LMFDB - Embedded newform 983.6.a.a.1.3

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			1.3
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)

$f(q)$	$=$	$q-10.9287 q^{2} +4.75838 q^{3} +87.4366 q^{4} -74.3663 q^{5} -52.0029 q^{6} -185.895 q^{7} -605.851 q^{8} -220.358 q^{9} +O(q^{10})$	\(q-10.9287 q^{2} +4.75838 q^{3} +87.4366 q^{4} -74.3663 q^{5} -52.0029 q^{6} -185.895 q^{7} -605.851 q^{8} -220.358 q^{9} +812.728 q^{10} +18.8981 q^{11} +416.056 q^{12} +51.9156 q^{13} +2031.59 q^{14} -353.863 q^{15} +3823.19 q^{16} -1195.92 q^{17} +2408.23 q^{18} -1826.67 q^{19} -6502.34 q^{20} -884.557 q^{21} -206.532 q^{22} -504.486 q^{23} -2882.87 q^{24} +2405.35 q^{25} -567.370 q^{26} -2204.83 q^{27} -16254.0 q^{28} +2902.30 q^{29} +3867.27 q^{30} +1566.55 q^{31} -22395.3 q^{32} +89.9243 q^{33} +13069.9 q^{34} +13824.3 q^{35} -19267.3 q^{36} -2952.72 q^{37} +19963.1 q^{38} +247.034 q^{39} +45054.9 q^{40} +11641.6 q^{41} +9667.07 q^{42} -4040.15 q^{43} +1652.39 q^{44} +16387.2 q^{45} +5513.38 q^{46} +14044.9 q^{47} +18192.2 q^{48} +17749.9 q^{49} -26287.4 q^{50} -5690.64 q^{51} +4539.33 q^{52} +19743.3 q^{53} +24096.0 q^{54} -1405.38 q^{55} +112624. q^{56} -8691.98 q^{57} -31718.3 q^{58} +27690.6 q^{59} -30940.6 q^{60} -9850.57 q^{61} -17120.4 q^{62} +40963.4 q^{63} +122410. q^{64} -3860.77 q^{65} -982.756 q^{66} -30617.9 q^{67} -104567. q^{68} -2400.54 q^{69} -151082. q^{70} +16217.8 q^{71} +133504. q^{72} -61877.8 q^{73} +32269.4 q^{74} +11445.6 q^{75} -159718. q^{76} -3513.06 q^{77} -2699.76 q^{78} +13209.9 q^{79} -284317. q^{80} +43055.5 q^{81} -127228. q^{82} +22720.8 q^{83} -77342.7 q^{84} +88936.2 q^{85} +44153.7 q^{86} +13810.2 q^{87} -11449.4 q^{88} +110072. q^{89} -179091. q^{90} -9650.84 q^{91} -44110.6 q^{92} +7454.23 q^{93} -153493. q^{94} +135843. q^{95} -106565. q^{96} +77641.9 q^{97} -193983. q^{98} -4164.34 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.9287	−1.93194	−0.965970	−	0.258653i	$-0.916721\pi$
$2$	−10.9287	−1.93194	−0.965970	+	0.258653i	$0.916721\pi$
$3$	4.75838	0.305250	0.152625	−	0.988284i	$-0.451227\pi$
$3$	4.75838	0.305250	0.152625	+	0.988284i	$0.451227\pi$
$4$	87.4366	2.73239
$5$	−74.3663	−1.33031	−0.665153	−	0.746707i	$-0.731634\pi$
$5$	−74.3663	−1.33031	−0.665153	+	0.746707i	$0.731634\pi$
$6$	−52.0029	−0.589725
$7$	−185.895	−1.43391	−0.716955	−	0.697119i	$-0.754465\pi$
$7$	−185.895	−1.43391	−0.716955	+	0.697119i	$0.754465\pi$
$8$	−605.851	−3.34688
$9$	−220.358	−0.906822
$10$	812.728	2.57007
$11$	18.8981	0.0470908	0.0235454	−	0.999723i	$-0.492505\pi$
