LMFDB - Embedded newform 983.6.a.a.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,6,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, 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("983.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	983.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:	$157.657294876$
Analytic rank:	$1$
Dimension:	$191$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-9.64751 q^{2} -11.8379 q^{3} +61.0744 q^{4} -72.0672 q^{5} +114.206 q^{6} -61.6914 q^{7} -280.496 q^{8} -102.865 q^{9} +O(q^{10})$	\(q-9.64751 q^{2} -11.8379 q^{3} +61.0744 q^{4} -72.0672 q^{5} +114.206 q^{6} -61.6914 q^{7} -280.496 q^{8} -102.865 q^{9} +695.269 q^{10} -635.686 q^{11} -722.991 q^{12} -807.568 q^{13} +595.168 q^{14} +853.121 q^{15} +751.705 q^{16} -1335.06 q^{17} +992.390 q^{18} -1147.56 q^{19} -4401.46 q^{20} +730.295 q^{21} +6132.78 q^{22} +2706.14 q^{23} +3320.47 q^{24} +2068.68 q^{25} +7791.02 q^{26} +4094.30 q^{27} -3767.77 q^{28} -5736.04 q^{29} -8230.50 q^{30} -7695.80 q^{31} +1723.79 q^{32} +7525.16 q^{33} +12880.0 q^{34} +4445.92 q^{35} -6282.42 q^{36} +3861.88 q^{37} +11071.1 q^{38} +9559.88 q^{39} +20214.5 q^{40} +8172.76 q^{41} -7045.52 q^{42} -14948.9 q^{43} -38824.1 q^{44} +7413.18 q^{45} -26107.5 q^{46} -875.701 q^{47} -8898.59 q^{48} -13001.2 q^{49} -19957.6 q^{50} +15804.2 q^{51} -49321.7 q^{52} -7898.62 q^{53} -39499.8 q^{54} +45812.1 q^{55} +17304.2 q^{56} +13584.7 q^{57} +55338.5 q^{58} +24763.4 q^{59} +52103.9 q^{60} +17222.2 q^{61} +74245.3 q^{62} +6345.88 q^{63} -40684.8 q^{64} +58199.1 q^{65} -72599.1 q^{66} -26515.7 q^{67} -81537.9 q^{68} -32034.9 q^{69} -42892.1 q^{70} -25210.3 q^{71} +28853.2 q^{72} +7566.37 q^{73} -37257.5 q^{74} -24488.7 q^{75} -70086.6 q^{76} +39216.3 q^{77} -92229.0 q^{78} +24259.7 q^{79} -54173.3 q^{80} -23471.6 q^{81} -78846.7 q^{82} -15585.1 q^{83} +44602.3 q^{84} +96213.8 q^{85} +144220. q^{86} +67902.5 q^{87} +178307. q^{88} -134132. q^{89} -71518.7 q^{90} +49820.0 q^{91} +165276. q^{92} +91101.9 q^{93} +8448.34 q^{94} +82701.4 q^{95} -20406.0 q^{96} -101709. q^{97} +125429. q^{98} +65389.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9}+O(q^{10}) $ 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9} - 2867 q^{10} - 1878 q^{11} - 3400 q^{12} - 6854 q^{13} - 1601 q^{14} - 3461 q^{15} + 38457 q^{16} - 10730 q^{17} - 17249 q^{18} - 5817 q^{19} - 9988 q^{20} - 15999 q^{21} - 20287 q^{22} - 15625 q^{23} - 19747 q^{24} + 67082 q^{25} - 9868 q^{26} - 22892 q^{27} - 72720 q^{28} - 17960 q^{29} - 27464 q^{30} - 25604 q^{31} - 68869 q^{32} - 60654 q^{33} - 42876 q^{34} - 30018 q^{35} + 172922 q^{36} - 114862 q^{37} + 4404 q^{38} - 73500 q^{39} - 137154 q^{40} - 90896 q^{41} - 10652 q^{42} - 121447 q^{43} - 57962 q^{44} - 109019 q^{45} - 136262 q^{46} - 86994 q^{47} - 133347 q^{48} + 278242 q^{49} - 93911 q^{50} - 66966 q^{51} - 284241 q^{52} - 122112 q^{53} - 130806 q^{54} - 134904 q^{55} - 100292 q^{56} - 423426 q^{57} - 307669 q^{58} - 85704 q^{59} - 238277 q^{60} - 206736 q^{61} - 190602 q^{62} - 387623 q^{63} + 411903 q^{64} - 244408 q^{65} - 113963 q^{66} - 337002 q^{67} - 388031 q^{68} - 165342 q^{69} - 183925 q^{70} - 174806 q^{71} - 753621 q^{72} - 1009738 q^{73} - 204958 q^{74} - 282676 q^{75} - 326869 q^{76} - 332288 q^{77} - 591801 q^{78} - 488092 q^{79} - 259068 q^{80} + 385959 q^{81} - 523996 q^{82} - 315720 q^{83} - 750486 q^{84} - 1001755 q^{85} - 287709 q^{86} - 316995 q^{87} - 836923 q^{88} - 298065 q^{89} - 751039 q^{90} - 521459 q^{91} - 640932 q^{92} - 554391 q^{93} - 623481 q^{94} - 491883 q^{95} - 767843 q^{96} - 1468693 q^{97} - 714146 q^{98} - 842507 q^{99}+O(q^{100}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9 - 2867 * q^10 - 1878 * q^11 - 3400 * q^12 - 6854 * q^13 - 1601 * q^14 - 3461 * q^15 + 38457 * q^16 - 10730 * q^17 - 17249 * q^18 - 5817 * q^19 - 9988 * q^20 - 15999 * q^21 - 20287 * q^22 - 15625 * q^23 - 19747 * q^24 + 67082 * q^25 - 9868 * q^26 - 22892 * q^27 - 72720 * q^28 - 17960 * q^29 - 27464 * q^30 - 25604 * q^31 - 68869 * q^32 - 60654 * q^33 - 42876 * q^34 - 30018 * q^35 + 172922 * q^36 - 114862 * q^37 + 4404 * q^38 - 73500 * q^39 - 137154 * q^40 - 90896 * q^41 - 10652 * q^42 - 121447 * q^43 - 57962 * q^44 - 109019 * q^45 - 136262 * q^46 - 86994 * q^47 - 133347 * q^48 + 278242 * q^49 - 93911 * q^50 - 66966 * q^51 - 284241 * q^52 - 122112 * q^53 - 130806 * q^54 - 134904 * q^55 - 100292 * q^56 - 423426 * q^57 - 307669 * q^58 - 85704 * q^59 - 238277 * q^60 - 206736 * q^61 - 190602 * q^62 - 387623 * q^63 + 411903 * q^64 - 244408 * q^65 - 113963 * q^66 - 337002 * q^67 - 388031 * q^68 - 165342 * q^69 - 183925 * q^70 - 174806 * q^71 - 753621 * q^72 - 1009738 * q^73 - 204958 * q^74 - 282676 * q^75 - 326869 * q^76 - 332288 * q^77 - 591801 * q^78 - 488092 * q^79 - 259068 * q^80 + 385959 * q^81 - 523996 * q^82 - 315720 * q^83 - 750486 * q^84 - 1001755 * q^85 - 287709 * q^86 - 316995 * q^87 - 836923 * q^88 - 298065 * q^89 - 751039 * q^90 - 521459 * q^91 - 640932 * q^92 - 554391 * q^93 - 623481 * q^94 - 491883 * q^95 - 767843 * q^96 - 1468693 * q^97 - 714146 * q^98 - 842507 * 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 $

$2$	−9.64751	−1.70545	−0.852727	−	0.522356i	$-0.825053\pi$
$2$	−9.64751	−1.70545	−0.852727	+	0.522356i	$0.825053\pi$
$3$	−11.8379	−0.759400	−0.379700	−	0.925110i	$-0.623973\pi$
$3$	−11.8379	−0.759400	−0.379700	+	0.925110i	$0.623973\pi$
$4$	61.0744	1.90858
$5$	−72.0672	−1.28918	−0.644588	−	0.764530i	$-0.722971\pi$
$5$	−72.0672	−1.28918	−0.644588	+	0.764530i	$0.722971\pi$
$6$	114.206	1.29512
$7$	−61.6914	−0.475860	−0.237930	−	0.971282i	$-0.576469\pi$
$7$	−61.6914	−0.475860	−0.237930	+	0.971282i	$0.576469\pi$
$8$	−280.496	−1.54954
$9$	−102.865	−0.423312
$10$	695.269	2.19863
$11$	−635.686	−1.58402	−0.792010	−	0.610508i	$-0.790965\pi$
$11$	−635.686	−1.58402	−0.792010	+	0.610508i	$0.790965\pi$
$12$	−722.991	−1.44937
$13$	−807.568	−1.32532	−0.662660	−	0.748921i	$-0.730572\pi$
$13$	−807.568	−1.32532	−0.662660	+	0.748921i	$0.730572\pi$
$14$	595.168	0.811558
$15$	853.121	0.979000
$16$	751.705	0.734087
$17$	−1335.06	−1.12041	−0.560206	−	0.828354i	$-0.689278\pi$
$17$	−1335.06	−1.12041	−0.560206	+	0.828354i	$0.689278\pi$
$18$	992.390	0.721940
$19$	−1147.56	−0.729275	−0.364638	−	0.931150i	$-0.618807\pi$
$19$	−1147.56	−0.729275	−0.364638	+	0.931150i	$0.618807\pi$
$20$	−4401.46	−2.46049
$21$	730.295	0.361368
$22$	6132.78	2.70147
$23$	2706.14	1.06667	0.533335	−	0.845904i	$-0.320938\pi$
