LMFDB - Embedded newform 1045.6.a.f.1.7

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:	$0$
Dimension:	$38$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
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)

$f(q)$	$=$	$q-7.46340 q^{2} +17.5503 q^{3} +23.7024 q^{4} +25.0000 q^{5} -130.985 q^{6} -243.020 q^{7} +61.9286 q^{8} +65.0117 q^{9} +O(q^{10})$	\(q-7.46340 q^{2} +17.5503 q^{3} +23.7024 q^{4} +25.0000 q^{5} -130.985 q^{6} -243.020 q^{7} +61.9286 q^{8} +65.0117 q^{9} -186.585 q^{10} -121.000 q^{11} +415.983 q^{12} -1204.11 q^{13} +1813.75 q^{14} +438.757 q^{15} -1220.67 q^{16} -472.894 q^{17} -485.209 q^{18} -361.000 q^{19} +592.559 q^{20} -4265.06 q^{21} +903.072 q^{22} +508.130 q^{23} +1086.86 q^{24} +625.000 q^{25} +8986.74 q^{26} -3123.74 q^{27} -5760.14 q^{28} -3630.11 q^{29} -3274.62 q^{30} -5726.09 q^{31} +7128.66 q^{32} -2123.58 q^{33} +3529.40 q^{34} -6075.49 q^{35} +1540.93 q^{36} +5115.06 q^{37} +2694.29 q^{38} -21132.4 q^{39} +1548.22 q^{40} -1605.02 q^{41} +31831.8 q^{42} -16725.2 q^{43} -2867.99 q^{44} +1625.29 q^{45} -3792.38 q^{46} -15083.3 q^{47} -21423.1 q^{48} +42251.5 q^{49} -4664.63 q^{50} -8299.42 q^{51} -28540.2 q^{52} -11207.2 q^{53} +23313.7 q^{54} -3025.00 q^{55} -15049.9 q^{56} -6335.65 q^{57} +27093.0 q^{58} +14310.0 q^{59} +10399.6 q^{60} -56973.2 q^{61} +42736.1 q^{62} -15799.1 q^{63} -14142.5 q^{64} -30102.7 q^{65} +15849.1 q^{66} +23648.5 q^{67} -11208.7 q^{68} +8917.82 q^{69} +45343.8 q^{70} -68868.8 q^{71} +4026.09 q^{72} +25302.8 q^{73} -38175.8 q^{74} +10968.9 q^{75} -8556.55 q^{76} +29405.4 q^{77} +157720. q^{78} -2995.10 q^{79} -30516.8 q^{80} -70620.3 q^{81} +11978.9 q^{82} -15820.6 q^{83} -101092. q^{84} -11822.4 q^{85} +124827. q^{86} -63709.4 q^{87} -7493.36 q^{88} -53675.8 q^{89} -12130.2 q^{90} +292622. q^{91} +12043.9 q^{92} -100494. q^{93} +112572. q^{94} -9025.00 q^{95} +125110. q^{96} +133629. q^{97} -315340. q^{98} -7866.42 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) $ 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9} + 200 q^{10} - 4598 q^{11} + 2312 q^{12} + 41 q^{13} + 23 q^{14} + 1575 q^{15} + 7196 q^{16} - 2431 q^{17} - 1689 q^{18} - 13718 q^{19} + 15400 q^{20} - 1577 q^{21} - 968 q^{22} + 9284 q^{23} + 7598 q^{24} + 23750 q^{25} + 13129 q^{26} + 9228 q^{27} - 1079 q^{28} - 559 q^{29} + 3725 q^{30} + 11147 q^{31} + 11051 q^{32} - 7623 q^{33} + 40895 q^{34} + 6875 q^{35} + 55887 q^{36} + 41579 q^{37} - 2888 q^{38} + 24982 q^{39} + 6600 q^{40} + 18597 q^{41} + 61360 q^{42} + 25353 q^{43} - 74536 q^{44} + 75725 q^{45} + 1611 q^{46} + 63516 q^{47} + 187737 q^{48} + 141609 q^{49} + 5000 q^{50} + 107546 q^{51} + 60018 q^{52} + 123045 q^{53} + 256696 q^{54} - 114950 q^{55} + 157335 q^{56} - 22743 q^{57} + 218938 q^{58} + 132925 q^{59} + 57800 q^{60} - 59107 q^{61} + 166982 q^{62} + 130582 q^{63} + 313126 q^{64} + 1025 q^{65} - 18029 q^{66} + 162534 q^{67} + 182980 q^{68} + 178552 q^{69} + 575 q^{70} + 157840 q^{71} + 98630 q^{72} - 63010 q^{73} + 122683 q^{74} + 39375 q^{75} - 222376 q^{76} - 33275 q^{77} + 277272 q^{78} - 16385 q^{79} + 179900 q^{80} + 290354 q^{81} + 362302 q^{82} + 138461 q^{83} + 446870 q^{84} - 60775 q^{85} + 643902 q^{86} + 291602 q^{87} - 31944 q^{88} + 224792 q^{89} - 42225 q^{90} + 498548 q^{91} + 581088 q^{92} + 134210 q^{93} + 35864 q^{94} - 342950 q^{95} + 377376 q^{96} + 292216 q^{97} - 58230 q^{98} - 366509 q^{99}+O(q^{100}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9 + 200 * q^10 - 4598 * q^11 + 2312 * q^12 + 41 * q^13 + 23 * q^14 + 1575 * q^15 + 7196 * q^16 - 2431 * q^17 - 1689 * q^18 - 13718 * q^19 + 15400 * q^20 - 1577 * q^21 - 968 * q^22 + 9284 * q^23 + 7598 * q^24 + 23750 * q^25 + 13129 * q^26 + 9228 * q^27 - 1079 * q^28 - 559 * q^29 + 3725 * q^30 + 11147 * q^31 + 11051 * q^32 - 7623 * q^33 + 40895 * q^34 + 6875 * q^35 + 55887 * q^36 + 41579 * q^37 - 2888 * q^38 + 24982 * q^39 + 6600 * q^40 + 18597 * q^41 + 61360 * q^42 + 25353 * q^43 - 74536 * q^44 + 75725 * q^45 + 1611 * q^46 + 63516 * q^47 + 187737 * q^48 + 141609 * q^49 + 5000 * q^50 + 107546 * q^51 + 60018 * q^52 + 123045 * q^53 + 256696 * q^54 - 114950 * q^55 + 157335 * q^56 - 22743 * q^57 + 218938 * q^58 + 132925 * q^59 + 57800 * q^60 - 59107 * q^61 + 166982 * q^62 + 130582 * q^63 + 313126 * q^64 + 1025 * q^65 - 18029 * q^66 + 162534 * q^67 + 182980 * q^68 + 178552 * q^69 + 575 * q^70 + 157840 * q^71 + 98630 * q^72 - 63010 * q^73 + 122683 * q^74 + 39375 * q^75 - 222376 * q^76 - 33275 * q^77 + 277272 * q^78 - 16385 * q^79 + 179900 * q^80 + 290354 * q^81 + 362302 * q^82 + 138461 * q^83 + 446870 * q^84 - 60775 * q^85 + 643902 * q^86 + 291602 * q^87 - 31944 * q^88 + 224792 * q^89 - 42225 * q^90 + 498548 * q^91 + 581088 * q^92 + 134210 * q^93 + 35864 * q^94 - 342950 * q^95 + 377376 * q^96 + 292216 * q^97 - 58230 * q^98 - 366509 * 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 $

$2$	−7.46340	−1.31936	−0.659678	−	0.751549i	$-0.729307\pi$
$2$	−7.46340	−1.31936	−0.659678	+	0.751549i	$0.729307\pi$
$3$	17.5503	1.12585	0.562925	−	0.826508i	$-0.309676\pi$
$3$	17.5503	1.12585	0.562925	+	0.826508i	$0.309676\pi$
$4$	23.7024	0.740699
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	−130.985	−1.48540
$7$	−243.020	−1.87455	−0.937273	−	0.348596i	$-0.886658\pi$
$7$	−243.020	−1.87455	−0.937273	+	0.348596i	$0.886658\pi$
$8$	61.9286	0.342111
$9$	65.0117	0.267538
$10$	−186.585	−0.590034
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	415.983	0.833916
$13$	−1204.11	−1.97609	−0.988045	−	0.154164i	$-0.950732\pi$
$13$	−1204.11	−1.97609	−0.988045	+	0.154164i	$0.950732\pi$
$14$	1813.75	2.47319
$15$	438.757	0.503495
$16$	−1220.67	−1.19206
$17$	−472.894	−0.396864	−0.198432	−	0.980115i	$-0.563585\pi$
$17$	−472.894	−0.396864	−0.198432	+	0.980115i	$0.563585\pi$
$18$	−485.209	−0.352978
$19$	−361.000	−0.229416
$19$	−361.000	−0.229416
$20$	592.559	0.331251
$21$	−4265.06	−2.11046
$22$	903.072	0.397801
$23$	508.130	0.200288	0.100144	−	0.994973i	$-0.468070\pi$
$23$	508.130	0.200288	0.100144	+	0.994973i	$0.468070\pi$
$24$	1086.86	0.385165
$25$	625.000	0.200000
$26$	8986.74	2.60717
$27$	−3123.74	−0.824642
$28$	−5760.14	−1.38847
$29$	−3630.11	−0.801539	−0.400769	−	0.916179i	$-0.631257\pi$
$29$	−3630.11	−0.801539	−0.400769	+	0.916179i	$0.631257\pi$
$30$	−3274.62	−0.664289
$31$	−5726.09	−1.07017	−0.535087	−	0.844797i	$-0.679721\pi$
$31$	−5726.09	−1.07017	−0.535087	+	0.844797i	$0.679721\pi$
