LMFDB - Embedded newform 29.6.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,6,Mod(1,29)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 6, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	29.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:	$4.65113077458$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 3x^{6} - 184x^{5} + 584x^{4} + 10145x^{3} - 34491x^{2} - 149754x + 524902 $ x^7 - 3x^6 - 184x^5 + 584x^4 + 10145x^3 - 34491x^2 - 149754x + 524902
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$9.56883$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.56883 q^{2} +18.3274 q^{3} +41.4249 q^{4} -84.3249 q^{5} -157.045 q^{6} +216.816 q^{7} -80.7606 q^{8} +92.8952 q^{9} +O(q^{10})$	\(q-8.56883 q^{2} +18.3274 q^{3} +41.4249 q^{4} -84.3249 q^{5} -157.045 q^{6} +216.816 q^{7} -80.7606 q^{8} +92.8952 q^{9} +722.566 q^{10} +380.662 q^{11} +759.213 q^{12} +1058.05 q^{13} -1857.86 q^{14} -1545.46 q^{15} -633.574 q^{16} +801.385 q^{17} -796.004 q^{18} -288.487 q^{19} -3493.15 q^{20} +3973.69 q^{21} -3261.83 q^{22} +334.571 q^{23} -1480.13 q^{24} +3985.69 q^{25} -9066.22 q^{26} -2751.04 q^{27} +8981.59 q^{28} +841.000 q^{29} +13242.8 q^{30} -3280.54 q^{31} +8013.32 q^{32} +6976.57 q^{33} -6866.93 q^{34} -18283.0 q^{35} +3848.18 q^{36} -11158.5 q^{37} +2472.00 q^{38} +19391.3 q^{39} +6810.13 q^{40} -887.943 q^{41} -34049.9 q^{42} +13247.9 q^{43} +15768.9 q^{44} -7833.38 q^{45} -2866.89 q^{46} -2338.13 q^{47} -11611.8 q^{48} +30202.3 q^{49} -34152.7 q^{50} +14687.3 q^{51} +43829.4 q^{52} +1850.38 q^{53} +23573.2 q^{54} -32099.3 q^{55} -17510.2 q^{56} -5287.23 q^{57} -7206.39 q^{58} +7102.05 q^{59} -64020.6 q^{60} +9622.02 q^{61} +28110.4 q^{62} +20141.2 q^{63} -48390.5 q^{64} -89219.6 q^{65} -59781.1 q^{66} +11714.6 q^{67} +33197.3 q^{68} +6131.84 q^{69} +156664. q^{70} -67084.1 q^{71} -7502.27 q^{72} -2340.00 q^{73} +95615.2 q^{74} +73047.5 q^{75} -11950.6 q^{76} +82533.8 q^{77} -166161. q^{78} +33928.9 q^{79} +53426.0 q^{80} -72993.0 q^{81} +7608.63 q^{82} -97350.5 q^{83} +164610. q^{84} -67576.7 q^{85} -113519. q^{86} +15413.4 q^{87} -30742.5 q^{88} +101586. q^{89} +67122.9 q^{90} +229401. q^{91} +13859.6 q^{92} -60124.0 q^{93} +20035.1 q^{94} +24326.7 q^{95} +146864. q^{96} -84674.6 q^{97} -258798. q^{98} +35361.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9}+O(q^{10}) $ 7 * q + 4 * q^2 + 26 * q^3 + 154 * q^4 + 32 * q^5 + 22 * q^6 + 184 * q^7 + 942 * q^8 + 1005 * q^9	\( 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9} + 922 q^{10} + 1106 q^{11} + 214 q^{12} + 408 q^{13} - 2008 q^{14} - 614 q^{15} + 242 q^{16} - 874 q^{17} - 5598 q^{18} + 4288 q^{19} - 6350 q^{20} - 4200 q^{21} - 6114 q^{22} - 4532 q^{23} - 4318 q^{24} + 5527 q^{25} - 19806 q^{26} + 5942 q^{27} - 496 q^{28} + 5887 q^{29} - 16734 q^{30} + 7794 q^{31} + 7898 q^{32} + 34410 q^{33} + 20840 q^{34} + 7088 q^{35} - 572 q^{36} + 5086 q^{37} + 23732 q^{38} + 33394 q^{39} + 22906 q^{40} + 19826 q^{41} - 55440 q^{42} + 19498 q^{43} - 6074 q^{44} + 7854 q^{45} - 12404 q^{46} + 14278 q^{47} - 16406 q^{48} + 38431 q^{49} - 41066 q^{50} + 23892 q^{51} - 34302 q^{52} - 58644 q^{53} - 31194 q^{54} - 25574 q^{55} - 79560 q^{56} - 88540 q^{57} + 3364 q^{58} + 12888 q^{59} - 180822 q^{60} + 102866 q^{61} - 42654 q^{62} - 88632 q^{63} - 10170 q^{64} - 149206 q^{65} + 7710 q^{66} + 102996 q^{67} + 85100 q^{68} - 107244 q^{69} + 349480 q^{70} - 51596 q^{71} + 135568 q^{72} - 17566 q^{73} + 12132 q^{74} + 39356 q^{75} + 360740 q^{76} - 94104 q^{77} + 46386 q^{78} + 212058 q^{79} + 142510 q^{80} - 128285 q^{81} + 201924 q^{82} - 122928 q^{83} - 12328 q^{84} - 109336 q^{85} - 63290 q^{86} + 21866 q^{87} + 136666 q^{88} - 66510 q^{89} + 56084 q^{90} + 194368 q^{91} - 110108 q^{92} - 474274 q^{93} + 438926 q^{94} - 131676 q^{95} - 117018 q^{96} - 118182 q^{97} - 29132 q^{98} + 300668 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 26 * q^3 + 154 * q^4 + 32 * q^5 + 22 * q^6 + 184 * q^7 + 942 * q^8 + 1005 * q^9 + 922 * q^10 + 1106 * q^11 + 214 * q^12 + 408 * q^13 - 2008 * q^14 - 614 * q^15 + 242 * q^16 - 874 * q^17 - 5598 * q^18 + 4288 * q^19 - 6350 * q^20 - 4200 * q^21 - 6114 * q^22 - 4532 * q^23 - 4318 * q^24 + 5527 * q^25 - 19806 * q^26 + 5942 * q^27 - 496 * q^28 + 5887 * q^29 - 16734 * q^30 + 7794 * q^31 + 7898 * q^32 + 34410 * q^33 + 20840 * q^34 + 7088 * q^35 - 572 * q^36 + 5086 * q^37 + 23732 * q^38 + 33394 * q^39 + 22906 * q^40 + 19826 * q^41 - 55440 * q^42 + 19498 * q^43 - 6074 * q^44 + 7854 * q^45 - 12404 * q^46 + 14278 * q^47 - 16406 * q^48 + 38431 * q^49 - 41066 * q^50 + 23892 * q^51 - 34302 * q^52 - 58644 * q^53 - 31194 * q^54 - 25574 * q^55 - 79560 * q^56 - 88540 * q^57 + 3364 * q^58 + 12888 * q^59 - 180822 * q^60 + 102866 * q^61 - 42654 * q^62 - 88632 * q^63 - 10170 * q^64 - 149206 * q^65 + 7710 * q^66 + 102996 * q^67 + 85100 * q^68 - 107244 * q^69 + 349480 * q^70 - 51596 * q^71 + 135568 * q^72 - 17566 * q^73 + 12132 * q^74 + 39356 * q^75 + 360740 * q^76 - 94104 * q^77 + 46386 * q^78 + 212058 * q^79 + 142510 * q^80 - 128285 * q^81 + 201924 * q^82 - 122928 * q^83 - 12328 * q^84 - 109336 * q^85 - 63290 * q^86 + 21866 * q^87 + 136666 * q^88 - 66510 * q^89 + 56084 * q^90 + 194368 * q^91 - 110108 * q^92 - 474274 * q^93 + 438926 * q^94 - 131676 * q^95 - 117018 * q^96 - 118182 * q^97 - 29132 * q^98 + 300668 * 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 $

$2$	−8.56883	−1.51477	−0.757385	−	0.652968i	$-0.773523\pi$
$2$	−8.56883	−1.51477	−0.757385	+	0.652968i	$0.773523\pi$
$3$	18.3274	1.17571	0.587853	−	0.808968i	$-0.299973\pi$
$3$	18.3274	1.17571	0.587853	+	0.808968i	$0.299973\pi$
$4$	41.4249	1.29453
$5$	−84.3249	−1.50845	−0.754225	−	0.656616i	$-0.771987\pi$
$5$	−84.3249	−1.50845	−0.754225	+	0.656616i	$0.771987\pi$
$6$	−157.045	−1.78092
$7$	216.816	1.67242	0.836212	−	0.548406i	$-0.184765\pi$
$7$	216.816	1.67242	0.836212	+	0.548406i	$0.184765\pi$
$8$	−80.7606	−0.446143
$9$	92.8952	0.382285
$10$	722.566	2.28496
$11$	380.662	0.948546	0.474273	−	0.880378i	$-0.342711\pi$
$11$	380.662	0.948546	0.474273	+	0.880378i	$0.342711\pi$
$12$	759.213	1.52199
$13$	1058.05	1.73638	0.868192	−	0.496228i	$-0.165282\pi$
$13$	1058.05	1.73638	0.868192	+	0.496228i	$0.165282\pi$
$14$	−1857.86	−2.53334
$15$	−1545.46	−1.77349
$16$	−633.574	−0.618724
$17$	801.385	0.672541	0.336271	−	0.941765i	$-0.390834\pi$
$17$	801.385	0.672541	0.336271	+	0.941765i	$0.390834\pi$
$18$	−796.004	−0.579074
$19$	−288.487	−0.183334	−0.0916669	−	0.995790i	$-0.529219\pi$
