02593e6	0.190564
$852$	1.35357e8	6.38827
$853$	−9.68970e6	−0.455971	−0.227986	−	0.973664i	$-0.573214\pi$
$853$	−9.68970e6	−0.455971	−0.227986	+	0.973664i	$0.573214\pi$
$854$	−8.98937e6	−0.421779
$855$	1.97042e6	0.0921817
$856$	−3.56752e7	−1.66411
$857$	−1.61699e7	−0.752063	−0.376032	−	0.926607i	$-0.622712\pi$
$857$	−1.61699e7	−0.752063	−0.376032	+	0.926607i	$0.622712\pi$
$858$	−7.47687e6	−0.346738
$859$	−1.98932e7	−0.919860	−0.459930	−	0.887955i	$-0.652125\pi$
$859$	−1.98932e7	−0.919860	−0.459930	+	0.887955i	$0.652125\pi$
$860$	1.74821e7	0.806024
$861$	9.11562e6	0.419062
$862$	3.76716e7	1.72681
$863$	1.56485e7	0.715229	0.357615	−	0.933869i	$-0.383590\pi$
$863$	1.56485e7	0.715229	0.357615	+	0.933869i	$0.383590\pi$
$864$	−1.00121e7	−0.456291
$865$	1.24741e7	0.566852
$866$	1.23599e7	0.560041
$867$	1.79039e7	0.808910
$868$	3.24222e7	1.46064
$869$	880357.	0.0395466
$870$	2.50585e7	1.12242
$871$	7.66622e6	0.342402
$872$	−5.82810e7	−2.59559
$873$	−1.99410e7	−0.885546
$874$	8.20478e6	0.363319
$875$	633094.	0.0279543
$876$	1.45192e8	6.39266
$877$	1.65529e7	0.726732	0.363366	−	0.931646i	$-0.381627\pi$
$877$	1.65529e7	0.726732	0.363366	+	0.931646i	$0.381627\pi$
$878$	7.26896e7	3.18226
$879$	−1.63354e7	−0.713112
$880$	−1.03895e7	−0.452262
$881$	−4.43391e7	−1.92463	−0.962315	−	0.271938i	$-0.912335\pi$
$881$	−4.43391e7	−1.92463	−0.962315	+	0.271938i	$0.912335\pi$
$882$	3.57626e7	1.54795
$883$	−3.52806e7	−1.52277	−0.761385	−	0.648300i	$-0.775480\pi$
$883$	−3.52806e7	−1.52277	−0.761385	+	0.648300i	$0.775480\pi$
$884$	−1.72667e7	−0.743155
$885$	−1.05361e7	−0.452190
$886$	−5.32994e7	−2.28107
$887$	4.57779e7	1.95365	0.976825	−	0.214040i	$-0.0686624\pi$
$887$	4.57779e7	1.95365	0.976825	+	0.214040i	$0.0686624\pi$
$888$	−2.33747e7	−0.994750
$889$	−4.95560e6	−0.210301
$890$	−1.28272e7	−0.542823
$891$	7.79667e6	0.329014
$892$	2.63237e7	1.10773
$893$	−7.37810e6	−0.309611
$894$	−3.45108e7	−1.44415
$895$	−1.72384e7	−0.719351
$896$	−1.67173e7	−0.695660
$897$	1.20382e7	0.499553
$898$	8.50026e7	3.51756
$899$	4.08363e7	1.68518
$900$	1.15527e7	0.475421
$901$	−1.29342e6	−0.0530796
$902$	−1.36894e7	−0.560231
$903$	−7.18814e6	−0.293357
$904$	−1.05977e8	−4.31313
$905$	1.38337e7	0.561458
$906$	1.42351e7	0.576155
$907$	−3.94523e7	−1.59241	−0.796204	−	0.605029i	$-0.793162\pi$
$907$	−3.94523e7	−1.59241	−0.796204	+	0.605029i	$0.793162\pi$
$908$	−1.28342e8	−5.16598
$909$	8.62928e6	0.346390
$910$	−2.91418e6	−0.116658
$911$	−2.01308e7	−0.803646	−0.401823	−	0.915717i	$-0.631623\pi$
$911$	−2.01308e7	−0.803646	−0.401823	+	0.915717i	$0.631623\pi$
$912$	−2.66308e7	−1.06022
$913$	8.48209e6	0.336764
$914$	−4.80740e7	−1.90346
$915$	−1.10296e7	−0.435520
$916$	3.71217e7	1.46180
