LMFDB - Embedded newform 869.6.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [869,6,Mod(1,869)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(869, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("869.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 869 = 11 \cdot 79 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	869.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:	$139.373539417$
Analytic rank:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	869.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-11.1509 q^{2} +14.5590 q^{3} +92.3430 q^{4} -52.3398 q^{5} -162.346 q^{6} -19.7989 q^{7} -672.881 q^{8} -31.0360 q^{9} +O(q^{10})$	\(q-11.1509 q^{2} +14.5590 q^{3} +92.3430 q^{4} -52.3398 q^{5} -162.346 q^{6} -19.7989 q^{7} -672.881 q^{8} -31.0360 q^{9} +583.637 q^{10} -121.000 q^{11} +1344.42 q^{12} -1193.52 q^{13} +220.777 q^{14} -762.014 q^{15} +4548.26 q^{16} -1005.47 q^{17} +346.080 q^{18} -375.802 q^{19} -4833.21 q^{20} -288.253 q^{21} +1349.26 q^{22} +3836.95 q^{23} -9796.46 q^{24} -385.549 q^{25} +13308.8 q^{26} -3989.69 q^{27} -1828.30 q^{28} -7486.21 q^{29} +8497.15 q^{30} +7055.98 q^{31} -29185.1 q^{32} -1761.64 q^{33} +11211.9 q^{34} +1036.27 q^{35} -2865.96 q^{36} -4944.36 q^{37} +4190.54 q^{38} -17376.4 q^{39} +35218.4 q^{40} -17034.4 q^{41} +3214.28 q^{42} -8598.24 q^{43} -11173.5 q^{44} +1624.42 q^{45} -42785.5 q^{46} -16833.1 q^{47} +66218.0 q^{48} -16415.0 q^{49} +4299.23 q^{50} -14638.6 q^{51} -110213. q^{52} -33151.7 q^{53} +44488.7 q^{54} +6333.11 q^{55} +13322.3 q^{56} -5471.30 q^{57} +83478.1 q^{58} +5883.43 q^{59} -70366.7 q^{60} +24201.2 q^{61} -78680.7 q^{62} +614.481 q^{63} +179897. q^{64} +62468.4 q^{65} +19643.9 q^{66} +33003.0 q^{67} -92848.0 q^{68} +55862.0 q^{69} -11555.4 q^{70} -23642.2 q^{71} +20883.6 q^{72} +4633.80 q^{73} +55134.1 q^{74} -5613.21 q^{75} -34702.7 q^{76} +2395.67 q^{77} +193763. q^{78} +6241.00 q^{79} -238055. q^{80} -50544.0 q^{81} +189950. q^{82} +59191.2 q^{83} -26618.1 q^{84} +52626.0 q^{85} +95878.3 q^{86} -108992. q^{87} +81418.5 q^{88} +15511.3 q^{89} -18113.8 q^{90} +23630.4 q^{91} +354315. q^{92} +102728. q^{93} +187705. q^{94} +19669.4 q^{95} -424906. q^{96} -125763. q^{97} +183042. q^{98} +3755.36 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q + 4 q^{2} + 78 q^{3} + 1530 q^{4} + 169 q^{5} - 78 q^{6} + 490 q^{7} - 192 q^{8} + 7632 q^{9}+O(q^{10}) $ 86 * q + 4 * q^2 + 78 * q^3 + 1530 * q^4 + 169 * q^5 - 78 * q^6 + 490 * q^7 - 192 * q^8 + 7632 * q^9	\( 86 q + 4 q^{2} + 78 q^{3} + 1530 q^{4} + 169 q^{5} - 78 q^{6} + 490 q^{7} - 192 q^{8} + 7632 q^{9} + 1019 q^{10} - 10406 q^{11} + 3369 q^{12} + 2992 q^{13} + 143 q^{14} + 3202 q^{15} + 29438 q^{16} - 4043 q^{17} + 2679 q^{18} + 16115 q^{19} + 8151 q^{20} + 909 q^{21} - 484 q^{22} - 403 q^{23} - 18745 q^{24} + 65143 q^{25} + 11635 q^{26} + 8841 q^{27} + 19998 q^{28} - 9797 q^{29} - 7753 q^{30} + 34557 q^{31} - 6195 q^{32} - 9438 q^{33} + 55362 q^{34} + 26255 q^{35} + 174892 q^{36} + 5322 q^{37} + 34138 q^{38} + 20246 q^{39} + 44862 q^{40} - 29897 q^{41} + 32393 q^{42} + 36010 q^{43} - 185130 q^{44} + 141885 q^{45} + 144330 q^{46} + 32330 q^{47} + 153596 q^{48} + 338884 q^{49} + 9642 q^{50} + 58559 q^{51} + 301121 q^{52} + 38487 q^{53} + 25966 q^{54} - 20449 q^{55} + 72298 q^{56} + 67302 q^{57} + 277501 q^{58} + 180602 q^{59} + 361842 q^{60} + 170221 q^{61} - 52231 q^{62} + 228776 q^{63} + 633510 q^{64} - 47719 q^{65} + 9438 q^{66} + 307210 q^{67} + 26244 q^{68} + 135307 q^{69} + 92715 q^{70} + 213698 q^{71} + 372144 q^{72} + 94636 q^{73} + 298200 q^{74} + 253758 q^{75} + 531922 q^{76} - 59290 q^{77} + 427545 q^{78} + 536726 q^{79} + 699157 q^{80} + 753290 q^{81} + 619268 q^{82} + 282139 q^{83} + 39834 q^{84} - 52876 q^{85} - 203149 q^{86} - 130307 q^{87} + 23232 q^{88} + 10087 q^{89} + 159005 q^{90} + 887428 q^{91} - 156182 q^{92} + 107249 q^{93} + 473622 q^{94} - 132719 q^{95} - 308216 q^{96} + 75639 q^{97} - 66857 q^{98} - 923472 q^{99}+O(q^{100}) \) 86 * q + 4 * q^2 + 78 * q^3 + 1530 * q^4 + 169 * q^5 - 78 * q^6 + 490 * q^7 - 192 * q^8 + 7632 * q^9 + 1019 * q^10 - 10406 * q^11 + 3369 * q^12 + 2992 * q^13 + 143 * q^14 + 3202 * q^15 + 29438 * q^16 - 4043 * q^17 + 2679 * q^18 + 16115 * q^19 + 8151 * q^20 + 909 * q^21 - 484 * q^22 - 403 * q^23 - 18745 * q^24 + 65143 * q^25 + 11635 * q^26 + 8841 * q^27 + 19998 * q^28 - 9797 * q^29 - 7753 * q^30 + 34557 * q^31 - 6195 * q^32 - 9438 * q^33 + 55362 * q^34 + 26255 * q^35 + 174892 * q^36 + 5322 * q^37 + 34138 * q^38 + 20246 * q^39 + 44862 * q^40 - 29897 * q^41 + 32393 * q^42 + 36010 * q^43 - 185130 * q^44 + 141885 * q^45 + 144330 * q^46 + 32330 * q^47 + 153596 * q^48 + 338884 * q^49 + 9642 * q^50 + 58559 * q^51 + 301121 * q^52 + 38487 * q^53 + 25966 * q^54 - 20449 * q^55 + 72298 * q^56 + 67302 * q^57 + 277501 * q^58 + 180602 * q^59 + 361842 * q^60 + 170221 * q^61 - 52231 * q^62 + 228776 * q^63 + 633510 * q^64 - 47719 * q^65 + 9438 * q^66 + 307210 * q^67 + 26244 * q^68 + 135307 * q^69 + 92715 * q^70 + 213698 * q^71 + 372144 * q^72 + 94636 * q^73 + 298200 * q^74 + 253758 * q^75 + 531922 * q^76 - 59290 * q^77 + 427545 * q^78 + 536726 * q^79 + 699157 * q^80 + 753290 * q^81 + 619268 * q^82 + 282139 * q^83 + 39834 * q^84 - 52876 * q^85 - 203149 * q^86 - 130307 * q^87 + 23232 * q^88 + 10087 * q^89 + 159005 * q^90 + 887428 * q^91 - 156182 * q^92 + 107249 * q^93 + 473622 * q^94 - 132719 * q^95 - 308216 * q^96 + 75639 * q^97 - 66857 * q^98 - 923472 * 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 $

$2$	−11.1509	−1.97122	−0.985612	−	0.169026i	$-0.945938\pi$
$2$	−11.1509	−1.97122	−0.985612	+	0.169026i	$0.945938\pi$
$3$	14.5590	0.933959	0.466980	−	0.884268i	$-0.345342\pi$
$3$	14.5590	0.933959	0.466980	+	0.884268i	$0.345342\pi$
$4$	92.3430	2.88572
$5$	−52.3398	−0.936282	−0.468141	−	0.883654i	$-0.655076\pi$
$5$	−52.3398	−0.936282	−0.468141	+	0.883654i	$0.655076\pi$
$6$	−162.346	−1.84104
$7$	−19.7989	−0.152720	−0.0763602	−	0.997080i	$-0.524330\pi$
$7$	−19.7989	−0.152720	−0.0763602	+	0.997080i	$0.524330\pi$
$8$	−672.881	−3.71718
$9$	−31.0360	−0.127720
$10$	583.637	1.84562
$11$	−121.000	−0.301511
$11$	−121.000	−0.301511
$12$	1344.42	2.69514
$13$	−1193.52	−1.95871	−0.979356	−	0.202145i	$-0.935209\pi$
$13$	−1193.52	−1.95871	−0.979356	+	0.202145i	$0.935209\pi$
$14$	220.777	0.301046
$15$	−762.014	−0.874449
$16$	4548.26	4.44166
$17$	−1005.47	−0.843813	−0.421906	−	0.906639i	$-0.638639\pi$
$17$	−1005.47	−0.843813	−0.421906	+	0.906639i	$0.638639\pi$
$18$	346.080	0.251765