$23$	2706.14	1.06667	0.533335	+	0.845904i	$0.320938\pi$
$24$	3320.47	1.17672
$25$	2068.68	0.661976
$26$	7791.02	2.26027
$27$	4094.30	1.08086
$28$	−3767.77	−0.908216
$29$	−5736.04	−1.26654	−0.633268	−	0.773933i	$-0.718287\pi$
$29$	−5736.04	−1.26654	−0.633268	+	0.773933i	$0.718287\pi$
$30$	−8230.50	−1.66964
$31$	−7695.80	−1.43830	−0.719150	−	0.694855i	$-0.755469\pi$
$31$	−7695.80	−1.43830	−0.719150	+	0.694855i	$0.755469\pi$
$32$	1723.79	0.297583
$33$	7525.16	1.20290
$34$	12880.0	1.91081
$35$	4445.92	0.613468
$36$	−6282.42	−0.807924
$37$	3861.88	0.463761	0.231881	−	0.972744i	$-0.425512\pi$
$37$	3861.88	0.463761	0.231881	+	0.972744i	$0.425512\pi$
$38$	11071.1	1.24375
$39$	9559.88	1.00645
$40$	20214.5	1.99763
$41$	8172.76	0.759292	0.379646	−	0.925132i	$-0.376046\pi$
$41$	8172.76	0.759292	0.379646	+	0.925132i	$0.376046\pi$
$42$	−7045.52	−0.616297
$43$	−14948.9	−1.23293	−0.616466	−	0.787381i	$-0.711436\pi$
$43$	−14948.9	−1.23293	−0.616466	+	0.787381i	$0.711436\pi$
$44$	−38824.1	−3.02322
$45$	7413.18	0.545724
$46$	−26107.5	−1.81916
$47$	−875.701	−0.0578244	−0.0289122	−	0.999582i	$-0.509204\pi$
$47$	−875.701	−0.0578244	−0.0289122	+	0.999582i	$0.509204\pi$
$48$	−8898.59	−0.557465
$49$	−13001.2	−0.773557
$50$	−19957.6	−1.12897
$51$	15804.2	0.850840
$52$	−49321.7	−2.52947
$53$	−7898.62	−0.386244	−0.193122	−	0.981175i	$-0.561861\pi$
$53$	−7898.62	−0.386244	−0.193122	+	0.981175i	$0.561861\pi$
$54$	−39499.8	−1.84336
$55$	45812.1	2.04208
$56$	17304.2	0.737363
$57$	13584.7	0.553811
$58$	55338.5	2.16002
$59$	24763.4	0.926148	0.463074	−	0.886320i	$-0.346746\pi$
$59$	24763.4	0.926148	0.463074	+	0.886320i	$0.346746\pi$
$60$	52103.9	1.86850
$61$	17222.2	0.592603	0.296302	−	0.955094i	$-0.404247\pi$
$61$	17222.2	0.592603	0.296302	+	0.955094i	$0.404247\pi$
$62$	74245.3	2.45296
$63$	6345.88	0.201438
$64$	−40684.8	−1.24160
$65$	58199.1	1.70857
$66$	−72599.1	−2.05150
$67$	−26515.7	−0.721633	−0.360817	−	0.932637i	$-0.617502\pi$
$67$	−26515.7	−0.721633	−0.360817	+	0.932637i	$0.617502\pi$
$68$	−81537.9	−2.13839
$69$	−32034.9	−0.810029
$70$	−42892.1	−1.04624
$71$	−25210.3	−0.593515	−0.296757	−	0.954953i	$-0.595905\pi$
$71$	−25210.3	−0.593515	−0.296757	+	0.954953i	$0.595905\pi$
$72$	28853.2	0.655938
$73$	7566.37	0.166181	0.0830903	−	0.996542i	$-0.473521\pi$
$73$	7566.37	0.166181	0.0830903	+	0.996542i	$0.473521\pi$
$74$	−37257.5	−0.790924
$75$	−24488.7	−0.502704
$76$	−70086.6	−1.39188
$77$	39216.3	0.753772
$78$	−92229.0	−1.71645
$79$	24259.7	0.437339	0.218670	−	0.975799i	$-0.429828\pi$
$79$	24259.7	0.437339	0.218670	+	0.975799i	$0.429828\pi$
$80$	−54173.3	−0.946368
$81$	−23471.6	−0.397494
$82$	−78846.7	−1.29494
$83$	−15585.1	−0.248322	−0.124161	−	0.992262i	$-0.539624\pi$
$83$	−15585.1	−0.248322	−0.124161	+	0.992262i	$0.539624\pi$
$84$	44602.3	0.689699
$85$	96213.8	1.44441
$86$	144220.	2.10271
$87$	67902.5	0.961806
$88$	178307.	2.45450
$89$	−134132.	−1.79497	−0.897485	−	0.441045i	$-0.854608\pi$
$89$	−134132.	−1.79497	−0.897485	+	0.441045i	$0.854608\pi$
$90$	−71518.7	−0.930708
$91$	49820.0	0.630667
$92$	165276.	2.03582
$93$	91101.9	1.09224
$94$	8448.34	0.0986169
$95$	82701.4	0.940165
$96$	−20406.0	−0.225985
$97$	−101709.	−1.09757	−0.548784	−	0.835964i	$-0.684909\pi$
$97$	−101709.	−1.09757	−0.548784	+	0.835964i	$0.684909\pi$
$98$	125429.	1.31927
$99$	65389.7	0.670535
$100$	126343.	1.26343
$101$	65741.9	0.641267	0.320633	−	0.947203i	$-0.396104\pi$
$101$	65741.9	0.641267	0.320633	+	0.947203i	$0.396104\pi$
$102$	−152471.	−1.45107
$103$	−89694.9	−0.833057	−0.416528	−	0.909123i	$-0.636753\pi$
$103$	−89694.9	−0.833057	−0.416528	+	0.909123i	$0.636753\pi$
$104$	226519.	2.05363
$105$	−52630.3	−0.465867
$106$	76202.0	0.658721
$107$	161690.	1.36528	0.682642	−	0.730753i	$-0.260831\pi$
$107$	161690.	1.36528	0.682642	+	0.730753i	$0.260831\pi$
$108$	250057.	2.06291
$109$	88851.8	0.716309	0.358154	−	0.933662i	$-0.383406\pi$
$109$	88851.8	0.716309	0.358154	+	0.933662i	$0.383406\pi$
$110$	−441972.	−3.48268
$111$	−45716.4	−0.352180
$112$	−46373.7	−0.349323
$113$	49335.0	0.363462	0.181731	−	0.983348i	$-0.441830\pi$
$113$	49335.0	0.363462	0.181731	+	0.983348i	$0.441830\pi$
$114$	−131058.	−0.944500
$115$	−195024.	−1.37513
$116$	−350326.	−2.41728
$117$	83070.4	0.561024
$118$	−238905.	−1.57950
$119$	82361.5	0.533159
$120$	−239297.	−1.51700
$121$	243045.	1.50912
$122$	−166151.	−1.01066
$123$	−96748.0	−0.576606
$124$	−470017.	−2.74511
$125$	76126.3	0.435772
$126$	−61221.9	−0.343543
$127$	−257157.	−1.41478	−0.707390	−	0.706823i	$-0.750128\pi$
$127$	−257157.	−1.41478	−0.707390	+	0.706823i	$0.750128\pi$
$128$	337346.	1.81991
$129$	176964.	0.936288
$130$	−561476.	−2.91389
$131$	72128.3	0.367221	0.183610	−	0.982999i	$-0.441222\pi$
$131$	72128.3	0.367221	0.183610	+	0.982999i	$0.441222\pi$
$132$	459595.	2.29583
$133$	70794.6	0.347033
$134$	255811.	1.23071
$135$	−295065.	−1.39342
$136$	374478.	1.73612
$137$	175381.	0.798330	0.399165	−	0.916879i	$-0.369300\pi$
$137$	175381.	0.798330	0.399165	+	0.916879i	$0.369300\pi$
$138$	309057.	1.38147
$139$	291305.	1.27882	0.639412	−	0.768865i	$-0.279178\pi$
$139$	291305.	1.27882	0.639412	+	0.768865i	$0.279178\pi$
$140$	271532.	1.17085
$141$	10366.4	0.0439118
$142$	243216.	1.01221
$143$	513359.	2.09933
$144$	−77324.1	−0.310748
$145$	413380.	1.63279
$146$	−72996.6	−0.283414
$147$	153906.	0.587439
$148$	235862.	0.885124
$149$	49533.5	0.182782	0.0913910	−	0.995815i	$-0.470869\pi$
$149$	49533.5	0.182782	0.0913910	+	0.995815i	$0.470869\pi$
$150$	236255.	0.857340
$151$	257331.	0.918438	0.459219	−	0.888323i	$-0.348129\pi$
$151$	257331.	0.918438	0.459219	+	0.888323i	$0.348129\pi$
$152$	321886.	1.13004
$153$	137331.	0.474284
$154$	−378340.	−1.28552
$155$	554615.	1.85422
$156$	583864.	1.92088
$157$	−115166.	−0.372884	−0.186442	−	0.982466i	$-0.559696\pi$
$157$	−115166.	−0.372884	−0.186442	+	0.982466i	$0.559696\pi$
$158$	−234046.	−0.745862
$159$	93502.8	0.293313
$160$	−124228.	−0.383638
$161$	−166945.	−0.507586
$162$	226443.	0.677909
$163$	−476828.	−1.40570	−0.702850	−	0.711338i	$-0.748090\pi$
$163$	−476828.	−1.40570	−0.702850	+	0.711338i	$0.748090\pi$
$164$	499146.	1.44917
$165$	−542317.	−1.55076
$166$	150358.	0.423502
$167$	615831.	1.70872	0.854359	−	0.519683i	$-0.173950\pi$
$167$	615831.	1.70872	0.854359	+	0.519683i	$0.173950\pi$
$168$	−204845.	−0.559953
$169$	280872.	0.756471
$170$	−928223.	−2.46337
$171$	118044.	0.308711
$172$	−912998.	−2.35315
$173$	417031.	1.05938	0.529691	−	0.848191i	$-0.322308\pi$
