LMFDB - Embedded newform 1045.6.a.h.1.15

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:	$40$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-2.77766 q^{2} -22.7115 q^{3} -24.2846 q^{4} +25.0000 q^{5} +63.0848 q^{6} -147.613 q^{7} +156.340 q^{8} +272.811 q^{9} +O(q^{10})$	\(q-2.77766 q^{2} -22.7115 q^{3} -24.2846 q^{4} +25.0000 q^{5} +63.0848 q^{6} -147.613 q^{7} +156.340 q^{8} +272.811 q^{9} -69.4415 q^{10} +121.000 q^{11} +551.539 q^{12} +639.175 q^{13} +410.019 q^{14} -567.787 q^{15} +342.849 q^{16} -659.486 q^{17} -757.777 q^{18} +361.000 q^{19} -607.115 q^{20} +3352.51 q^{21} -336.097 q^{22} +4675.18 q^{23} -3550.70 q^{24} +625.000 q^{25} -1775.41 q^{26} -677.054 q^{27} +3584.72 q^{28} +5066.41 q^{29} +1577.12 q^{30} +4496.85 q^{31} -5955.18 q^{32} -2748.09 q^{33} +1831.83 q^{34} -3690.32 q^{35} -6625.11 q^{36} +12358.5 q^{37} -1002.74 q^{38} -14516.6 q^{39} +3908.49 q^{40} +17965.0 q^{41} -9312.13 q^{42} +13840.7 q^{43} -2938.44 q^{44} +6820.28 q^{45} -12986.1 q^{46} -6956.38 q^{47} -7786.60 q^{48} +4982.57 q^{49} -1736.04 q^{50} +14977.9 q^{51} -15522.1 q^{52} +20615.9 q^{53} +1880.63 q^{54} +3025.00 q^{55} -23077.7 q^{56} -8198.84 q^{57} -14072.8 q^{58} +5808.65 q^{59} +13788.5 q^{60} -29010.9 q^{61} -12490.7 q^{62} -40270.4 q^{63} +5570.32 q^{64} +15979.4 q^{65} +7633.26 q^{66} -15642.2 q^{67} +16015.4 q^{68} -106180. q^{69} +10250.5 q^{70} +45233.9 q^{71} +42651.2 q^{72} -39182.9 q^{73} -34327.6 q^{74} -14194.7 q^{75} -8766.74 q^{76} -17861.2 q^{77} +40322.2 q^{78} -8183.99 q^{79} +8571.22 q^{80} -50916.2 q^{81} -49900.8 q^{82} +35339.3 q^{83} -81414.3 q^{84} -16487.2 q^{85} -38444.8 q^{86} -115066. q^{87} +18917.1 q^{88} -34162.3 q^{89} -18944.4 q^{90} -94350.5 q^{91} -113535. q^{92} -102130. q^{93} +19322.5 q^{94} +9025.00 q^{95} +135251. q^{96} -23325.9 q^{97} -13839.9 q^{98} +33010.1 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) $ 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * 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 $

$2$	−2.77766	−0.491026	−0.245513	−	0.969393i	$-0.578956\pi$
$2$	−2.77766	−0.491026	−0.245513	+	0.969393i	$0.578956\pi$
$3$	−22.7115	−1.45694	−0.728471	−	0.685077i	$-0.759769\pi$
$3$	−22.7115	−1.45694	−0.728471	+	0.685077i	$0.759769\pi$
$4$	−24.2846	−0.758894
$5$	25.0000	0.447214
$5$	25.0000	0.447214
$6$	63.0848	0.715396
$7$	−147.613	−1.13862	−0.569311	−	0.822123i	$-0.692790\pi$
$7$	−147.613	−1.13862	−0.569311	+	0.822123i	$0.692790\pi$
$8$	156.340	0.863662
$9$	272.811	1.12268
$10$	−69.4415	−0.219593
$11$	121.000	0.301511
$11$	121.000	0.301511
$12$	551.539	1.10566
$13$	639.175	1.04897	0.524483	−	0.851421i	$-0.324259\pi$
$13$	639.175	1.04897	0.524483	+	0.851421i	$0.324259\pi$
$14$	410.019	0.559092
$15$	−567.787	−0.651564
$16$	342.849	0.334813
$17$	−659.486	−0.553456	−0.276728	−	0.960948i	$-0.589250\pi$
$17$	−659.486	−0.553456	−0.276728	+	0.960948i	$0.589250\pi$
$18$	−757.777	−0.551265
$19$	361.000	0.229416
$19$	361.000	0.229416
$20$	−607.115	−0.339388
$21$	3352.51	1.65890
$22$	−336.097	−0.148050
$23$	4675.18	1.84280	0.921401	−	0.388614i	$-0.127046\pi$
$23$	4675.18	1.84280	0.921401	+	0.388614i	$0.127046\pi$
$24$	−3550.70	−1.25831
$25$	625.000	0.200000
$26$	−1775.41	−0.515069
$27$	−677.054	−0.178737
$28$	3584.72	0.864092
$29$	5066.41	1.11868	0.559340	−	0.828939i	$-0.311055\pi$
$29$	5066.41	1.11868	0.559340	+	0.828939i	$0.311055\pi$
$30$	1577.12	0.319935
$31$	4496.85	0.840435	0.420218	−	0.907423i	$-0.361954\pi$
$31$	4496.85	0.840435	0.420218	+	0.907423i	$0.361954\pi$
$32$	−5955.18	−1.02806
$33$	−2748.09	−0.439284
$34$	1831.83	0.271761
$35$	−3690.32	−0.509207
$36$	−6625.11	−0.851994
$37$	12358.5	1.48409	0.742045	−	0.670350i	$-0.233856\pi$
$37$	12358.5	1.48409	0.742045	+	0.670350i	$0.233856\pi$
$38$	−1002.74	−0.112649
$39$	−14516.6	−1.52828
$40$	3908.49	0.386241
$41$	17965.0	1.66905	0.834523	−	0.550973i	$-0.185743\pi$
$41$	17965.0	1.66905	0.834523	+	0.550973i	$0.185743\pi$
$42$	−9312.13	−0.814565
$43$	13840.7	1.14153	0.570764	−	0.821114i	$-0.306647\pi$
$43$	13840.7	1.14153	0.570764	+	0.821114i	$0.306647\pi$
$44$	−2938.44	−0.228815
$45$	6820.28	0.502078
$46$	−12986.1	−0.904863
$47$	−6956.38	−0.459345	−0.229672	−	0.973268i	$-0.573765\pi$
$47$	−6956.38	−0.459345	−0.229672	+	0.973268i	$0.573765\pi$
$48$	−7786.60	−0.487803
$49$	4982.57	0.296458
$50$	−1736.04	−0.0982052
$51$	14977.9	0.806354
$52$	−15522.1	−0.796054
$53$	20615.9	1.00812	0.504060	−	0.863669i	$-0.331839\pi$
$53$	20615.9	1.00812	0.504060	+	0.863669i	$0.331839\pi$
$54$	1880.63	0.0877644
$55$	3025.00	0.134840
$56$	−23077.7	−0.983384
$57$	−8198.84	−0.334245
$58$	−14072.8	−0.549300
$59$	5808.65	0.217243	0.108621	−	0.994083i	$-0.465356\pi$
$59$	5808.65	0.217243	0.108621	+	0.994083i	$0.465356\pi$
$60$	13788.5	0.494468
$61$	−29010.9	−0.998243	−0.499121	−	0.866532i	$-0.666344\pi$
$61$	−29010.9	−0.998243	−0.499121	+	0.866532i	$0.666344\pi$
$62$	−12490.7	−0.412675
$63$	−40270.4	−1.27831
$64$	5570.32	0.169993
$65$	15979.4	0.469112
$66$	7633.26	0.215700
$67$	−15642.2	−0.425706	−0.212853	−	0.977084i	$-0.568276\pi$
$67$	−15642.2	−0.425706	−0.212853	+	0.977084i	$0.568276\pi$
$68$	16015.4	0.420015
$69$	−106180.	−2.68485
$70$	10250.5	0.250034
$71$	45233.9	1.06492	0.532462	−	0.846454i	$-0.321267\pi$
$71$	45233.9	1.06492	0.532462	+	0.846454i	$0.321267\pi$
$72$	42651.2	0.969616
$73$	−39182.9	−0.860576	−0.430288	−	0.902692i	$-0.641588\pi$
$73$	−39182.9	−0.860576	−0.430288	+	0.902692i	$0.641588\pi$
$74$	−34327.6	−0.728726
$75$	−14194.7	−0.291388
$76$	−8766.74	−0.174102
$77$	−17861.2	−0.343307
$78$	40322.2	0.750426
$79$	−8183.99	−0.147536	−0.0737679	−	0.997275i	$-0.523502\pi$
$79$	−8183.99	−0.147536	−0.0737679	+	0.997275i	$0.523502\pi$
$80$	8571.22	0.149733
$81$	−50916.2	−0.862270
$82$	−49900.8	−0.819545
$83$	35339.3	0.563071	0.281535	−	0.959551i	$-0.409156\pi$
$83$	35339.3	0.563071	0.281535	+	0.959551i	$0.409156\pi$
$84$	−81414.3	−1.25893
$85$	−16487.2	−0.247513
$86$	−38444.8	−0.560520
$87$	−115066.	−1.62985
$88$	18917.1	0.260404
$89$	−34162.3	−0.457164	−0.228582	−	0.973525i	$-0.573409\pi$