$19$	−375.802	−0.238823	−0.119411	−	0.992845i	$-0.538101\pi$
$19$	−375.802	−0.238823	−0.119411	+	0.992845i	$0.538101\pi$
$20$	−4833.21	−2.70185
$21$	−288.253	−0.142635
$22$	1349.26	0.594346
$23$	3836.95	1.51240	0.756199	−	0.654342i	$-0.227054\pi$
$23$	3836.95	1.51240	0.756199	+	0.654342i	$0.227054\pi$
$24$	−9796.46	−3.47169
$25$	−385.549	−0.123376
$26$	13308.8	3.86106
$27$	−3989.69	−1.05324
$28$	−1828.30	−0.440708
$29$	−7486.21	−1.65298	−0.826489	−	0.562953i	$-0.809665\pi$
$29$	−7486.21	−1.65298	−0.826489	+	0.562953i	$0.809665\pi$
$30$	8497.15	1.72373
$31$	7055.98	1.31872	0.659361	−	0.751826i	$-0.270827\pi$
$31$	7055.98	1.31872	0.659361	+	0.751826i	$0.270827\pi$
$32$	−29185.1	−5.03833
$33$	−1761.64	−0.281599
$34$	11211.9	1.66334
$35$	1036.27	0.142989
$36$	−2865.96	−0.368565
$37$	−4944.36	−0.593753	−0.296876	−	0.954916i	$-0.595945\pi$
$37$	−4944.36	−0.593753	−0.296876	+	0.954916i	$0.595945\pi$
$38$	4190.54	0.470773
$39$	−17376.4	−1.82936
$40$	35218.4	3.48032
$41$	−17034.4	−1.58259	−0.791294	−	0.611436i	$-0.790592\pi$
$41$	−17034.4	−1.58259	−0.791294	+	0.611436i	$0.790592\pi$
$42$	3214.28	0.281165
$43$	−8598.24	−0.709151	−0.354575	−	0.935027i	$-0.615375\pi$
$43$	−8598.24	−0.709151	−0.354575	+	0.935027i	$0.615375\pi$
$44$	−11173.5	−0.870077
$45$	1624.42	0.119582
$46$	−42785.5	−2.98127
$47$	−16833.1	−1.11153	−0.555763	−	0.831341i	$-0.687574\pi$
$47$	−16833.1	−1.11153	−0.555763	+	0.831341i	$0.687574\pi$
$48$	66218.0	4.14833
$49$	−16415.0	−0.976676
$50$	4299.23	0.243201
$51$	−14638.6	−0.788087
$52$	−110213.	−5.65229
$53$	−33151.7	−1.62112	−0.810562	−	0.585654i	$-0.800838\pi$
$53$	−33151.7	−1.62112	−0.810562	+	0.585654i	$0.800838\pi$
$54$	44488.7	2.07618
$55$	6333.11	0.282300
$56$	13322.3	0.567688
$57$	−5471.30	−0.223051
$58$	83478.1	3.25839
$59$	5883.43	0.220039	0.110020	−	0.993929i	$-0.464909\pi$
$59$	5883.43	0.220039	0.110020	+	0.993929i	$0.464909\pi$
$60$	−70366.7	−2.52342
$61$	24201.2	0.832746	0.416373	−	0.909194i	$-0.363301\pi$
$61$	24201.2	0.832746	0.416373	+	0.909194i	$0.363301\pi$
$62$	−78680.7	−2.59950
$63$	614.481	0.0195055
$64$	179897.	5.49001
$65$	62468.4	1.83391
$66$	19643.9	0.555095
$67$	33003.0	0.898186	0.449093	−	0.893485i	$-0.351747\pi$
$67$	33003.0	0.898186	0.449093	+	0.893485i	$0.351747\pi$
$68$	−92848.0	−2.43501
$69$	55862.0	1.41252
$70$	−11555.4	−0.281864
$71$	−23642.2	−0.556598	−0.278299	−	0.960495i	$-0.589771\pi$
$71$	−23642.2	−0.556598	−0.278299	+	0.960495i	$0.589771\pi$
$72$	20883.6	0.474759
$73$	4633.80	0.101772	0.0508862	−	0.998704i	$-0.483795\pi$
$73$	4633.80	0.101772	0.0508862	+	0.998704i	$0.483795\pi$
$74$	55134.1	1.17042
$75$	−5613.21	−0.115228
$76$	−34702.7	−0.689175
$77$	2395.67	0.0460469
$78$	193763.	3.60607
$79$	6241.00	0.112509
$79$	6241.00	0.112509
$80$	−238055.	−4.15865
$81$	−50544.0	−0.855967
$82$	189950.	3.11963
$83$	59191.2	0.943108	0.471554	−	0.881837i	$-0.343693\pi$
$83$	59191.2	0.943108	0.471554	+	0.881837i	$0.343693\pi$
$84$	−26618.1	−0.411604
$85$	52626.0	0.790047
$86$	95878.3	1.39789
$87$	−108992.	−1.54381
$88$	81418.5	1.12077
$89$	15511.3	0.207574	0.103787	−	0.994600i	$-0.466904\pi$
$89$	15511.3	0.207574	0.103787	+	0.994600i	$0.466904\pi$
$90$	−18113.8	−0.235723
$91$	23630.4	0.299135
$92$	354315.	4.36436
$93$	102728.	1.23163
$94$	187705.	2.19107
$95$	19669.4	0.223605
$96$	−424906.	−4.70559
$97$	−125763.	−1.35714	−0.678569	−	0.734537i	$-0.737399\pi$
$97$	−125763.	−1.35714	−0.678569	+	0.734537i	$0.737399\pi$
$98$	183042.	1.92525
$99$	3755.36	0.0385091
$100$	−35602.8	−0.356028
$101$	−161858.	−1.57881	−0.789405	−	0.613873i	$-0.789611\pi$
$101$	−161858.	−1.57881	−0.789405	+	0.613873i	$0.789611\pi$
$102$	163234.	1.55349
$103$	−114622.	−1.06457	−0.532286	−	0.846564i	$-0.678667\pi$
$103$	−114622.	−1.06457	−0.532286	+	0.846564i	$0.678667\pi$
$104$	803095.	7.28087
$105$	15087.1	0.133546
$106$	369672.	3.19560
$107$	−47790.1	−0.403532	−0.201766	−	0.979434i	$-0.564668\pi$
$107$	−47790.1	−0.403532	−0.201766	+	0.979434i	$0.564668\pi$
$108$	−368420.	−3.03937
$109$	33154.1	0.267283	0.133642	−	0.991030i	$-0.457333\pi$
$109$	33154.1	0.267283	0.133642	+	0.991030i	$0.457333\pi$
$110$	−70620.0	−0.556476
$111$	−71984.8	−0.554541
$112$	−90050.8	−0.678332
$113$	−50610.3	−0.372857	−0.186429	−	0.982469i	$-0.559691\pi$
$113$	−50610.3	−0.372857	−0.186429	+	0.982469i	$0.559691\pi$
$114$	61010.0	0.439683
$115$	−200825.	−1.41603
$116$	−691299.	−4.77003
$117$	37042.1	0.250167
$118$	−65605.6	−0.433746
$119$	19907.2	0.128867
$120$	512744.	3.25048
$121$	14641.0	0.0909091
$122$	−269866.	−1.64153
$123$	−248004.	−1.47807
$124$	651571.	3.80546
$125$	183741.	1.05180
$126$	−6852.03	−0.0384497
$127$	−65041.0	−0.357831	−0.178916	−	0.983864i	$-0.557259\pi$
$127$	−65041.0	−0.357831	−0.178916	+	0.983864i	$0.557259\pi$
$128$	−1.07209e6	−5.78370
$129$	−125182.	−0.662318
$130$	−696581.	−3.61504
$131$	164171.	0.835832	0.417916	−	0.908486i	$-0.362761\pi$
$131$	164171.	0.835832	0.417916	+	0.908486i	$0.362761\pi$
$132$	−162675.	−0.812617
$133$	7440.49	0.0364731
$134$	−368014.	−1.77053
$135$	208819.	0.986134
$136$	676560.	3.13660
$137$	204597.	0.931317	0.465659	−	0.884964i	$-0.345817\pi$
$137$	204597.	0.931317	0.465659	+	0.884964i	$0.345817\pi$
$138$	−622913.	−2.78439
$139$	69880.8	0.306776	0.153388	−	0.988166i	$-0.450982\pi$
$139$	69880.8	0.306776	0.153388	+	0.988166i	$0.450982\pi$
$140$	95692.5	0.412627
$141$	−245073.	−1.03812
$142$	263632.	1.09718
$143$	144416.	0.590574
$144$	−141160.	−0.567290
$145$	391826.	1.54765
$146$	−51671.1	−0.200616
$147$	−238986.	−0.912176
$148$	−456577.	−1.71340
$149$	−334175.	−1.23313	−0.616564	−	0.787305i	$-0.711476\pi$
$149$	−334175.	−1.23313	−0.616564	+	0.787305i	$0.711476\pi$
$150$	62592.4	0.227140
$151$	253564.	0.904994	0.452497	−	0.891766i	$-0.350533\pi$
$151$	253564.	0.904994	0.452497	+	0.891766i	$0.350533\pi$
$152$	252870.	0.887746
$153$	31205.8	0.107772
$154$	−26714.0	−0.0907688
$155$	−369308.	−1.23470
$156$	−1.60459e6	−5.27901
$157$	180474.	0.584341	0.292170	−	0.956366i	$-0.405623\pi$
$157$	180474.	0.584341	0.292170	+	0.956366i	$0.405623\pi$
$158$	−69592.9	−0.221780
$159$	−482655.	−1.51406
$160$	1.52754e6	4.71730
$161$	−75967.5	−0.230974
$162$	563612.	1.68730
$163$	−467655.	−1.37866	−0.689329	−	0.724449i	$-0.742094\pi$
$163$	−467655.	−1.37866	−0.689329	+	0.724449i	$0.742094\pi$
$164$	−1.57301e6	−4.56691
$165$	92203.7	0.263656
$166$	−660036.	−1.85908
$167$	−69240.5	−0.192118	−0.0960592	−	0.995376i	$-0.530624\pi$
$167$	−69240.5	−0.192118	−0.0960592	+	0.995376i	$0.530624\pi$
$168$	193960.	0.530198
$169$	1.05319e6	2.83655