$173$	417031.	1.05938	0.529691	+	0.848191i	$0.322308\pi$
$174$	−655090.	−1.64032
$175$	−127619.	−0.315008
$176$	−477848.	−1.16281
$177$	−293146.	−0.703316
$178$	1.29404e6	3.06124
$179$	86859.3	0.202621	0.101310	−	0.994855i	$-0.467696\pi$
$179$	86859.3	0.202621	0.101310	+	0.994855i	$0.467696\pi$
$180$	452756.	1.04156
$181$	173225.	0.393019	0.196510	−	0.980502i	$-0.437039\pi$
$181$	173225.	0.393019	0.196510	+	0.980502i	$0.437039\pi$
$182$	−480639.	−1.07557
$183$	−203874.	−0.450023
$184$	−759061.	−1.65284
$185$	−278315.	−0.597870
$186$	−878906.	−1.86277
$187$	848677.	1.77475
$188$	−53483.0	−0.110362
$189$	−252583.	−0.514340
$190$	−797863.	−1.60341
$191$	128324.	0.254521	0.127261	−	0.991869i	$-0.459382\pi$
$191$	128324.	0.254521	0.127261	+	0.991869i	$0.459382\pi$
$192$	481621.	0.942872
$193$	250350.	0.483787	0.241893	−	0.970303i	$-0.422232\pi$
$193$	250350.	0.483787	0.241893	+	0.970303i	$0.422232\pi$
$194$	981241.	1.87185
$195$	−688953.	−1.29749
$196$	−794039.	−1.47639
$197$	−88154.7	−0.161838	−0.0809189	−	0.996721i	$-0.525785\pi$
$197$	−88154.7	−0.161838	−0.0809189	+	0.996721i	$0.525785\pi$
$198$	−630848.	−1.14357
$199$	−115539.	−0.206821	−0.103410	−	0.994639i	$-0.532976\pi$
$199$	−115539.	−0.206821	−0.103410	+	0.994639i	$0.532976\pi$
$200$	−580255.	−1.02576
$201$	313890.	0.548008
$202$	−634246.	−1.09365
$203$	353864.	0.602694
$204$	965234.	1.62389
$205$	−588987.	−0.978862
$206$	865332.	1.42074
$207$	−278367.	−0.451535
$208$	−607053.	−0.972900
$209$	729488.	1.15519
$210$	507751.	0.794516
$211$	455557.	0.704429	0.352214	−	0.935919i	$-0.385429\pi$
$211$	455557.	0.704429	0.352214	+	0.935919i	$0.385429\pi$
$212$	−482404.	−0.737175
$213$	298436.	0.450715
$214$	−1.55990e6	−2.32843
$215$	1.07733e6	1.58947
$216$	−1.14844e6	−1.67484
$217$	474765.	0.684430
$218$	−857199.	−1.22163
$219$	−89569.7	−0.126197
$220$	2.79795e6	3.89747
$221$	1.07815e6	1.48490
$222$	441050.	0.600627
$223$	129005.	0.173718	0.0868589	−	0.996221i	$-0.472317\pi$
$223$	129005.	0.173718	0.0868589	+	0.996221i	$0.472317\pi$
$224$	−106343.	−0.141608
$225$	−212794.	−0.280223
$226$	−475960.	−0.619868
$227$	−1.04042e6	−1.34012	−0.670059	−	0.742308i	$-0.733731\pi$
$227$	−1.04042e6	−1.34012	−0.670059	+	0.742308i	$0.733731\pi$
$228$	829676.	1.05699
$229$	−823514.	−1.03773	−0.518863	−	0.854858i	$-0.673644\pi$
$229$	−823514.	−1.03773	−0.518863	+	0.854858i	$0.673644\pi$
$230$	1.88149e6	2.34522
$231$	−464238.	−0.572414
$232$	1.60894e6	1.96254
$233$	1.16947e6	1.41123	0.705615	−	0.708596i	$-0.250671\pi$
$233$	1.16947e6	1.41123	0.705615	+	0.708596i	$0.250671\pi$
$234$	−801422.	−0.956801
$235$	63109.3	0.0745459
$236$	1.51241e6	1.76762
$237$	−287183.	−0.332115
$238$	−794584.	−0.909279
$239$	−1.57889e6	−1.78796	−0.893981	−	0.448105i	$-0.852099\pi$
$239$	−1.57889e6	−1.78796	−0.893981	+	0.448105i	$0.852099\pi$
$240$	641296.	0.718671
$241$	506324.	0.561546	0.280773	−	0.959774i	$-0.409409\pi$
$241$	506324.	0.561546	0.280773	+	0.959774i	$0.409409\pi$
$242$	−2.34478e6	−2.57374
$243$	−717061.	−0.779006
$244$	1.05184e6	1.13103
$245$	936958.	0.997252
$246$	933377.	0.983376
$247$	926732.	0.966522
$248$	2.15864e6	2.22870
$249$	184495.	0.188576
$250$	−734429.	−0.743190
$251$	−1.25729e6	−1.25966	−0.629828	−	0.776735i	$-0.716875\pi$
$251$	−1.25729e6	−1.25966	−0.629828	+	0.776735i	$0.716875\pi$
$252$	387571.	0.384459
$253$	−1.72025e6	−1.68963
$254$	2.48092e6	2.41284
$255$	−1.13897e6	−1.09688
$256$	−1.95263e6	−1.86218
$257$	500248.	0.472446	0.236223	−	0.971699i	$-0.424090\pi$
$257$	500248.	0.472446	0.236223	+	0.971699i	$0.424090\pi$
$258$	−1.70726e6	−1.59680
$259$	−238245.	−0.220686
$260$	3.55448e6	3.26094
$261$	590037.	0.536140
$262$	−695858.	−0.626279
$263$	−1.03674e6	−0.924235	−0.462117	−	0.886819i	$-0.652910\pi$
$263$	−1.03674e6	−0.924235	−0.462117	+	0.886819i	$0.652910\pi$
$264$	−2.11078e6	−1.86394
$265$	569231.	0.497936
$266$	−682991.	−0.591849
$267$	1.58784e6	1.36310
$268$	−1.61943e6	−1.37729
$269$	1.47768e6	1.24509	0.622543	−	0.782585i	$-0.286099\pi$
$269$	1.47768e6	1.24509	0.622543	+	0.782585i	$0.286099\pi$
$270$	2.84664e6	2.37642
$271$	−1.73140e6	−1.43210	−0.716052	−	0.698047i	$-0.754053\pi$
$271$	−1.73140e6	−1.43210	−0.716052	+	0.698047i	$0.754053\pi$
$272$	−1.00357e6	−0.822480
$273$	−589762.	−0.478928
$274$	−1.69199e6	−1.36152
$275$	−1.31503e6	−1.04858
$276$	−1.95651e6	−1.54600
$277$	−1.64654e6	−1.28936	−0.644679	−	0.764454i	$-0.723009\pi$
$277$	−1.64654e6	−1.28936	−0.644679	+	0.764454i	$0.723009\pi$
$278$	−2.81036e6	−2.18098
$279$	791628.	0.608850
$280$	−1.24706e6	−0.950591
$281$	1.45921e6	1.10243	0.551217	−	0.834362i	$-0.314164\pi$
$281$	1.45921e6	1.10243	0.551217	+	0.834362i	$0.314164\pi$
$282$	−100010.	−0.0748897
$283$	53645.3	0.0398168	0.0199084	−	0.999802i	$-0.493663\pi$
$283$	53645.3	0.0398168	0.0199084	+	0.999802i	$0.493663\pi$
$284$	−1.53970e6	−1.13277
$285$	−979008.	−0.713961
$286$	−4.95264e6	−3.58032
$287$	−504189.	−0.361317
$288$	−177317.	−0.125971
$289$	362520.	0.255322
$290$	−3.98809e6	−2.78465
$291$	1.20402e6	0.833492
$292$	462112.	0.317168
$293$	−526746.	−0.358453	−0.179226	−	0.983808i	$-0.557359\pi$
$293$	−526746.	−0.358453	−0.179226	+	0.983808i	$0.557359\pi$
$294$	−1.48481e6	−1.00185
$295$	−1.78463e6	−1.19397
$296$	−1.08324e6	−0.718615
$297$	−2.60269e6	−1.71211
$298$	−477875.	−0.311727
$299$	−2.18539e6	−1.41368
$300$	−1.49563e6	−0.959450
$301$	922221.	0.586704
$302$	−2.48260e6	−1.56635
$303$	−778244.	−0.486978
$304$	−862627.	−0.535352
$305$	−1.24116e6	−0.763971
$306$	−1.32490e6	−0.808870
$307$	1.54132e6	0.933352	0.466676	−	0.884428i	$-0.345451\pi$
$307$	1.54132e6	0.933352	0.466676	+	0.884428i	$0.345451\pi$
$308$	2.39512e6	1.43863
$309$	1.06180e6	0.632623
$310$	−5.35065e6	−3.16229
$311$	807495.	0.473412	0.236706	−	0.971581i	$-0.423932\pi$
$311$	807495.	0.473412	0.236706	+	0.971581i	$0.423932\pi$
$312$	−2.68151e6	−1.55953
$313$	−124016.	−0.0715513	−0.0357756	−	0.999360i	$-0.511390\pi$
$313$	−124016.	−0.0715513	−0.0357756	+	0.999360i	$0.511390\pi$
$314$	1.11106e6	0.635938
$315$	−457329.	−0.259689
$316$	1.48165e6	0.834695
$317$	−2.45925e6	−1.37453	−0.687266	−	0.726406i	$-0.741189\pi$
$317$	−2.45925e6	−1.37453	−0.687266	+	0.726406i	$0.741189\pi$
$318$	−902069.	−0.500232
$319$	3.64632e6	2.00622
$320$	2.93204e6	1.60064
$321$	−1.91406e6	−1.03680
$322$	1.61061e6	0.865665
$323$	1.53206e6	0.817088
$324$	−1.43352e6	−0.758648
$325$	−1.67060e6	−0.877330
$326$	4.60020e6	2.39736
$327$	−1.05182e6	−0.543964
$328$	−2.29242e6	−1.17655
$329$	54023.2	0.0275163