$19$	−288.487	−0.183334	−0.0916669	+	0.995790i	$0.529219\pi$
$20$	−3493.15	−1.95273
$21$	3973.69	1.96628
$22$	−3261.83	−1.43683
$23$	334.571	0.131877	0.0659385	−	0.997824i	$-0.478996\pi$
$23$	334.571	0.131877	0.0659385	+	0.997824i	$0.478996\pi$
$24$	−1480.13	−0.524533
$25$	3985.69	1.27542
$26$	−9066.22	−2.63022
$27$	−2751.04	−0.726252
$28$	8981.59	2.16500
$29$	841.000	0.185695
$29$	841.000	0.185695
$30$	13242.8	2.68644
$31$	−3280.54	−0.613115	−0.306557	−	0.951852i	$-0.599177\pi$
$31$	−3280.54	−0.613115	−0.306557	+	0.951852i	$0.599177\pi$
$32$	8013.32	1.38337
$33$	6976.57	1.11521
$34$	−6866.93	−1.01875
$35$	−18283.0	−2.52277
$36$	3848.18	0.494879
$37$	−11158.5	−1.33999	−0.669994	−	0.742366i	$-0.733703\pi$
$37$	−11158.5	−1.33999	−0.669994	+	0.742366i	$0.733703\pi$
$38$	2472.00	0.277709
$39$	19391.3	2.04148
$40$	6810.13	0.672985
$41$	−887.943	−0.0824946	−0.0412473	−	0.999149i	$-0.513133\pi$
$41$	−887.943	−0.0824946	−0.0412473	+	0.999149i	$0.513133\pi$
$42$	−34049.9	−2.97846
$43$	13247.9	1.09264	0.546318	−	0.837578i	$-0.316029\pi$
$43$	13247.9	1.09264	0.546318	+	0.837578i	$0.316029\pi$
$44$	15768.9	1.22792
$45$	−7833.38	−0.576657
$46$	−2866.89	−0.199763
$47$	−2338.13	−0.154392	−0.0771959	−	0.997016i	$-0.524597\pi$
$47$	−2338.13	−0.154392	−0.0771959	+	0.997016i	$0.524597\pi$
$48$	−11611.8	−0.727438
$49$	30202.3	1.79700
$50$	−34152.7	−1.93197
$51$	14687.3	0.790711
$52$	43829.4	2.24780
$53$	1850.38	0.0904840	0.0452420	−	0.998976i	$-0.485594\pi$
$53$	1850.38	0.0904840	0.0452420	+	0.998976i	$0.485594\pi$
$54$	23573.2	1.10010
$55$	−32099.3	−1.43083
$56$	−17510.2	−0.746141
$57$	−5287.23	−0.215547
$58$	−7206.39	−0.281286
$59$	7102.05	0.265616	0.132808	−	0.991142i	$-0.457601\pi$
$59$	7102.05	0.265616	0.132808	+	0.991142i	$0.457601\pi$
$60$	−64020.6	−2.29584
$61$	9622.02	0.331087	0.165543	−	0.986203i	$-0.447062\pi$
$61$	9622.02	0.331087	0.165543	+	0.986203i	$0.447062\pi$
$62$	28110.4	0.928728
$63$	20141.2	0.639343
$64$	−48390.5	−1.47676
$65$	−89219.6	−2.61925
$66$	−59781.1	−1.68929
$67$	11714.6	0.318816	0.159408	−	0.987213i	$-0.449042\pi$
$67$	11714.6	0.318816	0.159408	+	0.987213i	$0.449042\pi$
$68$	33197.3	0.870624
$69$	6131.84	0.155049
$70$	156664.	3.82142
$71$	−67084.1	−1.57933	−0.789667	−	0.613536i	$-0.789747\pi$
$71$	−67084.1	−1.57933	−0.789667	+	0.613536i	$0.789747\pi$
$72$	−7502.27	−0.170554
$73$	−2340.00	−0.0513935	−0.0256967	−	0.999670i	$-0.508180\pi$
$73$	−2340.00	−0.0513935	−0.0256967	+	0.999670i	$0.508180\pi$
$74$	95615.2	2.02977
$75$	73047.5	1.49952
$76$	−11950.6	−0.237331
$77$	82533.8	1.58637
$78$	−166161.	−3.09237
$79$	33928.9	0.611649	0.305825	−	0.952088i	$-0.401068\pi$
$79$	33928.9	0.611649	0.305825	+	0.952088i	$0.401068\pi$
$80$	53426.0	0.933314
$81$	−72993.0	−1.23614
$82$	7608.63	0.124960
$83$	−97350.5	−1.55111	−0.775555	−	0.631279i	$-0.782530\pi$
$83$	−97350.5	−1.55111	−0.775555	+	0.631279i	$0.782530\pi$
$84$	164610.	2.54541
$85$	−67576.7	−1.01449
$86$	−113519.	−1.65509
$87$	15413.4	0.218323
$88$	−30742.5	−0.423187
$89$	101586.	1.35943	0.679716	−	0.733475i	$-0.262103\pi$
$89$	101586.	1.35943	0.679716	+	0.733475i	$0.262103\pi$
$90$	67122.9	0.873504
$91$	229401.	2.90397
$92$	13859.6	0.170719
$93$	−60124.0	−0.720843
$94$	20035.1	0.233868
$95$	24326.7	0.276550
$96$	146864.	1.62643
$97$	−84674.6	−0.913743	−0.456871	−	0.889533i	$-0.651030\pi$
$97$	−84674.6	−0.913743	−0.456871	+	0.889533i	$0.651030\pi$
$98$	−258798.	−2.72205
$99$	35361.7	0.362615
$100$	165107.	1.65107
$101$	59936.3	0.584637	0.292318	−	0.956321i	$-0.405573\pi$
$101$	59936.3	0.584637	0.292318	+	0.956321i	$0.405573\pi$
$102$	−125853.	−1.19774
$103$	−196075.	−1.82108	−0.910542	−	0.413417i	$-0.864335\pi$
$103$	−196075.	−1.82108	−0.910542	+	0.413417i	$0.864335\pi$
$104$	−85448.3	−0.774676
$105$	−335081.	−2.96604
$106$	−15855.6	−0.137063
$107$	82447.0	0.696170	0.348085	−	0.937463i	$-0.386832\pi$
$107$	82447.0	0.696170	0.348085	+	0.937463i	$0.386832\pi$
$108$	−113961.	−0.940153
$109$	−152195.	−1.22697	−0.613484	−	0.789707i	$-0.710233\pi$
$109$	−152195.	−1.22697	−0.613484	+	0.789707i	$0.710233\pi$
$110$	275054.	2.16738
$111$	−204507.	−1.57543
$112$	−137369.	−1.03477
$113$	168561.	1.24182	0.620912	−	0.783880i	$-0.286762\pi$
$113$	168561.	1.24182	0.620912	+	0.783880i	$0.286762\pi$
$114$	45305.4	0.326504
$115$	−28212.7	−0.198930
$116$	34838.4	0.240388
$117$	98287.3	0.663793
$118$	−60856.3	−0.402347
$119$	173753.	1.12477
$120$	124812.	0.791232
$121$	−16147.1	−0.100261
$122$	−82449.5	−0.501520
$123$	−16273.7	−0.0969893
$124$	−135896.	−0.793695
$125$	−72577.8	−0.415460
$126$	−172586.	−0.968457
$127$	−21587.4	−0.118766	−0.0593829	−	0.998235i	$-0.518913\pi$
$127$	−21587.4	−0.118766	−0.0593829	+	0.998235i	$0.518913\pi$
$128$	158224.	0.853585
$129$	242800.	1.28462
$130$	764508.	3.96756
$131$	137802.	0.701581	0.350790	−	0.936454i	$-0.385913\pi$
$131$	137802.	0.701581	0.350790	+	0.936454i	$0.385913\pi$
$132$	289004.	1.44367
$133$	−62548.7	−0.306612
$134$	−100380.	−0.482933
$135$	231981.	1.09551
$136$	−64720.3	−0.300050
$137$	−422084.	−1.92131	−0.960654	−	0.277747i	$-0.910412\pi$
$137$	−422084.	−1.92131	−0.960654	+	0.277747i	$0.910412\pi$
$138$	−52542.7	−0.234863
$139$	79419.8	0.348652	0.174326	−	0.984688i	$-0.444225\pi$
$139$	79419.8	0.348652	0.174326	+	0.984688i	$0.444225\pi$
$140$	−757372.	−3.26580
$141$	−42852.0	−0.181519
$142$	574833.	2.39233
$143$	402758.	1.64704
$144$	−58855.9	−0.236529
$145$	−70917.3	−0.280112
$146$	20051.0	0.0778493
$147$	553530.	2.11275
$148$	−462239.	−1.73465
$149$	−144641.	−0.533736	−0.266868	−	0.963733i	$-0.585989\pi$
$149$	−144641.	−0.533736	−0.266868	+	0.963733i	$0.585989\pi$
$150$	−625932.	−2.27143
$151$	−446697.	−1.59430	−0.797152	−	0.603779i	$-0.793661\pi$
$151$	−446697.	−1.59430	−0.797152	+	0.603779i	$0.793661\pi$
$152$	23298.4	0.0817931
$153$	74444.8	0.257102
$154$	−707218.	−2.40299
$155$	276632.	0.924853
$156$	803282.	2.64275
$157$	−136908.	−0.443282	−0.221641	−	0.975128i	$-0.571141\pi$
$157$	−136908.	−0.443282	−0.221641	+	0.975128i	$0.571141\pi$
$158$	−290731.	−0.926508
$159$	33912.8	0.106383
$160$	−675723.	−2.08674
$161$	72540.5	0.220554
$162$	625465.	1.87247
$163$	5407.16	0.0159404	0.00797022	−	0.999968i	$-0.497463\pi$
$163$	5407.16	0.0159404	0.00797022	+	0.999968i	$0.497463\pi$
$164$	−36783.0	−0.106792
$165$	−588299.	−1.68224
$166$	834180.	2.34958
$167$	−303826.	−0.843013	−0.421506	−	0.906825i	$-0.638498\pi$
$167$	−303826.	−0.843013	−0.421506	+	0.906825i	$0.638498\pi$
$168$	−320917.	−0.877243
$169$	748167.	2.01503
$170$	579054.	1.53673
$171$	−26799.1	−0.0700857