$11$	18.8981	0.0470908	0.0235454	+	0.999723i	$0.492505\pi$
$12$	416.056	0.834064
$13$	51.9156	0.0852000	0.0426000	−	0.999092i	$-0.486436\pi$
$13$	51.9156	0.0852000	0.0426000	+	0.999092i	$0.486436\pi$
$14$	2031.59	2.77023
$15$	−353.863	−0.406076
$16$	3823.19	3.73359
$17$	−1195.92	−1.00364	−0.501822	−	0.864971i	$-0.667337\pi$
$17$	−1195.92	−1.00364	−0.501822	+	0.864971i	$0.667337\pi$
$18$	2408.23	1.75193
$19$	−1826.67	−1.16085	−0.580425	−	0.814314i	$-0.697114\pi$
$19$	−1826.67	−1.16085	−0.580425	+	0.814314i	$0.697114\pi$
$20$	−6502.34	−3.63492
$21$	−884.557	−0.437701
$22$	−206.532	−0.0909767
$23$	−504.486	−0.198852	−0.0994259	−	0.995045i	$-0.531701\pi$
$23$	−504.486	−0.198852	−0.0994259	+	0.995045i	$0.531701\pi$
$24$	−2882.87	−1.02164
$25$	2405.35	0.769713
$26$	−567.370	−0.164601
$27$	−2204.83	−0.582058
$28$	−16254.0	−3.91801
$29$	2902.30	0.640836	0.320418	−	0.947276i	$-0.396177\pi$
$29$	2902.30	0.640836	0.320418	+	0.947276i	$0.396177\pi$
$30$	3867.27	0.784514
$31$	1566.55	0.292779	0.146389	−	0.989227i	$-0.453235\pi$
$31$	1566.55	0.292779	0.146389	+	0.989227i	$0.453235\pi$
$32$	−22395.3	−3.86618
$33$	89.9243	0.0143745
$34$	13069.9	1.93898
$35$	13824.3	1.90754
$36$	−19267.3	−2.47780
$37$	−2952.72	−0.354583	−0.177292	−	0.984158i	$-0.556734\pi$
$37$	−2952.72	−0.354583	−0.177292	+	0.984158i	$0.556734\pi$
$38$	19963.1	2.24269
$39$	247.034	0.0260073
$40$	45054.9	4.45238
$41$	11641.6	1.08157	0.540783	−	0.841162i	$-0.318128\pi$
$41$	11641.6	1.08157	0.540783	+	0.841162i	$0.318128\pi$
$42$	9667.07	0.845613
$43$	−4040.15	−0.333217	−0.166608	−	0.986023i	$-0.553282\pi$
$43$	−4040.15	−0.333217	−0.166608	+	0.986023i	$0.553282\pi$
$44$	1652.39	0.128671
$45$	16387.2	1.20635
$46$	5513.38	0.384170
$47$	14044.9	0.927414	0.463707	−	0.885989i	$-0.346519\pi$
$47$	14044.9	0.927414	0.463707	+	0.885989i	$0.346519\pi$
$48$	18192.2	1.13968
$49$	17749.9	1.05610
$50$	−26287.4	−1.48704
$51$	−5690.64	−0.306362
$52$	4539.33	0.232800
$53$	19743.3	0.965452	0.482726	−	0.875771i	$-0.339647\pi$
$53$	19743.3	0.965452	0.482726	+	0.875771i	$0.339647\pi$
$54$	24096.0	1.12450
$55$	−1405.38	−0.0626452
$56$	112624.	4.79913
$57$	−8691.98	−0.354349
$58$	−31718.3	−1.23806
$59$	27690.6	1.03563	0.517813	−	0.855494i	$-0.326746\pi$
$59$	27690.6	1.03563	0.517813	+	0.855494i	$0.326746\pi$
$60$	−30940.6	−1.10956
$61$	−9850.57	−0.338951	−0.169475	−	0.985534i	$-0.554207\pi$
$61$	−9850.57	−0.338951	−0.169475	+	0.985534i	$0.554207\pi$
$62$	−17120.4	−0.565631
$63$	40963.4	1.30030
$64$	122410.	3.73565
$65$	−3860.77	−0.113342
$66$	−982.756	−0.0277706