$330$	5.23201e6	2.64474
$331$	−1.03170e6	−0.517587	−0.258793	−	0.965933i	$-0.583325\pi$
$331$	−1.03170e6	−0.517587	−0.258793	+	0.965933i	$0.583325\pi$
$332$	−951854.	−0.473942
$333$	−397252.	−0.196316
$334$	−5.94124e6	−2.91414
$335$	1.91091e6	0.930313
$336$	548966.	0.265276
$337$	−552823.	−0.265162	−0.132581	−	0.991172i	$-0.542326\pi$
$337$	−552823.	−0.265162	−0.132581	+	0.991172i	$0.542326\pi$
$338$	−2.70972e6	−1.29013
$339$	−584021.	−0.276013
$340$	5.87620e6	2.75676
$341$	4.89211e6	2.27830
$342$	−1.13883e6	−0.526493
$343$	1.83891e6	0.843965
$344$	4.19312e6	1.91047
$345$	2.30866e6	1.04427
$346$	−4.02331e6	−1.80673
$347$	387674.	0.172839	0.0864196	−	0.996259i	$-0.472457\pi$
$347$	387674.	0.172839	0.0864196	+	0.996259i	$0.472457\pi$
$348$	4.14711e6	1.83568
$349$	1.17543e6	0.516573	0.258286	−	0.966068i	$-0.416842\pi$
$349$	1.17543e6	0.516573	0.258286	+	0.966068i	$0.416842\pi$
$350$	1.23121e6	0.537232
$351$	−3.30643e6	−1.43249
$352$	−1.09579e6	−0.471378
$353$	−3.95708e6	−1.69020	−0.845100	−	0.534608i	$-0.820459\pi$
$353$	−3.95708e6	−1.69020	−0.845100	+	0.534608i	$0.820459\pi$
$354$	2.82813e6	1.19947
$355$	1.81683e6	0.765146
$356$	−8.19203e6	−3.42584
$357$	−974985.	−0.404881
$358$	−837976.	−0.345561
$359$	−3.54016e6	−1.44973	−0.724865	−	0.688891i	$-0.758098\pi$
$359$	−3.54016e6	−1.44973	−0.724865	+	0.688891i	$0.758098\pi$
$360$	−2.07937e6	−0.845619
$361$	−1.15920e6	−0.468158
$362$	−1.67119e6	−0.670277
$363$	−2.87714e6	−1.14603
$364$	3.04273e6	1.20368
$365$	−545287.	−0.214236
$366$	1.96688e6	0.767494
$367$	−1.51119e6	−0.585672	−0.292836	−	0.956163i	$-0.594599\pi$
$367$	−1.51119e6	−0.585672	−0.292836	+	0.956163i	$0.594599\pi$
$368$	2.03422e6	0.783029
$369$	−840690.	−0.321418
$370$	2.68504e6	1.01964
$371$	487277.	0.183798
$372$	5.56400e6	2.08463
$373$	−3.61282e6	−1.34454	−0.672270	−	0.740306i	$-0.734681\pi$
$373$	−3.61282e6	−1.34454	−0.672270	+	0.740306i	$0.734681\pi$
$374$	−8.18762e6	−3.02676
$375$	−901173.	−0.330925
$376$	245631.	0.0896010
$377$	4.63224e6	1.67856
$378$	2.43680e6	0.877183
$379$	3.25399e6	1.16364	0.581819	−	0.813319i	$-0.302341\pi$
$379$	3.25399e6	1.16364	0.581819	+	0.813319i	$0.302341\pi$
$380$	5.05094e6	1.79438
$381$	3.04419e6	1.07438
$382$	−1.23801e6	−0.434074
$383$	−4.33030e6	−1.50842	−0.754208	−	0.656636i	$-0.771979\pi$
$383$	−4.33030e6	−1.50842	−0.754208	+	0.656636i	$0.771979\pi$
$384$	−3.99346e6	−1.38204
$385$	−2.82621e6	−0.971746
$386$	−2.41525e6	−0.825076
$387$	1.53772e6	0.521915
$388$	−6.21184e6	−2.09479
$389$	5.09732e6	1.70792	0.853961	−	0.520337i	$-0.174193\pi$
$389$	5.09732e6	1.70792	0.853961	+	0.520337i	$0.174193\pi$
$390$	6.64668e6	2.21281
$391$	−3.61285e6	−1.19511
$392$	3.64678e6	1.19865
$393$	−853845.	−0.278867
$394$	850473.	0.276007
$395$	−1.74833e6	−0.563807
$396$	3.99364e6	1.27977
$397$	1.46835e6	0.467579	0.233789	−	0.972287i	$-0.424887\pi$
$397$	1.46835e6	0.467579	0.233789	+	0.972287i	$0.424887\pi$
$398$	1.11466e6	0.352724
$399$	−838057.	−0.263537
$400$	1.55503e6	0.485948
$401$	5.49186e6	1.70553	0.852764	−	0.522297i	$-0.174925\pi$
$401$	5.49186e6	1.70553	0.852764	+	0.522297i	$0.174925\pi$
$402$	−3.02825e6	−0.934603
$403$	6.21488e6	1.90621
$404$	4.01515e6	1.22391
$405$	1.69153e6	0.512440
$406$	−3.41391e6	−1.02787
$407$	−2.45494e6	−0.734607
$408$	−4.43302e6	−1.31841
$409$	−2.00518e6	−0.592714	−0.296357	−	0.955077i	$-0.595772\pi$
$409$	−2.00518e6	−0.592714	−0.296357	+	0.955077i	$0.595772\pi$
$410$	5.68226e6	1.66940
$411$	−2.07614e6	−0.606251
$412$	−5.47807e6	−1.58995
$413$	−1.52769e6	−0.440717
$414$	2.68554e6	0.770072
$415$	1.12318e6	0.320131
$416$	−1.39207e6	−0.394393
$417$	−3.44843e6	−0.971138
$418$	−7.03774e6	−1.97012
$419$	466190.	0.129726	0.0648631	−	0.997894i	$-0.479339\pi$
$419$	466190.	0.129726	0.0648631	+	0.997894i	$0.479339\pi$
$420$	−3.21436e6	−0.889143
$421$	169326.	0.0465607	0.0232803	−	0.999729i	$-0.492589\pi$
$421$	169326.	0.0465607	0.0232803	+	0.999729i	$0.492589\pi$
$422$	−4.39499e6	−1.20137
$423$	90078.9	0.0244778
$424$	2.21553e6	0.598498
$425$	−2.76180e6	−0.741686
$426$	−2.87916e6	−0.768674
$427$	−1.06246e6	−0.281996
$428$	9.87510e6	2.60575
$429$	−6.07708e6	−1.59423
$430$	−1.03935e7	−2.71076
$431$	−3.64961e6	−0.946353	−0.473177	−	0.880968i	$-0.656893\pi$
$431$	−3.64961e6	−0.946353	−0.473177	+	0.880968i	$0.656893\pi$
$432$	3.07771e6	0.793447
$433$	−3.84768e6	−0.986233	−0.493116	−	0.869963i	$-0.664142\pi$
$433$	−3.84768e6	−0.986233	−0.493116	+	0.869963i	$0.664142\pi$
$434$	−4.58030e6	−1.16726
$435$	−4.89354e6	−1.23994
$436$	5.42658e6	1.36713
$437$	−3.10546e6	−0.777896
$438$	864124.	0.215224
$439$	6.54292e6	1.62036	0.810178	−	0.586184i	$-0.199370\pi$
$439$	6.54292e6	1.62036	0.810178	+	0.586184i	$0.199370\pi$
$440$	−1.28501e7	−3.16428
$441$	1.33736e6	0.327456
$442$	−1.04015e7	−2.53243
$443$	1.61192e6	0.390242	0.195121	−	0.980779i	$-0.437490\pi$
$443$	1.61192e6	0.390242	0.195121	+	0.980779i	$0.437490\pi$
$444$	−2.79211e6	−0.672163
$445$	9.66651e6	2.31403
$446$	−1.24458e6	−0.296268
$447$	−586371.	−0.138805
$448$	2.50990e6	0.590829
$449$	−5.22174e6	−1.22236	−0.611181	−	0.791491i	$-0.709305\pi$
$449$	−5.22174e6	−1.22236	−0.611181	+	0.791491i	$0.709305\pi$
$450$	2.05293e6	0.477907
$451$	−5.19530e6	−1.20273
$452$	3.01311e6	0.693695
$453$	−3.04625e6	−0.697462
$454$	1.00374e7	2.28551
$455$	−3.59038e6	−0.813041
$456$	−3.81044e6	−0.858150
$457$	−1.70497e6	−0.381880	−0.190940	−	0.981602i	$-0.561154\pi$
$457$	−1.70497e6	−0.381880	−0.190940	+	0.981602i	$0.561154\pi$
$458$	7.94486e6	1.76979
$459$	−5.46613e6	−1.21101
$460$	−1.19110e7	−2.62453
$461$	6.46632e6	1.41711	0.708557	−	0.705653i	$-0.249346\pi$
$461$	6.46632e6	1.41711	0.708557	+	0.705653i	$0.249346\pi$
$462$	4.47874e6	0.976227
$463$	2.77710e6	0.602058	0.301029	−	0.953615i	$-0.402670\pi$
$463$	2.77710e6	0.602058	0.301029	+	0.953615i	$0.402670\pi$
$464$	−4.31181e6	−0.929747
$465$	−6.56545e6	−1.40810
$466$	−1.12824e7	−2.40679
$467$	−6.15589e6	−1.30617	−0.653083	−	0.757286i	$-0.726525\pi$
$467$	−6.15589e6	−1.30617	−0.653083	+	0.757286i	$0.726525\pi$
$468$	5.07348e6	1.07076
$469$	1.63579e6	0.343397
$470$	−608848.	−0.127135
$471$	1.36332e6	0.283168
$472$	−6.94603e6	−1.43510
$473$	9.50283e6	1.95299
$474$	2.77061e6	0.566407
$475$	−2.37393e6	−0.482763
$476$	5.03018e6	1.01758
$477$	812490.	0.163502
$478$	1.52324e7	3.04929
$479$	6.05256e6	1.20531	0.602657	−	0.798000i	$-0.294109\pi$
$479$	6.05256e6	1.20531	0.602657	+	0.798000i	$0.294109\pi$
$480$	1.47060e6	0.291334
$481$	−3.11873e6	−0.614632
$482$	−4.88476e6	−0.957692