$917$	1.56068e7	0.612900
$918$	4.38231e6	0.171631
$919$	−5.48978e6	−0.214420	−0.107210	−	0.994236i	$-0.534192\pi$
$919$	−5.48978e6	−0.214420	−0.107210	+	0.994236i	$0.534192\pi$
$920$	2.99228e7	1.16556
$921$	4.86088e7	1.88828
$922$	−7.93796e7	−3.07526
$923$	−1.98266e7	−0.766025
$924$	8.91520e6	0.343519
$925$	−1.19578e6	−0.0459513
$926$	9.78837e6	0.375131
$927$	−6.64854e6	−0.254113
$928$	−8.16371e7	−3.11184
$929$	3.29443e7	1.25239	0.626196	−	0.779666i	$-0.284611\pi$
$929$	3.29443e7	1.25239	0.626196	+	0.779666i	$0.284611\pi$
$930$	5.48169e7	2.07829
$931$	−5.47467e6	−0.207006
$932$	4.72763e7	1.78281
$933$	1.22572e6	0.0460984
$934$	4.82858e7	1.81114
$935$	2.31622e6	0.0866466
$936$	−3.30784e7	−1.23411
$937$	2.87312e7	1.06907	0.534533	−	0.845147i	$-0.320487\pi$
$937$	2.87312e7	1.06907	0.534533	+	0.845147i	$0.320487\pi$
$938$	−1.25960e7	−0.467439
$939$	4.01300e6	0.148527
$940$	−4.32583e7	−1.59680
$941$	−4.01528e7	−1.47823	−0.739114	−	0.673580i	$-0.764756\pi$
$941$	−4.01528e7	−1.47823	−0.739114	+	0.673580i	$0.764756\pi$
$942$	6.22302e7	2.28494
$943$	2.20407e7	0.807137
$944$	6.73914e7	2.46136
$945$	536748.	0.0195520
$946$	1.07948e7	0.392180
$947$	4.79512e6	0.173750	0.0868749	−	0.996219i	$-0.472312\pi$
$947$	4.79512e6	0.173750	0.0868749	+	0.996219i	$0.472312\pi$
$948$	1.32303e7	0.478134
$949$	−2.12671e7	−0.766553
$950$	−2.43699e6	−0.0876081
$951$	7.99996e6	0.286838
$952$	1.76470e7	0.631073
$953$	−2.36888e7	−0.844909	−0.422454	−	0.906384i	$-0.638831\pi$
$953$	−2.36888e7	−0.844909	−0.422454	+	0.906384i	$0.638831\pi$
$954$	−3.98349e6	−0.141707
$955$	−1.26290e7	−0.448084
$956$	−6.65869e6	−0.235637
$957$	1.12288e7	0.396328
$958$	3.95330e7	1.39170
$959$	201473.	0.00707409
$960$	−5.05705e7	−1.77100
$961$	6.07026e7	2.12031
$962$	5.50428e6	0.191762
$963$	1.36934e7	0.475822
$964$	1.32038e8	4.57621
$965$	−2.06791e7	−0.714847
$966$	−1.97794e7	−0.681979
$967$	1.08317e7	0.372504	0.186252	−	0.982502i	$-0.440366\pi$
$967$	1.08317e7	0.372504	0.186252	+	0.982502i	$0.440366\pi$
$968$	−8.32797e6	−0.285661
$969$	5.93701e6	0.203123
$970$	2.46627e7	0.841609
$971$	2.21614e7	0.754309	0.377154	−	0.926150i	$-0.376903\pi$
$971$	2.21614e7	0.754309	0.377154	+	0.926150i	$0.376903\pi$
$972$	1.06270e8	3.60782
$973$	−770475.	−0.0260902
$974$	−1.56266e7	−0.527797
$975$	−3.57560e6	−0.120458
$976$	7.05482e7	2.37062
$977$	−2.95729e7	−0.991191	−0.495596	−	0.868553i	$-0.665050\pi$
$977$	−2.95729e7	−0.991191	−0.495596	+	0.868553i	$0.665050\pi$
$978$	−9.28766e6	−0.310498
$979$	−5.74794e6	−0.191671
$980$	−3.20983e7	−1.06762
$981$	2.23703e7	0.742162
$982$	4.68860e7	1.55154
$983$	−4.58942e7	−1.51487	−0.757433	−	0.652912i	$-0.773547\pi$
$983$	−4.58942e7	−1.51487	−0.757433	+	0.652912i	$0.773547\pi$