$67$	−30617.9	−0.833275	−0.416638	−	0.909073i	$-0.636792\pi$
$67$	−30617.9	−0.833275	−0.416638	+	0.909073i	$0.636792\pi$
$68$	−104567.	−2.74235
$69$	−2400.54	−0.0606995
$70$	−151082.	−3.68525
$71$	16217.8	0.381810	0.190905	−	0.981609i	$-0.438858\pi$
$71$	16217.8	0.381810	0.190905	+	0.981609i	$0.438858\pi$
$72$	133504.	3.03503
$73$	−61877.8	−1.35903	−0.679513	−	0.733664i	$-0.737809\pi$
$73$	−61877.8	−1.35903	−0.679513	+	0.733664i	$0.737809\pi$
$74$	32269.4	0.685034
$75$	11445.6	0.234955
$76$	−159718.	−3.17190
$77$	−3513.06	−0.0675240
$78$	−2699.76	−0.0502446
$79$	13209.9	0.238141	0.119070	−	0.992886i	$-0.462009\pi$
$79$	13209.9	0.238141	0.119070	+	0.992886i	$0.462009\pi$
$80$	−284317.	−4.96681
$81$	43055.5	0.729149
$82$	−127228.	−2.08952
$83$	22720.8	0.362016	0.181008	−	0.983482i	$-0.442064\pi$
$83$	22720.8	0.362016	0.181008	+	0.983482i	$0.442064\pi$
$84$	−77342.7	−1.19597
$85$	88936.2	1.33515
$86$	44153.7	0.643755
$87$	13810.2	0.195615
$88$	−11449.4	−0.157608
$89$	110072.	1.47300	0.736499	−	0.676438i	$-0.236477\pi$
$89$	110072.	1.47300	0.736499	+	0.676438i	$0.236477\pi$
$90$	−179091.	−2.33060
$91$	−9650.84	−0.122169
$92$	−44110.6	−0.543342
$93$	7454.23	0.0893708
$94$	−153493.	−1.79171
$95$	135843.	1.54429
$96$	−106565.	−1.18015
$97$	77641.9	0.837851	0.418925	−	0.908021i	$-0.362407\pi$
$97$	77641.9	0.837851	0.418925	+	0.908021i	$0.362407\pi$
$98$	−193983.	−2.04032
$99$	−4164.34	−0.0427030
$100$	210316.	2.10316
$101$	−159141.	−1.55231	−0.776154	−	0.630543i	$-0.782832\pi$
$101$	−159141.	−1.55231	−0.776154	+	0.630543i	$0.782832\pi$
$102$	62191.3	0.591874
$103$	−69513.4	−0.645618	−0.322809	−	0.946464i	$-0.604627\pi$
$103$	−69513.4	−0.645618	−0.322809	+	0.946464i	$0.604627\pi$
$104$	−31453.1	−0.285154
$105$	65781.3	0.582276
$106$	−215769.	−1.86520
$107$	−118447.	−1.00015	−0.500076	−	0.865981i	$-0.666695\pi$
$107$	−118447.	−1.00015	−0.500076	+	0.865981i	$0.666695\pi$
$108$	−192783.	−1.59041
$109$	−107477.	−0.866465	−0.433233	−	0.901282i	$-0.642627\pi$
$109$	−107477.	−0.866465	−0.433233	+	0.901282i	$0.642627\pi$
$110$	15359.0	0.121027
$111$	−14050.2	−0.108237
$112$	−710711.	−5.35363
$113$	220751.	1.62632	0.813161	−	0.582039i	$-0.197745\pi$
$113$	220751.	1.62632	0.813161	+	0.582039i	$0.197745\pi$
$114$	94992.1	0.684582
$115$	37516.8	0.264534
$116$	253767.	1.75102
$117$	−11440.0	−0.0772613
$118$	−302623.	−2.00077
$119$	222315.	1.43914
$120$	214388.	1.35909
$121$	−160694.	−0.997782
$122$	107654.	0.654833
$123$	55395.2	0.330148
$124$	136974.	0.799987
$125$	53517.4	0.306352
$126$	−447677.	−2.51211
$127$	290260.	1.59690	0.798450	−	0.602062i	$-0.205654\pi$