$483$	1.97628e6	0.385461
$484$	1.48439e7	2.88027
$485$	7.32990e6	1.41496
$486$	6.91786e6	1.32856
$487$	−5.45532e6	−1.04231	−0.521156	−	0.853461i	$-0.674499\pi$
$487$	−5.45532e6	−1.04231	−0.521156	+	0.853461i	$0.674499\pi$
$488$	−4.83076e6	−0.918260
$489$	5.64463e6	1.06749
$490$	−9.03931e6	−1.70077
$491$	−2.00571e6	−0.375462	−0.187731	−	0.982221i	$-0.560113\pi$
$491$	−2.00571e6	−0.375462	−0.187731	+	0.982221i	$0.560113\pi$
$492$	−5.90883e6	−1.10050
$493$	7.65794e6	1.41904
$494$	−8.94066e6	−1.64836
$495$	−4.71245e6	−0.864438
$496$	−5.78497e6	−1.05584
$497$	1.55526e6	0.282430
$498$	−1.77992e6	−0.321607
$499$	3.54270e6	0.636917	0.318459	−	0.947937i	$-0.396835\pi$
$499$	3.54270e6	0.636917	0.318459	+	0.947937i	$0.396835\pi$
$500$	4.64937e6	0.831705
$501$	−7.29013e6	−1.29760
$502$	1.21297e7	2.14829
$503$	−3.79143e6	−0.668164	−0.334082	−	0.942544i	$-0.608426\pi$
$503$	−3.79143e6	−0.668164	−0.334082	+	0.942544i	$0.608426\pi$
$504$	−1.77999e6	−0.312135
$505$	−4.73783e6	−0.826706
$506$	1.65962e7	2.88158
$507$	−3.32493e6	−0.574464
$508$	−1.57057e7	−2.70022
$509$	−100544.	−0.0172013	−0.00860067	−	0.999963i	$-0.502738\pi$
$509$	−100544.	−0.0172013	−0.00860067	+	0.999963i	$0.502738\pi$
$510$	1.09882e7	1.87068
$511$	−466780.	−0.0790788
$512$	8.04299e6	1.35595
$513$	−4.69846e6	−0.788246
$514$	−4.82615e6	−0.805736
$515$	6.46406e6	1.07396
$516$	1.08080e7	1.78698
$517$	556671.	0.0915950
$518$	2.29847e6	0.376369
$519$	−4.93675e6	−0.804494
$520$	−1.63246e7	−2.64749
$521$	6.14234e6	0.991378	0.495689	−	0.868500i	$-0.334916\pi$
$521$	6.14234e6	0.991378	0.495689	+	0.868500i	$0.334916\pi$
$522$	−5.69239e6	−0.914363
$523$	6.81346e6	1.08921	0.544607	−	0.838691i	$-0.316679\pi$
$523$	6.81346e6	1.08921	0.544607	+	0.838691i	$0.316679\pi$
$524$	4.40519e6	0.700869
$525$	1.51074e6	0.239217
$526$	1.00020e7	1.57624
$527$	1.02743e7	1.61149
$528$	5.65670e6	0.883036
$529$	886837.	0.137786
$530$	−5.49166e6	−0.849208
$531$	−2.54729e6	−0.392050
$532$	4.32374e6	0.662339
$533$	−6.60005e6	−1.00630
$534$	−1.53187e7	−2.32470
$535$	−1.16525e7	−1.76009
$536$	7.43755e6	1.11820
$537$	−1.02823e6	−0.153870
$538$	−1.42559e7	−2.12344
$539$	8.26466e6	1.22533
$540$	−1.80209e7	−2.65945
$541$	1.10773e6	0.162719	0.0813597	−	0.996685i	$-0.474074\pi$
$541$	1.10773e6	0.162719	0.0813597	+	0.996685i	$0.474074\pi$
$542$	1.67037e7	2.44239
$543$	−2.05061e6	−0.298459
$544$	−2.30135e6	−0.333416
$545$	−6.40330e6	−0.923448
$546$	5.68974e6	0.816790
$547$	−1.05662e7	−1.50990	−0.754951	−	0.655781i	$-0.772340\pi$
$547$	−1.05662e7	−1.50990	−0.754951	+	0.655781i	$0.772340\pi$
$548$	1.07113e7	1.52367
$549$	−1.77156e6	−0.250856
$550$	1.26867e7	1.78831
$551$	6.58245e6	0.923653
$552$	8.98566e6	1.25517
$553$	−1.49662e6	−0.208112
$554$	1.58850e7	2.19894
$555$	3.29465e6	0.454022
$556$	1.77913e7	2.44073
$557$	9.00702e6	1.23011	0.615054	−	0.788485i	$-0.289134\pi$
$557$	9.00702e6	1.23011	0.615054	+	0.788485i	$0.289134\pi$
$558$	−7.63724e6	−1.03837
$559$	1.20723e7	1.63403
$560$	3.34202e6	0.450339
$561$	−1.00465e7	−1.34775
$562$	−1.40778e7	−1.88015
$563$	6.24863e6	0.830833	0.415417	−	0.909631i	$-0.363636\pi$
$563$	6.24863e6	0.830833	0.415417	+	0.909631i	$0.363636\pi$
$564$	633124.	0.0838091
$565$	−3.55543e6	−0.468567
$566$	−517544.	−0.0679057
$567$	1.44800e6	0.189152
$568$	7.07138e6	0.919673
$569$	−3.45544e6	−0.447428	−0.223714	−	0.974655i	$-0.571818\pi$
$569$	−3.45544e6	−0.447428	−0.223714	+	0.974655i	$0.571818\pi$
$570$	9.44499e6	1.21763
$571$	9.15225e6	1.17473	0.587365	−	0.809322i	$-0.300165\pi$
$571$	9.15225e6	1.17473	0.587365	+	0.809322i	$0.300165\pi$
$572$	3.13531e7	4.00674
$573$	−1.51908e6	−0.193283
$574$	4.86417e6	0.616210
$575$	5.59812e6	0.706110
$576$	4.18504e6	0.525586
$577$	−4.68496e6	−0.585823	−0.292912	−	0.956140i	$-0.594624\pi$
$577$	−4.68496e6	−0.585823	−0.292912	+	0.956140i	$0.594624\pi$
$578$	−3.49742e6	−0.435440
$579$	−2.96361e6	−0.367387
$580$	2.52470e7	3.11630
$581$	961469.	0.118167
$582$	−1.16158e7	−1.42148
$583$	5.02104e6	0.611818
$584$	−2.12234e6	−0.257503
$585$	−5.98664e6	−0.723259
$586$	5.08178e6	0.611325
$587$	1.44477e7	1.73063	0.865313	−	0.501231i	$-0.167119\pi$
$587$	1.44477e7	1.73063	0.865313	+	0.501231i	$0.167119\pi$
$588$	9.39973e6	1.12117
$589$	8.83139e6	1.04892
$590$	1.72172e7	2.03626
$591$	1.04356e6	0.122899
$592$	2.90300e6	0.340441
$593$	−1.17003e7	−1.36634	−0.683171	−	0.730258i	$-0.739400\pi$
$593$	−1.17003e7	−1.36634	−0.683171	+	0.730258i	$0.739400\pi$
$594$	2.51095e7	2.91992
$595$	−5.93556e6	−0.687336
$596$	3.02523e6	0.348853
$597$	1.36773e6	0.157060
$598$	2.10836e7	2.41097
$599$	−4.74765e6	−0.540645	−0.270322	−	0.962770i	$-0.587130\pi$
$599$	−4.74765e6	−0.540645	−0.270322	+	0.962770i	$0.587130\pi$
$600$	6.86898e6	0.778958
$601$	−2.96582e6	−0.334933	−0.167467	−	0.985878i	$-0.553559\pi$
$601$	−2.96582e6	−0.334933	−0.167467	+	0.985878i	$0.553559\pi$
$602$	−8.89713e6	−1.00060
$603$	2.72754e6	0.305476
$604$	1.57164e7	1.75291
$605$	−1.75156e7	−1.94552
$606$	7.50811e6	0.830518
$607$	−4.42946e6	−0.487954	−0.243977	−	0.969781i	$-0.578452\pi$
$607$	−4.42946e6	−0.487954	−0.243977	+	0.969781i	$0.578452\pi$
$608$	−1.97815e6	−0.217020
$609$	−4.18900e6	−0.457685
$610$	1.19741e7	1.30292
$611$	707188.	0.0766358
$612$	8.38738e6	0.905207
$613$	−1.52129e7	−1.63516	−0.817582	−	0.575812i	$-0.804686\pi$
$613$	−1.52129e7	−1.63516	−0.817582	+	0.575812i	$0.804686\pi$
$614$	−1.48699e7	−1.59179
$615$	6.97235e6	0.743347
$616$	−1.10000e7	−1.16800
$617$	6.77463e6	0.716428	0.358214	−	0.933640i	$-0.383386\pi$
$617$	6.77463e6	0.716428	0.358214	+	0.933640i	$0.383386\pi$
$618$	−1.02437e7	−1.07891
$619$	−2.59611e6	−0.272331	−0.136165	−	0.990686i	$-0.543478\pi$
$619$	−2.59611e6	−0.272331	−0.136165	+	0.990686i	$0.543478\pi$
$620$	3.38728e7	3.53893
$621$	1.10797e7	1.15292
$622$	−7.79032e6	−0.807382
$623$	8.27479e6	0.854155
$624$	7.18621e6	0.738820
$625$	−1.19508e7	−1.22376
$626$	1.19645e6	0.122027
$627$	−8.63558e6	−0.877248
$628$	−7.03369e6	−0.711678
$629$	−5.15583e6	−0.519603
$630$	4.41209e6	0.442887
$631$	1.49877e7	1.49852	0.749260	−	0.662276i	$-0.230410\pi$
$631$	1.49877e7	1.49852	0.749260	+	0.662276i	$0.230410\pi$
$632$	−6.80476e6	−0.677673
$633$	−5.39283e6	−0.534943
$634$	2.37257e7	2.34420
$635$	1.85326e7	1.82390
$636$	5.71063e6	0.559811
$637$	1.04993e7	1.02521
$638$	−3.51779e7	−3.42151
$639$	2.59325e6	0.251242
$640$	−2.43116e7	−2.34619
$641$	3.51577e6	0.337968	0.168984	−	0.985619i	$-0.445951\pi$
$641$	3.51577e6	0.337968	0.168984	+	0.985619i	$0.445951\pi$