$170$	−586828.	−1.55736
$171$	11663.4	0.0305025
$172$	−793988.	−2.04641
$173$	11251.6	0.0285824	0.0142912	−	0.999898i	$-0.495451\pi$
$173$	11251.6	0.0285824	0.0142912	+	0.999898i	$0.495451\pi$
$174$	1.21536e6	3.04320
$175$	7633.47	0.0188420
$176$	−550340.	−1.33921
$177$	85656.7	0.205508
$178$	−172966.	−0.409175
$179$	−510678.	−1.19128	−0.595641	−	0.803251i	$-0.703102\pi$
$179$	−510678.	−1.19128	−0.595641	+	0.803251i	$0.703102\pi$
$180$	150004.	0.345081
$181$	208959.	0.474094	0.237047	−	0.971498i	$-0.423821\pi$
$181$	208959.	0.474094	0.237047	+	0.971498i	$0.423821\pi$
$182$	−263501.	−0.589662
$183$	352345.	0.777751
$184$	−2.58181e6	−5.62185
$185$	258786.	0.555920
$186$	−1.14551e6	−2.42782
$187$	121662.	0.254419
$188$	−1.55442e6	−3.20755
$189$	78991.6	0.160852
$190$	−219332.	−0.440776
$191$	−801035.	−1.58880	−0.794398	−	0.607398i	$-0.792213\pi$
$191$	−801035.	−1.58880	−0.794398	+	0.607398i	$0.792213\pi$
$192$	2.61911e6	5.12744
$193$	−452484.	−0.874400	−0.437200	−	0.899364i	$-0.644030\pi$
$193$	−452484.	−0.874400	−0.437200	+	0.899364i	$0.644030\pi$
$194$	1.40237e6	2.67522
$195$	909477.	1.71279
$196$	−1.51581e6	−2.81842
$197$	−566671.	−1.04032	−0.520158	−	0.854070i	$-0.674127\pi$
$197$	−566671.	−1.04032	−0.520158	+	0.854070i	$0.674127\pi$
$198$	−41875.7	−0.0759101
$199$	−72791.4	−0.130301	−0.0651505	−	0.997875i	$-0.520753\pi$
$199$	−72791.4	−0.130301	−0.0651505	+	0.997875i	$0.520753\pi$
$200$	259429.	0.458609
$201$	480490.	0.838869
$202$	1.80486e6	3.11219
$203$	148219.	0.252443
$204$	−1.35177e6	−2.27420
$205$	891578.	1.48175
$206$	1.27814e6	2.09851
$207$	−119084.	−0.193164
$208$	−5.42843e6	−8.69993
$209$	45472.1	0.0720077
$210$	−168235.	−0.263249
$211$	236293.	0.365380	0.182690	−	0.983171i	$-0.441520\pi$
$211$	236293.	0.365380	0.182690	+	0.983171i	$0.441520\pi$
$212$	−3.06133e6	−4.67811
$213$	−344206.	−0.519840
$214$	532904.	0.795453
$215$	450030.	0.663965
$216$	2.68458e6	3.91510
$217$	−139701.	−0.201396
$218$	−369699.	−0.526875
$219$	67463.4	0.0950513
$220$	584819.	0.814638
$221$	1.20004e6	1.65279
$222$	802697.	1.09312
$223$	366354.	0.493331	0.246665	−	0.969101i	$-0.420665\pi$
$223$	366354.	0.493331	0.246665	+	0.969101i	$0.420665\pi$
$224$	577835.	0.769456
$225$	11965.9	0.0157576
$226$	564351.	0.734985
$227$	−141278.	−0.181975	−0.0909874	−	0.995852i	$-0.529002\pi$
$227$	−141278.	−0.181975	−0.0909874	+	0.995852i	$0.529002\pi$
$228$	−505237.	−0.643662
$229$	528816.	0.666370	0.333185	−	0.942861i	$-0.391877\pi$
$229$	528816.	0.666370	0.333185	+	0.942861i	$0.391877\pi$
$230$	2.23938e6	2.79131
$231$	34878.6	0.0430060
$232$	5.03732e6	6.14441
$233$	373338.	0.450518	0.225259	−	0.974299i	$-0.427677\pi$
$233$	373338.	0.450518	0.225259	+	0.974299i	$0.427677\pi$
$234$	−413053.	−0.493136
$235$	881041.	1.04070
$236$	543293.	0.634972
$237$	90862.6	0.105079
$238$	−221984.	−0.254026
$239$	1.33830e6	1.51551	0.757756	−	0.652538i	$-0.226296\pi$
$239$	1.33830e6	1.51551	0.757756	+	0.652538i	$0.226296\pi$
$240$	−3.46584e6	−3.88401
$241$	−775783.	−0.860394	−0.430197	−	0.902735i	$-0.641556\pi$
$241$	−775783.	−0.860394	−0.430197	+	0.902735i	$0.641556\pi$
$242$	−163261.	−0.179202
$243$	233624.	0.253806
$244$	2.23482e6	2.40307
$245$	859157.	0.914445
$246$	2.76547e6	2.91361
$247$	448527.	0.467785
$248$	−4.74783e6	−4.90192
$249$	861763.	0.880825
$250$	−2.04888e6	−2.07333
$251$	−1.08872e6	−1.09077	−0.545385	−	0.838185i	$-0.683617\pi$
$251$	−1.08872e6	−1.09077	−0.545385	+	0.838185i	$0.683617\pi$
$252$	56743.1	0.0562874
$253$	−464270.	−0.456005
$254$	725267.	0.705365
$255$	766181.	0.737871
$256$	6.19809e6	5.91096
$257$	−75988.6	−0.0717655	−0.0358827	−	0.999356i	$-0.511424\pi$
$257$	−75988.6	−0.0717655	−0.0358827	+	0.999356i	$0.511424\pi$
$258$	1.39589e6	1.30558
$259$	97893.1	0.0906781
$260$	5.76852e6	5.29214
$261$	232342.	0.211119
$262$	−1.83066e6	−1.64761
$263$	−623615.	−0.555939	−0.277969	−	0.960590i	$-0.589661\pi$
$263$	−623615.	−0.555939	−0.277969	+	0.960590i	$0.589661\pi$
$264$	1.18537e6	1.04675
$265$	1.73515e6	1.51783
$266$	−82968.3	−0.0718966
$267$	225829.	0.193866
$268$	3.04760e6	2.59191
$269$	−398272.	−0.335582	−0.167791	−	0.985823i	$-0.553663\pi$
$269$	−398272.	−0.335582	−0.167791	+	0.985823i	$0.553663\pi$
$270$	−2.32853e6	−1.94389
$271$	2.20315e6	1.82230	0.911152	−	0.412071i	$-0.135194\pi$
$271$	2.20315e6	1.82230	0.911152	+	0.412071i	$0.135194\pi$
$272$	−4.57313e6	−3.74793
$273$	344034.	0.279380
$274$	−2.28144e6	−1.83583
$275$	46651.5	0.0371992
$276$	5.15847e6	4.07613
$277$	−345208.	−0.270322	−0.135161	−	0.990824i	$-0.543155\pi$
$277$	−345208.	−0.270322	−0.135161	+	0.990824i	$0.543155\pi$
$278$	−779235.	−0.604723
$279$	−218990.	−0.168428
$280$	−697287.	−0.531517
$281$	2.02876e6	1.53273	0.766365	−	0.642405i	$-0.222063\pi$
$281$	2.02876e6	1.53273	0.766365	+	0.642405i	$0.222063\pi$
$282$	2.73279e6	2.04637
$283$	1.78574e6	1.32542	0.662709	−	0.748877i	$-0.269407\pi$
$283$	1.78574e6	1.32542	0.662709	+	0.748877i	$0.269407\pi$
$284$	−2.18319e6	−1.60619
$285$	286367.	0.208838
$286$	−1.61037e6	−1.16415
$287$	337264.	0.241694
$288$	905791.	0.643497
$289$	−408890.	−0.287980
$290$	−4.36922e6	−3.05077
$291$	−1.83098e6	−1.26751
$292$	427899.	0.293687
$293$	−1.78129e6	−1.21218	−0.606089	−	0.795397i	$-0.707262\pi$
$293$	−1.78129e6	−1.21218	−0.606089	+	0.795397i	$0.707262\pi$
$294$	2.66491e6	1.79810
$295$	−307937.	−0.206019
$296$	3.32696e6	2.20708
$297$	482752.	0.317565
$298$	3.72636e6	2.43077
$299$	−4.57946e6	−2.96235
$300$	−518341.	−0.332516
$301$	170236.	0.108302
$302$	−2.82747e6	−1.78394
$303$	−2.35648e6	−1.47454
$304$	−1.70925e6	−1.06077
$305$	−1.26669e6	−0.779686
$306$	−347973.	−0.212443
$307$	55848.6	0.0338194	0.0169097	−	0.999857i	$-0.494617\pi$
$307$	55848.6	0.0338194	0.0169097	+	0.999857i	$0.494617\pi$
$308$	221224.	0.132879
$309$	−1.66878e6	−0.994268
$310$	4.11813e6	2.43386
$311$	−2.24247e6	−1.31470	−0.657348	−	0.753587i	$-0.728322\pi$
$311$	−2.24247e6	−1.31470	−0.657348	+	0.753587i	$0.728322\pi$
$312$	1.16922e7	6.80004
$313$	2.20188e6	1.27038	0.635189	−	0.772357i	$-0.280922\pi$
$313$	2.20188e6	1.27038	0.635189	+	0.772357i	$0.280922\pi$
$314$	−2.01245e6	−1.15187
$315$	−32161.8	−0.0182627
$316$	576313.	0.324669
$317$	1.76514e6	0.986579	0.493290	−	0.869865i	$-0.335794\pi$
$317$	1.76514e6	0.986579	0.493290	+	0.869865i	$0.335794\pi$
$318$	5.38205e6	2.98456
$319$	905831.	0.498391
$320$	−9.41575e6	−5.14020
$321$	−695775.	−0.376883
$322$	847107.	0.455301
$323$	377857.	0.201522
$324$	−4.66739e6	−2.47008
$325$	460160.	0.241658
$326$	5.21478e6	2.71764
$327$	482690.	0.249631
$328$	1.14621e7	5.88276