$127$	290260.	1.59690	0.798450	+	0.602062i	$0.205654\pi$
$128$	−621130.	−3.35087
$129$	−19224.6	−0.101714
$130$	42193.3	0.218970
$131$	171578.	0.873541	0.436770	−	0.899573i	$-0.356122\pi$
$131$	171578.	0.873541	0.436770	+	0.899573i	$0.356122\pi$
$132$	7862.67	0.0392767
$133$	339568.	1.66455
$134$	334614.	1.60984
$135$	163965.	0.774315
$136$	724549.	3.35908
$137$	−290129.	−1.32066	−0.660328	−	0.750977i	$-0.729583\pi$
$137$	−290129.	−1.32066	−0.660328	+	0.750977i	$0.729583\pi$
$138$	26234.7	0.117268
$139$	235583.	1.03421	0.517104	−	0.855923i	$-0.327010\pi$
$139$	235583.	1.03421	0.517104	+	0.855923i	$0.327010\pi$
$140$	1.20875e6	5.21215
$141$	66830.9	0.283093
$142$	−177240.	−0.737634
$143$	981.106	0.00401214
$144$	−842470.	−3.38570
$145$	−215833.	−0.852507
$146$	676244.	2.62556
$147$	84460.5	0.322374
$148$	−258176.	−0.968861
$149$	432096.	1.59446	0.797232	−	0.603673i	$-0.206297\pi$
$149$	432096.	1.59446	0.797232	+	0.603673i	$0.206297\pi$
$150$	−125085.	−0.453919
$151$	−422919.	−1.50943	−0.754717	−	0.656050i	$-0.772226\pi$
$151$	−422919.	−1.50943	−0.754717	+	0.656050i	$0.772226\pi$
$152$	1.10669e6	3.88523
$153$	263530.	0.910127
$154$	38393.2	0.130452
$155$	−116499.	−0.389485
$156$	21599.8	0.0710622
$157$	180705.	0.585087	0.292544	−	0.956252i	$-0.405498\pi$
$157$	180705.	0.585087	0.292544	+	0.956252i	$0.405498\pi$
$158$	−144368.	−0.460073
$159$	93946.2	0.294704
$160$	1.66546e6	5.14321
$161$	93781.3	0.285136
$162$	−470541.	−1.40867
$163$	263185.	0.775876	0.387938	−	0.921685i	$-0.373187\pi$
$163$	263185.	0.775876	0.387938	+	0.921685i	$0.373187\pi$
$164$	1.01790e6	2.95527
$165$	−6687.34	−0.0191224
$166$	−248309.	−0.699393
$167$	−386296.	−1.07184	−0.535919	−	0.844269i	$-0.680035\pi$
$167$	−386296.	−1.07184	−0.535919	+	0.844269i	$0.680035\pi$
$168$	535910.	1.46493
$169$	−368598.	−0.992741
$170$	−971958.	−2.57944
$171$	402521.	1.05268
$172$	−353257.	−0.910479
$173$	−350675.	−0.890818	−0.445409	−	0.895327i	$-0.646942\pi$
$173$	−350675.	−0.890818	−0.445409	+	0.895327i	$0.646942\pi$
$174$	−150928.	−0.377917
$175$	−447143.	−1.10370
$176$	72251.0	0.175818
$177$	131762.	0.316125
$178$	−1.20295e6	−2.84575
$179$	371758.	0.867217	0.433609	−	0.901101i	$-0.357240\pi$
$179$	371758.	0.867217	0.433609	+	0.901101i	$0.357240\pi$
$180$	1.43284e6	3.29623
$181$	225131.	0.510786	0.255393	−	0.966837i	$-0.417795\pi$
$181$	225131.	0.510786	0.255393	+	0.966837i	$0.417795\pi$
$182$	105471.	0.236024
$183$	−46872.7	−0.103465
$184$	305643.	0.665534
$185$	219583.	0.471704
$186$	−81465.1	−0.172659
$187$	−22600.6	−0.0472624