$89$	−34162.3	−0.457164	−0.228582	+	0.973525i	$0.573409\pi$
$90$	−18944.4	−0.246533
$91$	−94350.5	−1.19437
$92$	−113535.	−1.39849
$93$	−102130.	−1.22447
$94$	19322.5	0.225550
$95$	9025.00	0.102598
$96$	135251.	1.49783
$97$	−23325.9	−0.251715	−0.125858	−	0.992048i	$-0.540168\pi$
$97$	−23325.9	−0.251715	−0.125858	+	0.992048i	$0.540168\pi$
$98$	−13839.9	−0.145568
$99$	33010.1	0.338501
$100$	−15177.9	−0.151779
$101$	152832.	1.49077	0.745386	−	0.666633i	$-0.232265\pi$
$101$	152832.	1.49077	0.745386	+	0.666633i	$0.232265\pi$
$102$	−41603.6	−0.395941
$103$	197206.	1.83158	0.915791	−	0.401654i	$-0.131565\pi$
$103$	197206.	1.83158	0.915791	+	0.401654i	$0.131565\pi$
$104$	99928.4	0.905952
$105$	83812.7	0.741885
$106$	−57263.9	−0.495013
$107$	108757.	0.918327	0.459164	−	0.888352i	$-0.348149\pi$
$107$	108757.	0.918327	0.459164	+	0.888352i	$0.348149\pi$
$108$	16442.0	0.135642
$109$	−112523.	−0.907138	−0.453569	−	0.891221i	$-0.649850\pi$
$109$	−112523.	−0.907138	−0.453569	+	0.891221i	$0.649850\pi$
$110$	−8402.43	−0.0662099
$111$	−280679.	−2.16223
$112$	−50608.9	−0.381225
$113$	−148256.	−1.09224	−0.546119	−	0.837707i	$-0.683895\pi$
$113$	−148256.	−1.09224	−0.546119	+	0.837707i	$0.683895\pi$
$114$	22773.6	0.164123
$115$	116879.	0.824126
$116$	−123036.	−0.848959
$117$	174374.	1.17765
$118$	−16134.5	−0.106672
$119$	97348.7	0.630177
$120$	−88767.5	−0.562731
$121$	14641.0	0.0909091
$122$	80582.4	0.490163
$123$	−408012.	−2.43170
$124$	−109204.	−0.637801
$125$	15625.0	0.0894427
$126$	111858.	0.627681
$127$	210080.	1.15578	0.577891	−	0.816114i	$-0.303876\pi$
$127$	210080.	1.15578	0.577891	+	0.816114i	$0.303876\pi$
$128$	175093.	0.944593
$129$	−314343.	−1.66314
$130$	−44385.3	−0.230346
$131$	−10568.2	−0.0538052	−0.0269026	−	0.999638i	$-0.508564\pi$
$131$	−10568.2	−0.0538052	−0.0269026	+	0.999638i	$0.508564\pi$
$132$	66736.2	0.333370
$133$	−53288.3	−0.261218
$134$	43448.7	0.209033
$135$	−16926.4	−0.0799335
$136$	−103104.	−0.477999
$137$	−44366.9	−0.201956	−0.100978	−	0.994889i	$-0.532197\pi$
$137$	−44366.9	−0.201956	−0.100978	+	0.994889i	$0.532197\pi$
$138$	294933.	1.31833
$139$	93755.3	0.411584	0.205792	−	0.978596i	$-0.434023\pi$
$139$	93755.3	0.411584	0.205792	+	0.978596i	$0.434023\pi$
$140$	89618.0	0.386434
$141$	157990.	0.669238
$142$	−125645.	−0.522905
$143$	77340.2	0.316275
$144$	93533.0	0.375888
$145$	126660.	0.500289
$146$	108837.	0.422565
$147$	−113161.	−0.431922
$148$	−300120.	−1.12627
$149$	−459538.	−1.69573	−0.847863	−	0.530215i	$-0.822111\pi$
$149$	−459538.	−1.69573	−0.847863	+	0.530215i	$0.822111\pi$
$150$	39428.0	0.143079
$151$	100751.	0.359591	0.179796	−	0.983704i	$-0.442456\pi$
$151$	100751.	0.359591	0.179796	+	0.983704i	$0.442456\pi$
$152$	56438.6	0.198138
$153$	−179915.	−0.621354
$154$	49612.3	0.168573
$155$	112421.	0.375854
$156$	352530.	1.15980
$157$	−265063.	−0.858224	−0.429112	−	0.903251i	$-0.641173\pi$
$157$	−265063.	−0.858224	−0.429112	+	0.903251i	$0.641173\pi$
$158$	22732.4	0.0724439
$159$	−468217.	−1.46877
$160$	−148880.	−0.459764
$161$	−690117.	−2.09825
$162$	141428.	0.423397
$163$	423842.	1.24950	0.624749	−	0.780826i	$-0.285201\pi$
$163$	423842.	1.24950	0.624749	+	0.780826i	$0.285201\pi$
$164$	−436274.	−1.26663
$165$	−68702.2	−0.196454
$166$	−98160.7	−0.276482
$167$	127790.	0.354572	0.177286	−	0.984159i	$-0.443268\pi$
$167$	127790.	0.354572	0.177286	+	0.984159i	$0.443268\pi$
$168$	524129.	1.43273
$169$	37251.9	0.100330
$170$	45795.7	0.121535
$171$	98484.8	0.257560
$172$	−336116.	−0.866299
$173$	−739707.	−1.87908	−0.939539	−	0.342442i	$-0.888746\pi$
$173$	−739707.	−1.87908	−0.939539	+	0.342442i	$0.888746\pi$
$174$	319614.	0.800299
$175$	−92258.1	−0.227724
$176$	41484.7	0.100950
$177$	−131923.	−0.316510
$178$	94891.3	0.224479
$179$	−158041.	−0.368670	−0.184335	−	0.982863i	$-0.559013\pi$
$179$	−158041.	−0.368670	−0.184335	+	0.982863i	$0.559013\pi$
$180$	−165628.	−0.381023
$181$	98306.9	0.223042	0.111521	−	0.993762i	$-0.464428\pi$
$181$	98306.9	0.223042	0.111521	+	0.993762i	$0.464428\pi$
$182$	262074.	0.586469
$183$	658880.	1.45438
$184$	730915.	1.59156
$185$	308962.	0.663705
$186$	283683.	0.601244
$187$	−79797.8	−0.166873
$188$	168933.	0.348594
$189$	99941.9	0.203514
$190$	−25068.4	−0.0503782
$191$	−739015.	−1.46578	−0.732892	−	0.680345i	$-0.761830\pi$
$191$	−739015.	−1.46578	−0.732892	+	0.680345i	$0.761830\pi$
$192$	−126510.	−0.247670
$193$	−57053.8	−0.110253	−0.0551266	−	0.998479i	$-0.517556\pi$
$193$	−57053.8	−0.110253	−0.0551266	+	0.998479i	$0.517556\pi$
$194$	64791.5	0.123599
$195$	−362915.	−0.683469
$196$	−121000.	−0.224980
$197$	389659.	0.715351	0.357675	−	0.933846i	$-0.383569\pi$
$197$	389659.	0.715351	0.357675	+	0.933846i	$0.383569\pi$
$198$	−91691.0	−0.166213
$199$	541641.	0.969569	0.484784	−	0.874634i	$-0.338898\pi$
$199$	541641.	0.969569	0.484784	+	0.874634i	$0.338898\pi$
$200$	97712.2	0.172732
$201$	355257.	0.620229
$202$	−424516.	−0.732007
$203$	−747868.	−1.27375
$204$	−363732.	−0.611937
$205$	449126.	0.746420
$206$	−547771.	−0.899354
$207$	1.27544e6	2.06888
$208$	219140.	0.351208
$209$	43681.0	0.0691714
$210$	−232803.	−0.364285
$211$	1.05480e6	1.63104	0.815520	−	0.578729i	$-0.196451\pi$
$211$	1.05480e6	1.63104	0.815520	+	0.578729i	$0.196451\pi$
$212$	−500648.	−0.765056
$213$	−1.02733e6	−1.55153
$214$	−302090.	−0.450922
$215$	346017.	0.510507
$216$	−105850.	−0.154368
$217$	−663793.	−0.956937
$218$	312550.	0.445428
$219$	889901.	1.25381
$220$	−73460.9	−0.102329
$221$	−421527.	−0.580557
$222$	779631.	1.06171
$223$	645294.	0.868951	0.434475	−	0.900684i	$-0.356934\pi$
$223$	645294.	0.868951	0.434475	+	0.900684i	$0.356934\pi$
$224$	879062.	1.17058
$225$	170507.	0.224536
$226$	411806.	0.536317
$227$	397053.	0.511427	0.255714	−	0.966753i	$-0.417690\pi$
$227$	397053.	0.511427	0.255714	+	0.966753i	$0.417690\pi$
$228$	199106.	0.253657
$229$	433047.	0.545690	0.272845	−	0.962058i	$-0.412035\pi$
$229$	433047.	0.545690	0.272845	+	0.962058i	$0.412035\pi$
$230$	−324652.	−0.404667
$231$	405653.	0.500179
$232$	792081.	0.966161
$233$	775837.	0.936226	0.468113	−	0.883669i	$-0.344934\pi$