$329$	333278.	0.169753
$330$	−1.02816e6	−0.519725
$331$	716965.	0.359690	0.179845	−	0.983695i	$-0.442440\pi$
$331$	716965.	0.359690	0.179845	+	0.983695i	$0.442440\pi$
$332$	5.46589e6	2.72155
$333$	153453.	0.0758343
$334$	772096.	0.378708
$335$	−1.72737e6	−0.840956
$336$	−1.31105e6	−0.633535
$337$	−1.79715e6	−0.862006	−0.431003	−	0.902351i	$-0.641840\pi$
$337$	−1.79715e6	−0.862006	−0.431003	+	0.902351i	$0.641840\pi$
$338$	−1.17441e7	−5.59147
$339$	−736834.	−0.348233
$340$	4.85964e6	2.27985
$341$	−853774.	−0.397610
$342$	−130058.	−0.0601273
$343$	657761.	0.301879
$344$	5.78559e6	2.63604
$345$	−2.92380e6	−1.32252
$346$	−125465.	−0.0563422
$347$	−339180.	−0.151219	−0.0756096	−	0.997137i	$-0.524090\pi$
$347$	−339180.	−0.151219	−0.0756096	+	0.997137i	$0.524090\pi$
$348$	−1.00646e7	−4.45501
$349$	−1.98647e6	−0.873009	−0.436504	−	0.899702i	$-0.643784\pi$
$349$	−1.98647e6	−0.873009	−0.436504	+	0.899702i	$0.643784\pi$
$350$	−85120.2	−0.0371418
$351$	4.76176e6	2.06300
$352$	3.53140e6	1.51911
$353$	−933062.	−0.398542	−0.199271	−	0.979944i	$-0.563857\pi$
$353$	−933062.	−0.398542	−0.199271	+	0.979944i	$0.563857\pi$
$354$	−955151.	−0.405101
$355$	1.23743e6	0.521133
$356$	1.43236e6	0.599002
$357$	289829.	0.120357
$358$	5.69453e6	2.34828
$359$	2.90133e6	1.18812	0.594061	−	0.804420i	$-0.297524\pi$
$359$	2.90133e6	1.18812	0.594061	+	0.804420i	$0.297524\pi$
$360$	−1.09304e6	−0.444508
$361$	−2.33487e6	−0.942964
$362$	−2.33008e6	−0.934544
$363$	213158.	0.0849054
$364$	2.18210e6	0.863220
$365$	−242532.	−0.0952877
$366$	−3.92897e6	−1.53312
$367$	−893109.	−0.346130	−0.173065	−	0.984910i	$-0.555367\pi$
$367$	−893109.	−0.346130	−0.173065	+	0.984910i	$0.555367\pi$
$368$	1.74514e7	6.71756
$369$	528681.	0.202129
$370$	−2.88571e6	−1.09584
$371$	656369.	0.247579
$372$	9.48621e6	3.55415
$373$	−2.72156e6	−1.01285	−0.506426	−	0.862284i	$-0.669034\pi$
$373$	−2.72156e6	−1.01285	−0.506426	+	0.862284i	$0.669034\pi$
$374$	−1.35664e6	−0.501517
$375$	2.67509e6	0.982335
$376$	1.13267e7	4.13174
$377$	8.93492e6	3.23771
$378$	−880829.	−0.317075
$379$	3.84388e6	1.37458	0.687292	−	0.726381i	$-0.258799\pi$
$379$	3.84388e6	1.37458	0.687292	+	0.726381i	$0.258799\pi$
$380$	1.81633e6	0.645263
$381$	−946931.	−0.334200
$382$	8.93228e6	3.13187
$383$	−2.37846e6	−0.828514	−0.414257	−	0.910160i	$-0.635958\pi$
$383$	−2.37846e6	−0.828514	−0.414257	+	0.910160i	$0.635958\pi$
$384$	−1.56085e7	−5.40174
$385$	−125389.	−0.0431129
$386$	5.04561e6	1.72364
$387$	266855.	0.0905730
$388$	−1.16133e7	−3.91632
$389$	2.57796e6	0.863778	0.431889	−	0.901927i	$-0.357847\pi$
$389$	2.57796e6	0.863778	0.431889	+	0.901927i	$0.357847\pi$
$390$	−1.01415e7	−3.37630
$391$	−3.85793e6	−1.27618
$392$	1.10453e7	3.63048
$393$	2.39017e6	0.780633
$394$	6.31891e6	2.05070
$395$	−326652.	−0.105340
$396$	346782.	0.111127
$397$	−441573.	−0.140613	−0.0703065	−	0.997525i	$-0.522398\pi$
$397$	−441573.	−0.140613	−0.0703065	+	0.997525i	$0.522398\pi$
$398$	811691.	0.256852
$399$	108326.	0.0340644
$400$	−1.75358e6	−0.547993
$401$	−1.49324e6	−0.463735	−0.231867	−	0.972747i	$-0.574484\pi$
$401$	−1.49324e6	−0.463735	−0.231867	+	0.972747i	$0.574484\pi$
$402$	−5.35791e6	−1.65360
$403$	−8.42144e6	−2.58300
$404$	−1.49464e7	−4.55600
$405$	2.64546e6	0.801427
$406$	−1.65278e6	−0.497622
$407$	598267.	0.179023
$408$	9.85003e6	2.92946
$409$	3.78384e6	1.11847	0.559235	−	0.829009i	$-0.311095\pi$
$409$	3.78384e6	1.11847	0.559235	+	0.829009i	$0.311095\pi$
$410$	−9.94192e6	−2.92086
$411$	2.97872e6	0.869812
$412$	−1.05846e7	−3.07206
$413$	−116486.	−0.0336045
$414$	1.32789e6	0.380769
$415$	−3.09805e6	−0.883015
$416$	3.48330e7	9.86863
$417$	1.01739e6	0.286516
$418$	−507056.	−0.141943
$419$	6.27177e6	1.74524	0.872620	−	0.488400i	$-0.162419\pi$
$419$	6.27177e6	1.74524	0.872620	+	0.488400i	$0.162419\pi$
$420$	1.39319e6	0.385377
$421$	7.20964e6	1.98248	0.991239	−	0.132081i	$-0.0421660\pi$
$421$	7.20964e6	1.98248	0.991239	+	0.132081i	$0.0421660\pi$
$422$	−2.63488e6	−0.720245
$423$	522433.	0.141965
$424$	2.23071e7	6.02600
$425$	387658.	0.104106
$426$	3.83821e6	1.02472
$427$	−479159.	−0.127177
$428$	−4.41308e6	−1.16448
$429$	2.10254e6	0.551572
$430$	−5.01825e6	−1.30882
$431$	−2.94603e6	−0.763912	−0.381956	−	0.924180i	$-0.624749\pi$
$431$	−2.94603e6	−0.763912	−0.381956	+	0.924180i	$0.624749\pi$
$432$	−1.81461e7	−4.67816
$433$	−5.17110e6	−1.32545	−0.662724	−	0.748864i	$-0.730600\pi$
$433$	−5.17110e6	−1.32545	−0.662724	+	0.748864i	$0.730600\pi$
$434$	1.55780e6	0.396996
$435$	5.70459e6	1.44544
$436$	3.06155e6	0.771304
$437$	−1.44193e6	−0.361195
$438$	−752279.	−0.187367
$439$	−3.98651e6	−0.987259	−0.493630	−	0.869672i	$-0.664330\pi$
$439$	−3.98651e6	−0.987259	−0.493630	+	0.869672i	$0.664330\pi$
$440$	−4.26143e6	−1.04936
$441$	509457.	0.124741
$442$	−1.33816e7	−3.25801
$443$	−2.84769e6	−0.689418	−0.344709	−	0.938710i	$-0.612022\pi$
$443$	−2.84769e6	−0.689418	−0.344709	+	0.938710i	$0.612022\pi$
$444$	−6.64730e6	−1.60025
$445$	−811859.	−0.194348
$446$	−4.08518e6	−0.972465
$447$	−4.86525e6	−1.15169
$448$	−3.56176e6	−0.838436
$449$	−6.31198e6	−1.47758	−0.738788	−	0.673938i	$-0.764601\pi$
$449$	−6.31198e6	−1.47758	−0.738788	+	0.673938i	$0.764601\pi$
$450$	−133431.	−0.0310617
$451$	2.06117e6	0.477168
$452$	−4.67351e6	−1.07596
$453$	3.69164e6	0.845227
$454$	1.57539e6	0.358713
$455$	−1.23681e6	−0.280075
$456$	3.68153e6	0.829118
$457$	−7.39075e6	−1.65538	−0.827690	−	0.561185i	$-0.810346\pi$
$457$	−7.39075e6	−1.65538	−0.827690	+	0.561185i	$0.810346\pi$
$458$	−5.89678e6	−1.31356
$459$	4.01150e6	0.888741
$460$	−1.85448e7	−4.08627
$461$	−1.78088e6	−0.390286	−0.195143	−	0.980775i	$-0.562517\pi$
$461$	−1.78088e6	−0.390286	−0.195143	+	0.980775i	$0.562517\pi$
$462$	−388928.	−0.0847743
$463$	6.51636e6	1.41271	0.706354	−	0.707859i	$-0.250339\pi$
$463$	6.51636e6	1.41271	0.706354	+	0.707859i	$0.250339\pi$
$464$	−3.40492e7	−7.34197
$465$	−5.37676e6	−1.15316
$466$	−4.16306e6	−0.888072
$467$	3.61380e6	0.766783	0.383391	−	0.923586i	$-0.374756\pi$
$467$	3.61380e6	0.766783	0.383391	+	0.923586i	$0.374756\pi$
$468$	3.42058e6	0.721913
$469$	−653425.	−0.137171
$470$	−9.82442e6	−2.05146
$471$	2.62752e6	0.545750
$472$	−3.95884e6	−0.817925
$473$	1.04039e6	0.213817
$474$	−1.01320e6	−0.207133
$475$	144890.	0.0294649
$476$	1.83829e6	0.371875
$477$	1.02890e6	0.207050
$478$	−1.49233e7	−2.98741
$479$	−5.64766e6	−1.12468	−0.562341	−	0.826906i	$-0.690099\pi$
$479$	−5.64766e6	−1.12468	−0.562341	+	0.826906i	$0.690099\pi$
$480$	2.22395e7	4.40576
$481$	5.90118e6	1.16299
$482$	8.65069e6	1.69603
$483$	−1.10601e6	−0.215720