$188$	1.22804e6	2.53406
$189$	409867.	0.834618
$190$	−1.48459e6	−2.98347
$191$	−33719.1	−0.0668794	−0.0334397	−	0.999441i	$-0.510646\pi$
$191$	−33719.1	−0.0668794	−0.0334397	+	0.999441i	$0.510646\pi$
$192$	582472.	1.14031
$193$	174099.	0.336436	0.168218	−	0.985750i	$-0.446199\pi$
$193$	174099.	0.336436	0.168218	+	0.985750i	$0.446199\pi$
$194$	−848525.	−1.61868
$195$	−18371.0	−0.0345977
$196$	1.55199e6	2.88568
$197$	−755260.	−1.38654	−0.693268	−	0.720680i	$-0.743830\pi$
$197$	−755260.	−1.38654	−0.693268	+	0.720680i	$0.743830\pi$
$198$	45510.9	0.0824997
$199$	89156.6	0.159596	0.0797978	−	0.996811i	$-0.474573\pi$
$199$	89156.6	0.159596	0.0797978	+	0.996811i	$0.474573\pi$
$200$	−1.45729e6	−2.57614
$201$	−145692.	−0.254357
$202$	1.73920e6	2.99897
$203$	−539521.	−0.918901
$204$	−497570.	−0.837103
$205$	−865744.	−1.43881
$206$	759692.	1.24730
$207$	111167.	0.180323
$208$	198483.	0.318102
$209$	−34520.6	−0.0546654
$210$	−718904.	−1.12492
$211$	1.16738e6	1.80511	0.902557	−	0.430570i	$-0.141687\pi$
$211$	1.16738e6	1.80511	0.902557	+	0.430570i	$0.141687\pi$
$212$	1.72629e6	2.63800
$213$	77170.6	0.116547
$214$	1.29448e6	1.93224
$215$	300451.	0.443280
$216$	1.33580e6	1.94808
$217$	−291213.	−0.419819
$218$	1.17459e6	1.67396
$219$	−294438.	−0.414843
$220$	−122882.	−0.171171
$221$	−62086.9	−0.0855105
$222$	153550.	0.209107
$223$	−463595.	−0.624276	−0.312138	−	0.950037i	$-0.601045\pi$
$223$	−463595.	−0.624276	−0.312138	+	0.950037i	$0.601045\pi$
$224$	4.16317e6	5.54376
$225$	−530039.	−0.697993
$226$	−2.41252e6	−3.14196
$227$	−534274.	−0.688176	−0.344088	−	0.938937i	$-0.611812\pi$
$227$	−534274.	−0.688176	−0.344088	+	0.938937i	$0.611812\pi$
$228$	−759998.	−0.968222
$229$	226993.	0.286038	0.143019	−	0.989720i	$-0.454319\pi$
$229$	226993.	0.286038	0.143019	+	0.989720i	$0.454319\pi$
$230$	−410010.	−0.511064
$231$	−16716.4	−0.0206117
$232$	−1.75836e6	−2.14480
$233$	607593.	0.733201	0.366600	−	0.930378i	$-0.380522\pi$
$233$	607593.	0.733201	0.366600	+	0.930378i	$0.380522\pi$
$234$	125025.	0.149264
$235$	−1.04447e6	−1.23374
$236$	2.42117e6	2.82974
$237$	62857.9	0.0726924
$238$	−2.42962e6	−2.78032
$239$	−1.13292e6	−1.28294	−0.641469	−	0.767149i	$-0.721675\pi$
$239$	−1.13292e6	−1.28294	−0.641469	+	0.767149i	$0.721675\pi$
$240$	−1.35289e6	−1.51612
$241$	538065.	0.596750	0.298375	−	0.954449i	$-0.403555\pi$
$241$	538065.	0.596750	0.298375	+	0.954449i	$0.403555\pi$
$242$	1.75618e6	1.92766
$243$	740648.	0.804630
$244$	−861301.	−0.926147
$245$	−1.31999e6	−1.40493
$246$	−605397.	−0.637827
$247$	−94832.7	−0.0989044
$248$	−949095.	−0.979897