$172$	548792.	1.41445
$173$	−45069.8	−0.114491	−0.0572454	−	0.998360i	$-0.518232\pi$
$173$	−45069.8	−0.114491	−0.0572454	+	0.998360i	$0.518232\pi$
$174$	−132075.	−0.330709
$175$	864163.	2.13305
$176$	−241178.	−0.586888
$177$	130162.	0.312286
$178$	−870471.	−2.05923
$179$	348392.	0.812710	0.406355	−	0.913715i	$-0.366800\pi$
$179$	348392.	0.812710	0.406355	+	0.913715i	$0.366800\pi$
$180$	−324497.	−0.746500
$181$	−754876.	−1.71269	−0.856346	−	0.516403i	$-0.827271\pi$
$181$	−754876.	−1.71269	−0.856346	+	0.516403i	$0.827271\pi$
$182$	−1.96570e6	−4.39885
$183$	176347.	0.389261
$184$	−27020.2	−0.0588361
$185$	940939.	2.02131
$186$	515193.	1.09191
$187$	305057.	0.637936
$188$	−96856.9	−0.199865
$189$	−596469.	−1.21460
$190$	−208451.	−0.418909
$191$	−559504.	−1.10974	−0.554868	−	0.831938i	$-0.687231\pi$
$191$	−559504.	−1.10974	−0.554868	+	0.831938i	$0.687231\pi$
$192$	−886874.	−1.73624
$193$	915469.	1.76909	0.884546	−	0.466453i	$-0.154468\pi$
$193$	915469.	1.76909	0.884546	+	0.466453i	$0.154468\pi$
$194$	725563.	1.38411
$195$	−1.63517e6	−3.07947
$196$	1.25113e6	2.32627
$197$	149660.	0.274751	0.137375	−	0.990519i	$-0.456133\pi$
$197$	149660.	0.274751	0.137375	+	0.990519i	$0.456133\pi$
$198$	−303009.	−0.549278
$199$	2043.12	0.00365731	0.00182865	−	0.999998i	$-0.499418\pi$
$199$	2043.12	0.00365731	0.00182865	+	0.999998i	$0.499418\pi$
$200$	−321887.	−0.569021
$201$	214698.	0.374834
$202$	−513584.	−0.885591
$203$	182342.	0.310562
$204$	608422.	1.02360
$205$	74875.7	0.124439
$206$	1.68014e6	2.75852
$207$	31080.1	0.0504146
$208$	−670350.	−1.07434
$209$	−109816.	−0.173900
$210$	2.87125e6	4.49286
$211$	−94629.7	−0.146326	−0.0731630	−	0.997320i	$-0.523309\pi$
$211$	−94629.7	−0.146326	−0.0731630	+	0.997320i	$0.523309\pi$
$212$	76652.0	0.117134
$213$	−1.22948e6	−1.85683
$214$	−706474.	−1.05454
$215$	−1.11713e6	−1.64819
$216$	222175.	0.324012
$217$	−711275.	−1.02539
$218$	1.30413e6	1.85857
$219$	−42886.1	−0.0604236
$220$	−1.32971e6	−1.85226
$221$	847902.	1.16779
$222$	1.75238e6	2.38642
$223$	33151.7	0.0446420	0.0223210	−	0.999751i	$-0.492894\pi$
$223$	33151.7	0.0446420	0.0223210	+	0.999751i	$0.492894\pi$
$224$	1.73742e6	2.31358
$225$	370252.	0.487574
$226$	−1.44437e6	−1.88108
$227$	−886146.	−1.14141	−0.570704	−	0.821156i	$-0.693329\pi$
$227$	−886146.	−1.14141	−0.570704	+	0.821156i	$0.693329\pi$
$228$	−219023.	−0.279031
$229$	−51324.5	−0.0646749	−0.0323375	−	0.999477i	$-0.510295\pi$
$229$	−51324.5	−0.0646749	−0.0323375	+	0.999477i	$0.510295\pi$
$230$	241750.	0.301333
$231$	1.51263e6	1.86511
$232$	−67919.6	−0.0828467
$233$	−854399.	−1.03103	−0.515515	−	0.856881i	$-0.672399\pi$
$233$	−854399.	−1.03103	−0.515515	+	0.856881i	$0.672399\pi$
$234$	−842208.	−1.00549
$235$	197163.	0.232892
$236$	294202.	0.343847
$237$	621831.	0.719120
$238$	−1.48886e6	−1.70377
$239$	750885.	0.850313	0.425156	−	0.905120i	$-0.360219\pi$
$239$	750885.	0.850313	0.425156	+	0.905120i	$0.360219\pi$
$240$	979163.	1.09730
$241$	−71808.1	−0.0796400	−0.0398200	−	0.999207i	$-0.512678\pi$
$241$	−71808.1	−0.0796400	−0.0398200	+	0.999207i	$0.512678\pi$
$242$	138362.	0.151872
$243$	−669273.	−0.727089
$244$	398591.	0.428601
$245$	−2.54680e6	−2.71069
$246$	139447.	0.146917
$247$	−305233.	−0.318338
$248$	264939.	0.273537
$249$	−1.78419e6	−1.82365
$250$	621907.	0.629326
$251$	897843.	0.899531	0.449765	−	0.893147i	$-0.351508\pi$
$251$	897843.	0.899531	0.449765	+	0.893147i	$0.351508\pi$
$252$	834347.	0.827647
$253$	127359.	0.125091
$254$	184979.	0.179903
$255$	−1.23851e6	−1.19275
$256$	192703.	0.183776
$257$	848562.	0.801402	0.400701	−	0.916209i	$-0.368767\pi$
$257$	848562.	0.801402	0.400701	+	0.916209i	$0.368767\pi$
$258$	−2.08051e6	−1.94590
$259$	−2.41934e6	−2.24103
$260$	−3.69591e6	−3.39069
$261$	78124.9	0.0709885
$262$	−1.18080e6	−1.06273
$263$	−592909.	−0.528565	−0.264283	−	0.964445i	$-0.585135\pi$
$263$	−592909.	−0.528565	−0.264283	+	0.964445i	$0.585135\pi$
$264$	−563432.	−0.497544
$265$	−156033.	−0.136491
$266$	535969.	0.464447
$267$	1.86181e6	1.59829
$268$	485276.	0.412716
$269$	833107.	0.701973	0.350986	−	0.936381i	$-0.385846\pi$
$269$	833107.	0.701973	0.350986	+	0.936381i	$0.385846\pi$
$270$	−1.98781e6	−1.65945
$271$	728989.	0.602973	0.301487	−	0.953470i	$-0.402517\pi$
$271$	728989.	0.602973	0.301487	+	0.953470i	$0.402517\pi$
$272$	−507736.	−0.416117
$273$	4.20434e6	3.41422
$274$	3.61676e6	2.91034
$275$	1.51720e6	1.20980
$276$	254011.	0.200715
$277$	1.44549e6	1.13192	0.565961	−	0.824432i	$-0.308505\pi$
$277$	1.44549e6	1.13192	0.565961	+	0.824432i	$0.308505\pi$
$278$	−680535.	−0.528127
$279$	−304747.	−0.234384
$280$	1.47655e6	1.12552
$281$	1.71312e6	1.29426	0.647131	−	0.762379i	$-0.275969\pi$
$281$	1.71312e6	1.29426	0.647131	+	0.762379i	$0.275969\pi$
$282$	367191.	0.274960
$283$	2.14168e6	1.58960	0.794799	−	0.606872i	$-0.207576\pi$
$283$	2.14168e6	1.58960	0.794799	+	0.606872i	$0.207576\pi$
$284$	−2.77896e6	−2.04449
$285$	445845.	0.325141
$286$	−3.45117e6	−2.49489
$287$	−192520.	−0.137966
$288$	744399.	0.528841
$289$	−777639.	−0.547688
$290$	607678.	0.424306
$291$	−1.55187e6	−1.07429
$292$	−96934.1	−0.0665303
$293$	663344.	0.451408	0.225704	−	0.974196i	$-0.427532\pi$
$293$	663344.	0.451408	0.225704	+	0.974196i	$0.427532\pi$
$294$	−4.74311e6	−3.20033
$295$	−598880.	−0.400668
$296$	901166.	0.597827
$297$	−1.04722e6	−0.688883
$298$	1.23941e6	0.808488
$299$	353992.	0.228989
$300$	3.02599e6	1.94117
$301$	2.87236e6	1.82735
$302$	3.82768e6	2.41500
$303$	1.09848e6	0.687361
$304$	182778.	0.113433
$305$	−811376.	−0.499428
$306$	−637905.	−0.389451
$307$	615215.	0.372547	0.186274	−	0.982498i	$-0.440359\pi$
$307$	615215.	0.372547	0.186274	+	0.982498i	$0.440359\pi$
$308$	3.41896e6	2.05360
$309$	−3.59356e6	−2.14106
$310$	−2.37041e6	−1.40094
$311$	−1.17303e6	−0.687712	−0.343856	−	0.939022i	$-0.611733\pi$
$311$	−1.17303e6	−0.687712	−0.343856	+	0.939022i	$0.611733\pi$
$312$	−1.56605e6	−0.910792
$313$	−2.58664e6	−1.49237	−0.746184	−	0.665740i	$-0.768116\pi$
$313$	−2.58664e6	−1.49237	−0.746184	+	0.665740i	$0.768116\pi$
$314$	1.17314e6	0.671470
$315$	−1.69840e6	−0.964416
$316$	1.40550e6	0.791798
$317$	−934239.	−0.522167	−0.261084	−	0.965316i	$-0.584080\pi$
$317$	−934239.	−0.522167	−0.261084	+	0.965316i	$0.584080\pi$
$318$	−290593.	−0.161145
$319$	320137.	0.176141
$320$	4.08052e6	2.22762
$321$	1.51104e6	0.818491
$322$	−621587.	−0.334089
$323$	−231189.	−0.123299
$324$	−3.02373e6	−1.60022
$325$	4.21704e6	2.21462
$326$	−46333.1	−0.0241461
$327$	−2.78934e6	−1.44255
$328$	71710.7	0.0368044
$329$	−506945.	−0.258209
$330$	5.04103e6	2.54821