$32$	7128.66	1.23065
$33$	−2123.58	−0.339457
$34$	3529.40	0.523605
$35$	−6075.49	−0.838322
$36$	1540.93	0.198165
$37$	5115.06	0.614252	0.307126	−	0.951669i	$-0.400633\pi$
$37$	5115.06	0.614252	0.307126	+	0.951669i	$0.400633\pi$
$38$	2694.29	0.302681
$39$	−21132.4	−2.22478
$40$	1548.22	0.152996
$41$	−1605.02	−0.149115	−0.0745574	−	0.997217i	$-0.523754\pi$
$41$	−1605.02	−0.149115	−0.0745574	+	0.997217i	$0.523754\pi$
$42$	31831.8	2.78444
$43$	−16725.2	−1.37943	−0.689717	−	0.724079i	$-0.742265\pi$
$43$	−16725.2	−1.37943	−0.689717	+	0.724079i	$0.742265\pi$
$44$	−2867.99	−0.223329
$45$	1625.29	0.119647
$46$	−3792.38	−0.264251
$47$	−15083.3	−0.995979	−0.497990	−	0.867183i	$-0.665928\pi$
$47$	−15083.3	−0.995979	−0.497990	+	0.867183i	$0.665928\pi$
$48$	−21423.1	−1.34209
$49$	42251.5	2.51392
$50$	−4664.63	−0.263871
$51$	−8299.42	−0.446809
$52$	−28540.2	−1.46369
$53$	−11207.2	−0.548033	−0.274016	−	0.961725i	$-0.588352\pi$
$53$	−11207.2	−0.548033	−0.274016	+	0.961725i	$0.588352\pi$
$54$	23313.7	1.08800
$55$	−3025.00	−0.134840
$56$	−15049.9	−0.641302
$57$	−6335.65	−0.258288
$58$	27093.0	1.05751
$59$	14310.0	0.535192	0.267596	−	0.963531i	$-0.413771\pi$
$59$	14310.0	0.535192	0.267596	+	0.963531i	$0.413771\pi$
$60$	10399.6	0.372938
$61$	−56973.2	−1.96040	−0.980202	−	0.197999i	$-0.936556\pi$
$61$	−56973.2	−1.96040	−0.980202	+	0.197999i	$0.936556\pi$
$62$	42736.1	1.41194
$63$	−15799.1	−0.501512
$64$	−14142.5	−0.431595
$65$	−30102.7	−0.883735
$66$	15849.1	0.447864
$67$	23648.5	0.643600	0.321800	−	0.946808i	$-0.395712\pi$
$67$	23648.5	0.643600	0.321800	+	0.946808i	$0.395712\pi$
$68$	−11208.7	−0.293957
$69$	8917.82	0.225495
$70$	45343.8	1.10605
$71$	−68868.8	−1.62135	−0.810675	−	0.585496i	$-0.800900\pi$
$71$	−68868.8	−1.62135	−0.810675	+	0.585496i	$0.800900\pi$
$72$	4026.09	0.0915276
$73$	25302.8	0.555726	0.277863	−	0.960621i	$-0.410374\pi$
$73$	25302.8	0.555726	0.277863	+	0.960621i	$0.410374\pi$
$74$	−38175.8	−0.810417
$75$	10968.9	0.225170
$76$	−8556.55	−0.169928
$77$	29405.4	0.565197
$78$	157720.	2.93528
$79$	−2995.10	−0.0539937	−0.0269969	−	0.999636i	$-0.508594\pi$
$79$	−2995.10	−0.0539937	−0.0269969	+	0.999636i	$0.508594\pi$
$80$	−30516.8	−0.533107
$81$	−70620.3	−1.19596
$82$	11978.9	0.196735
$83$	−15820.6	−0.252074	−0.126037	−	0.992026i	$-0.540226\pi$
$83$	−15820.6	−0.252074	−0.126037	+	0.992026i	$0.540226\pi$
$84$	−101092.	−1.56321
$85$	−11822.4	−0.177483
$86$	124827.	1.81996
$87$	−63709.4	−0.902412
$88$	−7493.36	−0.103150
$89$	−53675.8	−0.718296	−0.359148	−	0.933281i	$-0.616933\pi$
$89$	−53675.8	−0.718296	−0.359148	+	0.933281i	$0.616933\pi$
$90$	−12130.2	−0.157856
$91$	292622.	3.70427
$92$	12043.9	0.148353
$93$	−100494.	−1.20485
$94$	112572.	1.31405
$95$	−9025.00	−0.102598
$96$	125110.	1.38552
$97$	133629.	1.44202	0.721010	−	0.692925i	$-0.243678\pi$
$97$	133629.	1.44202	0.721010	+	0.692925i	$0.243678\pi$
$98$	−315340.	−3.31676
$99$	−7866.42	−0.0806658
$100$	14814.0	0.148140
$101$	−40541.4	−0.395453	−0.197727	−	0.980257i	$-0.563356\pi$
$101$	−40541.4	−0.395453	−0.197727	+	0.980257i	$0.563356\pi$
$102$	61941.9	0.589500
$103$	157436.	1.46221	0.731107	−	0.682262i	$-0.239004\pi$
$103$	157436.	1.46221	0.731107	+	0.682262i	$0.239004\pi$
$104$	−74568.7	−0.676041
$105$	−106626.	−0.943825
$106$	83643.6	0.723050
$107$	202449.	1.70945	0.854725	−	0.519081i	$-0.173726\pi$
$107$	202449.	1.70945	0.854725	+	0.519081i	$0.173726\pi$
$108$	−74040.0	−0.610811
$109$	42723.6	0.344430	0.172215	−	0.985059i	$-0.444908\pi$
$109$	42723.6	0.344430	0.172215	+	0.985059i	$0.444908\pi$
$110$	22576.8	0.177902
$111$	89770.7	0.691555
$112$	296648.	2.23458
$113$	39439.8	0.290562	0.145281	−	0.989390i	$-0.453591\pi$
$113$	39439.8	0.290562	0.145281	+	0.989390i	$0.453591\pi$
$114$	47285.5	0.340773
$115$	12703.3	0.0895717
$116$	−86042.1	−0.593699
$117$	−78281.1	−0.528679
$118$	−106801.	−0.706109
$119$	114923.	0.743940
$120$	27171.6	0.172251
$121$	14641.0	0.0909091
$122$	425214.	2.58647
$123$	−28168.5	−0.167881
$124$	−135722.	−0.792676
$125$	15625.0	0.0894427
$126$	117915.	0.661673
$127$	68321.8	0.375881	0.187940	−	0.982180i	$-0.439819\pi$
$127$	68321.8	0.375881	0.187940	+	0.982180i	$0.439819\pi$
$128$	−122566.	−0.661219
$129$	−293532.	−1.55304
$130$	224668.	1.16596
$131$	372055.	1.89421	0.947106	−	0.320920i	$-0.103992\pi$
$131$	372055.	1.89421	0.947106	+	0.320920i	$0.103992\pi$
$132$	−50333.9	−0.251435
$133$	87730.0	0.430050
$134$	−176498.	−0.849137
$135$	−78093.5	−0.368791
$136$	−29285.7	−0.135771
$137$	−389.802	−0.00177436	−0.000887181	−	1.00000i	$-0.500282\pi$
$137$	−389.802	−0.00177436	−0.000887181		1.00000i	$0.500282\pi$
$138$	−66557.3	−0.297507
$139$	−22065.4	−0.0968669	−0.0484335	−	0.998826i	$-0.515423\pi$
$139$	−22065.4	−0.0968669	−0.0484335	+	0.998826i	$0.515423\pi$
$140$	−144003.	−0.620944
$141$	−264715.	−1.12132
$142$	513996.	2.13914
$143$	145697.	0.595814
$144$	−79358.1	−0.318923
$145$	−90752.7	−0.358459
$146$	−188845.	−0.733200
$147$	741525.	2.83030
$148$	121239.	0.454976
$149$	−497782.	−1.83685	−0.918425	−	0.395595i	$-0.870538\pi$
$149$	−497782.	−1.83685	−0.918425	+	0.395595i	$0.870538\pi$
$150$	−81865.4	−0.297079
$151$	−459918.	−1.64149	−0.820745	−	0.571295i	$-0.806441\pi$
$151$	−459918.	−1.64149	−0.820745	+	0.571295i	$0.806441\pi$
$152$	−22356.2	−0.0784855
$153$	−30743.7	−0.106176
$154$	−219464.	−0.745696
$155$	−143152.	−0.478596
$156$	−500888.	−1.64789
$157$	−427755.	−1.38499	−0.692494	−	0.721423i	$-0.743488\pi$
$157$	−427755.	−1.38499	−0.692494	+	0.721423i	$0.743488\pi$
$158$	22353.6	0.0712369
$159$	−196689.	−0.617002
$160$	178217.	0.550361
$161$	−123486.	−0.375450
$162$	527068.	1.57790
$163$	−390486.	−1.15116	−0.575581	−	0.817745i	$-0.695224\pi$
$163$	−390486.	−1.15116	−0.575581	+	0.817745i	$0.695224\pi$
$164$	−38042.7	−0.110449
$165$	−53089.5	−0.151810
$166$	118076.	0.332575
$167$	−475034.	−1.31806	−0.659028	−	0.752119i	$-0.729032\pi$
$167$	−475034.	−1.31806	−0.659028	+	0.752119i	$0.729032\pi$
$168$	−264129.	−0.722010
$169$	1.07858e6	2.90493
$170$	88235.0	0.234163
$171$	−23469.2	−0.0613774
$172$	−396427.	−1.02175
$173$	−218264.	−0.554455	−0.277227	−	0.960804i	$-0.589416\pi$
$173$	−218264.	−0.554455	−0.277227	+	0.960804i	$0.589416\pi$
$174$	475488.	1.19060
$175$	−151887.	−0.374909
$176$	147702.	0.359421
$177$	251145.	0.602546
$178$	400604.	0.947688
$179$	−747453.	−1.74362	−0.871809	−	0.489846i	$-0.837053\pi$
$179$	−747453.	−1.74362	−0.871809	+	0.489846i	$0.837053\pi$