$249$	108114.	0.110505
$250$	−584876.	−0.591853
$251$	1.59679e6	1.59979	0.799896	−	0.600139i	$-0.204888\pi$
$251$	1.59679e6	1.59979	0.799896	+	0.600139i	$0.204888\pi$
$252$	3.58170e6	3.55294
$253$	−9533.83	−0.00936410
$254$	−3.17216e6	−3.08511
$255$	423192.	0.407556
$256$	2.87104e6	2.73803
$257$	292050.	0.275819	0.137910	−	0.990445i	$-0.455962\pi$
$257$	292050.	0.275819	0.137910	+	0.990445i	$0.455962\pi$
$258$	210100.	0.196506
$259$	548895.	0.508440
$260$	−337573.	−0.309695
$261$	−639544.	−0.581124
$262$	−1.87512e6	−1.68763
$263$	468633.	0.417776	0.208888	−	0.977940i	$-0.433016\pi$
$263$	468633.	0.417776	0.208888	+	0.977940i	$0.433016\pi$
$264$	−54480.7	−0.0481097
$265$	−1.46824e6	−1.28435
$266$	−3.71104e6	−3.21582
$267$	523765.	0.449633
$268$	−2.67713e6	−2.27684
$269$	−179526.	−0.151268	−0.0756338	−	0.997136i	$-0.524098\pi$
$269$	−179526.	−0.151268	−0.0756338	+	0.997136i	$0.524098\pi$
$270$	−1.79193e6	−1.49593
$271$	690804.	0.571389	0.285694	−	0.958321i	$-0.407776\pi$
$271$	690804.	0.571389	0.285694	+	0.958321i	$0.407776\pi$
$272$	−4.57223e6	−3.74719
$273$	−45922.3	−0.0372921
$274$	3.17074e6	2.55143
$275$	45456.6	0.0362464
$276$	−209895.	−0.165855
$277$	1.11764e6	0.875191	0.437595	−	0.899172i	$-0.355830\pi$
$277$	1.11764e6	0.875191	0.437595	+	0.899172i	$0.355830\pi$
$278$	−2.57462e6	−1.99803
$279$	−345201.	−0.265498
$280$	−8.37547e6	−6.38431
$281$	−174816.	−0.132073	−0.0660367	−	0.997817i	$-0.521035\pi$
$281$	−174816.	−0.132073	−0.0660367	+	0.997817i	$0.521035\pi$
$282$	−730375.	−0.546919
$283$	142652.	0.105879	0.0529396	−	0.998598i	$-0.483141\pi$
$283$	142652.	0.105879	0.0529396	+	0.998598i	$0.483141\pi$
$284$	1.41803e6	1.04326
$285$	646391.	0.471393
$286$	−10722.2	−0.00775121
$287$	−2.16411e6	−1.55087
$288$	4.93499e6	3.50594
$289$	10367.1	0.00730149
$290$	2.35878e6	1.64699
$291$	369449.	0.255754
$292$	−5.41038e6	−3.71339
$293$	1.14997e6	0.782562	0.391281	−	0.920271i	$-0.372032\pi$
$293$	1.14997e6	0.782562	0.391281	+	0.920271i	$0.372032\pi$
$294$	−923044.	−0.622808
$295$	−2.05925e6	−1.37770
$296$	1.78891e6	1.18675
$297$	−41667.1	−0.0274096
$298$	−4.72225e6	−3.08041
$299$	−26190.7	−0.0169422
$300$	1.00076e6	0.641990
$301$	751043.	0.477803
$302$	4.62195e6	2.91614
$303$	−757252.	−0.473842
$304$	−6.98371e6	−4.33413
$305$	732551.	0.450908
$306$	−2.88005e6	−1.75831
$307$	448711.	0.271719	0.135860	−	0.990728i	$-0.456620\pi$
$307$	448711.	0.271719	0.135860	+	0.990728i	$0.456620\pi$
$308$	−307170.	−0.184502
$309$	−330771.	−0.197075
$310$	1.27318e6	0.752463
$311$	−1.15874e6	−0.679339	−0.339669	−	0.940545i	$-0.610315\pi$