$233$	775837.	0.936226	0.468113	+	0.883669i	$0.344934\pi$
$234$	−484352.	−0.578258
$235$	−173909.	−0.205425
$236$	−141061.	−0.164864
$237$	185871.	0.214951
$238$	−270402.	−0.309433
$239$	−16141.9	−0.0182794	−0.00913968	−	0.999958i	$-0.502909\pi$
$239$	−16141.9	−0.0182794	−0.00913968	+	0.999958i	$0.502909\pi$
$240$	−194665.	−0.218152
$241$	1.58738e6	1.76051	0.880255	−	0.474500i	$-0.157371\pi$
$241$	1.58738e6	1.76051	0.880255	+	0.474500i	$0.157371\pi$
$242$	−40667.7	−0.0446387
$243$	1.32091e6	1.43501
$244$	704517.	0.757560
$245$	124564.	0.132580
$246$	1.13332e6	1.19403
$247$	230742.	0.240649
$248$	703036.	0.725852
$249$	−802608.	−0.820362
$250$	−43401.0	−0.0439187
$251$	−1.39816e6	−1.40079	−0.700393	−	0.713758i	$-0.746992\pi$
$251$	−1.39816e6	−1.40079	−0.700393	+	0.713758i	$0.746992\pi$
$252$	977951.	0.970099
$253$	565697.	0.555626
$254$	−583532.	−0.567519
$255$	374448.	0.360612
$256$	−664601.	−0.633812
$257$	1.62648e6	1.53608	0.768042	−	0.640400i	$-0.221231\pi$
$257$	1.62648e6	1.53608	0.768042	+	0.640400i	$0.221231\pi$
$258$	873137.	0.816645
$259$	−1.82427e6	−1.68982
$260$	−388053.	−0.356006
$261$	1.38217e6	1.25592
$262$	29355.0	0.0264197
$263$	516461.	0.460413	0.230207	−	0.973142i	$-0.426060\pi$
$263$	516461.	0.460413	0.230207	+	0.973142i	$0.426060\pi$
$264$	−429635.	−0.379393
$265$	515397.	0.450845
$266$	148017.	0.128265
$267$	775876.	0.666061
$268$	379864.	0.323066
$269$	−340562.	−0.286956	−0.143478	−	0.989653i	$-0.545829\pi$
$269$	−340562.	−0.286956	−0.143478	+	0.989653i	$0.545829\pi$
$270$	47015.7	0.0392494
$271$	−934573.	−0.773019	−0.386509	−	0.922285i	$-0.626319\pi$
$271$	−934573.	−0.773019	−0.386509	+	0.922285i	$0.626319\pi$
$272$	−226104.	−0.185305
$273$	2.14284e6	1.74013
$274$	123236.	0.0991657
$275$	75625.0	0.0603023
$276$	2.57854e6	2.03752
$277$	228804.	0.179169	0.0895846	−	0.995979i	$-0.471446\pi$
$277$	228804.	0.179169	0.0895846	+	0.995979i	$0.471446\pi$
$278$	−260420.	−0.202099
$279$	1.22679e6	0.943540
$280$	−576943.	−0.439783
$281$	592380.	0.447543	0.223771	−	0.974642i	$-0.428163\pi$
$281$	592380.	0.447543	0.223771	+	0.974642i	$0.428163\pi$
$282$	−438842.	−0.328613
$283$	1.98654e6	1.47445	0.737226	−	0.675647i	$-0.236135\pi$
$283$	1.98654e6	1.47445	0.737226	+	0.675647i	$0.236135\pi$
$284$	−1.09849e6	−0.808164
$285$	−204971.	−0.149479
$286$	−214825.	−0.155299
$287$	−2.65187e6	−1.90041
$288$	−1.62464e6	−1.15419
$289$	−984935.	−0.693686
$290$	−351819.	−0.245655
$291$	529766.	0.366734
$292$	951541.	0.653086
$293$	1.14978e6	0.782433	0.391216	−	0.920299i	$-0.372054\pi$
$293$	1.14978e6	0.782433	0.391216	+	0.920299i	$0.372054\pi$
$294$	314324.	0.212085
$295$	145216.	0.0971538
$296$	1.93212e6	1.28175
$297$	−81923.6	−0.0538912
$298$	1.27644e6	0.832645
$299$	2.98826e6	1.93304
$300$	344712.	0.221133
$301$	−2.04307e6	−1.29977
$302$	−279853.	−0.176569
$303$	−3.47104e6	−2.17197
$304$	123768.	0.0768114
$305$	−725272.	−0.446428
$306$	499743.	0.305101
$307$	−2.53376e6	−1.53433	−0.767165	−	0.641449i	$-0.778333\pi$
$307$	−2.53376e6	−1.53433	−0.767165	+	0.641449i	$0.778333\pi$
$308$	433751.	0.260534
$309$	−4.47883e6	−2.66851
$310$	−312268.	−0.184554
$311$	−502306.	−0.294488	−0.147244	−	0.989100i	$-0.547040\pi$
$311$	−502306.	−0.294488	−0.147244	+	0.989100i	$0.547040\pi$
$312$	−2.26952e6	−1.31992
$313$	978417.	0.564499	0.282250	−	0.959341i	$-0.408919\pi$
$313$	978417.	0.564499	0.282250	+	0.959341i	$0.408919\pi$
$314$	736256.	0.421410
$315$	−1.00676e6	−0.571676
$316$	198745.	0.111964
$317$	661270.	0.369599	0.184799	−	0.982776i	$-0.440836\pi$
$317$	661270.	0.369599	0.184799	+	0.982776i	$0.440836\pi$
$318$	1.30055e6	0.721205
$319$	613036.	0.337294
$320$	139258.	0.0760231
$321$	−2.47003e6	−1.33795
$322$	1.91691e6	1.03030
$323$	−238075.	−0.126972
$324$	1.23648e6	0.654371
$325$	399484.	0.209793
$326$	−1.17729e6	−0.613535
$327$	2.55555e6	1.32165
$328$	2.80864e6	1.44149
$329$	1.02685e6	0.523019
$330$	190831.	0.0964640
$331$	−837776.	−0.420299	−0.210149	−	0.977669i	$-0.567395\pi$
$331$	−837776.	−0.420299	−0.210149	+	0.977669i	$0.567395\pi$
$332$	−858201.	−0.427311
$333$	3.37153e6	1.66616
$334$	−354956.	−0.174104
$335$	−391054.	−0.190382
$336$	1.14940e6	0.555423
$337$	1.06270e6	0.509726	0.254863	−	0.966977i	$-0.417970\pi$
$337$	1.06270e6	0.509726	0.254863	+	0.966977i	$0.417970\pi$
$338$	−103473.	−0.0492647
$339$	3.36712e6	1.59133
$340$	400384.	0.187836
$341$	544119.	0.253401
$342$	−273557.	−0.126469
$343$	1.74544e6	0.801068
$344$	2.16385e6	0.985895
$345$	−2.65450e6	−1.20070
$346$	2.05466e6	0.922676
$347$	−2.77621e6	−1.23774	−0.618870	−	0.785494i	$-0.712409\pi$
$347$	−2.77621e6	−1.23774	−0.618870	+	0.785494i	$0.712409\pi$
$348$	2.79432e6	1.23688
$349$	3.96795e6	1.74382	0.871911	−	0.489664i	$-0.162881\pi$
$349$	3.96795e6	1.74382	0.871911	+	0.489664i	$0.162881\pi$
$350$	256262.	0.111818
$351$	−432756.	−0.187489
$352$	−720577.	−0.309973
$353$	411422.	0.175732	0.0878660	−	0.996132i	$-0.471995\pi$
$353$	411422.	0.175732	0.0878660	+	0.996132i	$0.471995\pi$
$354$	366437.	0.155414
$355$	1.13085e6	0.476248
$356$	829618.	0.346939
$357$	−2.21093e6	−0.918131
$358$	438985.	0.181026
$359$	1.47089e6	0.602343	0.301172	−	0.953570i	$-0.402622\pi$
$359$	1.47089e6	0.602343	0.301172	+	0.953570i	$0.402622\pi$
$360$	1.06628e6	0.433625
$361$	130321.	0.0526316
$362$	−273063.	−0.109520
$363$	−332519.	−0.132449
$364$	2.29126e6	0.906404
$365$	−979572.	−0.384861
$366$	−1.83014e6	−0.714139
$367$	−3.81255e6	−1.47758	−0.738790	−	0.673936i	$-0.764602\pi$
$367$	−3.81255e6	−1.47758	−0.738790	+	0.673936i	$0.764602\pi$
$368$	1.60288e6	0.616994
$369$	4.90106e6	1.87380
$370$	−858191.	−0.325896
$371$	−3.04317e6	−1.14787
$372$	2.48019e6	0.929239
$373$	131393.	0.0488990	0.0244495	−	0.999701i	$-0.492217\pi$
$373$	131393.	0.0488990	0.0244495	+	0.999701i	$0.492217\pi$
$374$	221651.	0.0819391
$375$	−354867.	−0.130313
$376$	−1.08756e6	−0.396719
$377$	3.23833e6	1.17346
$378$	−277605.	−0.0999304
$379$	−993434.	−0.355256	−0.177628	−	0.984098i	$-0.556842\pi$
$379$	−993434.	−0.355256	−0.177628	+	0.984098i	$0.556842\pi$
$380$	−219168.	−0.0778608
$381$	−4.77123e6	−1.68391