$484$	1.35199e6	0.262338
$485$	6.58241e6	1.27066
$486$	−2.60513e6	−0.500309
$487$	−5.79562e6	−1.10733	−0.553665	−	0.832739i	$-0.686771\pi$
$487$	−5.79562e6	−1.10733	−0.553665	+	0.832739i	$0.686771\pi$
$488$	−1.62845e7	−3.09546
$489$	−6.80858e6	−1.28761
$490$	−9.58040e6	−1.80257
$491$	−7.42279e6	−1.38952	−0.694758	−	0.719244i	$-0.744488\pi$
$491$	−7.42279e6	−1.38952	−0.694758	+	0.719244i	$0.744488\pi$
$492$	−2.29014e7	−4.26530
$493$	7.52715e6	1.39480
$494$	−5.00149e6	−0.922108
$495$	−196555.	−0.0360554
$496$	3.20925e7	5.85732
$497$	468090.	0.0850038
$498$	−9.60945e6	−1.73630
$499$	1.26702e6	0.227789	0.113894	−	0.993493i	$-0.463667\pi$
$499$	1.26702e6	0.227789	0.113894	+	0.993493i	$0.463667\pi$
$500$	1.69672e7	3.03519
$501$	−1.00807e6	−0.179431
$502$	1.21403e7	2.15015
$503$	5.43331e6	0.957513	0.478757	−	0.877948i	$-0.341088\pi$
$503$	5.43331e6	0.957513	0.478757	+	0.877948i	$0.341088\pi$
$504$	−413472.	−0.0725054
$505$	8.47159e6	1.47821
$506$	5.17704e6	0.898888
$507$	1.53334e7	2.64922
$508$	−6.00609e6	−1.03260
$509$	5.12584e6	0.876941	0.438470	−	0.898746i	$-0.355520\pi$
$509$	5.12584e6	0.876941	0.438470	+	0.898746i	$0.355520\pi$
$510$	−8.54362e6	−1.45451
$511$	−91744.3	−0.0155427
$512$	−3.48076e7	−5.86812
$513$	1.49933e6	0.251539
$514$	847343.	0.141466
$515$	5.99930e6	0.996741
$516$	−1.15597e7	−1.91126
$517$	2.03681e6	0.335138
$518$	−1.09160e6	−0.178747
$519$	163811.	0.0266947
$520$	−4.20338e7	−6.81695
$521$	−2.42503e6	−0.391402	−0.195701	−	0.980664i	$-0.562698\pi$
$521$	−2.42503e6	−0.391402	−0.195701	+	0.980664i	$0.562698\pi$
$522$	−2.59083e6	−0.416162
$523$	−1.30312e6	−0.208320	−0.104160	−	0.994561i	$-0.533215\pi$
$523$	−1.30312e6	−0.208320	−0.104160	+	0.994561i	$0.533215\pi$
$524$	1.51601e7	2.41198
$525$	111136.	0.0175977
$526$	6.95388e6	1.09588
$527$	−7.09457e6	−1.11275
$528$	−8.01238e6	−1.25077
$529$	8.28581e6	1.28735
$530$	−1.93485e7	−2.99198
$531$	−182598.	−0.0281035
$532$	687078.	0.105251
$533$	2.03309e7	3.09983
$534$	−2.51820e6	−0.382153
$535$	2.50132e6	0.377820
$536$	−2.22071e7	−3.33872
$537$	−7.43495e6	−1.11261
$538$	4.44110e6	0.661507
$539$	1.98622e6	0.294479
$540$	1.92830e7	2.84571
$541$	8.20171e6	1.20479	0.602395	−	0.798198i	$-0.294213\pi$
$541$	8.20171e6	1.20479	0.602395	+	0.798198i	$0.294213\pi$
$542$	−2.45671e7	−3.59217
$543$	3.04223e6	0.442784
$544$	2.93447e7	4.25141
$545$	−1.73528e6	−0.250252
$546$	−3.83630e6	−0.550720
$547$	−2.62406e6	−0.374977	−0.187489	−	0.982267i	$-0.560035\pi$
$547$	−2.62406e6	−0.374977	−0.187489	+	0.982267i	$0.560035\pi$
$548$	1.88931e7	2.68752
$549$	−751110.	−0.106359
$550$	−520207.	−0.0733279
$551$	2.81334e6	0.394768
$552$	−3.75885e7	−5.25058
$553$	−123565.	−0.0171824
$554$	3.84938e6	0.532865
$555$	3.76767e6	0.519207
$556$	6.45300e6	0.885268
$557$	1.24875e7	1.70544	0.852722	−	0.522365i	$-0.174950\pi$
$557$	1.24875e7	1.70544	0.852722	+	0.522365i	$0.174950\pi$
$558$	2.44194e6	0.332008
$559$	1.02622e7	1.38902
$560$	4.71324e6	0.635110
$561$	1.77127e6	0.237617
$562$	−2.26226e7	−3.02135
$563$	7.37604e6	0.980736	0.490368	−	0.871515i	$-0.336862\pi$
$563$	7.37604e6	0.980736	0.490368	+	0.871515i	$0.336862\pi$
$564$	−2.26308e7	−2.99572
$565$	2.64893e6	0.349099
$566$	−1.99127e7	−2.61270
$567$	1.00072e6	0.130724
$568$	1.59084e7	2.06897
$569$	1.05938e7	1.37174	0.685869	−	0.727725i	$-0.259422\pi$
$569$	1.05938e7	1.37174	0.685869	+	0.727725i	$0.259422\pi$
$570$	−3.19325e6	−0.411667
$571$	1.05437e7	1.35333	0.676664	−	0.736292i	$-0.263425\pi$
$571$	1.05437e7	1.35333	0.676664	+	0.736292i	$0.263425\pi$
$572$	1.33358e7	1.70423
$573$	−1.16623e7	−1.48387
$574$	−3.76080e6	−0.476432
$575$	−1.47933e6	−0.186593
$576$	−5.58328e6	−0.701186
$577$	1.09213e7	1.36563	0.682816	−	0.730591i	$-0.260755\pi$
$577$	1.09213e7	1.36563	0.682816	+	0.730591i	$0.260755\pi$
$578$	4.55950e6	0.567673
$579$	−6.58771e6	−0.816654
$580$	3.61824e7	4.46609
$581$	−1.17192e6	−0.144032
$582$	2.04171e7	2.49855
$583$	4.01135e6	0.488787
$584$	−3.11799e6	−0.378306
$585$	−1.93877e6	−0.234227
$586$	1.98631e7	2.38947
$587$	−915441.	−0.109657	−0.0548283	−	0.998496i	$-0.517461\pi$
$587$	−915441.	−0.109657	−0.0548283	+	0.998496i	$0.517461\pi$
$588$	−2.20687e7	−2.63228
$589$	−2.65166e6	−0.314941
$590$	3.43378e6	0.406109
$591$	−8.25016e6	−0.971613
$592$	−2.24882e7	−2.63725
$593$	−1.13278e7	−1.32285	−0.661425	−	0.750011i	$-0.730048\pi$
$593$	−1.13278e7	−1.32285	−0.661425	+	0.750011i	$0.730048\pi$
$594$	−5.38313e6	−0.625992
$595$	−1.04194e6	−0.120656
$596$	−3.08587e7	−3.55846
$597$	−1.05977e6	−0.121696
$598$	5.10652e7	5.83945
$599$	6.76527e6	0.770403	0.385202	−	0.922832i	$-0.374132\pi$
$599$	6.76527e6	0.770403	0.385202	+	0.922832i	$0.374132\pi$
$600$	3.77702e6	0.428322
$601$	−1.31690e7	−1.48719	−0.743594	−	0.668631i	$-0.766880\pi$
$601$	−1.31690e7	−1.48719	−0.743594	+	0.668631i	$0.766880\pi$
$602$	−1.89829e6	−0.213487
$603$	−1.02428e6	−0.114717
$604$	2.34149e7	2.61156
$605$	−766306.	−0.0851166
$606$	2.62769e7	2.90665
$607$	−5.04987e6	−0.556299	−0.278150	−	0.960538i	$-0.589721\pi$
$607$	−5.04987e6	−0.556299	−0.278150	+	0.960538i	$0.589721\pi$
$608$	1.09678e7	1.20327
$609$	2.15792e6	0.235772
$610$	1.41247e7	1.53693
$611$	2.00906e7	2.17716
$612$	2.88164e6	0.311000
$613$	−1.60443e6	−0.172453	−0.0862265	−	0.996276i	$-0.527481\pi$
$613$	−1.60443e6	−0.172453	−0.0862265	+	0.996276i	$0.527481\pi$
$614$	−622763.	−0.0666656
$615$	1.29805e7	1.38389
$616$	−1.61200e6	−0.171165
$617$	−1.67741e7	−1.77389	−0.886945	−	0.461875i	$-0.847177\pi$
$617$	−1.67741e7	−1.77389	−0.886945	+	0.461875i	$0.847177\pi$
$618$	1.86085e7	1.95992
$619$	−1.24995e7	−1.31120	−0.655598	−	0.755110i	$-0.727583\pi$
$619$	−1.24995e7	−1.31120	−0.655598	+	0.755110i	$0.727583\pi$
$620$	−3.41031e7	−3.56299
$621$	−1.53082e7	−1.59293
$622$	2.50056e7	2.59156
$623$	−307108.	−0.0317008
$624$	−7.90324e7	−8.12538
$625$	−8.41213e6	−0.861403
$626$	−2.45530e7	−2.50420
$627$	662027.	0.0672523
$628$	1.66655e7	1.68624
$629$	4.97140e6	0.501016
$630$	358634.	0.0359998
$631$	−3.71302e6	−0.371240	−0.185620	−	0.982622i	$-0.559429\pi$
$631$	−3.71302e6	−0.371240	−0.185620	+	0.982622i	$0.559429\pi$
$632$	−4.19945e6	−0.418215
$633$	3.44018e6	0.341250
$634$	−1.96830e7	−1.94477
$635$	3.40423e6	0.335031
$636$	−4.45698e7	−4.36916
$637$	1.95916e7	1.91303
$638$	−1.01009e7	−0.982441
$639$	733760.	0.0710889
$640$	5.61129e7	5.41518
$641$	−1.85765e7	−1.78574	−0.892872	−	0.450311i	$-0.851313\pi$
$641$	−1.85765e7	−1.78574	−0.892872	+	0.450311i	$0.851313\pi$
$642$	7.75853e6	0.742920
$643$	−4.36391e6	−0.416245	−0.208122	−	0.978103i	$-0.566735\pi$