$180$	38523.3	0.0886221
$181$	−224414.	−0.509160	−0.254580	−	0.967052i	$-0.581937\pi$
$181$	−224414.	−0.509160	−0.254580	+	0.967052i	$0.581937\pi$
$182$	−2.18395e6	−4.88725
$183$	−999894.	−2.20712
$184$	31467.8	0.0685207
$185$	127877.	0.274702
$186$	750030.	1.58963
$187$	57220.2	0.119659
$188$	−357509.	−0.737721
$189$	759130.	1.54583
$190$	67357.2	0.135363
$191$	965602.	1.91520	0.957601	−	0.288097i	$-0.0930226\pi$
$191$	965602.	1.91520	0.957601	+	0.288097i	$0.0930226\pi$
$192$	−248205.	−0.485911
$193$	964485.	1.86381	0.931906	−	0.362700i	$-0.118145\pi$
$193$	964485.	1.86381	0.931906	+	0.362700i	$0.118145\pi$
$194$	−997326.	−1.90254
$195$	−528310.	−0.994952
$196$	1.00146e6	1.86206
$197$	−672183.	−1.23402	−0.617009	−	0.786956i	$-0.711656\pi$
$197$	−672183.	−1.23402	−0.617009	+	0.786956i	$0.711656\pi$
$198$	58710.3	0.106427
$199$	478393.	0.856352	0.428176	−	0.903695i	$-0.359156\pi$
$199$	478393.	0.856352	0.428176	+	0.903695i	$0.359156\pi$
$200$	38705.4	0.0684221
$201$	415037.	0.724597
$202$	302577.	0.521744
$203$	882187.	1.50252
$204$	−196716.	−0.330951
$205$	−40125.5	−0.0666861
$206$	−1.17501e6	−1.92918
$207$	33034.4	0.0535847
$208$	1.46982e6	2.35563
$209$	43681.0	0.0691714
$210$	795796.	1.24524
$211$	−1.05668e6	−1.63394	−0.816970	−	0.576680i	$-0.804348\pi$
$211$	−1.05668e6	−1.63394	−0.816970	+	0.576680i	$0.804348\pi$
$212$	−265636.	−0.405927
$213$	−1.20867e6	−1.82540
$214$	−1.51096e6	−2.25537
$215$	−418131.	−0.616902
$216$	−193449.	−0.282119
$217$	1.39155e6	2.00609
$218$	−318863.	−0.454426
$219$	444070.	0.625664
$220$	−71699.6	−0.0998758
$221$	569415.	0.784239
$222$	−669995.	−0.912407
$223$	−1.03071e6	−1.38795	−0.693974	−	0.720000i	$-0.744142\pi$
$223$	−1.03071e6	−1.38795	−0.693974	+	0.720000i	$0.744142\pi$
$224$	−1.73240e6	−2.30690
$225$	40632.3	0.0535076
$226$	−294355.	−0.383355
$227$	673207.	0.867129	0.433565	−	0.901122i	$-0.357256\pi$
$227$	673207.	0.867129	0.433565	+	0.901122i	$0.357256\pi$
$228$	−150170.	−0.191313
$229$	188186.	0.237137	0.118568	−	0.992946i	$-0.462170\pi$
$229$	188186.	0.237137	0.118568	+	0.992946i	$0.462170\pi$
$230$	−94809.5	−0.118177
$231$	516072.	0.636327
$232$	−224808.	−0.274215
$233$	−432237.	−0.521594	−0.260797	−	0.965394i	$-0.583985\pi$
$233$	−432237.	−0.521594	−0.260797	+	0.965394i	$0.583985\pi$
$234$	584243.	0.697516
$235$	−377081.	−0.445416
$236$	339181.	0.396416
$237$	−52564.8	−0.0607888
$238$	−857713.	−0.981521
$239$	1.42934e6	1.61860	0.809301	−	0.587394i	$-0.199846\pi$
$239$	1.42934e6	1.61860	0.809301	+	0.587394i	$0.199846\pi$
$240$	−535579.	−0.600199
$241$	425451.	0.471853	0.235926	−	0.971771i	$-0.424188\pi$
$241$	425451.	0.471853	0.235926	+	0.971771i	$0.424188\pi$
$242$	−109272.	−0.119941
$243$	−480336.	−0.521831
$244$	−1.35040e6	−1.45207
$245$	1.05629e6	1.12426
$246$	210233.	0.221494
$247$	434683.	0.453346
$248$	−354609.	−0.366117
$249$	−277656.	−0.283798
$250$	−116616.	−0.118007
$251$	−148068.	−0.148346	−0.0741729	−	0.997245i	$-0.523632\pi$
$251$	−148068.	−0.148346	−0.0741729	+	0.997245i	$0.523632\pi$
$252$	−374476.	−0.371470
$253$	−61483.8	−0.0603892
$254$	−509913.	−0.495920
$255$	−207485.	−0.199819
$256$	1.36732e6	1.30398
$257$	−314590.	−0.297107	−0.148553	−	0.988904i	$-0.547462\pi$
$257$	−314590.	−0.297107	−0.148553	+	0.988904i	$0.547462\pi$
$258$	2.19075e6	2.04901
$259$	−1.24306e6	−1.15144
$260$	−713505.	−0.654581
$261$	−236000.	−0.214442
$262$	−2.77679e6	−2.49914
$263$	−1.01214e6	−0.902297	−0.451149	−	0.892449i	$-0.648986\pi$
$263$	−1.01214e6	−0.902297	−0.451149	+	0.892449i	$0.648986\pi$
$264$	−131511.	−0.116132
$265$	−280179.	−0.245088
$266$	−654765.	−0.567389
$267$	−942024.	−0.808694
$268$	560524.	0.476713
$269$	−1.94187e6	−1.63621	−0.818106	−	0.575068i	$-0.804976\pi$
$269$	−1.94187e6	−1.63621	−0.818106	+	0.575068i	$0.804976\pi$
$270$	582843.	0.486567
$271$	117194.	0.0969356	0.0484678	−	0.998825i	$-0.484566\pi$
$271$	117194.	0.0969356	0.0484678	+	0.998825i	$0.484566\pi$
$272$	577249.	0.473087
$273$	5.13559e6	4.17045
$274$	2909.25	0.00234101
$275$	−75625.0	−0.0603023
$276$	211373.	0.167024
$277$	−336367.	−0.263399	−0.131700	−	0.991290i	$-0.542043\pi$
$277$	−336367.	−0.263399	−0.131700	+	0.991290i	$0.542043\pi$
$278$	164683.	0.127802
$279$	−372263.	−0.286312
$280$	−376247.	−0.286799
$281$	−79792.8	−0.0602834	−0.0301417	−	0.999546i	$-0.509596\pi$
$281$	−79792.8	−0.0602834	−0.0301417	+	0.999546i	$0.509596\pi$
$282$	1.97567e6	1.47942
$283$	660282.	0.490076	0.245038	−	0.969513i	$-0.421200\pi$
$283$	660282.	0.490076	0.245038	+	0.969513i	$0.421200\pi$
$284$	−1.63235e6	−1.20093
$285$	−158391.	−0.115510
$286$	−1.08740e6	−0.786090
$287$	390051.	0.279522
$288$	463447.	0.329245
$289$	−1.19623e6	−0.842499
$290$	677324.	0.472935
$291$	2.34522e6	1.62350
$292$	599735.	0.411626
$293$	1.29197e6	0.879188	0.439594	−	0.898197i	$-0.355122\pi$
$293$	1.29197e6	0.879188	0.439594	+	0.898197i	$0.355122\pi$
$294$	−5.53430e6	−3.73417
$295$	357750.	0.239345
$296$	316769.	0.210142
$297$	377973.	0.248639
$298$	3.71515e6	2.42346
$299$	−611844.	−0.395788
$300$	259989.	0.166783
$301$	4.06456e6	2.58581
$302$	3.43255e6	2.16571
$303$	−711512.	−0.445221
$304$	440663.	0.273478
$305$	−1.42433e6	−0.876720
$306$	229452.	0.140084
$307$	−113466.	−0.0687103	−0.0343551	−	0.999410i	$-0.510938\pi$
$307$	−113466.	−0.0687103	−0.0343551	+	0.999410i	$0.510938\pi$
$308$	696976.	0.418641
$309$	2.76304e6	1.64623
$310$	1.06840e6	0.631438
$311$	916401.	0.537260	0.268630	−	0.963243i	$-0.413429\pi$
$311$	916401.	0.537260	0.268630	+	0.963243i	$0.413429\pi$
$312$	−1.30870e6	−0.761121
$313$	2.92319e6	1.68654	0.843269	−	0.537491i	$-0.180628\pi$
$313$	2.92319e6	1.68654	0.843269	+	0.537491i	$0.180628\pi$
$314$	3.19251e6	1.82729
$315$	−394978.	−0.224283
$316$	−70990.9	−0.0399931
$317$	1.14755e6	0.641394	0.320697	−	0.947182i	$-0.396083\pi$
$317$	1.14755e6	0.641394	0.320697	+	0.947182i	$0.396083\pi$
$318$	1.46797e6	0.814045
$319$	439243.	0.241673
$320$	−353563.	−0.193015
$321$	3.55303e6	1.92458
$322$	921623.	0.495351
$323$	170715.	0.0910468
$324$	−1.67387e6	−0.885847
$325$	−752567.	−0.395218
$326$	2.91435e6	1.51879
$327$	749810.	0.387777
$328$	−99396.6	−0.0510137
$329$	3.66552e6	1.86701
$330$	396229.	0.200291
$331$	1.74430e6	0.875086	0.437543	−	0.899198i	$-0.355849\pi$
$331$	1.74430e6	0.875086	0.437543	+	0.899198i	$0.355849\pi$
$332$	−374986.	−0.186711
$333$	332539.	0.164336
$334$	3.54537e6	1.73898
$335$	591211.	0.287827
$336$	5.20624e6	2.51580