$331$	−3.77955e6	−1.89614	−0.948070	−	0.318061i	$-0.896968\pi$
$331$	−3.77955e6	−1.89614	−0.948070	+	0.318061i	$0.896968\pi$
$332$	−4.03274e6	−2.00796
$333$	−1.03657e6	−0.512257
$334$	2.60344e6	1.27697
$335$	−987831.	−0.480918
$336$	−2.51762e6	−1.21658
$337$	2.10980e6	1.01197	0.505983	−	0.862544i	$-0.331130\pi$
$337$	2.10980e6	1.01197	0.505983	+	0.862544i	$0.331130\pi$
$338$	−6.41092e6	−3.05231
$339$	3.08929e6	1.46002
$340$	−2.79936e6	−1.31329
$341$	−1.24878e6	−0.581567
$342$	229637.	0.106164
$343$	2.90431e6	1.33293
$344$	−1.06991e6	−0.487472
$345$	−517067.	−0.233883
$346$	386196.	0.173427
$347$	37808.7	0.0168565	0.00842827	−	0.999964i	$-0.497317\pi$
$347$	37808.7	0.0168565	0.00842827	+	0.999964i	$0.497317\pi$
$348$	638498.	0.282626
$349$	632608.	0.278017	0.139008	−	0.990291i	$-0.455608\pi$
$349$	632608.	0.278017	0.139008	+	0.990291i	$0.455608\pi$
$350$	−7.40487e6	−3.23108
$351$	−2.91072e6	−1.26105
$352$	3.05037e6	1.31219
$353$	−2.76871e6	−1.18261	−0.591304	−	0.806449i	$-0.701387\pi$
$353$	−2.76871e6	−1.18261	−0.591304	+	0.806449i	$0.701387\pi$
$354$	−1.11534e6	−0.473041
$355$	5.65687e6	2.38235
$356$	4.20818e6	1.75982
$357$	3.18445e6	1.32240
$358$	−2.98531e6	−1.23107
$359$	−2.50490e6	−1.02578	−0.512889	−	0.858455i	$-0.671425\pi$
$359$	−2.50490e6	−1.02578	−0.512889	+	0.858455i	$0.671425\pi$
$360$	632628.	0.257272
$361$	−2.39287e6	−0.966389
$362$	6.46841e6	2.59433
$363$	−295935.	−0.117877
$364$	9.50293e6	3.75928
$365$	197320.	0.0775245
$366$	−1.51109e6	−0.589640
$367$	3.09219e6	1.19840	0.599199	−	0.800600i	$-0.295486\pi$
$367$	3.09219e6	1.19840	0.599199	+	0.800600i	$0.295486\pi$
$368$	−211976.	−0.0815955
$369$	−82485.6	−0.0315364
$370$	−8.06275e6	−3.06181
$371$	401193.	0.151328
$372$	−2.49063e6	−0.933151
$373$	2.44054e6	0.908266	0.454133	−	0.890934i	$-0.349949\pi$
$373$	2.44054e6	0.908266	0.454133	+	0.890934i	$0.349949\pi$
$374$	−2.61398e6	−0.966327
$375$	−1.33017e6	−0.488458
$376$	188829.	0.0688809
$377$	889816.	0.322439
$378$	5.11105e6	1.83984
$379$	2.64306e6	0.945168	0.472584	−	0.881286i	$-0.343321\pi$
$379$	2.64306e6	0.945168	0.472584	+	0.881286i	$0.343321\pi$
$380$	1.00773e6	0.358002
$381$	−395642.	−0.139634
$382$	4.79430e6	1.68099
$383$	−460287.	−0.160336	−0.0801682	−	0.996781i	$-0.525546\pi$
$383$	−460287.	−0.160336	−0.0801682	+	0.996781i	$0.525546\pi$
$384$	2.89984e6	1.00356
$385$	−6.95965e6	−2.39296
$386$	−7.84450e6	−2.67977
$387$	1.23066e6	0.417698
$388$	−3.50764e6	−1.18287
$389$	−2.72948e6	−0.914547	−0.457273	−	0.889326i	$-0.651174\pi$
$389$	−2.72948e6	−0.914547	−0.457273	+	0.889326i	$0.651174\pi$
$390$	1.40115e7	4.66469
$391$	268120.	0.0886927
$392$	−2.43915e6	−0.801722
$393$	2.52556e6	0.824853
$394$	−1.28241e6	−0.416184
$395$	−2.86106e6	−0.922643
$396$	1.46486e6	0.469415
$397$	530743.	0.169008	0.0845041	−	0.996423i	$-0.473069\pi$
$397$	530743.	0.169008	0.0845041	+	0.996423i	$0.473069\pi$
$398$	−17507.2	−0.00553998
$399$	−1.14636e6	−0.360486
$400$	−2.52523e6	−0.789134
$401$	1.65453e6	0.513822	0.256911	−	0.966435i	$-0.417295\pi$
$401$	1.65453e6	0.513822	0.256911	+	0.966435i	$0.417295\pi$
$402$	−1.83971e6	−0.567787
$403$	−3.47097e6	−1.06460
$404$	2.48286e6	0.756829
$405$	6.15513e6	1.86466
$406$	−1.56246e6	−0.470429
$407$	−4.24762e6	−1.27104
$408$	−1.18616e6	−0.352770
$409$	−5.20484e6	−1.53851	−0.769253	−	0.638944i	$-0.779372\pi$
$409$	−5.20484e6	−1.53851	−0.769253	+	0.638944i	$0.779372\pi$
$410$	−641597.	−0.188496
$411$	−7.73571e6	−2.25889
$412$	−8.12240e6	−2.35744
$413$	1.53984e6	0.444222
$414$	−266320.	−0.0763665
$415$	8.20907e6	2.33977
$416$	8.47846e6	2.40206
$417$	1.45556e6	0.409912
$418$	940997.	0.263419
$419$	191911.	0.0534030	0.0267015	−	0.999643i	$-0.491500\pi$
$419$	191911.	0.0534030	0.0267015	+	0.999643i	$0.491500\pi$
$420$	−1.38807e7	−3.83962
$421$	5.00002e6	1.37488	0.687442	−	0.726239i	$-0.258734\pi$
$421$	5.00002e6	1.37488	0.687442	+	0.726239i	$0.258734\pi$
$422$	810866.	0.221650
$423$	−217201.	−0.0590216
$424$	−149438.	−0.0403688
$425$	3.19407e6	0.857773
$426$	1.05352e7	2.81267
$427$	2.08621e6	0.553718
$428$	3.41536e6	0.901212
$429$	7.38153e6	1.93644
$430$	9.57247e6	2.49662
$431$	−3.04923e6	−0.790672	−0.395336	−	0.918537i	$-0.629372\pi$
$431$	−3.04923e6	−0.790672	−0.395336	+	0.918537i	$0.629372\pi$
$432$	1.74298e6	0.449349
$433$	3.79886e6	0.973719	0.486860	−	0.873480i	$-0.338142\pi$
$433$	3.79886e6	0.973719	0.486860	+	0.873480i	$0.338142\pi$
$434$	6.09480e6	1.55323
$435$	−1.29973e6	−0.329330
$436$	−6.30465e6	−1.58835
$437$	−96519.5	−0.0241775
$438$	367484.	0.0915279
$439$	3.28829e6	0.814345	0.407173	−	0.913351i	$-0.366515\pi$
$439$	3.28829e6	0.814345	0.407173	+	0.913351i	$0.366515\pi$
$440$	2.59236e6	0.638357
$441$	2.80565e6	0.686968
$442$	−7.26553e6	−1.76893
$443$	97599.9	0.0236287	0.0118144	−	0.999930i	$-0.496239\pi$
$443$	97599.9	0.0236287	0.0118144	+	0.999930i	$0.496239\pi$
$444$	−8.47167e6	−2.03944
$445$	−8.56621e6	−2.05064
$446$	−284072.	−0.0676224
$447$	−2.65091e6	−0.627517
$448$	−1.04918e7	−2.46977
$449$	4.55742e6	1.06685	0.533424	−	0.845848i	$-0.320905\pi$
$449$	4.55742e6	1.06685	0.533424	+	0.845848i	$0.320905\pi$
$450$	−3.17263e6	−0.738563
$451$	−338006.	−0.0782499
$452$	6.98261e6	1.60758
$453$	−8.18682e6	−1.87443
$454$	7.59324e6	1.72897
$455$	−1.93443e7	−4.38050
$456$	427000.	0.0961647
$457$	491699.	0.110131	0.0550654	−	0.998483i	$-0.482463\pi$
$457$	491699.	0.110131	0.0550654	+	0.998483i	$0.482463\pi$
$458$	439791.	0.0979677
$459$	−2.20464e6	−0.488434
$460$	−1.16871e6	−0.257520
$461$	2.55180e6	0.559234	0.279617	−	0.960112i	$-0.409792\pi$
$461$	2.55180e6	0.559234	0.279617	+	0.960112i	$0.409792\pi$
$462$	−1.29615e7	−2.82521
$463$	−6.25797e6	−1.35669	−0.678345	−	0.734743i	$-0.737303\pi$
$463$	−6.25797e6	−1.35669	−0.678345	+	0.734743i	$0.737303\pi$
$464$	−532835.	−0.114894
$465$	5.06995e6	1.08736
$466$	7.32120e6	1.56177
$467$	2.34350e6	0.497247	0.248624	−	0.968600i	$-0.420022\pi$
$467$	2.34350e6	0.497247	0.248624	+	0.968600i	$0.420022\pi$
$468$	4.07155e6	0.859300
$469$	2.53991e6	0.533195
$470$	−1.68945e6	−0.352778
$471$	−2.50918e6	−0.521169
$472$	−573565.	−0.118503
$473$	5.04297e6	1.03641
$474$	−5.32837e6	−1.08930
$475$	−1.14982e6	−0.233828
$476$	7.19771e6	1.45605
$477$	171892.	0.0345907
$478$	−6.43421e6	−1.28803
$479$	4.98927e6	0.993570	0.496785	−	0.867874i	$-0.334514\pi$
$479$	4.98927e6	0.993570	0.496785	+	0.867874i	$0.334514\pi$
$480$	−1.23843e7	−2.45339
$481$	−1.18062e7	−2.32674
$482$	615312.	0.120636
$483$	1.32948e6	0.259307
$484$	−668892.	−0.129790
$485$	7.14018e6	1.37834
$486$	5.73489e6	1.10137