$642$	1.84659e7	1.76821
$643$	−1.27015e6	−0.121151	−0.0605754	−	0.998164i	$-0.519294\pi$
$643$	−1.27015e6	−0.121151	−0.0605754	+	0.998164i	$0.519294\pi$
$644$	−1.01961e7	−0.968767
$645$	−1.27533e7	−1.20704
$646$	−1.47805e7	−1.39351
$647$	−4.71069e6	−0.442409	−0.221204	−	0.975227i	$-0.570999\pi$
$647$	−4.71069e6	−0.442409	−0.221204	+	0.975227i	$0.570999\pi$
$648$	6.58370e6	0.615932
$649$	−1.57417e7	−1.46704
$650$	1.61171e7	1.49625
$651$	−5.62020e6	−0.519756
$652$	−2.91220e7	−2.68289
$653$	1.79642e7	1.64863	0.824317	−	0.566128i	$-0.191559\pi$
$653$	1.79642e7	1.64863	0.824317	+	0.566128i	$0.191559\pi$
$654$	1.01474e7	0.927707
$655$	−5.19808e6	−0.473413
$656$	6.14350e6	0.557387
$657$	−778314.	−0.0703463
$658$	−521190.	−0.0469279
$659$	1.27459e6	0.114329	0.0571646	−	0.998365i	$-0.481794\pi$
$659$	1.27459e6	0.114329	0.0571646	+	0.998365i	$0.481794\pi$
$660$	−3.31217e7	−2.95974
$661$	7.94828e6	0.707570	0.353785	−	0.935327i	$-0.384894\pi$
$661$	7.94828e6	0.707570	0.353785	+	0.935327i	$0.384894\pi$
$662$	9.95333e6	0.882721
$663$	−1.27630e7	−1.12763
$664$	4.37157e6	0.384784
$665$	−5.10196e6	−0.447387
$666$	3.83249e6	0.334808
$667$	−1.55225e7	−1.35098
$668$	3.76115e7	3.26122
$669$	−1.52714e6	−0.131921
$670$	−1.84356e7	−1.58661
$671$	−1.09479e7	−0.938696
$672$	1.25887e6	0.107537
$673$	−2.15067e7	−1.83036	−0.915179	−	0.403047i	$-0.867951\pi$
$673$	−2.15067e7	−1.83036	−0.915179	+	0.403047i	$0.867951\pi$
$674$	5.33337e6	0.452222
$675$	8.46978e6	0.715505
$676$	1.71541e7	1.44378
$677$	−5.36879e6	−0.450199	−0.225100	−	0.974336i	$-0.572271\pi$
$677$	−5.36879e6	−0.450199	−0.225100	+	0.974336i	$0.572271\pi$
$678$	5.63435e6	0.470728
$679$	6.27459e6	0.522289
$680$	−2.69876e7	−2.23816
$681$	1.23163e7	1.01769
$682$	−4.71967e7	−3.88553
$683$	−2.29510e6	−0.188257	−0.0941283	−	0.995560i	$-0.530006\pi$
$683$	−2.29510e6	−0.188257	−0.0941283	+	0.995560i	$0.530006\pi$
$684$	7.20945e6	0.589199
$685$	−1.26392e7	−1.02919
$686$	−1.77409e7	−1.43934
$687$	9.74865e6	0.788048
$688$	−1.12372e7	−0.905080
$689$	6.37867e6	0.511896
$690$	−2.22729e7	−1.78096
$691$	−3.36103e6	−0.267780	−0.133890	−	0.990996i	$-0.542747\pi$
$691$	−3.36103e6	−0.267780	−0.133890	+	0.990996i	$0.542747\pi$
$692$	2.54699e7	2.02191
$693$	−4.03398e6	−0.319081
$694$	−3.74008e6	−0.294770
$695$	−2.09935e7	−1.64863
$696$	−1.90464e7	−1.49035
$697$	−1.09111e7	−0.850720
$698$	−1.13399e7	−0.880992
$699$	−1.38440e7	−1.07169
$700$	−7.79429e6	−0.601217
$701$	−2.31418e7	−1.77870	−0.889348	−	0.457231i	$-0.848841\pi$
$701$	−2.31418e7	−1.77870	−0.889348	+	0.457231i	$0.848841\pi$
$702$	3.18988e7	2.44304
$703$	−4.43174e6	−0.338210
$704$	2.58628e7	1.96672
$705$	−747079.	−0.0566101
$706$	3.81760e7	2.88256
$707$	−4.05571e6	−0.305153
$708$	−1.79037e7	−1.34233
$709$	1.52355e7	1.13826	0.569130	−	0.822248i	$-0.307280\pi$
$709$	1.52355e7	1.13826	0.569130	+	0.822248i	$0.307280\pi$
$710$	−1.75279e7	−1.30492
$711$	−2.49548e6	−0.185131
$712$	3.76235e7	2.78137
$713$	−2.08259e7	−1.53419
$714$	9.40618e6	0.690506
$715$	−3.69963e7	−2.70641
$716$	5.30489e6	0.386717
$717$	1.86907e7	1.35778
$718$	3.41538e7	2.47245
$719$	−1.28037e7	−0.923659	−0.461830	−	0.886969i	$-0.652807\pi$
$719$	−1.28037e7	−0.923659	−0.461830	+	0.886969i	$0.652807\pi$
$720$	5.57253e6	0.400609
$721$	5.53340e6	0.396419
$722$	1.11834e7	0.798422
$723$	−5.99379e6	−0.426438
$724$	1.05796e7	0.750107
$725$	−1.18660e7	−0.838416
$726$	2.77572e7	1.95449
$727$	1.41470e7	0.992720	0.496360	−	0.868117i	$-0.334670\pi$
$727$	1.41470e7	0.992720	0.496360	+	0.868117i	$0.334670\pi$
$728$	−1.39743e7	−0.977241
$729$	1.41921e7	0.989071
$730$	5.26066e6	0.365370
$731$	1.99577e7	1.38139
$732$	−1.24515e7	−0.858903
$733$	−1.05634e7	−0.726179	−0.363089	−	0.931754i	$-0.618278\pi$
$733$	−1.05634e7	−0.726179	−0.363089	+	0.931754i	$0.618278\pi$
$734$	1.45792e7	0.998836
$735$	−1.10916e7	−0.757312
$736$	4.66481e6	0.317423
$737$	1.68557e7	1.14308
$738$	8.11056e6	0.548163
$739$	1.71004e7	1.15185	0.575925	−	0.817502i	$-0.304642\pi$
$739$	1.71004e7	1.15185	0.575925	+	0.817502i	$0.304642\pi$
$740$	−1.69979e7	−1.14108
$741$	−1.09705e7	−0.733977
$742$	−4.70101e6	−0.313459
$743$	−1.18162e7	−0.785243	−0.392622	−	0.919700i	$-0.628432\pi$
$743$	−1.18162e7	−0.785243	−0.392622	+	0.919700i	$0.628432\pi$
$744$	−2.55537e7	−1.69247
$745$	−3.56974e6	−0.235638
$746$	3.48547e7	2.29305
$747$	1.60316e6	0.105118
$748$	5.18325e7	3.38725
$749$	−9.97486e6	−0.649684
$750$	8.69407e6	0.564378
$751$	−1.17091e7	−0.757569	−0.378784	−	0.925485i	$-0.623658\pi$
$751$	−1.17091e7	−0.757569	−0.378784	+	0.925485i	$0.623658\pi$
$752$	−658269.	−0.0424482
$753$	1.48837e7	0.956582
$754$	−4.46896e7	−2.86271
$755$	−1.85451e7	−1.18403
$756$	−1.54264e7	−0.981656
$757$	516963.	0.0327884	0.0163942	−	0.999866i	$-0.494781\pi$
$757$	516963.	0.0327884	0.0163942	+	0.999866i	$0.494781\pi$
$758$	−3.13929e7	−1.98453
$759$	2.03641e7	1.28310
$760$	−2.31974e7	−1.45682
$761$	−1.30886e7	−0.819279	−0.409640	−	0.912247i	$-0.634346\pi$
$761$	−1.30886e7	−0.819279	−0.409640	+	0.912247i	$0.634346\pi$
$762$	−2.93689e7	−1.83231
$763$	−5.48139e6	−0.340863
$764$	7.83731e6	0.485773
$765$	−9.89702e6	−0.611436
$766$	4.17766e7	2.57254
$767$	−1.99981e7	−1.22744
$768$	2.31150e7	1.41414
$769$	−1.23673e7	−0.754154	−0.377077	−	0.926182i	$-0.623071\pi$
$769$	−1.23673e7	−0.754154	−0.377077	+	0.926182i	$0.623071\pi$
$770$	2.72659e7	1.65727
$771$	−5.92187e6	−0.358775
$772$	1.52900e7	0.923344
$773$	−9.47903e6	−0.570578	−0.285289	−	0.958442i	$-0.592090\pi$
$773$	−9.47903e6	−0.570578	−0.285289	+	0.958442i	$0.592090\pi$
$774$	−1.48352e7	−0.890103
$775$	−1.59201e7	−0.952121
$776$	2.85290e7	1.70072
$777$	2.82031e6	0.167589
$778$	−4.91765e7	−2.91278
$779$	−9.37873e6	−0.553733
$780$	−4.20774e7	−2.47635
$781$	1.60258e7	0.940140
$782$	3.48550e7	2.03821
$783$	−2.34851e7	−1.36895
$784$	−9.77305e6	−0.567858
$785$	8.29967e6	0.480714
$786$	8.23748e6	0.475596
$787$	−2.37596e7	−1.36742	−0.683709	−	0.729754i	$-0.739634\pi$
$787$	−2.37596e7	−1.36742	−0.683709	+	0.729754i	$0.739634\pi$
$788$	−5.38400e6	−0.308880
$789$	1.22728e7	0.701863
$790$	1.68670e7	0.961548
$791$	−3.04355e6	−0.172957
$792$	−1.83416e7	−1.03902
$793$	−1.39081e7	−0.785389
$794$	−1.41660e7	−0.797434
$795$	−6.73848e6	−0.378133
$796$	−7.05645e6	−0.394733
$797$	−1.95843e7	−1.09210	−0.546051	−	0.837752i	$-0.683870\pi$
$797$	−1.95843e7	−1.09210	−0.546051	+	0.837752i	$0.683870\pi$
$798$	8.08516e6	0.449450
$799$	1.16911e6	0.0647871
$800$	3.56596e6	0.196993
$801$	1.37975e7	0.759833
$802$	−5.29828e7	−2.90870