$337$	−2.16954e6	−1.04062	−0.520310	−	0.853978i	$-0.674184\pi$
$337$	−2.16954e6	−1.04062	−0.520310	+	0.853978i	$0.674184\pi$
$338$	−8.04989e6	−3.83264
$339$	692179.	0.327129
$340$	−280218.	−0.131461
$341$	692857.	0.322669
$342$	175160.	0.0809787
$343$	−6.18351e6	−2.83792
$344$	−1.03577e6	−0.471919
$345$	222946.	0.100844
$346$	1.62899e6	0.731523
$347$	−1.74636e6	−0.778593	−0.389296	−	0.921113i	$-0.627282\pi$
$347$	−1.74636e6	−0.778593	−0.389296	+	0.921113i	$0.627282\pi$
$348$	−1.51006e6	−0.668416
$349$	967776.	0.425316	0.212658	−	0.977127i	$-0.431788\pi$
$349$	967776.	0.425316	0.212658	+	0.977127i	$0.431788\pi$
$350$	1.13360e6	0.494638
$351$	3.76132e6	1.62957
$352$	−862568.	−0.371054
$353$	−323059.	−0.137989	−0.0689947	−	0.997617i	$-0.521979\pi$
$353$	−323059.	−0.137989	−0.0689947	+	0.997617i	$0.521979\pi$
$354$	−1.87439e6	−0.794973
$355$	−1.72172e6	−0.725090
$356$	−1.27224e6	−0.532041
$357$	2.01692e6	0.837564
$358$	5.57854e6	2.30045
$359$	−991685.	−0.406104	−0.203052	−	0.979168i	$-0.565086\pi$
$359$	−991685.	−0.406104	−0.203052	+	0.979168i	$0.565086\pi$
$360$	100652.	0.0409324
$361$	130321.	0.0526316
$362$	1.67489e6	0.671762
$363$	256953.	0.102350
$364$	6.93582e6	2.74375
$365$	632569.	0.248528
$366$	7.46261e6	2.91198
$367$	2.31936e6	0.898881	0.449441	−	0.893310i	$-0.351623\pi$
$367$	2.31936e6	0.898881	0.449441	+	0.893310i	$0.351623\pi$
$368$	−620261.	−0.238756
$369$	−104345.	−0.0398939
$370$	−954394.	−0.362429
$371$	2.72356e6	1.02731
$372$	−2.38195e6	−0.892434
$373$	2.66820e6	0.992993	0.496497	−	0.868039i	$-0.334619\pi$
$373$	2.66820e6	0.992993	0.496497	+	0.868039i	$0.334619\pi$
$374$	−427057.	−0.157873
$375$	274223.	0.100699
$376$	−934085.	−0.340735
$377$	4.37104e6	1.58391
$378$	−5.66569e6	−2.03950
$379$	−1.40954e6	−0.504057	−0.252028	−	0.967720i	$-0.581098\pi$
$379$	−1.40954e6	−0.504057	−0.252028	+	0.967720i	$0.581098\pi$
$380$	−213914.	−0.0759941
$381$	1.19907e6	0.423185
$382$	−7.20667e6	−2.52683
$383$	−2.64080e6	−0.919896	−0.459948	−	0.887946i	$-0.652132\pi$
$383$	−2.64080e6	−0.919896	−0.459948	+	0.887946i	$0.652132\pi$
$384$	−2.15107e6	−0.744433
$385$	735134.	0.252764
$386$	−7.19834e6	−2.45903
$387$	−1.08734e6	−0.369051
$388$	3.16732e6	1.06810
$389$	3.83800e6	1.28597	0.642985	−	0.765879i	$-0.277696\pi$
$389$	3.83800e6	1.28597	0.642985	+	0.765879i	$0.277696\pi$
$390$	3.94299e6	1.31270
$391$	−240292.	−0.0794872
$392$	2.61658e6	0.860039
$393$	6.52966e6	2.13260
$394$	5.01677e6	1.62811
$395$	−74877.5	−0.0241467
$396$	−186453.	−0.0597490
$397$	−893657.	−0.284574	−0.142287	−	0.989825i	$-0.545446\pi$
$397$	−893657.	−0.284574	−0.142287	+	0.989825i	$0.545446\pi$
$398$	−3.57044e6	−1.12983
$399$	1.53969e6	0.484172
$400$	−762921.	−0.238413
$401$	1.25078e6	0.388438	0.194219	−	0.980958i	$-0.437783\pi$
$401$	1.25078e6	0.388438	0.194219	+	0.980958i	$0.437783\pi$
$402$	−3.09759e6	−0.956001
$403$	6.89483e6	2.11476
$404$	−960927.	−0.292912
$405$	−1.76551e6	−0.534850
$406$	−6.58412e6	−1.98236
$407$	−618922.	−0.185204
$408$	−513971.	−0.152858
$409$	−3.91607e6	−1.15756	−0.578778	−	0.815485i	$-0.696470\pi$
$409$	−3.91607e6	−1.15756	−0.578778	+	0.815485i	$0.696470\pi$
$410$	299472.	0.0879827
$411$	−6841.12	−0.00199767
$412$	3.73161e6	1.08306
$413$	−3.47761e6	−1.00324
$414$	−246549.	−0.0706973
$415$	−395515.	−0.112731
$416$	−8.58367e6	−2.43187
$417$	−387254.	−0.109058
$418$	−326009.	−0.0912617
$419$	4.59413e6	1.27840	0.639202	−	0.769039i	$-0.279265\pi$
$419$	4.59413e6	1.27840	0.639202	+	0.769039i	$0.279265\pi$
$420$	−2.52730e6	−0.699090
$421$	5.77910e6	1.58911	0.794557	−	0.607190i	$-0.207703\pi$
$421$	5.77910e6	1.58911	0.794557	+	0.607190i	$0.207703\pi$
$422$	7.88641e6	2.15575
$423$	−980589.	−0.266462
$424$	−694045.	−0.187488
$425$	−295559.	−0.0793728
$426$	9.02076e6	2.40835
$427$	1.38456e7	3.67487
$428$	4.79852e6	1.26619
$429$	2.55702e6	0.670797
$430$	3.12068e6	0.813913
$431$	4.61563e6	1.19684	0.598422	−	0.801181i	$-0.295795\pi$
$431$	4.61563e6	1.19684	0.598422	+	0.801181i	$0.295795\pi$
$432$	3.81307e6	0.983026
$433$	670432.	0.171844	0.0859221	−	0.996302i	$-0.472616\pi$
$433$	670432.	0.171844	0.0859221	+	0.996302i	$0.472616\pi$
$434$	−1.03857e7	−2.64674
$435$	−1.59273e6	−0.403571
$436$	1.01265e6	0.255119
$437$	−183435.	−0.0459493
$438$	−3.31427e6	−0.825474
$439$	−7.27727e6	−1.80222	−0.901109	−	0.433592i	$-0.857246\pi$
$439$	−7.27727e6	−1.80222	−0.901109	+	0.433592i	$0.857246\pi$
$440$	−187334.	−0.0461302
$441$	2.74684e6	0.672570
$442$	−4.24977e6	−1.03469
$443$	3.91771e6	0.948469	0.474234	−	0.880399i	$-0.342725\pi$
$443$	3.91771e6	0.948469	0.474234	+	0.880399i	$0.342725\pi$
$444$	2.12778e6	0.512234
$445$	−1.34189e6	−0.321232
$446$	7.69258e6	1.83120
$447$	−8.73621e6	−2.06802
$448$	3.43690e6	0.809045
$449$	−7.85443e6	−1.83865	−0.919324	−	0.393501i	$-0.871264\pi$
$449$	−7.85443e6	−1.83865	−0.919324	+	0.393501i	$0.871264\pi$
$450$	−303255.	−0.0705956
$451$	194207.	0.0449598
$452$	934817.	0.215219
$453$	−8.07169e6	−1.84807
$454$	−5.02441e6	−1.14405
$455$	7.31554e6	1.65660
$456$	−392358.	−0.0883629
$457$	1.10215e6	0.246860	0.123430	−	0.992353i	$-0.460611\pi$
$457$	1.10215e6	0.246860	0.123430	+	0.992353i	$0.460611\pi$
$458$	−1.40451e6	−0.312868
$459$	1.47720e6	0.327271
$460$	301097.	0.0663456
$461$	−5.06100e6	−1.10913	−0.554567	−	0.832139i	$-0.687116\pi$
$461$	−5.06100e6	−1.10913	−0.554567	+	0.832139i	$0.687116\pi$
$462$	−3.85165e6	−0.839541
$463$	3.45457e6	0.748931	0.374466	−	0.927241i	$-0.377826\pi$
$463$	3.45457e6	0.748931	0.374466	+	0.927241i	$0.377826\pi$
$464$	4.43118e6	0.955486
$465$	−2.51236e6	−0.538827
$466$	3.22596e6	0.688167
$467$	−121044.	−0.0256834	−0.0128417	−	0.999918i	$-0.504088\pi$
$467$	−121044.	−0.0256834	−0.0128417	+	0.999918i	$0.504088\pi$
$468$	−1.85545e6	−0.391592
$469$	−5.74704e6	−1.20646
$470$	2.81431e6	0.587661
$471$	−7.50722e6	−1.55929
$472$	886199.	0.183095
$473$	2.02375e6	0.415915
$474$	392312.	0.0802021
$475$	−225625.	−0.0458831
$476$	2.72393e6	0.551035
$477$	−728598.	−0.146620
$478$	−1.06677e7	−2.13551
$479$	1.97911e6	0.394123	0.197061	−	0.980391i	$-0.436860\pi$
$479$	1.97911e6	0.394123	0.197061	+	0.980391i	$0.436860\pi$
$480$	3.12775e6	0.619624
$481$	−6.15908e6	−1.21382
$482$	−3.17531e6	−0.622542
$483$	−2.16720e6	−0.422700
$484$	347026.	0.0673362
$485$	3.34072e6	0.644891
$486$	3.58494e6	0.688480
$487$	−3.55335e6	−0.678916	−0.339458	−	0.940621i	$-0.610244\pi$
$487$	−3.55335e6	−0.678916	−0.339458	+	0.940621i	$0.610244\pi$
$488$	−3.52827e6	−0.670675