$487$	−1.75440e6	−0.335202	−0.167601	−	0.985855i	$-0.553602\pi$
$487$	−1.75440e6	−0.335202	−0.167601	+	0.985855i	$0.553602\pi$
$488$	−777080.	−0.147712
$489$	99099.5	0.0187413
$490$	2.18231e7	4.10608
$491$	2.28688e6	0.428094	0.214047	−	0.976823i	$-0.431335\pi$
$491$	2.28688e6	0.428094	0.214047	+	0.976823i	$0.431335\pi$
$492$	−674137.	−0.125555
$493$	673965.	0.124888
$494$	2.61549e6	0.482209
$495$	−2.98187e6	−0.546986
$496$	2.07847e6	0.379349
$497$	−1.45449e7	−2.64132
$498$	1.52884e7	2.76241
$499$	6.03762e6	1.08546	0.542730	−	0.839907i	$-0.317391\pi$
$499$	6.03762e6	1.08546	0.542730	+	0.839907i	$0.317391\pi$
$500$	−3.00653e6	−0.537824
$501$	−5.56836e6	−0.991135
$502$	−7.69347e6	−1.36258
$503$	−1.11239e6	−0.196036	−0.0980182	−	0.995185i	$-0.531250\pi$
$503$	−1.11239e6	−0.196036	−0.0980182	+	0.995185i	$0.531250\pi$
$504$	−1.62661e6	−0.285238
$505$	−5.05412e6	−0.881896
$506$	−1.09132e6	−0.189485
$507$	1.37120e7	2.36909
$508$	−894257.	−0.153746
$509$	−3.45813e6	−0.591625	−0.295813	−	0.955246i	$-0.595590\pi$
$509$	−3.45813e6	−0.591625	−0.295813	+	0.955246i	$0.595590\pi$
$510$	1.06126e7	1.80674
$511$	−507349.	−0.0859517
$512$	−6.71440e6	−1.13196
$513$	793639.	0.133146
$514$	−7.27118e6	−1.21394
$515$	1.65340e7	2.74701
$516$	1.00580e7	1.66298
$517$	−890039.	−0.146448
$518$	2.07309e7	3.39465
$519$	−826015.	−0.134608
$520$	7.20542e6	1.16856
$521$	−9.29125e6	−1.49961	−0.749807	−	0.661656i	$-0.769854\pi$
$521$	−9.29125e6	−1.49961	−0.749807	+	0.661656i	$0.769854\pi$
$522$	−669439.	−0.107531
$523$	1.62992e6	0.260563	0.130282	−	0.991477i	$-0.458412\pi$
$523$	1.62992e6	0.260563	0.130282	+	0.991477i	$0.458412\pi$
$524$	5.70844e6	0.908216
$525$	1.58379e7	2.50784
$526$	5.08054e6	0.800655
$527$	−2.62898e6	−0.412345
$528$	−4.42017e6	−0.690008
$529$	−6.32441e6	−0.982608
$530$	1.33702e6	0.206752
$531$	659746.	0.101541
$532$	−2.59107e6	−0.396918
$533$	−939484.	−0.143242
$534$	−1.59535e7	−2.42105
$535$	−6.95233e6	−1.05014
$536$	−946076.	−0.142238
$537$	6.38514e6	0.955509
$538$	−7.13876e6	−1.06333
$539$	1.14969e7	1.70454
$540$	9.60979e6	1.41817
$541$	−1.04884e7	−1.54070	−0.770348	−	0.637624i	$-0.779917\pi$
$541$	−1.04884e7	−1.54070	−0.770348	+	0.637624i	$0.779917\pi$
$542$	−6.24659e6	−0.913366
$543$	−1.38349e7	−2.01362
$544$	6.42176e6	0.930372
$545$	1.28338e7	1.85082
$546$	−3.60263e7	−5.17176
$547$	4.48107e6	0.640345	0.320172	−	0.947359i	$-0.396259\pi$
$547$	4.48107e6	0.640345	0.320172	+	0.947359i	$0.396259\pi$
$548$	−1.74848e7	−2.48719
$549$	893839.	0.126569
$550$	−1.30007e7	−1.83256
$551$	−242618.	−0.0340442
$552$	−495211.	−0.0691739
$553$	7.35634e6	1.02294
$554$	−1.23862e7	−1.71460
$555$	1.72450e7	2.37646
$556$	3.28996e6	0.451339
$557$	−720322.	−0.0983759	−0.0491879	−	0.998790i	$-0.515663\pi$
$557$	−720322.	−0.0983759	−0.0491879	+	0.998790i	$0.515663\pi$
$558$	2.61132e6	0.355038
$559$	1.40169e7	1.89724
$560$	1.15836e7	1.56090
$561$	5.59092e6	0.750025
$562$	−1.46795e7	−1.96051
$563$	1.26872e7	1.68692	0.843458	−	0.537196i	$-0.180516\pi$
$563$	1.26872e7	1.68692	0.843458	+	0.537196i	$0.180516\pi$
$564$	−1.77514e6	−0.234982
$565$	−1.42139e7	−1.87323
$566$	−1.83517e7	−2.40788
$567$	−1.58261e7	−2.06736
$568$	5.41775e6	0.704609
$569$	−7.93605e6	−1.02760	−0.513799	−	0.857910i	$-0.671762\pi$
$569$	−7.93605e6	−1.02760	−0.513799	+	0.857910i	$0.671762\pi$
$570$	−3.82038e6	−0.492514
$571$	9.14124e6	1.17332	0.586658	−	0.809835i	$-0.300443\pi$
$571$	9.14124e6	1.17332	0.586658	+	0.809835i	$0.300443\pi$
$572$	1.66842e7	2.13214
$573$	−1.02543e7	−1.30472
$574$	1.64967e6	0.208987
$575$	1.33350e6	0.168199
$576$	−4.49524e6	−0.564543
$577$	2.52312e6	0.315499	0.157750	−	0.987479i	$-0.449576\pi$
$577$	2.52312e6	0.315499	0.157750	+	0.987479i	$0.449576\pi$
$578$	6.66346e6	0.829622
$579$	1.67782e7	2.07993
$580$	−2.93774e6	−0.362613
$581$	−2.11072e7	−2.59412
$582$	1.32977e7	1.62731
$583$	704371.	0.0858283
$584$	188979.	0.0229288
$585$	−8.28807e6	−1.00130
$586$	−5.68408e6	−0.683780
$587$	−1.02895e7	−1.23254	−0.616268	−	0.787536i	$-0.711356\pi$
$587$	−1.02895e7	−1.23254	−0.616268	+	0.787536i	$0.711356\pi$
$588$	2.29299e7	2.73502
$589$	946395.	0.112405
$590$	5.13170e6	0.606920
$591$	2.74288e6	0.323026
$592$	7.06972e6	0.829083
$593$	−573757.	−0.0670025	−0.0335013	−	0.999439i	$-0.510666\pi$
$593$	−573757.	−0.0670025	−0.0335013	+	0.999439i	$0.510666\pi$
$594$	8.97343e6	1.04350
$595$	−1.46517e7	−1.69667
$596$	−5.99176e6	−0.690937
$597$	37445.2	0.00429992
$598$	−3.03330e6	−0.346866
$599$	1.61434e7	1.83835	0.919173	−	0.393853i	$-0.128858\pi$
$599$	1.61434e7	1.83835	0.919173	+	0.393853i	$0.128858\pi$
$600$	−5.89936e6	−0.669001
$601$	3.97295e6	0.448670	0.224335	−	0.974512i	$-0.427979\pi$
$601$	3.97295e6	0.448670	0.224335	+	0.974512i	$0.427979\pi$
$602$	−2.46127e7	−2.76802
$603$	1.08823e6	0.121878
$604$	−1.85044e7	−2.06387
$605$	1.36160e6	0.151238
$606$	−9.41268e6	−1.04119
$607$	5.65644e6	0.623119	0.311560	−	0.950227i	$-0.399149\pi$
$607$	5.65644e6	0.623119	0.311560	+	0.950227i	$0.399149\pi$
$608$	−2.31174e6	−0.253618
$609$	3.34187e6	0.365129
$610$	6.95255e6	0.756518
$611$	−2.47385e6	−0.268084
$612$	3.08387e6	0.332826
$613$	7.65406e6	0.822699	0.411349	−	0.911478i	$-0.365058\pi$
$613$	7.65406e6	0.822699	0.411349	+	0.911478i	$0.365058\pi$
$614$	−5.27168e6	−0.564323
$615$	1.37228e6	0.146304
$616$	−6.66548e6	−0.707749
$617$	−1.06193e7	−1.12301	−0.561505	−	0.827473i	$-0.689778\pi$
$617$	−1.06193e7	−1.12301	−0.561505	+	0.827473i	$0.689778\pi$
$618$	3.07926e7	3.24321
$619$	−4.45953e6	−0.467802	−0.233901	−	0.972260i	$-0.575149\pi$
$619$	−4.45953e6	−0.467802	−0.233901	+	0.972260i	$0.575149\pi$
$620$	1.14594e7	1.19725
$621$	−920418.	−0.0957759
$622$	1.00515e7	1.04173
$623$	2.20254e7	2.27355
$624$	−1.22858e7	−1.26311
$625$	−6.33517e6	−0.648722
$626$	2.21645e7	2.26059
$627$	−2.01265e6	−0.204456
$628$	−5.67141e6	−0.573841
$629$	−8.94224e6	−0.901197
$630$	1.45533e7	1.46087
$631$	1.51771e7	1.51745	0.758725	−	0.651411i	$-0.225823\pi$
$631$	1.51771e7	1.51745	0.758725	+	0.651411i	$0.225823\pi$
$632$	−2.74012e6	−0.272883
$633$	−1.73432e6	−0.172036
$634$	8.00534e6	0.790964
$635$	1.82036e6	0.179152
$636$	1.40483e6	0.137715
$637$	3.19554e7	3.12029
$638$	−2.74320e6	−0.266812
$639$	−6.23180e6	−0.603755
$640$	−1.33422e7	−1.28759
$641$	1.33769e7	1.28591	0.642957	−	0.765903i	$-0.277708\pi$
$641$	1.33769e7	1.28591	0.642957	+	0.765903i	$0.277708\pi$
$642$	−1.29479e7	−1.23983
$643$	−5.68424e6	−0.542182	−0.271091	−	0.962554i	$-0.587384\pi$
$643$	−5.68424e6	−0.542182	−0.271091	+	0.962554i	$0.587384\pi$
$644$	3.00498e6	0.285514