$382$	2.05273e6	0.719738
$383$	5.31329e6	1.85083	0.925416	−	0.378953i	$-0.123716\pi$
$383$	5.31329e6	1.85083	0.925416	+	0.378953i	$0.123716\pi$
$384$	−3.97663e6	−1.37622
$385$	−446529.	−0.153532
$386$	158476.	0.0541372
$387$	3.77590e6	1.28157
$388$	566461.	0.191025
$389$	−1.80123e6	−0.603526	−0.301763	−	0.953383i	$-0.597575\pi$
$389$	−1.80123e6	−0.603526	−0.301763	+	0.953383i	$0.597575\pi$
$390$	1.00806e6	0.335601
$391$	−3.08322e6	−1.01991
$392$	778972.	0.256039
$393$	240020.	0.0783910
$394$	−1.08234e6	−0.351256
$395$	−204600.	−0.0659800
$396$	−801638.	−0.256886
$397$	3.13187e6	0.997304	0.498652	−	0.866802i	$-0.333829\pi$
$397$	3.13187e6	0.997304	0.498652	+	0.866802i	$0.333829\pi$
$398$	−1.50449e6	−0.476083
$399$	1.21025e6	0.380579
$400$	214280.	0.0669626
$401$	−3.59188e6	−1.11548	−0.557739	−	0.830017i	$-0.688331\pi$
$401$	−3.59188e6	−1.11548	−0.557739	+	0.830017i	$0.688331\pi$
$402$	−986783.	−0.304549
$403$	2.87428e6	0.881588
$404$	−3.71147e6	−1.13134
$405$	−1.27290e6	−0.385619
$406$	2.07732e6	0.625445
$407$	1.49537e6	0.447470
$408$	2.34164e6	0.696417
$409$	−751091.	−0.222016	−0.111008	−	0.993820i	$-0.535408\pi$
$409$	−751091.	−0.222016	−0.111008	+	0.993820i	$0.535408\pi$
$410$	−1.24752e6	−0.366512
$411$	1.00764e6	0.294239
$412$	−4.78906e6	−1.38998
$413$	−857431.	−0.247357
$414$	−3.54274e6	−1.01587
$415$	883483.	0.251813
$416$	−3.80641e6	−1.07840
$417$	−2.12932e6	−0.599654
$418$	−121331.	−0.0339650
$419$	1.14562e6	0.318790	0.159395	−	0.987215i	$-0.449046\pi$
$419$	1.14562e6	0.318790	0.159395	+	0.987215i	$0.449046\pi$
$420$	−2.03536e6	−0.563012
$421$	−6.27013e6	−1.72413	−0.862067	−	0.506794i	$-0.830830\pi$
$421$	−6.27013e6	−1.72413	−0.862067	+	0.506794i	$0.830830\pi$
$422$	−2.92988e6	−0.800883
$423$	−1.89778e6	−0.515697
$424$	3.22308e6	0.870675
$425$	−412179.	−0.110691
$426$	2.85357e6	0.761842
$427$	4.28238e6	1.13662
$428$	−2.64112e6	−0.696913
$429$	−1.75651e6	−0.460795
$430$	−961119.	−0.250672
$431$	−7.00508e6	−1.81643	−0.908217	−	0.418499i	$-0.862556\pi$
$431$	−7.00508e6	−1.81643	−0.908217	+	0.418499i	$0.862556\pi$
$432$	−232127.	−0.0598435
$433$	−3.02004e6	−0.774093	−0.387046	−	0.922060i	$-0.626505\pi$
$433$	−3.02004e6	−0.774093	−0.387046	+	0.922060i	$0.626505\pi$
$434$	1.84379e6	0.469881
$435$	−2.87664e6	−0.728891
$436$	2.73257e6	0.688422
$437$	1.68774e6	0.422768
$438$	−2.47184e6	−0.615653
$439$	5.26645e6	1.30424	0.652119	−	0.758116i	$-0.273880\pi$
$439$	5.26645e6	1.30424	0.652119	+	0.758116i	$0.273880\pi$
$440$	472927.	0.116456
$441$	1.35930e6	0.332827
$442$	1.17086e6	0.285069
$443$	−4.33126e6	−1.04859	−0.524294	−	0.851537i	$-0.675671\pi$
$443$	−4.33126e6	−1.04859	−0.524294	+	0.851537i	$0.675671\pi$
$444$	6.81617e6	1.64090
$445$	−854057.	−0.204450
$446$	−1.79241e6	−0.426677
$447$	1.04368e7	2.47057
$448$	−822252.	−0.193557
$449$	−3.07642e6	−0.720162	−0.360081	−	0.932921i	$-0.617251\pi$
$449$	−3.07642e6	−0.720162	−0.360081	+	0.932921i	$0.617251\pi$
$450$	−473611.	−0.110253
$451$	2.17377e6	0.503236
$452$	3.60035e6	0.828893
$453$	−2.28821e6	−0.523903
$454$	−1.10288e6	−0.251124
$455$	−2.35876e6	−0.534141
$456$	−1.28180e6	−0.288675
$457$	−5.20085e6	−1.16489	−0.582444	−	0.812871i	$-0.697903\pi$
$457$	−5.20085e6	−1.16489	−0.582444	+	0.812871i	$0.697903\pi$
$458$	−1.20286e6	−0.267948
$459$	446508.	0.0989231
$460$	−2.83837e6	−0.625424
$461$	−7.02031e6	−1.53852	−0.769261	−	0.638934i	$-0.779376\pi$
$461$	−7.02031e6	−1.53852	−0.769261	+	0.638934i	$0.779376\pi$
$462$	−1.12677e6	−0.245601
$463$	−1.26341e6	−0.273900	−0.136950	−	0.990578i	$-0.543730\pi$
$463$	−1.26341e6	−0.273900	−0.136950	+	0.990578i	$0.543730\pi$
$464$	1.73701e6	0.374549
$465$	−2.55325e6	−0.547598
$466$	−2.15501e6	−0.459711
$467$	3.77999e6	0.802045	0.401022	−	0.916068i	$-0.368655\pi$
$467$	3.77999e6	0.802045	0.401022	+	0.916068i	$0.368655\pi$
$468$	−4.23460e6	−0.893713
$469$	2.30899e6	0.484718
$470$	483062.	0.100869
$471$	6.01998e6	1.25038
$472$	908121.	0.187624
$473$	1.67472e6	0.344184
$474$	−516286.	−0.105547
$475$	225625.	0.0458831
$476$	−2.36407e6	−0.478237
$477$	5.62424e6	1.13180
$478$	44836.8	0.00897563
$479$	−277404.	−0.0552426	−0.0276213	−	0.999618i	$-0.508793\pi$
$479$	−277404.	−0.0552426	−0.0276213	+	0.999618i	$0.508793\pi$
$480$	3.38128e6	0.669850
$481$	7.89922e6	1.55676
$482$	−4.40921e6	−0.864456
$483$	1.56736e7	3.05703
$484$	−355551.	−0.0689903
$485$	−583148.	−0.112570
$486$	−3.66903e6	−0.704629
$487$	733481.	0.140141	0.0700707	−	0.997542i	$-0.477678\pi$
$487$	733481.	0.140141	0.0700707	+	0.997542i	$0.477678\pi$
$488$	−4.53555e6	−0.862144
$489$	−9.62609e6	−1.82044
$490$	−345997.	−0.0651002
$491$	−2.33920e6	−0.437888	−0.218944	−	0.975737i	$-0.570261\pi$
$491$	−2.33920e6	−0.437888	−0.218944	+	0.975737i	$0.570261\pi$
$492$	9.90842e6	1.84540
$493$	−3.34123e6	−0.619140
$494$	−640924.	−0.118165
$495$	825254.	0.151382
$496$	1.54174e6	0.281389
$497$	−6.67711e6	−1.21254
$498$	2.22937e6	0.402819
$499$	−4.49956e6	−0.808944	−0.404472	−	0.914550i	$-0.632545\pi$
$499$	−4.49956e6	−0.808944	−0.404472	+	0.914550i	$0.632545\pi$
$500$	−379447.	−0.0678775
$501$	−2.90229e6	−0.516590
$502$	3.88361e6	0.687822
$503$	−2.62082e6	−0.461868	−0.230934	−	0.972969i	$-0.574178\pi$
$503$	−2.62082e6	−0.461868	−0.230934	+	0.972969i	$0.574178\pi$
$504$	−6.29586e6	−1.10402
$505$	3.82080e6	0.666693
$506$	−1.57131e6	−0.272827
$507$	−846045.	−0.146175
$508$	−5.10172e6	−0.877116
$509$	4.58014e6	0.783582	0.391791	−	0.920054i	$-0.371856\pi$
$509$	4.58014e6	0.783582	0.391791	+	0.920054i	$0.371856\pi$
$510$	−1.04009e6	−0.177070
$511$	5.78390e6	0.979870
$512$	−3.75695e6	−0.633375
$513$	−244417.	−0.0410050
$514$	−4.51780e6	−0.754256
$515$	4.93014e6	0.819109
$516$	7.63368e6	1.26215
$517$	−841722.	−0.138498
$518$	5.06720e6	0.829743
$519$	1.67998e7	2.73771
$520$	2.49821e6	0.405154
$521$	−7.30964e6	−1.17978	−0.589891	−	0.807483i	$-0.700829\pi$
$521$	−7.30964e6	−1.17978	−0.589891	+	0.807483i	$0.700829\pi$
$522$	−3.83921e6	−0.616688
$523$	−3.94203e6	−0.630181	−0.315091	−	0.949062i	$-0.602035\pi$
$523$	−3.94203e6	−0.630181	−0.315091	+	0.949062i	$0.602035\pi$
$524$	256645.	0.0408324