$489$	−6.85313e6	−1.29603
$490$	−7.88350e6	−1.48330
$491$	−1.07469e6	−0.201178	−0.100589	−	0.994928i	$-0.532073\pi$
$491$	−1.07469e6	−0.201178	−0.100589	+	0.994928i	$0.532073\pi$
$492$	−667660.	−0.124349
$493$	1.71666e6	0.318102
$494$	−3.24421e6	−0.598125
$495$	−196661.	−0.0360748
$496$	6.98969e6	1.27571
$497$	1.67365e7	3.03930
$498$	2.07226e6	0.374430
$499$	−6.46554e6	−1.16239	−0.581197	−	0.813763i	$-0.697415\pi$
$499$	−6.46554e6	−1.16239	−0.581197	+	0.813763i	$0.697415\pi$
$500$	370349.	0.0662501
$501$	−8.33697e6	−1.48393
$502$	1.10509e6	0.195721
$503$	−965258.	−0.170108	−0.0850538	−	0.996376i	$-0.527106\pi$
$503$	−965258.	−0.170108	−0.0850538	+	0.996376i	$0.527106\pi$
$504$	−978418.	−0.171573
$505$	−1.01353e6	−0.176852
$506$	458878.	0.0796748
$507$	1.89294e7	3.27052
$508$	1.61939e6	0.278414
$509$	−6.56646e6	−1.12341	−0.561703	−	0.827339i	$-0.689854\pi$
$509$	−6.56646e6	−1.12341	−0.561703	+	0.827339i	$0.689854\pi$
$510$	1.54855e6	0.263632
$511$	−6.14907e6	−1.04173
$512$	−6.28274e6	−1.05919
$513$	1.12767e6	0.189186
$514$	2.34791e6	0.391989
$515$	3.93590e6	0.653922
$516$	−6.95741e6	−1.15033
$517$	1.82507e6	0.300299
$518$	9.27745e6	1.51916
$519$	−3.83058e6	−0.624233
$520$	−1.86422e6	−0.302335
$521$	−6.14413e6	−0.991667	−0.495834	−	0.868418i	$-0.665137\pi$
$521$	−6.14413e6	−0.991667	−0.495834	+	0.868418i	$0.665137\pi$
$522$	1.76136e6	0.282925
$523$	3.09188e6	0.494275	0.247138	−	0.968980i	$-0.420510\pi$
$523$	3.09188e6	0.494275	0.247138	+	0.968980i	$0.420510\pi$
$524$	8.81858e6	1.40304
$525$	−2.66566e6	−0.422091
$526$	7.55398e6	1.19045
$527$	2.70783e6	0.424713
$528$	2.59220e6	0.404654
$529$	−6.17815e6	−0.959885
$530$	2.09109e6	0.323358
$531$	930319.	0.143184
$532$	2.07941e6	0.318538
$533$	1.93261e6	0.294664
$534$	7.03071e6	1.06695
$535$	5.06123e6	0.764489
$536$	1.46452e6	0.220182
$537$	−1.31180e7	−1.96305
$538$	1.44930e7	2.15874
$539$	−5.11243e6	−0.757976
$540$	−1.85100e6	−0.273163
$541$	1.27977e7	1.87992	0.939959	−	0.341288i	$-0.110863\pi$
$541$	1.27977e7	1.87992	0.939959	+	0.341288i	$0.110863\pi$
$542$	−874668.	−0.127893
$543$	−3.93853e6	−0.573237
$544$	−3.37110e6	−0.488399
$545$	1.06809e6	0.154034
$546$	−3.83289e7	−5.50231
$547$	1.14963e7	1.64281	0.821407	−	0.570342i	$-0.193189\pi$
$547$	1.14963e7	1.64281	0.821407	+	0.570342i	$0.193189\pi$
$548$	−9239.22	−0.00131427
$549$	−3.70392e6	−0.524483
$550$	564420.	0.0795601
$551$	1.31047e6	0.183886
$552$	552268.	0.0771441
$553$	727867.	0.101214
$554$	2.51045e6	0.347517
$555$	2.24427e6	0.309273
$556$	−523003.	−0.0717492
$557$	7.26169e6	0.991744	0.495872	−	0.868395i	$-0.334848\pi$
$557$	7.26169e6	0.991744	0.495872	+	0.868395i	$0.334848\pi$
$558$	2.77835e6	0.377747
$559$	2.01390e7	2.72589
$560$	7.41619e6	0.999334
$561$	1.00423e6	0.134718
$562$	595525.	0.0795352
$563$	−4.31238e6	−0.573384	−0.286692	−	0.958023i	$-0.592556\pi$
$563$	−4.31238e6	−0.573384	−0.286692	+	0.958023i	$0.592556\pi$
$564$	−6.27437e6	−0.830563
$565$	985995.	0.129943
$566$	−4.92795e6	−0.646584
$567$	1.71621e7	2.24188
$568$	−4.26495e6	−0.554681
$569$	1.13499e7	1.46965	0.734824	−	0.678258i	$-0.237265\pi$
$569$	1.13499e7	1.46965	0.734824	+	0.678258i	$0.237265\pi$
$570$	1.18214e6	0.152398
$571$	−1.05538e7	−1.35463	−0.677314	−	0.735694i	$-0.736856\pi$
$571$	−1.05538e7	−1.35463	−0.677314	+	0.735694i	$0.736856\pi$
$572$	3.45336e6	0.441318
$573$	1.69466e7	2.15623
$574$	−2.91111e6	−0.368789
$575$	317581.	0.0400577
$576$	−919429.	−0.115468
$577$	−1.19152e7	−1.48992	−0.744959	−	0.667110i	$-0.767531\pi$
$577$	−1.19152e7	−1.48992	−0.744959	+	0.667110i	$0.767531\pi$
$578$	8.92793e6	1.11156
$579$	1.69270e7	2.09837
$580$	−2.15105e6	−0.265510
$581$	3.84472e6	0.472524
$582$	−1.75033e7	−2.14197
$583$	1.35607e6	0.165238
$584$	1.56697e6	0.190120
$585$	−1.95703e6	−0.236433
$586$	−9.64246e6	−1.15996
$587$	8.27396e6	0.991101	0.495551	−	0.868579i	$-0.334966\pi$
$587$	8.27396e6	0.991101	0.495551	+	0.868579i	$0.334966\pi$
$588$	1.75759e7	2.09640
$589$	2.06712e6	0.245515
$590$	−2.67003e6	−0.315782
$591$	−1.17970e7	−1.38932
$592$	−6.24382e6	−0.732228
$593$	1.09029e7	1.27323	0.636614	−	0.771182i	$-0.280334\pi$
$593$	1.09029e7	1.27323	0.636614	+	0.771182i	$0.280334\pi$
$594$	−2.82096e6	−0.328043
$595$	2.87306e6	0.332700
$596$	−1.17986e7	−1.36055
$597$	8.39592e6	0.964123
$598$	4.56643e6	0.522185
$599$	−1.23668e7	−1.40828	−0.704141	−	0.710060i	$-0.748668\pi$
$599$	−1.23668e7	−1.40828	−0.704141	+	0.710060i	$0.748668\pi$
$600$	679290.	0.0770330
$601$	−2.39529e6	−0.270502	−0.135251	−	0.990811i	$-0.543184\pi$
$601$	−2.39529e6	−0.270502	−0.135251	+	0.990811i	$0.543184\pi$
$602$	−3.03354e7	−3.41161
$603$	1.53743e6	0.172187
$604$	−1.09011e7	−1.21585
$605$	366025.	0.0406558
$606$	5.31030e6	0.587405
$607$	5.35241e6	0.589628	0.294814	−	0.955555i	$-0.404742\pi$
$607$	5.35241e6	0.589628	0.294814	+	0.955555i	$0.404742\pi$
$608$	−2.57345e6	−0.282329
$609$	1.54826e7	1.69161
$610$	1.06303e7	1.15670
$611$	1.81619e7	1.96815
$612$	−728698.	−0.0786446
$613$	−1.10953e7	−1.19259	−0.596293	−	0.802767i	$-0.703360\pi$
$613$	−1.10953e7	−1.19259	−0.596293	+	0.802767i	$0.703360\pi$
$614$	846846.	0.0906532
$615$	−704213.	−0.0750786
$616$	1.82103e6	0.193360
$617$	−3.42039e6	−0.361712	−0.180856	−	0.983510i	$-0.557887\pi$
$617$	−3.42039e6	−0.361712	−0.180856	+	0.983510i	$0.557887\pi$
$618$	−2.06217e7	−2.17197
$619$	−1.12682e7	−1.18203	−0.591014	−	0.806661i	$-0.701272\pi$
$619$	−1.12682e7	−1.18203	−0.591014	+	0.806661i	$0.701272\pi$
$620$	−3.39305e6	−0.354495
$621$	−1.58727e6	−0.165166
$622$	−6.83947e6	−0.708837
$623$	1.30443e7	1.34648
$624$	2.57958e7	2.65208
$625$	390625.	0.0400000
$626$	−2.18169e7	−2.22514
$627$	766613.	0.0778767
$628$	−1.01388e7	−1.02586
$629$	−2.41888e6	−0.243774
$630$	2.94788e6	0.295909
$631$	3.36865e6	0.336808	0.168404	−	0.985718i	$-0.446139\pi$
$631$	3.36865e6	0.336808	0.168404	+	0.985718i	$0.446139\pi$
$632$	−185482.	−0.0184718
$633$	−1.85450e7	−1.83957
$634$	−8.56465e6	−0.846227
$635$	1.70804e6	0.168099
$636$	−4.66199e6	−0.457013
$637$	−5.08753e7	−4.96774
$638$	−3.27825e6	−0.318853
$639$	−4.47728e6	−0.433773
$640$	−3.06415e6	−0.295706
$641$	−1.36912e7	−1.31613	−0.658063	−	0.752963i	$-0.728624\pi$
$641$	−1.36912e7	−1.31613	−0.658063	+	0.752963i	$0.728624\pi$
$642$	−2.65177e7	−2.53921
$643$	1.17373e7	1.11954	0.559772	−	0.828647i	$-0.310889\pi$
$643$	1.17373e7	1.11954	0.559772	+	0.828647i	$0.310889\pi$
$644$	−2.92690e6	−0.278095
$645$	−7.33831e6	−0.694539
$646$	−1.27411e6	−0.120123