$645$	−2.04741e7	−1.93778
$646$	1.98102e6	0.186770
$647$	−1.93095e7	−1.81347	−0.906735	−	0.421702i	$-0.861433\pi$
$647$	−1.93095e7	−1.81347	−0.906735	+	0.421702i	$0.861433\pi$
$648$	5.89496e6	0.551497
$649$	2.70348e6	0.251949
$650$	−3.61351e7	−3.35464
$651$	−1.30359e7	−1.20556
$652$	223991.	0.0206354
$653$	151435.	0.0138977	0.00694884	−	0.999976i	$-0.497788\pi$
$653$	151435.	0.0138977	0.00694884	+	0.999976i	$0.497788\pi$
$654$	2.39014e7	2.18514
$655$	−1.16201e7	−1.05830
$656$	562577.	0.0510414
$657$	−217374.	−0.0196469
$658$	4.34392e6	0.391127
$659$	−9.74503e6	−0.874117	−0.437058	−	0.899433i	$-0.643980\pi$
$659$	−9.74503e6	−0.874117	−0.437058	+	0.899433i	$0.643980\pi$
$660$	−2.43702e7	−2.17771
$661$	−8.52857e6	−0.759229	−0.379614	−	0.925145i	$-0.623943\pi$
$661$	−8.52857e6	−0.759229	−0.379614	+	0.925145i	$0.623943\pi$
$662$	3.23864e7	2.87222
$663$	1.55399e7	1.37298
$664$	7.86208e6	0.692018
$665$	5.27441e6	0.462509
$666$	8.88220e6	0.775952
$667$	281374.	0.0244889
$668$	−1.25860e7	−1.09130
$669$	607586.	0.0524859
$670$	8.46456e6	0.728480
$671$	3.66274e6	0.314051
$672$	3.18424e7	2.72009
$673$	−1.53606e7	−1.30729	−0.653643	−	0.756803i	$-0.726760\pi$
$673$	−1.53606e7	−1.30729	−0.653643	+	0.756803i	$0.726760\pi$
$674$	−1.80785e7	−1.53290
$675$	−1.09648e7	−0.926277
$676$	3.09928e7	2.60852
$677$	−2.37603e6	−0.199241	−0.0996207	−	0.995025i	$-0.531763\pi$
$677$	−2.37603e6	−0.199241	−0.0996207	+	0.995025i	$0.531763\pi$
$678$	−2.64716e7	−2.21159
$679$	−1.83588e7	−1.52817
$680$	5.45753e6	0.452610
$681$	−1.62408e7	−1.34196
$682$	1.07006e7	0.880941
$683$	−6.86181e6	−0.562842	−0.281421	−	0.959584i	$-0.590806\pi$
$683$	−6.86181e6	−0.562842	−0.281421	+	0.959584i	$0.590806\pi$
$684$	−1.11015e6	−0.0907280
$685$	3.55922e7	2.89820
$686$	−2.48865e7	−2.01908
$687$	−940647.	−0.0760387
$688$	−8.39351e6	−0.676040
$689$	1.95779e6	0.157115
$690$	4.43066e6	0.354279
$691$	1.86887e7	1.48896	0.744480	−	0.667645i	$-0.232698\pi$
$691$	1.86887e7	1.48896	0.744480	+	0.667645i	$0.232698\pi$
$692$	−1.86701e6	−0.148212
$693$	7.66699e6	0.606446
$694$	−323977.	−0.0255338
$695$	−6.69706e6	−0.525923
$696$	−1.24479e6	−0.0974034
$697$	−711584.	−0.0554810
$698$	−5.42071e6	−0.421132
$699$	−1.56589e7	−1.21219
$700$	3.57979e7	2.76129
$701$	−5.85780e6	−0.450235	−0.225118	−	0.974332i	$-0.572277\pi$
$701$	−5.85780e6	−0.450235	−0.225118	+	0.974332i	$0.572277\pi$
$702$	2.49415e7	1.91020
$703$	3.21908e6	0.245665
$704$	−1.84204e7	−1.40078
$705$	3.61349e6	0.273813
$706$	2.37246e7	1.79138
$707$	1.29952e7	0.977761
$708$	5.39197e6	0.404263
$709$	−3.17834e6	−0.237457	−0.118728	−	0.992927i	$-0.537882\pi$
$709$	−3.17834e6	−0.237457	−0.118728	+	0.992927i	$0.537882\pi$
$710$	−4.84727e7	−3.60871
$711$	3.15184e6	0.233824
$712$	−8.20412e6	−0.606502
$713$	−1.09758e6	−0.0808557
$714$	−2.72870e7	−2.00314
$715$	−3.39626e7	−2.48448
$716$	1.44321e7	1.05208
$717$	1.37618e7	0.999718
$718$	2.14640e7	1.55382
$719$	2.62515e7	1.89379	0.946894	−	0.321546i	$-0.104202\pi$
$719$	2.62515e7	1.89379	0.946894	+	0.321546i	$0.104202\pi$
$720$	4.96302e6	0.356792
$721$	−4.25123e7	−3.04563
$722$	2.05041e7	1.46386
$723$	−1.31606e6	−0.0936332
$724$	−3.12707e7	−2.21713
$725$	3.35197e6	0.236840
$726$	2.53582e6	0.178557
$727$	−1.53808e7	−1.07930	−0.539651	−	0.841889i	$-0.681444\pi$
$727$	−1.53808e7	−1.07930	−0.539651	+	0.841889i	$0.681444\pi$
$728$	−1.85266e7	−1.29559
$729$	5.47123e6	0.381300
$730$	−1.69080e6	−0.117432
$731$	1.06167e7	0.734842
$732$	7.30516e6	0.503909
$733$	1.07403e7	0.738338	0.369169	−	0.929362i	$-0.379642\pi$
$733$	1.07403e7	0.738338	0.369169	+	0.929362i	$0.379642\pi$
$734$	−2.64965e7	−1.81530
$735$	−4.66764e7	−3.18698
$736$	2.68103e6	0.182434
$737$	4.45930e6	0.302411
$738$	706805.	0.0477704
$739$	1.50225e7	1.01189	0.505943	−	0.862567i	$-0.331145\pi$
$739$	1.50225e7	1.01189	0.505943	+	0.862567i	$0.331145\pi$
$740$	3.89783e7	2.61664
$741$	−5.59413e6	−0.374272
$742$	−3.43776e6	−0.229227
$743$	−1.20298e7	−0.799440	−0.399720	−	0.916637i	$-0.630893\pi$
$743$	−1.20298e7	−0.799440	−0.399720	+	0.916637i	$0.630893\pi$
$744$	4.85565e6	0.321599
$745$	1.21969e7	0.805115
$746$	−2.09126e7	−1.37581
$747$	−9.04339e6	−0.592966
$748$	1.26370e7	0.825827
$749$	1.78758e7	1.16429
$750$	1.13980e7	0.739902
$751$	1.27308e7	0.823674	0.411837	−	0.911258i	$-0.364887\pi$
$751$	1.27308e7	0.823674	0.411837	+	0.911258i	$0.364887\pi$
$752$	1.48138e6	0.0955259
$753$	1.64552e7	1.05758
$754$	−7.62469e6	−0.488420
$755$	3.76677e7	2.40493
$756$	−2.47087e7	−1.57234
$757$	−2.61540e7	−1.65882	−0.829408	−	0.558643i	$-0.811322\pi$
$757$	−2.61540e7	−1.65882	−0.829408	+	0.558643i	$0.811322\pi$
$758$	−2.26479e7	−1.43171
$759$	2.33416e6	0.147071
$760$	−1.96463e6	−0.123381
$761$	1.26786e7	0.793612	0.396806	−	0.917903i	$-0.370119\pi$
$761$	1.26786e7	0.793612	0.396806	+	0.917903i	$0.370119\pi$
$762$	3.39019e6	0.211513
$763$	−3.29983e7	−2.05201
$764$	−2.31774e7	−1.43658
$765$	−6.27755e6	−0.387826
$766$	3.94412e6	0.242873
$767$	7.51429e6	0.461211
$768$	3.53175e6	0.216066
$769$	2.28743e7	1.39486	0.697431	−	0.716652i	$-0.254326\pi$
$769$	2.28743e7	1.39486	0.697431	+	0.716652i	$0.254326\pi$
$770$	5.96361e7	3.62479
$771$	1.55520e7	0.942213
$772$	3.79232e7	2.29014
$773$	2.65876e7	1.60041	0.800204	−	0.599728i	$-0.204725\pi$
$773$	2.65876e7	1.60041	0.800204	+	0.599728i	$0.204725\pi$
$774$	−1.05454e7	−0.632716
$775$	−1.30752e7	−0.781980
$776$	6.83837e6	0.407660
$777$	−4.43403e7	−2.63479
$778$	2.33885e7	1.38533
$779$	256160.	0.0151240
$780$	−6.77367e7	−3.98646
$781$	−2.55364e7	−1.49807
$782$	−2.29748e6	−0.134349
$783$	−2.31362e6	−0.134862
$784$	−1.91354e7	−1.11185
$785$	1.15448e7	0.668669
$786$	−2.16411e7	−1.24946
$787$	−9.06273e6	−0.521582	−0.260791	−	0.965395i	$-0.583983\pi$
$787$	−9.06273e6	−0.521582	−0.260791	+	0.965395i	$0.583983\pi$
$788$	6.19963e6	0.355673
$789$	−1.08665e7	−0.621437
$790$	2.45159e7	1.39759
$791$	3.65467e7	2.07686
$792$	−2.85583e6	−0.161778
$793$	1.01805e7	0.574894
$794$	−4.54785e6	−0.256009
$795$	−2.85969e6	−0.160473
$796$	84636.1	0.00473449
$797$	−2.52271e7	−1.40676	−0.703382	−	0.710812i	$-0.748328\pi$
$797$	−2.52271e7	−1.40676	−0.703382	+	0.710812i	$0.748328\pi$
$798$	9.82295e6	0.546053
$799$	−1.87374e6	−0.103835
$800$	3.19386e7	1.76438
$801$	9.43683e6	0.519690
$802$	−1.41774e7	−0.778322
$803$	−890748.	−0.0487491
$804$	8.89386e6	0.485233
$805$	−6.11697e6	−0.332695
$806$	2.97421e7	1.61263
$807$	1.52687e7	0.825314
$808$	−4.84049e6	−0.260832
$809$	−8.69627e6	−0.467156	−0.233578	−	0.972338i	$-0.575043\pi$
$809$	−8.69627e6	−0.467156	−0.233578	+	0.972338i	$0.575043\pi$