$525$	2.09532e6	0.331781
$526$	−1.43455e6	−0.226075
$527$	−2.96561e6	−0.465144
$528$	−942179.	−0.147078
$529$	1.54209e7	2.39592
$530$	−1.43160e6	−0.221376
$531$	1.58466e6	0.243894
$532$	1.29408e6	0.198236
$533$	1.14828e7	1.75077
$534$	−2.15512e6	−0.327053
$535$	2.71892e6	0.410688
$536$	−2.44549e6	−0.367666
$537$	3.58935e6	0.537131
$538$	945967.	0.140903
$539$	602891.	0.0893854
$540$	411050.	0.0606611
$541$	4.42219e6	0.649598	0.324799	−	0.945783i	$-0.394703\pi$
$541$	4.42219e6	0.649598	0.324799	+	0.945783i	$0.394703\pi$
$542$	2.59593e6	0.379572
$543$	−2.23269e6	−0.324960
$544$	3.92736e6	0.568989
$545$	−2.81307e6	−0.405685
$546$	−5.95208e6	−0.854451
$547$	1.36377e7	1.94883	0.974414	−	0.224760i	$-0.0721597\pi$
$547$	1.36377e7	1.94883	0.974414	+	0.224760i	$0.0721597\pi$
$548$	1.07743e6	0.153263
$549$	−7.91449e6	−1.12071
$550$	−210061.	−0.0296100
$551$	1.82898e6	0.256643
$552$	−1.66002e7	−2.31881
$553$	1.20806e6	0.167987
$554$	−635539.	−0.0879767
$555$	−7.01697e6	−0.966980
$556$	−2.27681e6	−0.312349
$557$	−1.22341e7	−1.67084	−0.835421	−	0.549611i	$-0.814776\pi$
$557$	−1.22341e7	−1.67084	−0.835421	+	0.549611i	$0.814776\pi$
$558$	−3.40761e6	−0.463302
$559$	8.84663e6	1.19742
$560$	−1.26522e6	−0.170489
$561$	1.81233e6	0.243125
$562$	−1.64543e6	−0.219755
$563$	−7.67718e6	−1.02078	−0.510388	−	0.859944i	$-0.670498\pi$
$563$	−7.67718e6	−1.02078	−0.510388	+	0.859944i	$0.670498\pi$
$564$	−3.83671e6	−0.507881
$565$	−3.70641e6	−0.488464
$566$	−5.51793e6	−0.723994
$567$	7.51589e6	0.981799
$568$	7.07185e6	0.919734
$569$	1.41750e7	1.83545	0.917727	−	0.397212i	$-0.130022\pi$
$569$	1.41750e7	1.83545	0.917727	+	0.397212i	$0.130022\pi$
$570$	569340.	0.0733981
$571$	−7.51681e6	−0.964814	−0.482407	−	0.875947i	$-0.660237\pi$
$571$	−7.51681e6	−0.964814	−0.482407	+	0.875947i	$0.660237\pi$
$572$	−1.87818e6	−0.240019
$573$	1.67841e7	2.13556
$574$	7.36600e6	0.933151
$575$	2.92199e6	0.368560
$576$	1.51965e6	0.190847
$577$	−9.67827e6	−1.21020	−0.605102	−	0.796148i	$-0.706868\pi$
$577$	−9.67827e6	−1.21020	−0.605102	+	0.796148i	$0.706868\pi$
$578$	2.73582e6	0.340618
$579$	1.29578e6	0.160633
$580$	−3.07589e6	−0.379666
$581$	−5.21654e6	−0.641124
$582$	−1.47151e6	−0.180076
$583$	2.49452e6	0.303960
$584$	−6.12584e6	−0.743247
$585$	4.35935e6	0.526662
$586$	−3.19371e6	−0.384195
$587$	7.43801e6	0.890967	0.445483	−	0.895290i	$-0.353032\pi$
$587$	7.43801e6	0.890967	0.445483	+	0.895290i	$0.353032\pi$
$588$	2.74808e6	0.327783
$589$	1.62336e6	0.192809
$590$	−403361.	−0.0477050
$591$	−8.84973e6	−1.04222
$592$	4.23708e6	0.496893
$593$	−7.09183e6	−0.828174	−0.414087	−	0.910237i	$-0.635899\pi$
$593$	−7.09183e6	−0.828174	−0.414087	+	0.910237i	$0.635899\pi$
$594$	227556.	0.0264620
$595$	2.43372e6	0.281824
$596$	1.11597e7	1.28688
$597$	−1.23015e7	−1.41261
$598$	−8.30037e6	−0.949171
$599$	6.07424e6	0.691712	0.345856	−	0.938288i	$-0.387589\pi$
$599$	6.07424e6	0.691712	0.345856	+	0.938288i	$0.387589\pi$
$600$	−2.21919e6	−0.251661
$601$	3.66384e6	0.413762	0.206881	−	0.978366i	$-0.433669\pi$
$601$	3.66384e6	0.413762	0.206881	+	0.978366i	$0.433669\pi$
$602$	5.67494e6	0.638220
$603$	−4.26736e6	−0.477932
$604$	−2.44671e6	−0.272891
$605$	366025.	0.0406558
$606$	9.64138e6	1.06649
$607$	1.10632e7	1.21873	0.609366	−	0.792889i	$-0.291424\pi$
$607$	1.10632e7	1.21873	0.609366	+	0.792889i	$0.291424\pi$
$608$	−2.14982e6	−0.235854
$609$	1.69852e7	1.85578
$610$	2.01456e6	0.219208
$611$	−4.44634e6	−0.481837
$612$	4.36917e6	0.471542
$613$	−1.59812e7	−1.71775	−0.858873	−	0.512189i	$-0.828835\pi$
$613$	−1.59812e7	−1.71775	−0.858873	+	0.512189i	$0.828835\pi$
$614$	7.03792e6	0.753396
$615$	−1.02003e7	−1.08749
$616$	−2.79241e6	−0.296501
$617$	−8.35800e6	−0.883872	−0.441936	−	0.897047i	$-0.645708\pi$
$617$	−8.35800e6	−0.883872	−0.441936	+	0.897047i	$0.645708\pi$
$618$	1.24407e7	1.31031
$619$	−585900.	−0.0614606	−0.0307303	−	0.999528i	$-0.509783\pi$
$619$	−585900.	−0.0614606	−0.0307303	+	0.999528i	$0.509783\pi$
$620$	−2.73011e6	−0.285233
$621$	−3.16535e6	−0.329377
$622$	1.39524e6	0.144601
$623$	5.04280e6	0.520537
$624$	−4.97700e6	−0.511689
$625$	390625.	0.0400000
$626$	−2.71771e6	−0.277184
$627$	−992060.	−0.100779
$628$	6.43696e6	0.651301
$629$	−8.15024e6	−0.821379
$630$	2.79644e6	0.280708
$631$	1.18136e7	1.18116	0.590580	−	0.806979i	$-0.298899\pi$
$631$	1.18136e7	1.18116	0.590580	+	0.806979i	$0.298899\pi$
$632$	−1.27948e6	−0.127421
$633$	−2.39561e7	−2.37633
$634$	−1.83678e6	−0.181483
$635$	5.25201e6	0.516882
$636$	1.13705e7	1.11464
$637$	3.18473e6	0.310974
$638$	−1.70281e6	−0.165620
$639$	1.23403e7	1.19557
$640$	4.37733e6	0.422435
$641$	−1.70903e7	−1.64287	−0.821437	−	0.570299i	$-0.806828\pi$
$641$	−1.70903e7	−1.64287	−0.821437	+	0.570299i	$0.806828\pi$
$642$	6.86091e6	0.656968
$643$	−5.15697e6	−0.491889	−0.245945	−	0.969284i	$-0.579098\pi$
$643$	−5.15697e6	−0.491889	−0.245945	+	0.969284i	$0.579098\pi$
$644$	1.67592e7	1.59235
$645$	−7.85857e6	−0.743779
$646$	661290.	0.0623463
$647$	1.65395e7	1.55332	0.776661	−	0.629919i	$-0.216912\pi$
$647$	1.65395e7	1.55332	0.776661	+	0.629919i	$0.216912\pi$
$648$	−7.96022e6	−0.744710
$649$	702846.	0.0655011
$650$	−1.10963e6	−0.103014
$651$	1.50757e7	1.39420
$652$	−1.02928e7	−0.948236
$653$	2.10047e7	1.92767	0.963837	−	0.266492i	$-0.0858647\pi$
$653$	2.10047e7	1.92767	0.963837	+	0.266492i	$0.0858647\pi$
$654$	−7.09846e6	−0.648963
$655$	−264206.	−0.0240624
$656$	6.15929e6	0.558819
$657$	−1.06895e7	−0.966151
$658$	−2.85224e6	−0.256816
$659$	−1.76115e7	−1.57973	−0.789866	−	0.613280i	$-0.789850\pi$
$659$	−1.76115e7	−1.57973	−0.789866	+	0.613280i	$0.789850\pi$
$660$	1.66841e6	0.149088
$661$	1.20980e7	1.07699	0.538493	−	0.842630i	$-0.318994\pi$
$661$	1.20980e7	1.07699	0.538493	+	0.842630i	$0.318994\pi$
$662$	2.32706e6	0.206377
$663$	9.57351e6	0.845838
$664$	5.52494e6	0.486303
$665$	−1.33221e6	−0.116820
$666$	−9.36496e6	−0.818126
$667$	2.36864e7	2.06150
$668$	−3.10332e6	−0.269082
$669$	−1.46556e7	−1.26601
$670$	1.08622e6	0.0934823
$671$	−3.51032e6	−0.300981
$672$	−1.99648e7	−1.70546
$673$	−1.67169e6	−0.142271	−0.0711357	−	0.997467i	$-0.522662\pi$