$647$	1.56123e7	1.46625	0.733124	−	0.680095i	$-0.238062\pi$
$647$	1.56123e7	1.46625	0.733124	+	0.680095i	$0.238062\pi$
$648$	−4.37342e6	−0.409151
$649$	−1.73151e6	−0.161367
$650$	5.61671e6	0.521433
$651$	2.44221e7	2.25855
$652$	−9.25543e6	−0.852664
$653$	7.89449e6	0.724505	0.362252	−	0.932080i	$-0.382008\pi$
$653$	7.89449e6	0.724505	0.362252	+	0.932080i	$0.382008\pi$
$654$	−5.59614e6	−0.511616
$655$	9.30137e6	0.847118
$656$	1.95920e6	0.177754
$657$	1.64498e6	0.148678
$658$	−2.73573e7	−2.46325
$659$	−7.77485e6	−0.697395	−0.348697	−	0.937235i	$-0.613376\pi$
$659$	−7.77485e6	−0.697395	−0.348697	+	0.937235i	$0.613376\pi$
$660$	−1.25835e6	−0.112445
$661$	4.73782e6	0.421769	0.210885	−	0.977511i	$-0.432366\pi$
$661$	4.73782e6	0.421769	0.210885	+	0.977511i	$0.432366\pi$
$662$	−1.30184e7	−1.15455
$663$	9.99339e6	0.882935
$664$	−979749.	−0.0862372
$665$	2.19325e6	0.192324
$666$	−2.48187e6	−0.216817
$667$	−1.84457e6	−0.160539
$668$	−1.12594e7	−0.976282
$669$	−1.80892e7	−1.56262
$670$	−4.41245e6	−0.379746
$671$	6.89375e6	0.591084
$672$	−3.04041e7	−2.59723
$673$	−1.68755e7	−1.43622	−0.718108	−	0.695932i	$-0.754992\pi$
$673$	−1.68755e7	−1.43622	−0.718108	+	0.695932i	$0.754992\pi$
$674$	1.61921e7	1.37295
$675$	−1.95234e6	−0.164928
$676$	2.55649e7	2.15168
$677$	1.55000e7	1.29975	0.649875	−	0.760041i	$-0.274821\pi$
$677$	1.55000e7	1.29975	0.649875	+	0.760041i	$0.274821\pi$
$678$	−5.16601e6	−0.431600
$679$	−3.24744e7	−2.70313
$680$	−732142.	−0.0607188
$681$	1.18150e7	0.976257
$682$	−5.17107e6	−0.425716
$683$	2.20708e6	0.181036	0.0905182	−	0.995895i	$-0.471148\pi$
$683$	2.20708e6	0.181036	0.0905182	+	0.995895i	$0.471148\pi$
$684$	−556276.	−0.0454622
$685$	−9745.04	−0.000793519 0
$686$	4.61500e7	3.74422
$687$	3.30271e6	0.266980
$688$	2.04161e7	1.64437
$689$	1.34946e7	1.08296
$690$	−1.66393e6	−0.133049
$691$	−1.38014e7	−1.09958	−0.549790	−	0.835303i	$-0.685292\pi$
$691$	−1.38014e7	−1.09958	−0.549790	+	0.835303i	$0.685292\pi$
$692$	−5.17336e6	−0.410684
$693$	1.91169e6	0.151212
$694$	1.30338e7	1.02724
$695$	−551636.	−0.0433202
$696$	−3.94543e6	−0.308725
$697$	759004.	0.0591782
$698$	−7.22290e6	−0.561142
$699$	−7.58588e6	−0.587236
$700$	−3.60008e6	−0.277695
$701$	8.25725e6	0.634659	0.317329	−	0.948315i	$-0.397214\pi$
$701$	8.25725e6	0.634659	0.317329	+	0.948315i	$0.397214\pi$
$702$	−2.80722e7	−2.14998
$703$	−1.84654e6	−0.140919
$704$	1.71124e6	0.130131
$705$	−6.61788e6	−0.501471
$706$	2.41112e6	0.182057
$707$	9.85235e6	0.741295
$708$	5.95272e6	0.446305
$709$	−1.80125e6	−0.134573	−0.0672866	−	0.997734i	$-0.521434\pi$
$709$	−1.80125e6	−0.134573	−0.0672866	+	0.997734i	$0.521434\pi$
$710$	1.28499e7	0.956651
$711$	−194717.	−0.0144454
$712$	−3.32407e6	−0.245737
$713$	−2.90960e6	−0.214343
$714$	−1.50531e7	−1.10505
$715$	3.64242e6	0.266456
$716$	−1.77164e7	−1.29150
$717$	2.50853e7	1.82230
$718$	7.40135e6	0.535796
$719$	−2.34967e7	−1.69506	−0.847528	−	0.530751i	$-0.821910\pi$
$719$	−2.34967e7	−1.69506	−0.847528	+	0.530751i	$0.821910\pi$
$720$	−1.98395e6	−0.142626
$721$	−3.82600e7	−2.74099
$722$	−972638.	−0.0694398
$723$	7.46677e6	0.531235
$724$	−5.31915e6	−0.377134
$725$	−2.26882e6	−0.160308
$726$	−1.91775e6	−0.135036
$727$	−4.48887e6	−0.314993	−0.157496	−	0.987520i	$-0.550342\pi$
$727$	−4.48887e6	−0.314993	−0.157496	+	0.987520i	$0.550342\pi$
$728$	1.81217e7	1.26727
$729$	8.73071e6	0.608458
$730$	−4.72112e6	−0.327897
$731$	7.90926e6	0.547448
$732$	−2.36998e7	−1.63481
$733$	−5.21279e6	−0.358352	−0.179176	−	0.983817i	$-0.557343\pi$
$733$	−5.21279e6	−0.358352	−0.179176	+	0.983817i	$0.557343\pi$
$734$	−1.73103e7	−1.18594
$735$	1.85381e7	1.26575
$736$	3.62229e6	0.246484
$737$	−2.86146e6	−0.194053
$738$	778769.	0.0526342
$739$	5.82493e6	0.392355	0.196178	−	0.980568i	$-0.437147\pi$
$739$	5.82493e6	0.392355	0.196178	+	0.980568i	$0.437147\pi$
$740$	3.03098e6	0.203471
$741$	7.62880e6	0.510400
$742$	−2.03270e7	−1.35539
$743$	−9.62286e6	−0.639488	−0.319744	−	0.947504i	$-0.603597\pi$
$743$	−9.62286e6	−0.639488	−0.319744	+	0.947504i	$0.603597\pi$
$744$	−6.22348e6	−0.412193
$745$	−1.24446e7	−0.821464
$746$	−1.99139e7	−1.31011
$747$	−1.02853e6	−0.0674394
$748$	1.35625e6	0.0886313
$749$	−4.91991e7	−3.20444
$750$	−2.04664e6	−0.132858
$751$	2.97560e7	1.92520	0.962599	−	0.270930i	$-0.0873313\pi$
$751$	2.97560e7	1.92520	0.962599	+	0.270930i	$0.0873313\pi$
$752$	1.84117e7	1.18727
$753$	−2.59862e6	−0.167015
$754$	−3.26228e7	−2.08974
$755$	−1.14980e7	−0.734097
$756$	1.79932e7	1.14499
$757$	1.02348e7	0.649140	0.324570	−	0.945862i	$-0.394780\pi$
$757$	1.02348e7	0.649140	0.324570	+	0.945862i	$0.394780\pi$
$758$	1.05200e7	0.665030
$759$	−1.07906e6	−0.0679892
$760$	−558906.	−0.0350998
$761$	−1.95881e7	−1.22612	−0.613058	−	0.790038i	$-0.710061\pi$
$761$	−1.95881e7	−1.22612	−0.613058	+	0.790038i	$0.710061\pi$
$762$	−8.94910e6	−0.558332
$763$	−1.03827e7	−0.645651
$764$	2.28870e7	1.41859
$765$	−768592.	−0.0474834
$766$	1.97094e7	1.21367
$767$	−1.72308e7	−1.05759
$768$	2.39968e7	1.46808
$769$	1.08037e7	0.658804	0.329402	−	0.944190i	$-0.393153\pi$
$769$	1.08037e7	0.658804	0.329402	+	0.944190i	$0.393153\pi$
$770$	−5.48660e6	−0.333485
$771$	−5.52114e6	−0.334498
$772$	2.28606e7	1.38052
$773$	−5.57108e6	−0.335344	−0.167672	−	0.985843i	$-0.553625\pi$
$773$	−5.57108e6	−0.335344	−0.167672	+	0.985843i	$0.553625\pi$
$774$	8.11523e6	0.486910
$775$	−3.57881e6	−0.214035
$776$	8.27545e6	0.493330
$777$	−2.18160e7	−1.29635
$778$	−2.86445e7	−1.69665
$779$	579412.	0.0342093
$780$	−1.25222e7	−0.736960
$781$	8.33313e6	0.488855
$782$	1.79339e6	0.104872
$783$	1.13395e7	0.660983
$784$	−5.15753e7	−2.99676
$785$	−1.06939e7	−0.619386
$786$	−4.87335e7	−2.81366
$787$	1.91760e7	1.10363	0.551813	−	0.833968i	$-0.313936\pi$
$787$	1.91760e7	1.10363	0.551813	+	0.833968i	$0.313936\pi$
$788$	−1.59323e7	−0.914036
$789$	−1.77633e7	−1.01585
$790$	558841.	0.0318581
$791$	−9.58465e6	−0.544672
$792$	−487157.	−0.0275966
$793$	6.86018e7	3.87394
$794$	6.66972e6	0.375454
$795$	−4.91722e6	−0.275932
$796$	1.13390e7	0.634299
$797$	1.49102e6	0.0831455	0.0415727	−	0.999135i	$-0.486763\pi$
$797$	1.49102e6	0.0831455	0.0415727	+	0.999135i	$0.486763\pi$
$798$	−1.14913e7	−0.638795
$799$	7.13278e6	0.395268
$800$	4.45541e6	0.246129
$801$	−3.48956e6	−0.192172
$802$	−9.33510e6	−0.512487
$803$	−3.06163e6	−0.167558
$804$	9.83735e6	0.536708
$805$	−3.08714e6	−0.167906
$806$	−5.14589e7	−2.79012
$807$	−3.40803e7	−1.84213
$808$	−2.51067e6	−0.135289