$643$	−4.36391e6	−0.416245	−0.208122	+	0.978103i	$0.566735\pi$
$644$	−7.01507e6	−0.666526
$645$	6.55198e6	0.620116
$646$	−4.21346e6	−0.397244
$647$	−2.07962e7	−1.95310	−0.976549	−	0.215296i	$-0.930929\pi$
$647$	−2.07962e7	−1.95310	−0.976549	+	0.215296i	$0.930929\pi$
$648$	3.40101e7	3.18178
$649$	−711894.	−0.0663443
$650$	−5.13121e6	−0.476361
$651$	−2.03391e6	−0.188095
$652$	−4.31847e7	−3.97842
$653$	1.30542e7	1.19803	0.599016	−	0.800737i	$-0.295559\pi$
$653$	1.30542e7	1.19803	0.599016	+	0.800737i	$0.295559\pi$
$654$	−5.38244e6	−0.492079
$655$	−8.59268e6	−0.782574
$656$	−7.74770e7	−7.02932
$657$	−143815.	−0.0129984
$658$	−3.71636e6	−0.334620
$659$	−968247.	−0.0868506	−0.0434253	−	0.999057i	$-0.513827\pi$
$659$	−968247.	−0.0868506	−0.0434253	+	0.999057i	$0.513827\pi$
$660$	8.51437e6	0.760838
$661$	1.61638e7	1.43893	0.719464	−	0.694530i	$-0.244387\pi$
$661$	1.61638e7	1.43893	0.719464	+	0.694530i	$0.244387\pi$
$662$	−7.99482e6	−0.709029
$663$	1.74714e7	1.54363
$664$	−3.98286e7	−3.50570
$665$	−389434.	−0.0341491
$666$	−1.71115e6	−0.149486
$667$	−2.87242e7	−2.49996
$668$	−6.39388e6	−0.554400
$669$	5.33374e6	0.460751
$670$	1.92618e7	1.65771
$671$	−2.92835e6	−0.251083
$672$	8.41268e6	0.718640
$673$	1.67412e7	1.42478	0.712392	−	0.701782i	$-0.247612\pi$
$673$	1.67412e7	1.42478	0.712392	+	0.701782i	$0.247612\pi$
$674$	2.00399e7	1.69921
$675$	1.53822e6	0.129945
$676$	9.72549e7	8.18549
$677$	−5.97421e6	−0.500967	−0.250483	−	0.968121i	$-0.580590\pi$
$677$	−5.97421e6	−0.500967	−0.250483	+	0.968121i	$0.580590\pi$
$678$	8.21638e6	0.686446
$679$	2.48998e6	0.207263
$680$	−3.54110e7	−2.93674
$681$	−2.05687e6	−0.169957
$682$	9.52037e6	0.783777
$683$	1.68982e7	1.38608	0.693042	−	0.720897i	$-0.256270\pi$
$683$	1.68982e7	1.38608	0.693042	+	0.720897i	$0.256270\pi$
$684$	1.07704e6	0.0880217
$685$	−1.07086e7	−0.871976
$686$	−7.33464e6	−0.595070
$687$	7.69902e6	0.622363
$688$	−3.91071e7	−3.14981
$689$	3.95671e7	3.17531
$690$	3.26031e7	2.60697
$691$	−5.05614e6	−0.402832	−0.201416	−	0.979506i	$-0.564554\pi$
$691$	−5.05614e6	−0.402832	−0.201416	+	0.979506i	$0.564554\pi$
$692$	1.03900e6	0.0824807
$693$	−74352.2	−0.00588113
$694$	3.78217e6	0.298087
$695$	−3.65754e6	−0.287228
$696$	7.33383e7	5.73862
$697$	1.71276e7	1.33541
$698$	2.21510e7	1.72090
$699$	5.43542e6	0.420766
$700$	704898.	0.0543727
$701$	1.76476e7	1.35641	0.678206	−	0.734872i	$-0.262758\pi$
$701$	1.76476e7	1.35641	0.678206	+	0.734872i	$0.262758\pi$
$702$	−5.30980e7	−4.06664
$703$	1.85810e6	0.141802
$704$	−2.17675e7	−1.65530
$705$	1.28271e7	0.971973
$706$	1.04045e7	0.785615
$707$	3.20461e6	0.241116
$708$	7.90980e6	0.593038
$709$	−1.18572e6	−0.0885864	−0.0442932	−	0.999019i	$-0.514104\pi$
$709$	−1.18572e6	−0.0885864	−0.0442932	+	0.999019i	$0.514104\pi$
$710$	−1.37984e7	−1.02727
$711$	−193696.	−0.0143697
$712$	−1.04373e7	−0.771590
$713$	2.70734e7	1.99443
$714$	−3.23186e6	−0.237250
$715$	−7.55868e6	−0.552944
$716$	−4.71576e7	−3.43771
$717$	1.94843e7	1.41543
$718$	−3.23525e7	−2.34205
$719$	5.72243e6	0.412818	0.206409	−	0.978466i	$-0.433822\pi$
$719$	5.72243e6	0.412818	0.206409	+	0.978466i	$0.433822\pi$
$720$	7.38828e6	0.531144
$721$	2.26940e6	0.162582
$722$	2.60360e7	1.85879
$723$	−1.12946e7	−0.803573
$724$	1.92959e7	1.36810
$725$	2.88630e6	0.203937
$726$	−2.37691e6	−0.167367
$727$	−1.01849e6	−0.0714697	−0.0357349	−	0.999361i	$-0.511377\pi$
$727$	−1.01849e6	−0.0714697	−0.0357349	+	0.999361i	$0.511377\pi$
$728$	−1.59004e7	−1.11194
$729$	1.56835e7	1.09301
$730$	2.70445e6	0.187833
$731$	8.64526e6	0.598391
$732$	3.25366e7	2.24437
$733$	−7.13450e6	−0.490460	−0.245230	−	0.969465i	$-0.578863\pi$
$733$	−7.13450e6	−0.490460	−0.245230	+	0.969465i	$0.578863\pi$
$734$	9.95899e6	0.682300
$735$	1.25085e7	0.854054
$736$	−1.11982e8	−7.61996
$737$	−3.99336e6	−0.270813
$738$	−5.89528e6	−0.398441
$739$	−3.59057e6	−0.241853	−0.120927	−	0.992661i	$-0.538587\pi$
$739$	−3.59057e6	−0.241853	−0.120927	+	0.992661i	$0.538587\pi$
$740$	2.38971e7	1.60423
$741$	6.53009e6	0.436892
$742$	−7.31911e6	−0.488033
$743$	1.51342e7	1.00574	0.502872	−	0.864361i	$-0.332277\pi$
$743$	1.51342e7	1.00574	0.502872	+	0.864361i	$0.332277\pi$
$744$	−6.91236e7	−4.57819
$745$	1.74906e7	1.15456
$746$	3.03479e7	1.99656
$747$	−1.83706e6	−0.120454
$748$	1.12346e7	0.734182
$749$	946194.	0.0616276
$750$	−2.98297e7	−1.93640
$751$	−1.74032e7	−1.12598	−0.562989	−	0.826464i	$-0.690349\pi$
$751$	−1.74032e7	−1.12598	−0.562989	+	0.826464i	$0.690349\pi$
$752$	−7.65614e7	−4.93702
$753$	−1.58507e7	−1.01874
$754$	−9.96326e7	−6.38224
$755$	−1.32715e7	−0.847329
$756$	7.29432e6	0.464174
$757$	3.93063e6	0.249300	0.124650	−	0.992201i	$-0.460219\pi$
$757$	3.93063e6	0.249300	0.124650	+	0.992201i	$0.460219\pi$
$758$	−4.28628e7	−2.70961
$759$	−6.75930e6	−0.425890
$760$	−1.32352e7	−0.831180
$761$	9.69171e6	0.606651	0.303326	−	0.952887i	$-0.401903\pi$
$761$	9.69171e6	0.606651	0.303326	+	0.952887i	$0.401903\pi$
$762$	1.05592e7	0.658782
$763$	−656417.	−0.0408196
$764$	−7.39700e7	−4.58482
$765$	−1.63330e6	−0.100905
$766$	2.65221e7	1.63319
$767$	−7.02197e6	−0.430993
$768$	9.02379e7	5.52060
$769$	−2.73303e7	−1.66659	−0.833293	−	0.552831i	$-0.813547\pi$
$769$	−2.73303e7	−1.66659	−0.833293	+	0.552831i	$0.813547\pi$
$770$	1.39820e6	0.0849852
$771$	−1.10632e6	−0.0670260
$772$	−4.17838e7	−2.52327
$773$	1.22344e7	0.736432	0.368216	−	0.929740i	$-0.379969\pi$
$773$	1.22344e7	0.736432	0.368216	+	0.929740i	$0.379969\pi$
$774$	−2.97568e6	−0.178540
$775$	−2.72043e6	−0.162698
$776$	8.46235e7	5.04472
$777$	1.42522e6	0.0846897
$778$	−2.87466e7	−1.70270
$779$	6.40158e6	0.377958
$780$	8.39838e7	4.94264
$781$	2.86070e6	0.167821
$782$	4.30194e7	2.51564
$783$	2.98676e7	1.74099
$784$	−7.46597e7	−4.33807
$785$	−9.44598e6	−0.547108
$786$	−2.66526e7	−1.53880
$787$	−1.90957e6	−0.109900	−0.0549502	−	0.998489i	$-0.517500\pi$
$787$	−1.90957e6	−0.109900	−0.0549502	+	0.998489i	$0.517500\pi$
$788$	−5.23281e7	−3.00206
$789$	−9.07920e6	−0.519224
$790$	3.64248e6	0.207649
$791$	1.00203e6	0.0569429
$792$	−2.52691e6	−0.143145
$793$	−2.88846e7	−1.63111
$794$	4.92394e6	0.277180
$795$	2.52620e7	1.41759
$796$	−6.72178e6	−0.376012
$797$	2.42882e7	1.35441	0.677203	−	0.735796i	$-0.263192\pi$
$797$	2.42882e7	1.35441	0.677203	+	0.735796i	$0.263192\pi$
$798$	−1.20793e6	−0.0671485
$799$	1.69252e7	0.937920
$800$	1.12523e7	0.621608
$801$	−481410.	−0.0265115
$802$	1.66510e7	0.914125
$803$	−560690.	−0.0306855
$804$	4.43699e7	2.42074
$805$	3.97612e6	0.216257
$806$	9.39068e7	5.09166
$807$	−5.79843e6	−0.313420
$808$	1.08911e8	5.86871
$809$	−2.59536e7	−1.39421	−0.697103	−	0.716971i	$-0.745528\pi$