$803$	−4.80983e6	−0.263233
$804$	1.91706e7	1.04591
$805$	1.20313e7	0.654368
$806$	−5.99581e7	−3.25095
$807$	−1.74926e7	−0.945518
$808$	−1.84403e7	−0.993666
$809$	−1.03121e6	−0.0553959	−0.0276979	−	0.999616i	$-0.508818\pi$
$809$	−1.03121e6	−0.0553959	−0.0276979	+	0.999616i	$0.508818\pi$
$810$	−1.63191e7	−0.873944
$811$	−8.49374e6	−0.453468	−0.226734	−	0.973957i	$-0.572805\pi$
$811$	−8.49374e6	−0.453468	−0.226734	+	0.973957i	$0.572805\pi$
$812$	2.16121e7	1.15029
$813$	2.04961e7	1.08754
$814$	2.36841e7	1.25284
$815$	3.43636e7	1.81220
$816$	1.18801e7	0.624591
$817$	1.71548e7	0.899147
$818$	1.93450e7	1.01085
$819$	−5.12473e6	−0.266969
$820$	−3.59721e7	−1.86823
$821$	1.10131e7	0.570234	0.285117	−	0.958493i	$-0.407967\pi$
$821$	1.10131e7	0.570234	0.285117	+	0.958493i	$0.407967\pi$
$822$	2.00296e7	1.03393
$823$	−2.44593e6	−0.125876	−0.0629382	−	0.998017i	$-0.520047\pi$
$823$	−2.44593e6	−0.125876	−0.0629382	+	0.998017i	$0.520047\pi$
$824$	2.51591e7	1.29085
$825$	1.55671e7	0.796294
$826$	1.47384e7	0.751623
$827$	3.72044e6	0.189161	0.0945804	−	0.995517i	$-0.469849\pi$
$827$	3.72044e6	0.189161	0.0945804	+	0.995517i	$0.469849\pi$
$828$	−1.70011e7	−0.861789
$829$	1.06107e7	0.536237	0.268118	−	0.963386i	$-0.413598\pi$
$829$	1.06107e7	0.536237	0.268118	+	0.963386i	$0.413598\pi$
$830$	−1.08359e7	−0.545969
$831$	1.94915e7	0.979138
$832$	3.28557e7	1.64552
$833$	1.73573e7	0.866702
$834$	3.32687e7	1.65623
$835$	−4.43812e7	−2.20284
$836$	4.45530e7	2.20476
$837$	−3.15089e7	−1.55461
$838$	−4.49757e6	−0.221242
$839$	1.11970e7	0.549156	0.274578	−	0.961565i	$-0.411462\pi$
$839$	1.11970e7	0.549156	0.274578	+	0.961565i	$0.411462\pi$
$840$	1.47626e7	0.721878
$841$	1.23910e7	0.604112
$842$	−1.63358e6	−0.0794071
$843$	−1.72740e7	−0.837188
$844$	2.78229e7	1.34446
$845$	−2.02417e7	−0.975224
$846$	−869037.	−0.0417458
$847$	−1.49938e7	−0.718130
$848$	−5.93743e6	−0.283536
$849$	−635046.	−0.0302368
$850$	2.66445e7	1.26491
$851$	1.04508e7	0.494680
$852$	1.82268e7	0.860224
$853$	2.11418e7	0.994878	0.497439	−	0.867499i	$-0.334274\pi$
$853$	2.11418e7	0.994878	0.497439	+	0.867499i	$0.334274\pi$
$854$	1.02501e7	0.480932
$855$	−8.50707e6	−0.397983
$856$	−4.53533e7	−2.11556
$857$	1.11912e7	0.520502	0.260251	−	0.965541i	$-0.416195\pi$
$857$	1.11912e7	0.520502	0.260251	+	0.965541i	$0.416195\pi$
$858$	5.86287e7	2.71889
$859$	1.52318e7	0.704315	0.352158	−	0.935941i	$-0.385448\pi$
$859$	1.52318e7	0.704315	0.352158	+	0.935941i	$0.385448\pi$
$860$	6.57972e7	3.03362
$861$	5.96852e6	0.274384
$862$	3.52096e7	1.61396
$863$	3.14748e7	1.43859	0.719294	−	0.694706i	$-0.244465\pi$
$863$	3.14748e7	1.43859	0.719294	+	0.694706i	$0.244465\pi$
$864$	7.05771e6	0.321647
$865$	−3.00542e7	−1.36573
$866$	3.71206e7	1.68198
$867$	−4.29147e6	−0.193891
$868$	2.89960e7	1.30629
$869$	−1.54216e7	−0.692754
$870$	4.72105e7	2.11466
$871$	2.14132e7	0.956394
$872$	−2.49226e7	−1.10995
$873$	1.04623e7	0.464614
$874$	2.99599e7	1.32667
$875$	−4.69634e6	−0.207367
$876$	−5.47042e6	−0.240858
$877$	−4.37274e6	−0.191979	−0.0959897	−	0.995382i	$-0.530602\pi$
$877$	−4.37274e6	−0.191979	−0.0959897	+	0.995382i	$0.530602\pi$
$878$	−6.31229e7	−2.76344
$879$	6.23554e6	0.272209
$880$	3.44372e7	1.49907
$881$	2.62741e6	0.114048	0.0570239	−	0.998373i	$-0.481839\pi$
$881$	2.62741e6	0.114048	0.0570239	+	0.998373i	$0.481839\pi$
$882$	−1.29022e7	−0.558462
$883$	4.27948e7	1.84709	0.923547	−	0.383486i	$-0.125276\pi$
$883$	4.27948e7	1.84709	0.923547	+	0.383486i	$0.125276\pi$
$884$	6.58473e7	2.83405
$885$	2.11262e7	0.906699
$886$	−1.55510e7	−0.665540
$887$	−1.38511e7	−0.591119	−0.295560	−	0.955324i	$-0.595506\pi$
$887$	−1.38511e7	−0.591119	−0.295560	+	0.955324i	$0.595506\pi$
$888$	1.28233e7	0.545716
$889$	1.58644e7	0.673238
$890$	−9.32577e7	−3.94648
$891$	1.49206e7	0.629639
$892$	7.87890e6	0.331554
$893$	1.00492e6	0.0421699
$894$	5.65702e6	0.236725
$895$	−6.25971e6	−0.261214
$896$	−2.08113e7	−0.866024
$897$	2.58703e7	1.07355
$898$	5.03768e7	2.08468
$899$	4.41434e7	1.82166
$900$	−1.29963e7	−0.534826
$901$	1.05451e7	0.432752
$902$	5.01217e7	2.05121
$903$	−1.09171e7	−0.445542
$904$	−1.38383e7	−0.563198
$905$	−1.24838e7	−0.506671
$906$	2.93887e7	1.18949
$907$	3.80809e7	1.53705	0.768526	−	0.639819i	$-0.220991\pi$
$907$	3.80809e7	1.53705	0.768526	+	0.639819i	$0.220991\pi$
$908$	−6.35429e7	−2.55772
$909$	−6.76253e6	−0.271456
$910$	3.46383e7	1.38660
$911$	−3.19658e7	−1.27612	−0.638058	−	0.769988i	$-0.720262\pi$
$911$	−3.19658e7	−1.27612	−0.638058	+	0.769988i	$0.720262\pi$
$912$	1.02117e7	0.406546
$913$	9.90725e6	0.393347
$914$	1.64488e7	0.651280
$915$	1.46926e7	0.580159
$916$	−5.02957e7	−1.98058
$917$	−4.44969e6	−0.174746
$918$	5.27345e7	2.06532
$919$	7.10675e6	0.277576	0.138788	−	0.990322i	$-0.455679\pi$
$919$	7.10675e6	0.277576	0.138788	+	0.990322i	$0.455679\pi$
$920$	5.47033e7	2.13081
$921$	−1.82459e7	−0.708787
$922$	−6.23839e7	−2.41683
$923$	2.03590e7	0.786597
$924$	−2.83531e7	−1.09250
$925$	7.98898e6	0.306999
$926$	−2.67921e7	−1.02678
$927$	9.22646e6	0.352643
$928$	−9.88772e6	−0.376900
$929$	−7.82444e6	−0.297450	−0.148725	−	0.988879i	$-0.547517\pi$
$929$	−7.82444e6	−0.297450	−0.148725	+	0.988879i	$0.547517\pi$
$930$	6.33403e7	2.40144
$931$	1.49196e7	0.564136
$932$	7.14244e7	2.69344
$933$	−9.55902e6	−0.359509
$934$	5.93890e7	2.22761
$935$	−6.11617e7	−2.28797
$936$	−2.33009e7	−0.869327
$937$	4.49409e6	0.167222	0.0836109	−	0.996498i	$-0.473355\pi$
$937$	4.49409e6	0.167222	0.0836109	+	0.996498i	$0.473355\pi$
$938$	−1.57813e7	−0.585647
$939$	1.46809e6	0.0543360
$940$	3.85436e6	0.142277
$941$	−2.65094e7	−0.975944	−0.487972	−	0.872859i	$-0.662263\pi$
$941$	−2.65094e7	−0.975944	−0.487972	+	0.872859i	$0.662263\pi$
$942$	−1.31526e7	−0.482931
$943$	2.21166e7	0.809914
$944$	1.86148e7	0.679873
$945$	1.82030e7	0.663075
$946$	−9.16786e7	−3.33074
$947$	−2.42422e7	−0.878408	−0.439204	−	0.898387i	$-0.644739\pi$
$947$	−2.42422e7	−0.878408	−0.439204	+	0.898387i	$0.644739\pi$
$948$	−1.75396e7	−0.633867
$949$	−6.11035e6	−0.220242
$950$	2.29025e7	0.823330
$951$	2.91123e7	1.04382
$952$	−2.31021e7	−0.826149
$953$	−6.09648e6	−0.217444	−0.108722	−	0.994072i	$-0.534676\pi$
$953$	−6.09648e6	−0.217444	−0.108722	+	0.994072i	$0.534676\pi$
$954$	−7.83851e6	−0.278845
$955$	−9.24793e6	−0.328123
$956$	−9.64301e7	−3.41246
$957$	−4.31646e7	−1.52352
$958$	−5.83921e7	−2.05561
$959$	−1.08195e7	−0.379893
$960$	−3.47091e7	−1.21553
$961$	3.05962e7	1.06871
$962$	3.00880e7	1.04823
$963$	−1.66322e7	−0.577941
$964$	3.09234e7	1.07175
$965$	−1.80420e7	−0.623686