$809$	−7.63352e6	−0.410066	−0.205033	−	0.978755i	$-0.565730\pi$
$809$	−7.63352e6	−0.410066	−0.205033	+	0.978755i	$0.565730\pi$
$810$	1.31767e7	0.705658
$811$	−2.07631e7	−1.10851	−0.554254	−	0.832347i	$-0.686997\pi$
$811$	−2.07631e7	−1.10851	−0.554254	+	0.832347i	$0.686997\pi$
$812$	2.09099e7	1.11292
$813$	2.05679e6	0.109135
$814$	4.61927e6	0.244350
$815$	−9.76214e6	−0.514815
$816$	1.01309e7	0.532625
$817$	6.03781e6	0.316464
$818$	2.92272e7	1.52723
$819$	1.90238e7	0.991034
$820$	−951068.	−0.0493943
$821$	2.62920e7	1.36134	0.680668	−	0.732592i	$-0.261690\pi$
$821$	2.62920e7	1.36134	0.680668	+	0.732592i	$0.261690\pi$
$822$	51058.0	0.00263563
$823$	9.99526e6	0.514392	0.257196	−	0.966359i	$-0.417201\pi$
$823$	9.99526e6	0.514392	0.257196	+	0.966359i	$0.417201\pi$
$824$	9.74980e6	0.500239
$825$	−1.32724e6	−0.0678913
$826$	2.59548e7	1.32363
$827$	−1.66299e7	−0.845523	−0.422762	−	0.906241i	$-0.638939\pi$
$827$	−1.66299e7	−0.845523	−0.422762	+	0.906241i	$0.638939\pi$
$828$	782994.	0.0396901
$829$	5.98849e6	0.302643	0.151322	−	0.988485i	$-0.451647\pi$
$829$	5.98849e6	0.302643	0.151322	+	0.988485i	$0.451647\pi$
$830$	2.95189e6	0.148732
$831$	−5.90334e6	−0.296548
$832$	1.70291e7	0.852871
$833$	−1.99805e7	−0.997685
$834$	2.89023e6	0.143886
$835$	−1.18759e7	−0.589452
$836$	1.03534e6	0.0512352
$837$	1.78868e7	0.882510
$838$	−3.42878e7	−1.68667
$839$	−2.12620e7	−1.04279	−0.521397	−	0.853314i	$-0.674589\pi$
$839$	−2.12620e7	−1.04279	−0.521397	+	0.853314i	$0.674589\pi$
$840$	−6.60323e6	−0.322893
$841$	−7.33347e6	−0.357536
$842$	−4.31317e7	−2.09661
$843$	−1.40038e6	−0.0678700
$844$	−2.50457e7	−1.21026
$845$	2.69645e7	1.29913
$846$	7.31853e6	0.351559
$847$	−3.55805e6	−0.170413
$848$	1.36803e7	0.653290
$849$	1.15881e7	0.551752
$850$	2.20587e6	0.104721
$851$	2.59912e6	0.123027
$852$	−2.86482e7	−1.35207
$853$	9.83372e6	0.462749	0.231374	−	0.972865i	$-0.425678\pi$
$853$	9.83372e6	0.462749	0.231374	+	0.972865i	$0.425678\pi$
$854$	−1.03335e8	−4.84846
$855$	−586731.	−0.0274488
$856$	1.25374e7	0.584821
$857$	−1.15987e7	−0.539457	−0.269729	−	0.962936i	$-0.586934\pi$
$857$	−1.15987e7	−0.539457	−0.269729	+	0.962936i	$0.586934\pi$
$858$	−1.90841e7	−0.885019
$859$	−2.46575e7	−1.14016	−0.570080	−	0.821589i	$-0.693088\pi$
$859$	−2.46575e7	−1.14016	−0.570080	+	0.821589i	$0.693088\pi$
$860$	−9.91069e6	−0.456938
$861$	6.84550e6	0.314700
$862$	−3.44483e7	−1.57906
$863$	−2.15332e7	−0.984196	−0.492098	−	0.870540i	$-0.663770\pi$
$863$	−2.15332e7	−0.984196	−0.492098	+	0.870540i	$0.663770\pi$
$864$	−2.22681e7	−1.01484
$865$	−5.45659e6	−0.247960
$866$	−5.00370e6	−0.226724
$867$	−2.09941e7	−0.948527
$868$	3.29831e7	1.48591
$869$	362407.	0.0162797
$870$	1.18872e7	0.532454
$871$	−2.84753e7	−1.27181
$872$	2.64581e6	0.117833
$873$	8.68745e6	0.385795
$874$	1.36905e6	0.0606234
$875$	−3.79718e6	−0.167664
$876$	1.05255e7	0.463429
$877$	3.11654e7	1.36828	0.684138	−	0.729353i	$-0.260179\pi$
$877$	3.11654e7	1.36828	0.684138	+	0.729353i	$0.260179\pi$
$878$	5.43132e7	2.37777
$879$	2.26743e7	0.989834
$880$	3.69254e6	0.160738
$881$	2.09112e6	0.0907692	0.0453846	−	0.998970i	$-0.485549\pi$
$881$	2.09112e6	0.0907692	0.0453846	+	0.998970i	$0.485549\pi$
$882$	−2.05008e7	−0.887359
$883$	−1.98601e7	−0.857195	−0.428597	−	0.903496i	$-0.640992\pi$
$883$	−1.98601e7	−0.857195	−0.428597	+	0.903496i	$0.640992\pi$
$884$	1.34965e7	0.580885
$885$	6.27861e6	0.269467
$886$	−2.92395e7	−1.25137
$887$	3.29181e7	1.40484	0.702418	−	0.711764i	$-0.252104\pi$
$887$	3.29181e7	1.40484	0.702418	+	0.711764i	$0.252104\pi$
$888$	5.55937e6	0.236588
$889$	−1.66035e7	−0.704605
$890$	1.00151e7	0.423819
$891$	8.54506e6	0.360596
$892$	−2.44302e7	−1.02805
$893$	5.44505e6	0.228493
$894$	6.52018e7	2.72845
$895$	−1.86863e7	−0.779770
$896$	2.97859e7	1.23948
$897$	−1.07380e7	−0.445598
$898$	5.86208e7	2.42583
$899$	2.07863e7	0.857785
$900$	963082.	0.0396330
$901$	5.29981e6	0.217494
$902$	−1.44945e6	−0.0593179
$903$	7.13341e7	2.91124
$904$	2.44245e6	0.0994043
$905$	−5.61035e6	−0.227703
$906$	6.02422e7	2.43826
$907$	−2.42865e7	−0.980273	−0.490136	−	0.871646i	$-0.663053\pi$
$907$	−2.42865e7	−0.980273	−0.490136	+	0.871646i	$0.663053\pi$
$908$	1.59566e7	0.642281
$909$	−2.63567e6	−0.105799
$910$	−5.45988e7	−2.18565
$911$	−2.37784e6	−0.0949264	−0.0474632	−	0.998873i	$-0.515114\pi$
$911$	−2.37784e6	−0.0949264	−0.0474632	+	0.998873i	$0.515114\pi$
$912$	7.73376e6	0.307895
$913$	1.91429e6	0.0760032
$914$	−8.22578e6	−0.325695
$915$	−2.49973e7	−0.987055
$916$	4.46045e6	0.175647
$917$	−9.04166e7	−3.55079
$918$	−1.10249e7	−0.431786
$919$	8.06201e6	0.314887	0.157443	−	0.987528i	$-0.449675\pi$
$919$	8.06201e6	0.314887	0.157443	+	0.987528i	$0.449675\pi$
$920$	786695.	0.0306434
$921$	−1.99137e6	−0.0773574
$922$	3.77723e7	1.46334
$923$	8.29255e7	3.20393
$924$	1.22321e7	0.471326
$925$	3.19691e6	0.122850
$926$	−2.57829e7	−0.988106
$927$	1.02352e7	0.391198
$928$	−2.58778e7	−0.986410
$929$	−1.65395e7	−0.628757	−0.314378	−	0.949298i	$-0.601796\pi$
$929$	−1.65395e7	−0.628757	−0.314378	+	0.949298i	$0.601796\pi$
$930$	1.87508e7	0.710905
$931$	−1.52528e7	−0.576733
$932$	−1.02450e7	−0.386344
$933$	1.60831e7	0.604874
$934$	903402.	0.0338855
$935$	1.43050e6	0.0535131
$936$	−4.84784e6	−0.180867
$937$	−1.90569e7	−0.709091	−0.354546	−	0.935039i	$-0.615364\pi$
$937$	−1.90569e7	−0.709091	−0.354546	+	0.935039i	$0.615364\pi$
$938$	4.28924e7	1.59175
$939$	5.13028e7	1.89879
$940$	−8.93772e6	−0.329919
$941$	1.67445e7	0.616452	0.308226	−	0.951313i	$-0.400265\pi$
$941$	1.67445e7	0.616452	0.308226	+	0.951313i	$0.400265\pi$
$942$	5.60294e7	2.05726
$943$	−815559.	−0.0298659
$944$	−1.74679e7	−0.637984
$945$	1.89782e7	0.691316
$946$	−1.51041e7	−0.548740
$947$	4.79164e7	1.73624	0.868119	−	0.496357i	$-0.165329\pi$
$947$	4.79164e7	1.73624	0.868119	+	0.496357i	$0.165329\pi$
$948$	−1.24591e6	−0.0450262
$949$	−3.04672e7	−1.09817
$950$	1.68393e6	0.0605362
$951$	2.01399e7	0.722113
$952$	7.11699e6	0.254510
$953$	−4.16200e7	−1.48446	−0.742232	−	0.670143i	$-0.766233\pi$
$953$	−4.16200e7	−1.48446	−0.742232	+	0.670143i	$0.766233\pi$
$954$	5.43782e6	0.193443
$955$	2.41400e7	0.856505
$956$	3.38787e7	1.19890
$957$	7.70883e6	0.272088
$958$	−1.47709e7	−0.519988
$959$	94729.4	0.00332612
$960$	−6.20512e6	−0.217306
$961$	4.15897e6	0.145270
$962$	4.59677e7	1.60146
$963$	1.31616e7	0.457343
$964$	1.00842e7	0.349501
$965$	2.41121e7	0.833522
$966$	1.61747e7	0.557691
$967$	−3.72083e6	−0.127960	−0.0639799	−	0.997951i	$-0.520379\pi$