$809$	−2.59536e7	−1.39421	−0.697103	+	0.716971i	$0.745528\pi$
$810$	−2.94993e7	−1.57979
$811$	−572743.	−0.0305779	−0.0152889	−	0.999883i	$-0.504867\pi$
$811$	−572743.	−0.0305779	−0.0152889	+	0.999883i	$0.504867\pi$
$812$	1.36870e7	0.728481
$813$	3.20756e7	1.70196
$814$	−6.67123e6	−0.352895
$815$	2.44769e7	1.29081
$816$	−6.65802e7	−3.50041
$817$	3.23124e6	0.169361
$818$	−4.21933e7	−2.20475
$819$	−733394.	−0.0382056
$820$	8.23310e7	4.27591
$821$	1.04922e7	0.543260	0.271630	−	0.962402i	$-0.412437\pi$
$821$	1.04922e7	0.543260	0.271630	+	0.962402i	$0.412437\pi$
$822$	−3.32155e7	−1.71459
$823$	−8.27820e6	−0.426026	−0.213013	−	0.977049i	$-0.568328\pi$
$823$	−8.27820e6	−0.426026	−0.213013	+	0.977049i	$0.568328\pi$
$824$	7.71270e7	3.95720
$825$	679198.	0.0347425
$826$	1.29892e6	0.0662419
$827$	−1.16937e7	−0.594549	−0.297275	−	0.954792i	$-0.596078\pi$
$827$	−1.16937e7	−0.594549	−0.297275	+	0.954792i	$0.596078\pi$
$828$	−1.09965e7	−0.557417
$829$	−3.07089e7	−1.55195	−0.775975	−	0.630764i	$-0.782742\pi$
$829$	−3.07089e7	−1.55195	−0.775975	+	0.630764i	$0.782742\pi$
$830$	3.45461e7	1.74062
$831$	−5.02587e6	−0.252470
$832$	−2.14710e8	−10.7533
$833$	1.65048e7	0.824132
$834$	−1.13449e7	−0.564787
$835$	3.62403e6	0.179877
$836$	4.19903e6	0.207794
$837$	−2.81512e7	−1.38894
$838$	−6.99360e7	−3.44026
$839$	−3.64379e7	−1.78710	−0.893549	−	0.448965i	$-0.851793\pi$
$839$	−3.64379e7	−1.78710	−0.893549	+	0.448965i	$0.851793\pi$
$840$	−1.01518e7	−0.496415
$841$	3.55322e7	1.73233
$842$	−8.03941e7	−3.90791
$843$	2.95367e7	1.43151
$844$	2.18200e7	1.05438
$845$	−5.51238e7	−2.65581
$846$	−5.82561e6	−0.279844
$847$	−289876.	−0.0138837
$848$	−1.50783e8	−7.20048
$849$	2.59986e7	1.23789
$850$	−4.32274e6	−0.205216
$851$	−1.89712e7	−0.897990
$852$	−3.17850e7	−1.50011
$853$	−2.96834e7	−1.39682	−0.698410	−	0.715698i	$-0.746109\pi$
$853$	−2.96834e7	−1.39682	−0.698410	+	0.715698i	$0.746109\pi$
$854$	5.34306e6	0.250695
$855$	−610461.	−0.0285590
$856$	3.21570e7	1.50000
$857$	2.86070e7	1.33052	0.665258	−	0.746614i	$-0.268322\pi$
$857$	2.86070e7	1.33052	0.665258	+	0.746614i	$0.268322\pi$
$858$	−2.34453e7	−1.08727
$859$	2.50841e7	1.15989	0.579943	−	0.814657i	$-0.303075\pi$
$859$	2.50841e7	1.15989	0.579943	+	0.814657i	$0.303075\pi$
$860$	4.15571e7	1.91602
$861$	4.91022e6	0.225732
$862$	3.28509e7	1.50584
$863$	3.65805e7	1.67195	0.835973	−	0.548771i	$-0.184904\pi$
$863$	3.65805e7	1.67195	0.835973	+	0.548771i	$0.184904\pi$
$864$	1.16439e8	5.30659
$865$	−588905.	−0.0267611
$866$	5.76625e7	2.61275
$867$	−5.95303e6	−0.268961
$868$	−1.29004e7	−0.581172
$869$	−755161.	−0.0339227
$870$	−6.36115e7	−2.84929
$871$	−3.93897e7	−1.75929
$872$	−2.23088e7	−0.993538
$873$	3.90319e6	0.173334
$874$	1.60789e7	0.711996
$875$	−3.63788e6	−0.160631
$876$	6.22978e6	0.274291
$877$	−3.03877e7	−1.33413	−0.667066	−	0.744999i	$-0.732450\pi$
$877$	−3.03877e7	−1.33413	−0.667066	+	0.744999i	$0.732450\pi$
$878$	4.44532e7	1.94611
$879$	−2.59338e7	−1.13212
$880$	2.88046e7	1.25388
$881$	−1.82942e7	−0.794099	−0.397050	−	0.917797i	$-0.629966\pi$
$881$	−1.82942e7	−0.794099	−0.397050	+	0.917797i	$0.629966\pi$
$882$	−5.68091e6	−0.245893
$883$	2.45673e7	1.06037	0.530183	−	0.847883i	$-0.322123\pi$
$883$	2.45673e7	1.06037	0.530183	+	0.847883i	$0.322123\pi$
$884$	1.10816e8	4.76948
$885$	−4.48325e6	−0.192413
$886$	3.17543e7	1.35900
$887$	−1.56853e7	−0.669397	−0.334699	−	0.942325i	$-0.608635\pi$
$887$	−1.56853e7	−0.669397	−0.334699	+	0.942325i	$0.608635\pi$
$888$	4.84372e7	2.06132
$889$	1.28774e6	0.0546481
$890$	9.05297e6	0.383104
$891$	6.11582e6	0.258084
$892$	3.38302e7	1.42361
$893$	6.32592e6	0.265458
$894$	5.42520e7	2.27024
$895$	2.67288e7	1.11538
$896$	2.12262e7	0.883290
$897$	−6.66723e7	−2.76671
$898$	7.03844e7	2.91263
$899$	−5.28226e7	−2.17982
$900$	1.10497e6	0.0454720
$901$	3.33330e7	1.36792
$902$	−2.29839e7	−0.940605
$903$	2.47847e6	0.101149
$904$	3.40547e7	1.38598
$905$	−1.09368e7	−0.443885
$906$	−4.11651e7	−1.66613
$907$	−2.69869e7	−1.08927	−0.544635	−	0.838673i	$-0.683332\pi$
$907$	−2.69869e7	−1.08927	−0.544635	+	0.838673i	$0.683332\pi$
$908$	−1.30461e7	−0.525129
$909$	5.02342e6	0.201646
$910$	1.37916e7	0.552090
$911$	−2.50637e7	−1.00057	−0.500287	−	0.865860i	$-0.666772\pi$
$911$	−2.50637e7	−1.00057	−0.500287	+	0.865860i	$0.666772\pi$
$912$	−2.48849e7	−0.990715
$913$	−7.16213e6	−0.284358
$914$	8.24136e7	3.26312
$915$	−1.84417e7	−0.728195
$916$	4.88325e7	1.92296
$917$	−3.25042e6	−0.127649
$918$	−4.47320e7	−1.75191
$919$	3.60167e7	1.40674	0.703372	−	0.710822i	$-0.251677\pi$
$919$	3.60167e7	1.40674	0.703372	+	0.710822i	$0.251677\pi$
$920$	1.35131e8	5.26364
$921$	813099.	0.0315860
$922$	1.98585e7	0.769340
$923$	2.82174e7	1.09021
$924$	3.22079e6	0.124103
$925$	1.90629e6	0.0732547
$926$	−7.26634e7	−2.78476
$927$	3.55742e6	0.135968
$928$	2.18486e8	8.32824
$929$	3.08949e7	1.17449	0.587243	−	0.809411i	$-0.300213\pi$
$929$	3.08949e7	1.17449	0.587243	+	0.809411i	$0.300213\pi$
$930$	5.99558e7	2.27313
$931$	6.16880e6	0.233252
$932$	3.44752e7	1.30007
$933$	−3.26480e7	−1.22787
$934$	−4.02972e7	−1.51150
$935$	−6.36774e6	−0.238208
$936$	−2.49249e7	−0.929916
$937$	−3.79051e7	−1.41042	−0.705210	−	0.708999i	$-0.749147\pi$
$937$	−3.79051e7	−1.41042	−0.705210	+	0.708999i	$0.749147\pi$
$938$	7.28629e6	0.270395
$939$	3.20572e7	1.18648
$940$	8.13580e7	3.00318
$941$	−1.07258e6	−0.0394870	−0.0197435	−	0.999805i	$-0.506285\pi$
$941$	−1.07258e6	−0.0394870	−0.0197435	+	0.999805i	$0.506285\pi$
$942$	−2.92993e7	−1.07580
$943$	−6.53602e7	−2.39350
$944$	2.67594e7	0.977340
$945$	−4.13440e6	−0.150603
$946$	−1.16013e7	−0.421481
$947$	2.80951e7	1.01802	0.509010	−	0.860761i	$-0.330012\pi$
$947$	2.80951e7	1.01802	0.509010	+	0.860761i	$0.330012\pi$
$948$	8.39053e6	0.303227
$949$	−5.53052e6	−0.199343
$950$	−1.61566e6	−0.0580820
$951$	2.56987e7	0.921425
$952$	−1.33952e7	−0.479023
$953$	−3.94844e7	−1.40830	−0.704148	−	0.710054i	$-0.748671\pi$
$953$	−3.94844e7	−1.40830	−0.704148	+	0.710054i	$0.748671\pi$
$954$	−1.14732e7	−0.408143
$955$	4.19260e7	1.48756
$956$	1.23583e8	4.37334
$957$	1.31880e7	0.465477
$958$	6.29766e7	2.21700
$959$	−4.05080e6	−0.142231
$960$	−1.37084e8	−4.80073
$961$	2.11578e7	0.739028
$962$	−6.58036e7	−2.29251
$963$	1.48322e6	0.0515393
$964$	−7.16381e7	−2.48286
$965$	2.36829e7	0.818685
$966$	1.23330e7	0.425233
$967$	5.35044e6	0.184002	0.0920011	−	0.995759i	$-0.470674\pi$
$967$	5.35044e6	0.184002	0.0920011	+	0.995759i	$0.470674\pi$
$968$	−9.85164e6	−0.337925
$969$	5.50122e6	0.188213
$970$	−7.33999e7	−2.50476