$810$	−5.27423e7	−2.82453
$811$	1.94112e7	1.03633	0.518166	−	0.855280i	$-0.326615\pi$
$811$	1.94112e7	1.03633	0.518166	+	0.855280i	$0.326615\pi$
$812$	7.55352e6	0.402031
$813$	1.33605e7	0.708919
$814$	3.63971e7	1.92533
$815$	−455959.	−0.0240454
$816$	−9.30551e6	−0.489232
$817$	−3.82184e6	−0.200317
$818$	4.45994e7	2.33048
$819$	2.13103e7	1.11014
$820$	3.10172e6	0.161090
$821$	1.78189e7	0.922620	0.461310	−	0.887239i	$-0.347380\pi$
$821$	1.78189e7	0.922620	0.461310	+	0.887239i	$0.347380\pi$
$822$	6.62861e7	3.42171
$823$	−1.73515e7	−0.892969	−0.446485	−	0.894791i	$-0.647324\pi$
$823$	−1.73515e7	−0.892969	−0.446485	+	0.894791i	$0.647324\pi$
$824$	1.58352e7	0.812464
$825$	2.78065e7	1.42236
$826$	−1.31946e7	−0.672894
$827$	8.83226e6	0.449064	0.224532	−	0.974467i	$-0.427915\pi$
$827$	8.83226e6	0.449064	0.224532	+	0.974467i	$0.427915\pi$
$828$	1.28749e6	0.0652631
$829$	−1.69640e7	−0.857316	−0.428658	−	0.903467i	$-0.641014\pi$
$829$	−1.69640e7	−0.857316	−0.428658	+	0.903467i	$0.641014\pi$
$830$	−7.03422e7	−3.54422
$831$	2.64922e7	1.33081
$832$	−5.11993e7	−2.56422
$833$	2.42036e7	1.20856
$834$	−1.24725e7	−0.620922
$835$	2.56201e7	1.27164
$836$	−4.54913e6	−0.225119
$837$	9.02490e6	0.445275
$838$	−1.64446e6	−0.0808933
$839$	−2.68046e7	−1.31463	−0.657316	−	0.753615i	$-0.728308\pi$
$839$	−2.68046e7	−1.31463	−0.657316	+	0.753615i	$0.728308\pi$
$840$	2.70613e7	1.32328
$841$	707281.	0.0344828
$842$	−4.28443e7	−2.08263
$843$	3.13971e7	1.52167
$844$	−3.92003e6	−0.189423
$845$	−6.30891e7	−3.03957
$846$	1.86116e6	0.0894042
$847$	−3.50095e6	−0.167678
$848$	−1.17235e6	−0.0559847
$849$	3.92514e7	1.86890
$850$	−2.73695e7	−1.29933
$851$	−3.73331e6	−0.176714
$852$	−5.09311e7	−2.40372
$853$	2.65626e7	1.24997	0.624983	−	0.780638i	$-0.285106\pi$
$853$	2.65626e7	1.24997	0.624983	+	0.780638i	$0.285106\pi$
$854$	−1.78764e7	−0.838755
$855$	2.25983e6	0.105721
$856$	−6.65846e6	−0.310591
$857$	−1.81681e7	−0.845003	−0.422501	−	0.906362i	$-0.638848\pi$
$857$	−1.81681e7	−0.845003	−0.422501	+	0.906362i	$0.638848\pi$
$858$	−6.32511e7	−2.93325
$859$	2.68029e7	1.23936	0.619681	−	0.784854i	$-0.287262\pi$
$859$	2.68029e7	1.23936	0.619681	+	0.784854i	$0.287262\pi$
$860$	−4.62769e7	−2.13362
$861$	−3.52841e6	−0.162207
$862$	2.61283e7	1.19769
$863$	−2.87179e7	−1.31258	−0.656291	−	0.754508i	$-0.727876\pi$
$863$	−2.87179e7	−1.31258	−0.656291	+	0.754508i	$0.727876\pi$
$864$	−2.20450e7	−1.00467
$865$	3.80051e6	0.172704
$866$	−3.25518e7	−1.47496
$867$	−1.42521e7	−0.643921
$868$	−2.94645e7	−1.32739
$869$	1.29155e7	0.580178
$870$	1.11372e7	0.498859
$871$	1.23946e7	0.553587
$872$	1.22913e7	0.547404
$873$	−7.86586e6	−0.349310
$874$	827060.	0.0366234
$875$	−1.57360e7	−0.694825
$876$	−1.77655e6	−0.0782201
$877$	139217.	0.00611213	0.00305606	−	0.999995i	$-0.499027\pi$
$877$	139217.	0.00611213	0.00305606	+	0.999995i	$0.499027\pi$
$878$	−2.81768e7	−1.23355
$879$	1.21574e7	0.530723
$880$	2.03373e7	0.885292
$881$	−8.68118e6	−0.376824	−0.188412	−	0.982090i	$-0.560334\pi$
$881$	−8.68118e6	−0.376824	−0.188412	+	0.982090i	$0.560334\pi$
$882$	−2.40411e7	−1.04060
$883$	−2.65874e7	−1.14756	−0.573778	−	0.819011i	$-0.694523\pi$
$883$	−2.65874e7	−1.14756	−0.573778	+	0.819011i	$0.694523\pi$
$884$	3.51243e7	1.51174
$885$	−1.09759e7	−0.471068
$886$	−836317.	−0.0357921
$887$	−4.43687e7	−1.89351	−0.946754	−	0.321956i	$-0.895660\pi$
$887$	−4.43687e7	−1.89351	−0.946754	+	0.321956i	$0.895660\pi$
$888$	1.65161e7	0.702869
$889$	−4.68050e6	−0.198627
$890$	7.34024e7	3.10624
$891$	−2.77857e7	−1.17254
$892$	1.37331e6	0.0577904
$893$	674521.	0.0283052
$894$	2.27152e7	0.950544
$895$	−2.93781e7	−1.22593
$896$	3.43055e7	1.42756
$897$	6.48776e6	0.269224
$898$	−3.90517e7	−1.61603
$899$	−2.75894e6	−0.113853
$900$	1.53376e7	0.631179
$901$	1.48287e6	0.0608542
$902$	2.89632e6	0.118531
$903$	5.26429e7	2.14843
$904$	−1.36131e7	−0.554031
$905$	6.36548e7	2.58351
$906$	7.01515e7	2.83934
$907$	−1.96923e7	−0.794839	−0.397420	−	0.917637i	$-0.630094\pi$
$907$	−1.96923e7	−0.794839	−0.397420	+	0.917637i	$0.630094\pi$
$908$	−3.67085e7	−1.47758
$909$	5.56779e6	0.223498
$910$	1.65758e8	6.63545
$911$	4.33698e6	0.173138	0.0865688	−	0.996246i	$-0.472410\pi$
$911$	4.33698e6	0.173138	0.0865688	+	0.996246i	$0.472410\pi$
$912$	3.34985e6	0.133364
$913$	−3.70577e7	−1.47130
$914$	−4.21329e6	−0.166823
$915$	−1.48704e7	−0.587180
$916$	−2.12611e6	−0.0837236
$917$	2.98777e7	1.17334
$918$	1.88912e7	0.739865
$919$	2.13300e7	0.833110	0.416555	−	0.909110i	$-0.363237\pi$
$919$	2.13300e7	0.833110	0.416555	+	0.909110i	$0.363237\pi$
$920$	2.27847e6	0.0887512
$921$	1.12753e7	0.438006
$922$	−2.18659e7	−0.847112
$923$	−7.09781e7	−2.74233
$924$	6.26607e7	2.41443
$925$	−4.44743e7	−1.70905
$926$	5.36235e7	2.05507
$927$	−1.82145e7	−0.696172
$928$	6.73921e6	0.256885
$929$	4.41448e7	1.67819	0.839093	−	0.543988i	$-0.183086\pi$
$929$	4.41448e7	1.67819	0.839093	+	0.543988i	$0.183086\pi$
$930$	−4.34436e7	−1.64709
$931$	−8.71296e6	−0.329452
$932$	−3.53934e7	−1.33470
$933$	−2.14986e7	−0.808547
$934$	−2.00810e7	−0.753215
$935$	−2.57239e7	−0.962295
$936$	−7.93774e6	−0.296147
$937$	5.10338e7	1.89893	0.949466	−	0.313871i	$-0.101626\pi$
$937$	5.10338e7	1.89893	0.949466	+	0.313871i	$0.101626\pi$
$938$	−2.17641e7	−0.807669
$939$	−4.74066e7	−1.75459
$940$	8.16745e6	0.301486
$941$	4.69231e7	1.72748	0.863739	−	0.503939i	$-0.168116\pi$
$941$	4.69231e7	1.72748	0.863739	+	0.503939i	$0.168116\pi$
$942$	2.15007e7	0.789452
$943$	−297080.	−0.0108791
$944$	−4.49967e6	−0.164343
$945$	5.02972e7	1.83217
$946$	−4.32124e7	−1.56993
$947$	1.22405e7	0.443533	0.221766	−	0.975100i	$-0.428818\pi$
$947$	1.22405e7	0.443533	0.221766	+	0.975100i	$0.428818\pi$
$948$	2.57593e7	0.930922
$949$	−2.47582e6	−0.0892388
$950$	9.85263e6	0.354195
$951$	−1.71222e7	−0.613915
$952$	−1.40324e7	−0.501811
$953$	−4.02315e7	−1.43494	−0.717470	−	0.696590i	$-0.754700\pi$
$953$	−4.02315e7	−1.43494	−0.717470	+	0.696590i	$0.754700\pi$
$954$	−1.47291e6	−0.0523969
$955$	4.71801e7	1.67398
$956$	3.11053e7	1.10075
$957$	5.86730e6	0.207090
$958$	−4.27523e7	−1.50503
$959$	−9.15146e7	−3.21324
$960$	7.47856e7	2.61903
$961$	−1.78672e7	−0.624090
$962$	1.01165e8	3.52447
$963$	7.65893e6	0.266135
$964$	−2.97465e6	−0.103096
$965$	−7.71969e7	−2.66859
$966$	−1.13921e7	−0.392791
$967$	1.72628e7	0.593668	0.296834	−	0.954929i	$-0.404069\pi$
$967$	1.72628e7	0.593668	0.296834	+	0.954929i	$0.404069\pi$
$968$	1.30405e6	0.0447306
$969$	−4.23711e6	−0.144964
$970$	−6.11830e7	−2.08786
$971$	1.32907e7	0.452378	0.226189	−	0.974083i	$-0.427373\pi$