$967$	−3.72083e6	−0.127960	−0.0639799	+	0.997951i	$0.520379\pi$
$968$	906697.	0.0311010
$969$	2.99609e6	0.102505
$970$	−2.49332e7	−0.850840
$971$	−8.15619e6	−0.277613	−0.138806	−	0.990320i	$-0.544327\pi$
$971$	−8.15619e6	−0.277613	−0.138806	+	0.990320i	$0.544327\pi$
$972$	−1.13851e7	−0.386519
$973$	5.36233e6	0.181582
$974$	2.65201e7	0.895731
$975$	−1.32078e7	−0.444956
$976$	6.95456e7	2.33693
$977$	2.12844e7	0.713386	0.356693	−	0.934222i	$-0.383904\pi$
$977$	2.12844e7	0.713386	0.356693	+	0.934222i	$0.383904\pi$
$978$	5.11476e7	1.70993
$979$	6.49477e6	0.216574
$980$	2.50365e7	0.832738
$981$	2.77754e6	0.0921482
$982$	8.02085e6	0.265425
$983$	−3.84409e7	−1.26885	−0.634425	−	0.772985i	$-0.718763\pi$
$983$	−3.84409e7	−1.26885	−0.634425	+	0.772985i	$0.718763\pi$
$984$	−1.74444e6	−0.0574338
$985$	−1.68046e7	−0.551870
$986$	−1.28121e7	−0.419689
$987$	6.43309e7	2.10197
$988$	1.03030e7	0.335793
$989$	−8.49860e6	−0.276285
$990$	1.46776e6	0.0475955
$991$	2.88498e7	0.933166	0.466583	−	0.884478i	$-0.345485\pi$
$991$	2.88498e7	0.933166	0.466583	+	0.884478i	$0.345485\pi$
$992$	−4.08194e7	−1.31700
$993$	3.06129e7	0.985215
$994$	−1.24911e8	−4.00991
$995$	1.19598e7	0.382972
$996$	−6.58110e6	−0.210208
$997$	−5.27226e7	−1.67981	−0.839903	−	0.542736i	$-0.817388\pi$
$997$	−5.27226e7	−1.67981	−0.839903	+	0.542736i	$0.817388\pi$
$998$	4.82549e7	1.53361
$999$	−1.59781e7	−0.506538

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.f.1.7	✓	38

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.f.1.7	✓	38	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)

\(f(q)\)	\(=\)	\(q-7.46340 q^{2} +17.5503 q^{3} +23.7024 q^{4} +25.0000 q^{5} -130.985 q^{6} -243.020 q^{7} +61.9286 q^{8} +65.0117 q^{9} +O(q^{10})\)	\(q-7.46340 q^{2} +17.5503 q^{3} +23.7024 q^{4} +25.0000 q^{5} -130.985 q^{6} -243.020 q^{7} +61.9286 q^{8} +65.0117 q^{9} -186.585 q^{10} -121.000 q^{11} +415.983 q^{12} -1204.11 q^{13} +1813.75 q^{14} +438.757 q^{15} -1220.67 q^{16} -472.894 q^{17} -485.209 q^{18} -361.000 q^{19} +592.559 q^{20} -4265.06 q^{21} +903.072 q^{22} +508.130 q^{23} +1086.86 q^{24} +625.000 q^{25} +8986.74 q^{26} -3123.74 q^{27} -5760.14 q^{28} -3630.11 q^{29} -3274.62 q^{30} -5726.09 q^{31} +7128.66 q^{32} -2123.58 q^{33} +3529.40 q^{34} -6075.49 q^{35} +1540.93 q^{36} +5115.06 q^{37} +2694.29 q^{38} -21132.4 q^{39} +1548.22 q^{40} -1605.02 q^{41} +31831.8 q^{42} -16725.2 q^{43} -2867.99 q^{44} +1625.29 q^{45} -3792.38 q^{46} -15083.3 q^{47} -21423.1 q^{48} +42251.5 q^{49} -4664.63 q^{50} -8299.42 q^{51} -28540.2 q^{52} -11207.2 q^{53} +23313.7 q^{54} -3025.00 q^{55} -15049.9 q^{56} -6335.65 q^{57} +27093.0 q^{58} +14310.0 q^{59} +10399.6 q^{60} -56973.2 q^{61} +42736.1 q^{62} -15799.1 q^{63} -14142.5 q^{64} -30102.7 q^{65} +15849.1 q^{66} +23648.5 q^{67} -11208.7 q^{68} +8917.82 q^{69} +45343.8 q^{70} -68868.8 q^{71} +4026.09 q^{72} +25302.8 q^{73} -38175.8 q^{74} +10968.9 q^{75} -8556.55 q^{76} +29405.4 q^{77} +157720. q^{78} -2995.10 q^{79} -30516.8 q^{80} -70620.3 q^{81} +11978.9 q^{82} -15820.6 q^{83} -101092. q^{84} -11822.4 q^{85} +124827. q^{86} -63709.4 q^{87} -7493.36 q^{88} -53675.8 q^{89} -12130.2 q^{90} +292622. q^{91} +12043.9 q^{92} -100494. q^{93} +112572. q^{94} -9025.00 q^{95} +125110. q^{96} +133629. q^{97} -315340. q^{98} -7866.42 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9}+O(q^{10}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9	\( 38 q + 8 q^{2} + 63 q^{3} + 616 q^{4} + 950 q^{5} + 149 q^{6} + 275 q^{7} + 264 q^{8} + 3029 q^{9} + 200 q^{10} - 4598 q^{11} + 2312 q^{12} + 41 q^{13} + 23 q^{14} + 1575 q^{15} + 7196 q^{16} - 2431 q^{17} - 1689 q^{18} - 13718 q^{19} + 15400 q^{20} - 1577 q^{21} - 968 q^{22} + 9284 q^{23} + 7598 q^{24} + 23750 q^{25} + 13129 q^{26} + 9228 q^{27} - 1079 q^{28} - 559 q^{29} + 3725 q^{30} + 11147 q^{31} + 11051 q^{32} - 7623 q^{33} + 40895 q^{34} + 6875 q^{35} + 55887 q^{36} + 41579 q^{37} - 2888 q^{38} + 24982 q^{39} + 6600 q^{40} + 18597 q^{41} + 61360 q^{42} + 25353 q^{43} - 74536 q^{44} + 75725 q^{45} + 1611 q^{46} + 63516 q^{47} + 187737 q^{48} + 141609 q^{49} + 5000 q^{50} + 107546 q^{51} + 60018 q^{52} + 123045 q^{53} + 256696 q^{54} - 114950 q^{55} + 157335 q^{56} - 22743 q^{57} + 218938 q^{58} + 132925 q^{59} + 57800 q^{60} - 59107 q^{61} + 166982 q^{62} + 130582 q^{63} + 313126 q^{64} + 1025 q^{65} - 18029 q^{66} + 162534 q^{67} + 182980 q^{68} + 178552 q^{69} + 575 q^{70} + 157840 q^{71} + 98630 q^{72} - 63010 q^{73} + 122683 q^{74} + 39375 q^{75} - 222376 q^{76} - 33275 q^{77} + 277272 q^{78} - 16385 q^{79} + 179900 q^{80} + 290354 q^{81} + 362302 q^{82} + 138461 q^{83} + 446870 q^{84} - 60775 q^{85} + 643902 q^{86} + 291602 q^{87} - 31944 q^{88} + 224792 q^{89} - 42225 q^{90} + 498548 q^{91} + 581088 q^{92} + 134210 q^{93} + 35864 q^{94} - 342950 q^{95} + 377376 q^{96} + 292216 q^{97} - 58230 q^{98} - 366509 q^{99}+O(q^{100}) \) 38 * q + 8 * q^2 + 63 * q^3 + 616 * q^4 + 950 * q^5 + 149 * q^6 + 275 * q^7 + 264 * q^8 + 3029 * q^9 + 200 * q^10 - 4598 * q^11 + 2312 * q^12 + 41 * q^13 + 23 * q^14 + 1575 * q^15 + 7196 * q^16 - 2431 * q^17 - 1689 * q^18 - 13718 * q^19 + 15400 * q^20 - 1577 * q^21 - 968 * q^22 + 9284 * q^23 + 7598 * q^24 + 23750 * q^25 + 13129 * q^26 + 9228 * q^27 - 1079 * q^28 - 559 * q^29 + 3725 * q^30 + 11147 * q^31 + 11051 * q^32 - 7623 * q^33 + 40895 * q^34 + 6875 * q^35 + 55887 * q^36 + 41579 * q^37 - 2888 * q^38 + 24982 * q^39 + 6600 * q^40 + 18597 * q^41 + 61360 * q^42 + 25353 * q^43 - 74536 * q^44 + 75725 * q^45 + 1611 * q^46 + 63516 * q^47 + 187737 * q^48 + 141609 * q^49 + 5000 * q^50 + 107546 * q^51 + 60018 * q^52 + 123045 * q^53 + 256696 * q^54 - 114950 * q^55 + 157335 * q^56 - 22743 * q^57 + 218938 * q^58 + 132925 * q^59 + 57800 * q^60 - 59107 * q^61 + 166982 * q^62 + 130582 * q^63 + 313126 * q^64 + 1025 * q^65 - 18029 * q^66 + 162534 * q^67 + 182980 * q^68 + 178552 * q^69 + 575 * q^70 + 157840 * q^71 + 98630 * q^72 - 63010 * q^73 + 122683 * q^74 + 39375 * q^75 - 222376 * q^76 - 33275 * q^77 + 277272 * q^78 - 16385 * q^79 + 179900 * q^80 + 290354 * q^81 + 362302 * q^82 + 138461 * q^83 + 446870 * q^84 - 60775 * q^85 + 643902 * q^86 + 291602 * q^87 - 31944 * q^88 + 224792 * q^89 - 42225 * q^90 + 498548 * q^91 + 581088 * q^92 + 134210 * q^93 + 35864 * q^94 - 342950 * q^95 + 377376 * q^96 + 292216 * q^97 - 58230 * q^98 - 366509 * q^99

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