$673$	−1.67169e6	−0.142271	−0.0711357	+	0.997467i	$0.522662\pi$
$674$	−2.95183e6	−0.250289
$675$	−423159.	−0.0357474
$676$	−904647.	−0.0761399
$677$	−1.13500e7	−0.951753	−0.475877	−	0.879512i	$-0.657869\pi$
$677$	−1.13500e7	−0.951753	−0.475877	+	0.879512i	$0.657869\pi$
$678$	−9.35273e6	−0.781383
$679$	3.44321e6	0.286608
$680$	−2.57759e6	−0.213768
$681$	−9.01766e6	−0.745120
$682$	−1.51138e6	−0.124426
$683$	−5.37535e6	−0.440915	−0.220458	−	0.975397i	$-0.570755\pi$
$683$	−5.37535e6	−0.440915	−0.220458	+	0.975397i	$0.570755\pi$
$684$	−2.39166e6	−0.195461
$685$	−1.10917e6	−0.0903176
$686$	−4.84824e6	−0.393345
$687$	−9.83514e6	−0.795039
$688$	4.74527e6	0.382199
$689$	1.31772e7	1.05748
$690$	7.37332e6	0.589576
$691$	−1.10396e7	−0.879542	−0.439771	−	0.898110i	$-0.644940\pi$
$691$	−1.10396e7	−0.879542	−0.439771	+	0.898110i	$0.644940\pi$
$692$	1.79635e7	1.42602
$693$	−4.87272e6	−0.385424
$694$	7.71138e6	0.607762
$695$	2.34388e6	0.184066
$696$	−1.79893e7	−1.40764
$697$	−1.18477e7	−0.923744
$698$	−1.10216e7	−0.856262
$699$	−1.76204e7	−1.36403
$700$	2.24045e6	0.172818
$701$	−7.18378e6	−0.552151	−0.276075	−	0.961136i	$-0.589034\pi$
$701$	−7.18378e6	−0.552151	−0.276075	+	0.961136i	$0.589034\pi$
$702$	1.20205e6	0.0920619
$703$	4.46141e6	0.340474
$704$	674009.	0.0512547
$705$	3.94974e6	0.299292
$706$	−1.14279e6	−0.0862890
$707$	−2.25600e7	−1.69742
$708$	3.20369e6	0.240197
$709$	−72529.0	−0.00541871	−0.00270936	−	0.999996i	$-0.500862\pi$
$709$	−72529.0	−0.00541871	−0.00270936	+	0.999996i	$0.500862\pi$
$710$	−3.14111e6	−0.233850
$711$	−2.23268e6	−0.165635
$712$	−5.34092e6	−0.394835
$713$	2.10236e7	1.54876
$714$	6.14122e6	0.450826
$715$	1.93350e6	0.141443
$716$	3.83797e6	0.279781
$717$	366607.	0.0266320
$718$	−4.08563e6	−0.295766
$719$	−8.52315e6	−0.614862	−0.307431	−	0.951570i	$-0.599469\pi$
$719$	−8.52315e6	−0.614862	−0.307431	+	0.951570i	$0.599469\pi$
$720$	2.33832e6	0.168102
$721$	−2.91101e7	−2.08548
$722$	−361988.	−0.0258435
$723$	−3.60518e7	−2.56496
$724$	−2.38734e6	−0.169266
$725$	3.16651e6	0.223736
$726$	923624.	0.0650360
$727$	−1.22292e7	−0.858145	−0.429072	−	0.903270i	$-0.641159\pi$
$727$	−1.22292e7	−0.858145	−0.429072	+	0.903270i	$0.641159\pi$
$728$	−1.47507e7	−1.03154
$729$	−1.76271e7	−1.22846
$730$	2.72092e6	0.188977
$731$	−9.12775e6	−0.631786
$732$	−1.60006e7	−1.10372
$733$	−1.56294e7	−1.07444	−0.537219	−	0.843443i	$-0.680525\pi$
$733$	−1.56294e7	−1.07444	−0.537219	+	0.843443i	$0.680525\pi$
$734$	1.05900e7	0.725530
$735$	−2.82904e6	−0.193161
$736$	−2.78415e7	−1.89452
$737$	−1.89270e6	−0.128355
$738$	−1.36135e7	−0.920086
$739$	−8.31727e6	−0.560235	−0.280117	−	0.959966i	$-0.590373\pi$
$739$	−8.31727e6	−0.560235	−0.280117	+	0.959966i	$0.590373\pi$
$740$	−7.50301e6	−0.503682
$741$	−5.24050e6	−0.350612
$742$	8.45289e6	0.563632
$743$	2.91763e7	1.93891	0.969456	−	0.245266i	$-0.0788753\pi$
$743$	2.91763e7	1.93891	0.969456	+	0.245266i	$0.0788753\pi$
$744$	−1.59670e7	−1.05752
$745$	−1.14884e7	−0.758352
$746$	−364965.	−0.0240107
$747$	9.64096e6	0.632148
$748$	1.93786e6	0.126639
$749$	−1.60539e7	−1.04563
$750$	985700.	0.0639870
$751$	−2.28320e7	−1.47722	−0.738610	−	0.674133i	$-0.764517\pi$
$751$	−2.28320e7	−1.47722	−0.738610	+	0.674133i	$0.764517\pi$
$752$	−2.38499e6	−0.153795
$753$	3.17542e7	2.04086
$754$	−8.99497e6	−0.576198
$755$	2.51879e6	0.160814
$756$	−2.42705e6	−0.154445
$757$	2.14668e7	1.36153	0.680767	−	0.732500i	$-0.261647\pi$
$757$	2.14668e7	1.36153	0.680767	+	0.732500i	$0.261647\pi$
$758$	2.75942e6	0.174440
$759$	−1.28478e7	−0.809514
$760$	1.41096e6	0.0886099
$761$	7.29835e6	0.456839	0.228419	−	0.973563i	$-0.426644\pi$
$761$	7.29835e6	0.456839	0.228419	+	0.973563i	$0.426644\pi$
$762$	1.32529e7	0.826842
$763$	1.66098e7	1.03289
$764$	1.79467e7	1.11237
$765$	−4.49788e6	−0.277878
$766$	−1.47585e7	−0.908806
$767$	3.71274e6	0.227880
$768$	1.50941e7	0.923428
$769$	−1.77905e7	−1.08486	−0.542428	−	0.840103i	$-0.682495\pi$
$769$	−1.77905e7	−1.08486	−0.542428	+	0.840103i	$0.682495\pi$
$770$	1.24031e6	0.0753880
$771$	−3.69397e7	−2.23798
$772$	1.38553e6	0.0836705
$773$	2.07962e7	1.25180	0.625900	−	0.779903i	$-0.284732\pi$
$773$	2.07962e7	1.25180	0.625900	+	0.779903i	$0.284732\pi$
$774$	−1.04882e7	−0.629284
$775$	2.81053e6	0.168087
$776$	−3.64676e6	−0.217397
$777$	4.14318e7	2.46196
$778$	5.00322e6	0.296347
$779$	6.48538e6	0.382905
$780$	8.81325e6	0.518680
$781$	5.47330e6	0.321086
$782$	8.56413e6	0.500802
$783$	−3.43024e6	−0.199949
$784$	1.70827e6	0.0992580
$785$	−6.62658e6	−0.383809
$786$	−666695.	−0.0384920
$787$	−1.93347e7	−1.11276	−0.556378	−	0.830929i	$-0.687809\pi$
$787$	−1.93347e7	−1.11276	−0.556378	+	0.830929i	$0.687809\pi$
$788$	−9.46271e6	−0.542875
$789$	−1.17296e7	−0.670796
$790$	568309.	0.0323979
$791$	2.18846e7	1.24365
$792$	5.16079e6	0.292350
$793$	−1.85430e7	−1.04712
$794$	−8.69927e6	−0.489702
$795$	−1.17054e7	−0.656855
$796$	−1.31535e7	−0.735800
$797$	2.30780e7	1.28692	0.643462	−	0.765478i	$-0.277497\pi$
$797$	2.30780e7	1.28692	0.643462	+	0.765478i	$0.277497\pi$
$798$	−3.36168e6	−0.186874
$799$	4.58764e6	0.254227
$800$	−3.72199e6	−0.205613
$801$	−9.31985e6	−0.513249
$802$	9.97702e6	0.547728
$803$	−4.74113e6	−0.259473
$804$	−8.62727e6	−0.470688
$805$	−1.72529e7	−0.938367
$806$	−7.98377e6	−0.432883
$807$	7.73467e6	0.418079
$808$	2.38937e7	1.28752
$809$	−2.12625e7	−1.14220	−0.571102	−	0.820879i	$-0.693484\pi$
$809$	−2.12625e7	−1.14220	−0.571102	+	0.820879i	$0.693484\pi$
$810$	3.53570e6	0.189349
$811$	8.66812e6	0.462778	0.231389	−	0.972861i	$-0.425673\pi$
$811$	8.66812e6	0.462778	0.231389	+	0.972861i	$0.425673\pi$
$812$	1.81617e7	0.966642
$813$	2.12255e7	1.12624
$814$	−4.15364e6	−0.219719
$815$	1.05961e7	0.558792
$816$	5.13516e6	0.269978
$817$	4.99649e6	0.261885
$818$	2.08628e6	0.109016
$819$	−2.57399e7	−1.34090
$820$	−1.09068e7	−0.566453
$821$	−4.48129e6	−0.232031	−0.116015	−	0.993247i	$-0.537012\pi$
$821$	−4.48129e6	−0.232031	−0.116015	+	0.993247i	$0.537012\pi$
$822$	−2.79887e6	−0.144479
$823$	3.41551e7	1.75774	0.878872	−	0.477057i	$-0.158296\pi$
$823$	3.41551e7	1.75774	0.878872	+	0.477057i	$0.158296\pi$