$971$	1.32907e7	0.452378	0.226189	+	0.974083i	$0.427373\pi$
$972$	−2.77246e7	−0.941238
$973$	1.72195e7	0.583093
$974$	1.50332e7	0.507754
$975$	7.72876e7	2.60374
$976$	−6.09626e6	−0.204851
$977$	−4.16592e7	−1.39629	−0.698144	−	0.715957i	$-0.745990\pi$
$977$	−4.16592e7	−1.39629	−0.698144	+	0.715957i	$0.745990\pi$
$978$	−849167.	−0.0283887
$979$	3.86699e7	1.28948
$980$	−1.05501e8	−3.50907
$981$	−1.41382e7	−0.469051
$982$	−1.95959e7	−0.648464
$983$	2.91834e6	0.0963278	0.0481639	−	0.998839i	$-0.484663\pi$
$983$	2.91834e6	0.0963278	0.0481639	+	0.998839i	$0.484663\pi$
$984$	1.31427e6	0.0432711
$985$	−1.26200e7	−0.414448
$986$	−5.77509e6	−0.189176
$987$	−9.29100e6	−0.303577
$988$	−1.26442e7	−0.412098
$989$	4.43236e6	0.144094
$990$	2.55512e7	0.828558
$991$	−5.12994e7	−1.65931	−0.829657	−	0.558274i	$-0.811464\pi$
$991$	−5.12994e7	−1.65931	−0.829657	+	0.558274i	$0.811464\pi$
$992$	−2.62881e7	−0.848163
$993$	−6.92696e7	−2.22930
$994$	1.24633e8	4.00099
$995$	−172286.	−0.00551686
$996$	−7.39097e7	−2.36077
$997$	3.15013e7	1.00367	0.501834	−	0.864964i	$-0.332659\pi$
$997$	3.15013e7	1.00367	0.501834	+	0.864964i	$0.332659\pi$
$998$	−5.17353e7	−1.64422
$999$	3.06974e7	0.973169

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.6.a.b.1.1	✓	7
3.2	odd	2		261.6.a.e.1.7		7
4.3	odd	2		464.6.a.k.1.2		7
5.4	even	2		725.6.a.b.1.7		7
29.28	even	2		841.6.a.b.1.7		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.6.a.b.1.1	✓	7	1.1	even	1	trivial
261.6.a.e.1.7		7	3.2	odd	2
464.6.a.k.1.2		7	4.3	odd	2
725.6.a.b.1.7		7	5.4	even	2
841.6.a.b.1.7		7	29.28	even	2

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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-8.56883 q^{2} +18.3274 q^{3} +41.4249 q^{4} -84.3249 q^{5} -157.045 q^{6} +216.816 q^{7} -80.7606 q^{8} +92.8952 q^{9} +O(q^{10})\)	\(q-8.56883 q^{2} +18.3274 q^{3} +41.4249 q^{4} -84.3249 q^{5} -157.045 q^{6} +216.816 q^{7} -80.7606 q^{8} +92.8952 q^{9} +722.566 q^{10} +380.662 q^{11} +759.213 q^{12} +1058.05 q^{13} -1857.86 q^{14} -1545.46 q^{15} -633.574 q^{16} +801.385 q^{17} -796.004 q^{18} -288.487 q^{19} -3493.15 q^{20} +3973.69 q^{21} -3261.83 q^{22} +334.571 q^{23} -1480.13 q^{24} +3985.69 q^{25} -9066.22 q^{26} -2751.04 q^{27} +8981.59 q^{28} +841.000 q^{29} +13242.8 q^{30} -3280.54 q^{31} +8013.32 q^{32} +6976.57 q^{33} -6866.93 q^{34} -18283.0 q^{35} +3848.18 q^{36} -11158.5 q^{37} +2472.00 q^{38} +19391.3 q^{39} +6810.13 q^{40} -887.943 q^{41} -34049.9 q^{42} +13247.9 q^{43} +15768.9 q^{44} -7833.38 q^{45} -2866.89 q^{46} -2338.13 q^{47} -11611.8 q^{48} +30202.3 q^{49} -34152.7 q^{50} +14687.3 q^{51} +43829.4 q^{52} +1850.38 q^{53} +23573.2 q^{54} -32099.3 q^{55} -17510.2 q^{56} -5287.23 q^{57} -7206.39 q^{58} +7102.05 q^{59} -64020.6 q^{60} +9622.02 q^{61} +28110.4 q^{62} +20141.2 q^{63} -48390.5 q^{64} -89219.6 q^{65} -59781.1 q^{66} +11714.6 q^{67} +33197.3 q^{68} +6131.84 q^{69} +156664. q^{70} -67084.1 q^{71} -7502.27 q^{72} -2340.00 q^{73} +95615.2 q^{74} +73047.5 q^{75} -11950.6 q^{76} +82533.8 q^{77} -166161. q^{78} +33928.9 q^{79} +53426.0 q^{80} -72993.0 q^{81} +7608.63 q^{82} -97350.5 q^{83} +164610. q^{84} -67576.7 q^{85} -113519. q^{86} +15413.4 q^{87} -30742.5 q^{88} +101586. q^{89} +67122.9 q^{90} +229401. q^{91} +13859.6 q^{92} -60124.0 q^{93} +20035.1 q^{94} +24326.7 q^{95} +146864. q^{96} -84674.6 q^{97} -258798. q^{98} +35361.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9}+O(q^{10}) \) 7 * q + 4 * q^2 + 26 * q^3 + 154 * q^4 + 32 * q^5 + 22 * q^6 + 184 * q^7 + 942 * q^8 + 1005 * q^9	\( 7 q + 4 q^{2} + 26 q^{3} + 154 q^{4} + 32 q^{5} + 22 q^{6} + 184 q^{7} + 942 q^{8} + 1005 q^{9} + 922 q^{10} + 1106 q^{11} + 214 q^{12} + 408 q^{13} - 2008 q^{14} - 614 q^{15} + 242 q^{16} - 874 q^{17} - 5598 q^{18} + 4288 q^{19} - 6350 q^{20} - 4200 q^{21} - 6114 q^{22} - 4532 q^{23} - 4318 q^{24} + 5527 q^{25} - 19806 q^{26} + 5942 q^{27} - 496 q^{28} + 5887 q^{29} - 16734 q^{30} + 7794 q^{31} + 7898 q^{32} + 34410 q^{33} + 20840 q^{34} + 7088 q^{35} - 572 q^{36} + 5086 q^{37} + 23732 q^{38} + 33394 q^{39} + 22906 q^{40} + 19826 q^{41} - 55440 q^{42} + 19498 q^{43} - 6074 q^{44} + 7854 q^{45} - 12404 q^{46} + 14278 q^{47} - 16406 q^{48} + 38431 q^{49} - 41066 q^{50} + 23892 q^{51} - 34302 q^{52} - 58644 q^{53} - 31194 q^{54} - 25574 q^{55} - 79560 q^{56} - 88540 q^{57} + 3364 q^{58} + 12888 q^{59} - 180822 q^{60} + 102866 q^{61} - 42654 q^{62} - 88632 q^{63} - 10170 q^{64} - 149206 q^{65} + 7710 q^{66} + 102996 q^{67} + 85100 q^{68} - 107244 q^{69} + 349480 q^{70} - 51596 q^{71} + 135568 q^{72} - 17566 q^{73} + 12132 q^{74} + 39356 q^{75} + 360740 q^{76} - 94104 q^{77} + 46386 q^{78} + 212058 q^{79} + 142510 q^{80} - 128285 q^{81} + 201924 q^{82} - 122928 q^{83} - 12328 q^{84} - 109336 q^{85} - 63290 q^{86} + 21866 q^{87} + 136666 q^{88} - 66510 q^{89} + 56084 q^{90} + 194368 q^{91} - 110108 q^{92} - 474274 q^{93} + 438926 q^{94} - 131676 q^{95} - 117018 q^{96} - 118182 q^{97} - 29132 q^{98} + 300668 q^{99}+O(q^{100}) \) 7 * q + 4 * q^2 + 26 * q^3 + 154 * q^4 + 32 * q^5 + 22 * q^6 + 184 * q^7 + 942 * q^8 + 1005 * q^9 + 922 * q^10 + 1106 * q^11 + 214 * q^12 + 408 * q^13 - 2008 * q^14 - 614 * q^15 + 242 * q^16 - 874 * q^17 - 5598 * q^18 + 4288 * q^19 - 6350 * q^20 - 4200 * q^21 - 6114 * q^22 - 4532 * q^23 - 4318 * q^24 + 5527 * q^25 - 19806 * q^26 + 5942 * q^27 - 496 * q^28 + 5887 * q^29 - 16734 * q^30 + 7794 * q^31 + 7898 * q^32 + 34410 * q^33 + 20840 * q^34 + 7088 * q^35 - 572 * q^36 + 5086 * q^37 + 23732 * q^38 + 33394 * q^39 + 22906 * q^40 + 19826 * q^41 - 55440 * q^42 + 19498 * q^43 - 6074 * q^44 + 7854 * q^45 - 12404 * q^46 + 14278 * q^47 - 16406 * q^48 + 38431 * q^49 - 41066 * q^50 + 23892 * q^51 - 34302 * q^52 - 58644 * q^53 - 31194 * q^54 - 25574 * q^55 - 79560 * q^56 - 88540 * q^57 + 3364 * q^58 + 12888 * q^59 - 180822 * q^60 + 102866 * q^61 - 42654 * q^62 - 88632 * q^63 - 10170 * q^64 - 149206 * q^65 + 7710 * q^66 + 102996 * q^67 + 85100 * q^68 - 107244 * q^69 + 349480 * q^70 - 51596 * q^71 + 135568 * q^72 - 17566 * q^73 + 12132 * q^74 + 39356 * q^75 + 360740 * q^76 - 94104 * q^77 + 46386 * q^78 + 212058 * q^79 + 142510 * q^80 - 128285 * q^81 + 201924 * q^82 - 122928 * q^83 - 12328 * q^84 - 109336 * q^85 - 63290 * q^86 + 21866 * q^87 + 136666 * q^88 - 66510 * q^89 + 56084 * q^90 + 194368 * q^91 - 110108 * q^92 - 474274 * q^93 + 438926 * q^94 - 131676 * q^95 - 117018 * q^96 - 118182 * q^97 - 29132 * q^98 + 300668 * q^99

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