$984$	−1.27970e8	−4.21327
$985$	−5.44258e6	−0.178737
$986$	3.57326e7	1.17050
$987$	1.77865e7	0.581164
$988$	8.14070e6	0.265320
$989$	−1.73803e7	−0.565022
$990$	7.13352e6	0.231321
$991$	−4.15111e7	−1.34270	−0.671351	−	0.741140i	$-0.734286\pi$
$991$	−4.15111e7	−1.34270	−0.671351	+	0.741140i	$0.734286\pi$
$992$	−1.78586e8	−5.76192
$993$	3.26867e6	0.105196
$994$	3.25761e7	1.04576
$995$	2.12153e6	0.0679345
$996$	1.27472e8	4.07161
$997$	5.12150e7	1.63177	0.815886	−	0.578213i	$-0.196250\pi$
$997$	5.12150e7	1.63177	0.815886	+	0.578213i	$0.196250\pi$
$998$	2.71576e6	0.0863109
$999$	−1.01380e6	−0.0321396

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.b.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-10.8010 q^{2} -21.4786 q^{3} +84.6626 q^{4} +25.0000 q^{5} +231.991 q^{6} +40.5180 q^{7} -568.812 q^{8} +218.330 q^{9} +O(q^{10})\)	\(q-10.8010 q^{2} -21.4786 q^{3} +84.6626 q^{4} +25.0000 q^{5} +231.991 q^{6} +40.5180 q^{7} -568.812 q^{8} +218.330 q^{9} -270.026 q^{10} -121.000 q^{11} -1818.43 q^{12} +266.356 q^{13} -437.637 q^{14} -536.965 q^{15} +3434.56 q^{16} -765.694 q^{17} -2358.19 q^{18} +361.000 q^{19} +2116.57 q^{20} -870.270 q^{21} +1306.93 q^{22} -2104.23 q^{23} +12217.3 q^{24} +625.000 q^{25} -2876.93 q^{26} +529.886 q^{27} +3430.36 q^{28} +4320.60 q^{29} +5799.78 q^{30} +9451.55 q^{31} -18894.9 q^{32} +2598.91 q^{33} +8270.29 q^{34} +1012.95 q^{35} +18484.4 q^{36} -1913.25 q^{37} -3899.18 q^{38} -5720.96 q^{39} -14220.3 q^{40} -10474.5 q^{41} +9399.83 q^{42} +8259.66 q^{43} -10244.2 q^{44} +5458.24 q^{45} +22727.9 q^{46} -20438.0 q^{47} -73769.5 q^{48} -15165.3 q^{49} -6750.66 q^{50} +16446.0 q^{51} +22550.4 q^{52} +1689.21 q^{53} -5723.32 q^{54} -3025.00 q^{55} -23047.1 q^{56} -7753.77 q^{57} -46667.0 q^{58} +19621.6 q^{59} -45460.8 q^{60} +20540.7 q^{61} -102087. q^{62} +8846.28 q^{63} +94178.4 q^{64} +6658.91 q^{65} -28070.9 q^{66} +28781.8 q^{67} -64825.7 q^{68} +45196.0 q^{69} -10940.9 q^{70} -74436.2 q^{71} -124188. q^{72} -79844.4 q^{73} +20665.1 q^{74} -13424.1 q^{75} +30563.2 q^{76} -4902.68 q^{77} +61792.3 q^{78} -7275.68 q^{79} +85864.0 q^{80} -64435.3 q^{81} +113135. q^{82} -70099.9 q^{83} -73679.4 q^{84} -19142.3 q^{85} -89213.0 q^{86} -92800.3 q^{87} +68826.2 q^{88} +47503.7 q^{89} -58954.7 q^{90} +10792.2 q^{91} -178150. q^{92} -203006. q^{93} +220751. q^{94} +9025.00 q^{95} +405835. q^{96} -91334.3 q^{97} +163801. q^{98} -26417.9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 8 q^{2} - 63 q^{3} + 520 q^{4} + 900 q^{5} + 5 q^{6} - 509 q^{7} - 690 q^{8} + 1935 q^{9}+O(q^{10}) \) 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

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