$824$	3.08311e7	1.58187
$825$	−1.71756e6	−0.0878569
$826$	2.38165e6	0.121459
$827$	493047.	0.0250683	0.0125341	−	0.999921i	$-0.496010\pi$
$827$	493047.	0.0250683	0.0125341	+	0.999921i	$0.496010\pi$
$828$	−3.09736e7	−1.57006
$829$	−7.83379e6	−0.395900	−0.197950	−	0.980212i	$-0.563428\pi$
$829$	−7.83379e6	−0.395900	−0.197950	+	0.980212i	$0.563428\pi$
$830$	−2.45402e6	−0.123647
$831$	−5.19647e6	−0.261039
$832$	3.56041e6	0.178317
$833$	−3.28593e6	−0.164076
$834$	5.91453e6	0.294446
$835$	3.19474e6	0.158569
$836$	−1.06078e6	−0.0524938
$837$	−3.04461e6	−0.150217
$838$	−3.18213e6	−0.156534
$839$	−1.09993e7	−0.539459	−0.269729	−	0.962936i	$-0.586934\pi$
$839$	−1.09993e7	−0.539459	−0.269729	+	0.962936i	$0.586934\pi$
$840$	1.31032e7	0.640738
$841$	5.15739e6	0.251443
$842$	1.74163e7	0.846594
$843$	−1.34538e7	−0.652044
$844$	−2.56154e7	−1.23779
$845$	931297.	0.0448690
$846$	5.27138e6	0.253220
$847$	−2.16120e6	−0.103511
$848$	7.06813e6	0.337532
$849$	−4.51172e7	−2.14819
$850$	1.14489e6	0.0543523
$851$	5.77780e7	2.73488
$852$	2.49483e7	1.17745
$853$	1.18799e7	0.559035	0.279518	−	0.960141i	$-0.409825\pi$
$853$	1.18799e7	0.559035	0.279518	+	0.960141i	$0.409825\pi$
$854$	−1.18950e7	−0.558110
$855$	2.46212e6	0.115184
$856$	1.70030e7	0.793125
$857$	1.87188e6	0.0870614	0.0435307	−	0.999052i	$-0.486139\pi$
$857$	1.87188e6	0.0870614	0.0435307	+	0.999052i	$0.486139\pi$
$858$	4.87899e6	0.226262
$859$	−1.32533e7	−0.612831	−0.306415	−	0.951898i	$-0.599130\pi$
$859$	−1.32533e7	−0.612831	−0.306415	+	0.951898i	$0.599130\pi$
$860$	−8.40289e6	−0.387421
$861$	6.02279e7	2.76879
$862$	1.94577e7	0.891916
$863$	8.61616e6	0.393810	0.196905	−	0.980423i	$-0.436911\pi$
$863$	8.61616e6	0.393810	0.196905	+	0.980423i	$0.436911\pi$
$864$	4.03198e6	0.183753
$865$	−1.84927e7	−0.840349
$866$	8.38865e6	0.380099
$867$	2.23693e7	1.01066
$868$	1.61200e7	0.726214
$869$	−990263.	−0.0444837
$870$	7.99034e6	0.357904
$871$	−9.99809e6	−0.446551
$872$	−1.75917e7	−0.783461
$873$	−6.36357e6	−0.282596
$874$	−4.68797e6	−0.207590
$875$	−2.30645e6	−0.101841
$876$	−2.16109e7	−0.951508
$877$	−3.19796e7	−1.40402	−0.702012	−	0.712165i	$-0.747715\pi$
$877$	−3.19796e7	−1.40402	−0.702012	+	0.712165i	$0.747715\pi$
$878$	−1.46284e7	−0.640415
$879$	−2.61133e7	−1.13996
$880$	1.03712e6	0.0451462
$881$	5.05038e6	0.219222	0.109611	−	0.993975i	$-0.465039\pi$
$881$	5.05038e6	0.219222	0.109611	+	0.993975i	$0.465039\pi$
$882$	−3.77567e6	−0.163427
$883$	1.11703e7	0.482130	0.241065	−	0.970509i	$-0.422503\pi$
$883$	1.11703e7	0.482130	0.241065	+	0.970509i	$0.422503\pi$
$884$	1.02366e7	0.440581
$885$	−3.29807e6	−0.141547
$886$	1.20308e7	0.514884
$887$	2.80528e7	1.19720	0.598600	−	0.801048i	$-0.295724\pi$
$887$	2.80528e7	1.19720	0.598600	+	0.801048i	$0.295724\pi$
$888$	−4.38812e7	−1.86744
$889$	−3.10106e7	−1.31600
$890$	2.37228e6	0.100390
$891$	−6.16086e6	−0.259984
$892$	−1.56707e7	−0.659441
$893$	−2.51125e6	−0.105381
$894$	−2.89899e7	−1.21312
$895$	−3.95103e6	−0.164874
$896$	−2.58460e7	−1.07553
$897$	−6.78677e7	−2.81632
$898$	8.54527e6	0.353618
$899$	2.27829e7	0.940178
$900$	−4.14069e6	−0.170399
$901$	−1.35959e7	−0.557950
$902$	−6.03799e6	−0.247102
$903$	4.64010e7	1.89369
$904$	−2.31783e7	−0.943325
$905$	2.45767e6	0.0997476
$906$	6.35588e6	0.257250
$907$	3.38959e6	0.136814	0.0684068	−	0.997658i	$-0.478208\pi$
$907$	3.38959e6	0.136814	0.0684068	+	0.997658i	$0.478208\pi$
$908$	−9.64227e6	−0.388119
$909$	4.16943e7	1.67366
$910$	6.55184e6	0.262277
$911$	−3.70080e7	−1.47741	−0.738703	−	0.674031i	$-0.764561\pi$
$911$	−3.70080e7	−1.47741	−0.738703	+	0.674031i	$0.764561\pi$
$912$	−2.81096e6	−0.111910
$913$	4.27606e6	0.169772
$914$	1.44462e7	0.571990
$915$	1.64720e7	0.650419
$916$	−1.05164e7	−0.414121
$917$	1.56001e6	0.0612637
$918$	−1.24025e6	−0.0485738
$919$	1.57795e7	0.616316	0.308158	−	0.951335i	$-0.400287\pi$
$919$	1.57795e7	0.616316	0.308158	+	0.951335i	$0.400287\pi$
$920$	1.82729e7	0.711766
$921$	5.75454e7	2.23543
$922$	1.95000e7	0.755454
$923$	2.89124e7	1.11707
$924$	−9.85113e6	−0.379582
$925$	7.72404e6	0.296818
$926$	3.50933e6	0.134492
$927$	5.37999e7	2.05628
$928$	−3.01714e7	−1.15007
$929$	1.99445e7	0.758201	0.379101	−	0.925355i	$-0.376233\pi$
$929$	1.99445e7	0.758201	0.379101	+	0.925355i	$0.376233\pi$
$930$	7.09207e6	0.268885
$931$	1.79871e6	0.0680121
$932$	−1.88409e7	−0.710496
$933$	1.14081e7	0.429052
$934$	−1.04995e7	−0.393825
$935$	−1.99495e6	−0.0746281
$936$	2.72616e7	1.01709
$937$	3.56765e7	1.32749	0.663747	−	0.747957i	$-0.268965\pi$
$937$	3.56765e7	1.32749	0.663747	+	0.747957i	$0.268965\pi$
$938$	−6.41358e6	−0.238009
$939$	−2.22213e7	−0.822442
$940$	4.22332e6	0.155896
$941$	1.71799e7	0.632478	0.316239	−	0.948680i	$-0.397580\pi$
$941$	1.71799e7	0.632478	0.316239	+	0.948680i	$0.397580\pi$
$942$	−1.67215e7	−0.613970
$943$	8.39897e7	3.07572
$944$	1.99149e6	0.0727357
$945$	2.49855e6	0.0910140
$946$	−4.65182e6	−0.169003
$947$	−3.05290e7	−1.10621	−0.553105	−	0.833112i	$-0.686557\pi$
$947$	−3.05290e7	−1.10621	−0.553105	+	0.833112i	$0.686557\pi$
$948$	−4.51379e6	−0.163125
$949$	−2.50447e7	−0.902715
$950$	−626710.	−0.0225298
$951$	−1.50184e7	−0.538484
$952$	1.52194e7	0.544260
$953$	−4.87656e7	−1.73933	−0.869663	−	0.493646i	$-0.835664\pi$
$953$	−4.87656e7	−1.73933	−0.869663	+	0.493646i	$0.835664\pi$
$954$	−1.56222e7	−0.555741
$955$	−1.84754e7	−0.655519
$956$	392000.	0.0138721
$957$	−1.39230e7	−0.491418
$958$	770535.	0.0271256
$959$	6.54912e6	0.229952
$960$	−3.16276e6	−0.110761
$961$	−8.40747e6	−0.293668
$962$	−2.19414e7	−0.764409
$963$	2.96701e7	1.03099
$964$	−3.85489e7	−1.33604
$965$	−1.42634e6	−0.0493067
$966$	−4.35359e7	−1.50108
$967$	1.89646e7	0.652194	0.326097	−	0.945336i	$-0.394266\pi$
$967$	1.89646e7	0.652194	0.326097	+	0.945336i	$0.394266\pi$
$968$	2.28897e6	0.0785147
$969$	5.40702e6	0.184990
$970$	1.61979e6	0.0552750
$971$	−4.65960e7	−1.58599	−0.792995	−	0.609228i	$-0.791480\pi$
$971$	−4.65960e7	−1.58599	−0.792995	+	0.609228i	$0.791480\pi$
$972$	−3.20777e7	−1.08902
$973$	−1.38395e7	−0.468639
$974$	−2.03736e6	−0.0688131
$975$	−9.07288e6	−0.305657
$976$	−9.94634e6	−0.334225