$966$	−1.90662e7	−0.657386
$967$	−4.42320e7	−1.52115	−0.760573	−	0.649253i	$-0.775082\pi$
$967$	−4.42320e7	−1.52115	−0.760573	+	0.649253i	$0.775082\pi$
$968$	−6.81732e7	−2.33844
$969$	−1.81363e7	−0.620496
$970$	−7.07153e7	−2.41315
$971$	−5.06645e7	−1.72447	−0.862235	−	0.506508i	$-0.830936\pi$
$971$	−5.06645e7	−1.72447	−0.862235	+	0.506508i	$0.830936\pi$
$972$	−4.37941e7	−1.48679
$973$	−1.79710e7	−0.608541
$974$	5.26302e7	1.77762
$975$	1.97763e7	0.666244
$976$	1.29460e7	0.435023
$977$	1.43001e6	0.0479295	0.0239647	−	0.999713i	$-0.492371\pi$
$977$	1.43001e6	0.0479295	0.0239647	+	0.999713i	$0.492371\pi$
$978$	−5.44566e7	−1.82055
$979$	8.52658e7	2.84327
$980$	5.72242e7	1.90333
$981$	−9.13974e6	−0.303222
$982$	1.93502e7	0.640333
$983$	−966289.	−0.0318950
$983$	−966289.	−0.0318950
$984$	2.71374e7	0.893472
$985$	6.35306e6	0.208637
$986$	−7.38801e7	−2.42011
$987$	−639520.	−0.0208959
$988$	5.65997e7	1.84468
$989$	−4.04539e7	−1.31513
$990$	4.54634e7	1.47426
$991$	1.97080e7	0.637469	0.318734	−	0.947844i	$-0.396742\pi$
$991$	1.97080e7	0.637469	0.318734	+	0.947844i	$0.396742\pi$
$992$	−1.32659e7	−0.428014
$993$	1.22131e7	0.393055
$994$	−1.50044e7	−0.481672
$995$	8.32654e6	0.266629
$996$	1.12679e7	0.359911
$997$	5.95623e7	1.89772	0.948862	−	0.315690i	$-0.102236\pi$
$997$	5.95623e7	1.89772	0.948862	+	0.315690i	$0.102236\pi$
$998$	−3.41782e7	−1.08623
$999$	1.58117e7	0.501262

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.a.1.20	✓	191

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.a.1.20	✓	191	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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-9.64751 q^{2} -11.8379 q^{3} +61.0744 q^{4} -72.0672 q^{5} +114.206 q^{6} -61.6914 q^{7} -280.496 q^{8} -102.865 q^{9} +O(q^{10})\)	\(q-9.64751 q^{2} -11.8379 q^{3} +61.0744 q^{4} -72.0672 q^{5} +114.206 q^{6} -61.6914 q^{7} -280.496 q^{8} -102.865 q^{9} +695.269 q^{10} -635.686 q^{11} -722.991 q^{12} -807.568 q^{13} +595.168 q^{14} +853.121 q^{15} +751.705 q^{16} -1335.06 q^{17} +992.390 q^{18} -1147.56 q^{19} -4401.46 q^{20} +730.295 q^{21} +6132.78 q^{22} +2706.14 q^{23} +3320.47 q^{24} +2068.68 q^{25} +7791.02 q^{26} +4094.30 q^{27} -3767.77 q^{28} -5736.04 q^{29} -8230.50 q^{30} -7695.80 q^{31} +1723.79 q^{32} +7525.16 q^{33} +12880.0 q^{34} +4445.92 q^{35} -6282.42 q^{36} +3861.88 q^{37} +11071.1 q^{38} +9559.88 q^{39} +20214.5 q^{40} +8172.76 q^{41} -7045.52 q^{42} -14948.9 q^{43} -38824.1 q^{44} +7413.18 q^{45} -26107.5 q^{46} -875.701 q^{47} -8898.59 q^{48} -13001.2 q^{49} -19957.6 q^{50} +15804.2 q^{51} -49321.7 q^{52} -7898.62 q^{53} -39499.8 q^{54} +45812.1 q^{55} +17304.2 q^{56} +13584.7 q^{57} +55338.5 q^{58} +24763.4 q^{59} +52103.9 q^{60} +17222.2 q^{61} +74245.3 q^{62} +6345.88 q^{63} -40684.8 q^{64} +58199.1 q^{65} -72599.1 q^{66} -26515.7 q^{67} -81537.9 q^{68} -32034.9 q^{69} -42892.1 q^{70} -25210.3 q^{71} +28853.2 q^{72} +7566.37 q^{73} -37257.5 q^{74} -24488.7 q^{75} -70086.6 q^{76} +39216.3 q^{77} -92229.0 q^{78} +24259.7 q^{79} -54173.3 q^{80} -23471.6 q^{81} -78846.7 q^{82} -15585.1 q^{83} +44602.3 q^{84} +96213.8 q^{85} +144220. q^{86} +67902.5 q^{87} +178307. q^{88} -134132. q^{89} -71518.7 q^{90} +49820.0 q^{91} +165276. q^{92} +91101.9 q^{93} +8448.34 q^{94} +82701.4 q^{95} -20406.0 q^{96} -101709. q^{97} +125429. q^{98} +65389.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9}+O(q^{10}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9} - 2867 q^{10} - 1878 q^{11} - 3400 q^{12} - 6854 q^{13} - 1601 q^{14} - 3461 q^{15} + 38457 q^{16} - 10730 q^{17} - 17249 q^{18} - 5817 q^{19} - 9988 q^{20} - 15999 q^{21} - 20287 q^{22} - 15625 q^{23} - 19747 q^{24} + 67082 q^{25} - 9868 q^{26} - 22892 q^{27} - 72720 q^{28} - 17960 q^{29} - 27464 q^{30} - 25604 q^{31} - 68869 q^{32} - 60654 q^{33} - 42876 q^{34} - 30018 q^{35} + 172922 q^{36} - 114862 q^{37} + 4404 q^{38} - 73500 q^{39} - 137154 q^{40} - 90896 q^{41} - 10652 q^{42} - 121447 q^{43} - 57962 q^{44} - 109019 q^{45} - 136262 q^{46} - 86994 q^{47} - 133347 q^{48} + 278242 q^{49} - 93911 q^{50} - 66966 q^{51} - 284241 q^{52} - 122112 q^{53} - 130806 q^{54} - 134904 q^{55} - 100292 q^{56} - 423426 q^{57} - 307669 q^{58} - 85704 q^{59} - 238277 q^{60} - 206736 q^{61} - 190602 q^{62} - 387623 q^{63} + 411903 q^{64} - 244408 q^{65} - 113963 q^{66} - 337002 q^{67} - 388031 q^{68} - 165342 q^{69} - 183925 q^{70} - 174806 q^{71} - 753621 q^{72} - 1009738 q^{73} - 204958 q^{74} - 282676 q^{75} - 326869 q^{76} - 332288 q^{77} - 591801 q^{78} - 488092 q^{79} - 259068 q^{80} + 385959 q^{81} - 523996 q^{82} - 315720 q^{83} - 750486 q^{84} - 1001755 q^{85} - 287709 q^{86} - 316995 q^{87} - 836923 q^{88} - 298065 q^{89} - 751039 q^{90} - 521459 q^{91} - 640932 q^{92} - 554391 q^{93} - 623481 q^{94} - 491883 q^{95} - 767843 q^{96} - 1468693 q^{97} - 714146 q^{98} - 842507 q^{99}+O(q^{100}) \) 191 * q - 37 * q^2 - 74 * q^3 + 2821 * q^4 - 247 * q^5 - 335 * q^6 - 1569 * q^7 - 1761 * q^8 + 13251 * q^9 - 2867 * q^10 - 1878 * q^11 - 3400 * q^12 - 6854 * q^13 - 1601 * q^14 - 3461 * q^15 + 38457 * q^16 - 10730 * q^17 - 17249 * q^18 - 5817 * q^19 - 9988 * q^20 - 15999 * q^21 - 20287 * q^22 - 15625 * q^23 - 19747 * q^24 + 67082 * q^25 - 9868 * q^26 - 22892 * q^27 - 72720 * q^28 - 17960 * q^29 - 27464 * q^30 - 25604 * q^31 - 68869 * q^32 - 60654 * q^33 - 42876 * q^34 - 30018 * q^35 + 172922 * q^36 - 114862 * q^37 + 4404 * q^38 - 73500 * q^39 - 137154 * q^40 - 90896 * q^41 - 10652 * q^42 - 121447 * q^43 - 57962 * q^44 - 109019 * q^45 - 136262 * q^46 - 86994 * q^47 - 133347 * q^48 + 278242 * q^49 - 93911 * q^50 - 66966 * q^51 - 284241 * q^52 - 122112 * q^53 - 130806 * q^54 - 134904 * q^55 - 100292 * q^56 - 423426 * q^57 - 307669 * q^58 - 85704 * q^59 - 238277 * q^60 - 206736 * q^61 - 190602 * q^62 - 387623 * q^63 + 411903 * q^64 - 244408 * q^65 - 113963 * q^66 - 337002 * q^67 - 388031 * q^68 - 165342 * q^69 - 183925 * q^70 - 174806 * q^71 - 753621 * q^72 - 1009738 * q^73 - 204958 * q^74 - 282676 * q^75 - 326869 * q^76 - 332288 * q^77 - 591801 * q^78 - 488092 * q^79 - 259068 * q^80 + 385959 * q^81 - 523996 * q^82 - 315720 * q^83 - 750486 * q^84 - 1001755 * q^85 - 287709 * q^86 - 316995 * q^87 - 836923 * q^88 - 298065 * q^89 - 751039 * q^90 - 521459 * q^91 - 640932 * q^92 - 554391 * q^93 - 623481 * q^94 - 491883 * q^95 - 767843 * q^96 - 1468693 * q^97 - 714146 * q^98 - 842507 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more