$971$	−6.07784e6	−0.206872	−0.103436	−	0.994636i	$-0.532984\pi$
$971$	−6.07784e6	−0.206872	−0.103436	+	0.994636i	$0.532984\pi$
$972$	2.15736e7	0.732414
$973$	−1.38357e6	−0.0468509
$974$	6.46264e7	2.18279
$975$	6.69946e6	0.225698
$976$	1.10073e8	3.69878
$977$	3.62936e7	1.21645	0.608225	−	0.793765i	$-0.291882\pi$
$977$	3.62936e7	1.21645	0.608225	+	0.793765i	$0.291882\pi$
$978$	7.59219e7	2.53817
$979$	−1.87687e6	−0.0625860
$980$	7.93372e7	2.63883
$981$	−1.02897e6	−0.0341375
$982$	8.27709e7	2.73904
$983$	−3.26658e7	−1.07823	−0.539113	−	0.842234i	$-0.681240\pi$
$983$	−3.26658e7	−1.07823	−0.539113	+	0.842234i	$0.681240\pi$
$984$	1.66877e8	5.49426
$985$	2.96594e7	0.974030
$986$	−8.39346e7	−2.74947
$987$	4.85219e6	0.158542
$988$	4.14183e7	1.34990
$989$	−3.29910e7	−1.07252
$990$	2.19177e6	0.0710733
$991$	−3.34569e7	−1.08218	−0.541092	−	0.840963i	$-0.681989\pi$
$991$	−3.34569e7	−1.08218	−0.541092	+	0.840963i	$0.681989\pi$
$992$	−2.05930e8	−6.64416
$993$	1.04383e7	0.335935
$994$	−5.21964e6	−0.167562
$995$	3.80989e6	0.121998
$996$	7.95778e7	2.54181
$997$	1.90594e7	0.607257	0.303628	−	0.952791i	$-0.401802\pi$
$997$	1.90594e7	0.607257	0.303628	+	0.952791i	$0.401802\pi$
$998$	−1.41284e7	−0.449022
$999$	1.97264e7	0.625367

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	869.6.a.d.1.2	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
869.6.a.d.1.2	✓	86	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:	\( N \)	\(=\)	\( 869 = 11 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	869.a (trivial)

\(f(q)\)	\(=\)	\(q-11.1509 q^{2} +14.5590 q^{3} +92.3430 q^{4} -52.3398 q^{5} -162.346 q^{6} -19.7989 q^{7} -672.881 q^{8} -31.0360 q^{9} +O(q^{10})\)	\(q-11.1509 q^{2} +14.5590 q^{3} +92.3430 q^{4} -52.3398 q^{5} -162.346 q^{6} -19.7989 q^{7} -672.881 q^{8} -31.0360 q^{9} +583.637 q^{10} -121.000 q^{11} +1344.42 q^{12} -1193.52 q^{13} +220.777 q^{14} -762.014 q^{15} +4548.26 q^{16} -1005.47 q^{17} +346.080 q^{18} -375.802 q^{19} -4833.21 q^{20} -288.253 q^{21} +1349.26 q^{22} +3836.95 q^{23} -9796.46 q^{24} -385.549 q^{25} +13308.8 q^{26} -3989.69 q^{27} -1828.30 q^{28} -7486.21 q^{29} +8497.15 q^{30} +7055.98 q^{31} -29185.1 q^{32} -1761.64 q^{33} +11211.9 q^{34} +1036.27 q^{35} -2865.96 q^{36} -4944.36 q^{37} +4190.54 q^{38} -17376.4 q^{39} +35218.4 q^{40} -17034.4 q^{41} +3214.28 q^{42} -8598.24 q^{43} -11173.5 q^{44} +1624.42 q^{45} -42785.5 q^{46} -16833.1 q^{47} +66218.0 q^{48} -16415.0 q^{49} +4299.23 q^{50} -14638.6 q^{51} -110213. q^{52} -33151.7 q^{53} +44488.7 q^{54} +6333.11 q^{55} +13322.3 q^{56} -5471.30 q^{57} +83478.1 q^{58} +5883.43 q^{59} -70366.7 q^{60} +24201.2 q^{61} -78680.7 q^{62} +614.481 q^{63} +179897. q^{64} +62468.4 q^{65} +19643.9 q^{66} +33003.0 q^{67} -92848.0 q^{68} +55862.0 q^{69} -11555.4 q^{70} -23642.2 q^{71} +20883.6 q^{72} +4633.80 q^{73} +55134.1 q^{74} -5613.21 q^{75} -34702.7 q^{76} +2395.67 q^{77} +193763. q^{78} +6241.00 q^{79} -238055. q^{80} -50544.0 q^{81} +189950. q^{82} +59191.2 q^{83} -26618.1 q^{84} +52626.0 q^{85} +95878.3 q^{86} -108992. q^{87} +81418.5 q^{88} +15511.3 q^{89} -18113.8 q^{90} +23630.4 q^{91} +354315. q^{92} +102728. q^{93} +187705. q^{94} +19669.4 q^{95} -424906. q^{96} -125763. q^{97} +183042. q^{98} +3755.36 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q + 4 q^{2} + 78 q^{3} + 1530 q^{4} + 169 q^{5} - 78 q^{6} + 490 q^{7} - 192 q^{8} + 7632 q^{9}+O(q^{10}) \) 86 * q + 4 * q^2 + 78 * q^3 + 1530 * q^4 + 169 * q^5 - 78 * q^6 + 490 * q^7 - 192 * q^8 + 7632 * q^9	\( 86 q + 4 q^{2} + 78 q^{3} + 1530 q^{4} + 169 q^{5} - 78 q^{6} + 490 q^{7} - 192 q^{8} + 7632 q^{9} + 1019 q^{10} - 10406 q^{11} + 3369 q^{12} + 2992 q^{13} + 143 q^{14} + 3202 q^{15} + 29438 q^{16} - 4043 q^{17} + 2679 q^{18} + 16115 q^{19} + 8151 q^{20} + 909 q^{21} - 484 q^{22} - 403 q^{23} - 18745 q^{24} + 65143 q^{25} + 11635 q^{26} + 8841 q^{27} + 19998 q^{28} - 9797 q^{29} - 7753 q^{30} + 34557 q^{31} - 6195 q^{32} - 9438 q^{33} + 55362 q^{34} + 26255 q^{35} + 174892 q^{36} + 5322 q^{37} + 34138 q^{38} + 20246 q^{39} + 44862 q^{40} - 29897 q^{41} + 32393 q^{42} + 36010 q^{43} - 185130 q^{44} + 141885 q^{45} + 144330 q^{46} + 32330 q^{47} + 153596 q^{48} + 338884 q^{49} + 9642 q^{50} + 58559 q^{51} + 301121 q^{52} + 38487 q^{53} + 25966 q^{54} - 20449 q^{55} + 72298 q^{56} + 67302 q^{57} + 277501 q^{58} + 180602 q^{59} + 361842 q^{60} + 170221 q^{61} - 52231 q^{62} + 228776 q^{63} + 633510 q^{64} - 47719 q^{65} + 9438 q^{66} + 307210 q^{67} + 26244 q^{68} + 135307 q^{69} + 92715 q^{70} + 213698 q^{71} + 372144 q^{72} + 94636 q^{73} + 298200 q^{74} + 253758 q^{75} + 531922 q^{76} - 59290 q^{77} + 427545 q^{78} + 536726 q^{79} + 699157 q^{80} + 753290 q^{81} + 619268 q^{82} + 282139 q^{83} + 39834 q^{84} - 52876 q^{85} - 203149 q^{86} - 130307 q^{87} + 23232 q^{88} + 10087 q^{89} + 159005 q^{90} + 887428 q^{91} - 156182 q^{92} + 107249 q^{93} + 473622 q^{94} - 132719 q^{95} - 308216 q^{96} + 75639 q^{97} - 66857 q^{98} - 923472 q^{99}+O(q^{100}) \) 86 * q + 4 * q^2 + 78 * q^3 + 1530 * q^4 + 169 * q^5 - 78 * q^6 + 490 * q^7 - 192 * q^8 + 7632 * q^9 + 1019 * q^10 - 10406 * q^11 + 3369 * q^12 + 2992 * q^13 + 143 * q^14 + 3202 * q^15 + 29438 * q^16 - 4043 * q^17 + 2679 * q^18 + 16115 * q^19 + 8151 * q^20 + 909 * q^21 - 484 * q^22 - 403 * q^23 - 18745 * q^24 + 65143 * q^25 + 11635 * q^26 + 8841 * q^27 + 19998 * q^28 - 9797 * q^29 - 7753 * q^30 + 34557 * q^31 - 6195 * q^32 - 9438 * q^33 + 55362 * q^34 + 26255 * q^35 + 174892 * q^36 + 5322 * q^37 + 34138 * q^38 + 20246 * q^39 + 44862 * q^40 - 29897 * q^41 + 32393 * q^42 + 36010 * q^43 - 185130 * q^44 + 141885 * q^45 + 144330 * q^46 + 32330 * q^47 + 153596 * q^48 + 338884 * q^49 + 9642 * q^50 + 58559 * q^51 + 301121 * q^52 + 38487 * q^53 + 25966 * q^54 - 20449 * q^55 + 72298 * q^56 + 67302 * q^57 + 277501 * q^58 + 180602 * q^59 + 361842 * q^60 + 170221 * q^61 - 52231 * q^62 + 228776 * q^63 + 633510 * q^64 - 47719 * q^65 + 9438 * q^66 + 307210 * q^67 + 26244 * q^68 + 135307 * q^69 + 92715 * q^70 + 213698 * q^71 + 372144 * q^72 + 94636 * q^73 + 298200 * q^74 + 253758 * q^75 + 531922 * q^76 - 59290 * q^77 + 427545 * q^78 + 536726 * q^79 + 699157 * q^80 + 753290 * q^81 + 619268 * q^82 + 282139 * q^83 + 39834 * q^84 - 52876 * q^85 - 203149 * q^86 - 130307 * q^87 + 23232 * q^88 + 10087 * q^89 + 159005 * q^90 + 887428 * q^91 - 156182 * q^92 + 107249 * q^93 + 473622 * q^94 - 132719 * q^95 - 308216 * q^96 + 75639 * q^97 - 66857 * q^98 - 923472 * q^99

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