$977$	−1.52749e7	−0.511968	−0.255984	−	0.966681i	$-0.582399\pi$
$977$	−1.52749e7	−0.511968	−0.255984	+	0.966681i	$0.582399\pi$
$978$	2.67380e7	0.893885
$979$	−4.13364e6	−0.137840
$980$	−3.02499e6	−0.100614
$981$	−3.06974e7	−1.01843
$982$	6.49750e6	0.215014
$983$	3.09412e7	1.02130	0.510649	−	0.859789i	$-0.329405\pi$
$983$	3.09412e7	1.02130	0.510649	+	0.859789i	$0.329405\pi$
$984$	−6.37885e7	−2.10017
$985$	9.74148e6	0.319915
$986$	9.28080e6	0.304014
$987$	−2.33213e7	−0.762009
$988$	−5.60348e6	−0.182627
$989$	6.47077e7	2.10361
$990$	−2.29228e6	−0.0743325
$991$	−6.76991e6	−0.218977	−0.109489	−	0.993988i	$-0.534921\pi$
$991$	−6.76991e6	−0.218977	−0.109489	+	0.993988i	$0.534921\pi$
$992$	−2.67796e7	−0.864021
$993$	1.90271e7	0.612351
$994$	1.85467e7	0.595390
$995$	1.35410e7	0.433604
$996$	1.94910e7	0.622567
$997$	1.52639e6	0.0486326	0.0243163	−	0.999704i	$-0.492259\pi$
$997$	1.52639e6	0.0486326	0.0243163	+	0.999704i	$0.492259\pi$
$998$	1.24982e7	0.397212
$999$	−8.36735e6	−0.265261

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1045.6.a.h.1.15	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1045.6.a.h.1.15	✓	40	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)

\(f(q)\)	\(=\)	\(q-2.77766 q^{2} -22.7115 q^{3} -24.2846 q^{4} +25.0000 q^{5} +63.0848 q^{6} -147.613 q^{7} +156.340 q^{8} +272.811 q^{9} +O(q^{10})\)	\(q-2.77766 q^{2} -22.7115 q^{3} -24.2846 q^{4} +25.0000 q^{5} +63.0848 q^{6} -147.613 q^{7} +156.340 q^{8} +272.811 q^{9} -69.4415 q^{10} +121.000 q^{11} +551.539 q^{12} +639.175 q^{13} +410.019 q^{14} -567.787 q^{15} +342.849 q^{16} -659.486 q^{17} -757.777 q^{18} +361.000 q^{19} -607.115 q^{20} +3352.51 q^{21} -336.097 q^{22} +4675.18 q^{23} -3550.70 q^{24} +625.000 q^{25} -1775.41 q^{26} -677.054 q^{27} +3584.72 q^{28} +5066.41 q^{29} +1577.12 q^{30} +4496.85 q^{31} -5955.18 q^{32} -2748.09 q^{33} +1831.83 q^{34} -3690.32 q^{35} -6625.11 q^{36} +12358.5 q^{37} -1002.74 q^{38} -14516.6 q^{39} +3908.49 q^{40} +17965.0 q^{41} -9312.13 q^{42} +13840.7 q^{43} -2938.44 q^{44} +6820.28 q^{45} -12986.1 q^{46} -6956.38 q^{47} -7786.60 q^{48} +4982.57 q^{49} -1736.04 q^{50} +14977.9 q^{51} -15522.1 q^{52} +20615.9 q^{53} +1880.63 q^{54} +3025.00 q^{55} -23077.7 q^{56} -8198.84 q^{57} -14072.8 q^{58} +5808.65 q^{59} +13788.5 q^{60} -29010.9 q^{61} -12490.7 q^{62} -40270.4 q^{63} +5570.32 q^{64} +15979.4 q^{65} +7633.26 q^{66} -15642.2 q^{67} +16015.4 q^{68} -106180. q^{69} +10250.5 q^{70} +45233.9 q^{71} +42651.2 q^{72} -39182.9 q^{73} -34327.6 q^{74} -14194.7 q^{75} -8766.74 q^{76} -17861.2 q^{77} +40322.2 q^{78} -8183.99 q^{79} +8571.22 q^{80} -50916.2 q^{81} -49900.8 q^{82} +35339.3 q^{83} -81414.3 q^{84} -16487.2 q^{85} -38444.8 q^{86} -115066. q^{87} +18917.1 q^{88} -34162.3 q^{89} -18944.4 q^{90} -94350.5 q^{91} -113535. q^{92} -102130. q^{93} +19322.5 q^{94} +9025.00 q^{95} +135251. q^{96} -23325.9 q^{97} -13839.9 q^{98} +33010.1 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9}+O(q^{10}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9	\( 40 q + 24 q^{2} + 63 q^{3} + 690 q^{4} + 1000 q^{5} + 365 q^{6} + 839 q^{7} + 846 q^{8} + 3555 q^{9} + 600 q^{10} + 4840 q^{11} + 2312 q^{12} + 2661 q^{13} + 395 q^{14} + 1575 q^{15} + 15974 q^{16} + 8249 q^{17} + 7225 q^{18} + 14440 q^{19} + 17250 q^{20} + 6845 q^{21} + 2904 q^{22} + 13948 q^{23} + 9740 q^{24} + 25000 q^{25} + 11581 q^{26} + 27864 q^{27} + 37879 q^{28} + 12965 q^{29} + 9125 q^{30} + 4411 q^{31} + 30751 q^{32} + 7623 q^{33} - 17739 q^{34} + 20975 q^{35} + 71345 q^{36} + 5729 q^{37} + 8664 q^{38} - 23560 q^{39} + 21150 q^{40} + 34059 q^{41} + 48528 q^{42} + 68593 q^{43} + 83490 q^{44} + 88875 q^{45} + 43829 q^{46} + 91592 q^{47} + 26539 q^{48} + 152447 q^{49} + 15000 q^{50} - 23170 q^{51} + 46798 q^{52} + 24361 q^{53} + 136436 q^{54} + 121000 q^{55} - 35393 q^{56} + 22743 q^{57} + 77722 q^{58} + 212881 q^{59} + 57800 q^{60} + 137627 q^{61} + 82606 q^{62} + 243832 q^{63} + 259580 q^{64} + 66525 q^{65} + 44165 q^{66} + 78752 q^{67} + 565000 q^{68} + 46134 q^{69} + 9875 q^{70} + 28888 q^{71} - 65574 q^{72} + 291074 q^{73} + 151963 q^{74} + 39375 q^{75} + 249090 q^{76} + 101519 q^{77} - 136222 q^{78} + 87079 q^{79} + 399350 q^{80} + 471360 q^{81} - 74882 q^{82} + 346989 q^{83} - 159196 q^{84} + 206225 q^{85} - 207742 q^{86} + 294612 q^{87} + 102366 q^{88} + 126718 q^{89} + 180625 q^{90} - 239900 q^{91} + 274196 q^{92} + 321654 q^{93} - 418108 q^{94} + 361000 q^{95} + 342154 q^{96} + 137404 q^{97} - 89356 q^{98} + 430155 q^{99}+O(q^{100}) \) 40 * q + 24 * q^2 + 63 * q^3 + 690 * q^4 + 1000 * q^5 + 365 * q^6 + 839 * q^7 + 846 * q^8 + 3555 * q^9 + 600 * q^10 + 4840 * q^11 + 2312 * q^12 + 2661 * q^13 + 395 * q^14 + 1575 * q^15 + 15974 * q^16 + 8249 * q^17 + 7225 * q^18 + 14440 * q^19 + 17250 * q^20 + 6845 * q^21 + 2904 * q^22 + 13948 * q^23 + 9740 * q^24 + 25000 * q^25 + 11581 * q^26 + 27864 * q^27 + 37879 * q^28 + 12965 * q^29 + 9125 * q^30 + 4411 * q^31 + 30751 * q^32 + 7623 * q^33 - 17739 * q^34 + 20975 * q^35 + 71345 * q^36 + 5729 * q^37 + 8664 * q^38 - 23560 * q^39 + 21150 * q^40 + 34059 * q^41 + 48528 * q^42 + 68593 * q^43 + 83490 * q^44 + 88875 * q^45 + 43829 * q^46 + 91592 * q^47 + 26539 * q^48 + 152447 * q^49 + 15000 * q^50 - 23170 * q^51 + 46798 * q^52 + 24361 * q^53 + 136436 * q^54 + 121000 * q^55 - 35393 * q^56 + 22743 * q^57 + 77722 * q^58 + 212881 * q^59 + 57800 * q^60 + 137627 * q^61 + 82606 * q^62 + 243832 * q^63 + 259580 * q^64 + 66525 * q^65 + 44165 * q^66 + 78752 * q^67 + 565000 * q^68 + 46134 * q^69 + 9875 * q^70 + 28888 * q^71 - 65574 * q^72 + 291074 * q^73 + 151963 * q^74 + 39375 * q^75 + 249090 * q^76 + 101519 * q^77 - 136222 * q^78 + 87079 * q^79 + 399350 * q^80 + 471360 * q^81 - 74882 * q^82 + 346989 * q^83 - 159196 * q^84 + 206225 * q^85 - 207742 * q^86 + 294612 * q^87 + 102366 * q^88 + 126718 * q^89 + 180625 * q^90 - 239900 * q^91 + 274196 * q^92 + 321654 * q^93 - 418108 * q^94 + 361000 * q^95 + 342154 * q^96 + 137404 * q^97 - 89356 * q^98 + 430155 * q^99

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