$311$	−1.15874e6	−0.679339	−0.339669	+	0.940545i	$0.610315\pi$
$312$	−149666.	−0.0870434
$313$	−1.41345e6	−0.815492	−0.407746	−	0.913095i	$-0.633685\pi$
$313$	−1.41345e6	−0.815492	−0.407746	+	0.913095i	$0.633685\pi$
$314$	−1.97487e6	−1.13035
$315$	−3.04630e6	−1.72980
$316$	1.15503e6	0.650694
$317$	807140.	0.451129	0.225564	−	0.974228i	$-0.427577\pi$
$317$	807140.	0.451129	0.225564	+	0.974228i	$0.427577\pi$
$318$	−1.02671e6	−0.569351
$319$	54847.9	0.0301775
$320$	−9.10317e6	−4.96956
$321$	−563618.	−0.305297
$322$	−1.02491e6	−0.550865
$323$	2.18455e6	1.16508
$324$	3.76463e6	1.99232
$325$	124875.	0.0655796
$326$	−2.87627e6	−1.49895
$327$	−511418.	−0.264489
$328$	−7.05308e6	−3.61988
$329$	−2.61087e6	−1.32983
$330$	73084.0	0.0369434
$331$	−1.14468e6	−0.574269	−0.287135	−	0.957890i	$-0.592703\pi$
$331$	−1.14468e6	−0.574269	−0.287135	+	0.957890i	$0.592703\pi$
$332$	1.98663e6	0.989171
$333$	650655.	0.321544
$334$	4.22172e6	2.07073
$335$	2.27694e6	1.10851
$336$	−3.38183e6	−1.63419
$337$	3.05739e6	1.46648	0.733241	−	0.679969i	$-0.238007\pi$
$337$	3.05739e6	1.46648	0.733241	+	0.679969i	$0.238007\pi$
$338$	4.02830e6	1.91792
$339$	1.05042e6	0.496435
$340$	7.77628e6	3.64817
$341$	29604.8	0.0137872
$342$	−4.39903e6	−2.03372
$343$	−175271.	−0.0804407
$344$	2.44773e6	1.11524
$345$	178519.	0.0807489
$346$	3.83242e6	1.72101
$347$	−1.16976e6	−0.521521	−0.260760	−	0.965404i	$-0.583973\pi$
$347$	−1.16976e6	−0.521521	−0.260760	+	0.965404i	$0.583973\pi$
$348$	1.20752e6	0.534498
$349$	−4.28589e6	−1.88355	−0.941776	−	0.336240i	$-0.890845\pi$
$349$	−4.28589e6	−1.88355	−0.941776	+	0.336240i	$0.890845\pi$
$350$	4.88669e6	2.13228
$351$	−114465.	−0.0495913
$352$	−423229.	−0.182062
$353$	−74871.3	−0.0319800	−0.0159900	−	0.999872i	$-0.505090\pi$
$353$	−74871.3	−0.0319800	−0.0159900	+	0.999872i	$0.505090\pi$
$354$	−1.43999e6	−0.610734
$355$	−1.20606e6	−0.507924
$356$	9.62434e6	4.02481
$357$	1.05786e6	0.439296
$358$	−4.06284e6	−1.67541
$359$	945612.	0.387237	0.193619	−	0.981077i	$-0.437978\pi$
$359$	945612.	0.387237	0.193619	+	0.981077i	$0.437978\pi$
$360$	−9.92820e6	−4.03752
$361$	860623.	0.347572
$362$	−2.46039e6	−0.986807
$363$	−764642.	−0.304573
$364$	−843837.	−0.333814
$365$	4.60162e6	1.80792
$366$	512258.	0.199888
$367$	313040.	0.121321	0.0606603	−	0.998158i	$-0.480679\pi$
$367$	313040.	0.121321	0.0606603	+	0.998158i	$0.480679\pi$
$368$	−1.92875e6	−0.742431
$369$	−2.56532e6	−0.980789
$370$	−2.39976e6	−0.911304
$371$	−3.67018e6	−1.38437
$372$	651773.	0.244196
$373$	4.92548e6	1.83306	0.916530	−	0.399967i	$-0.130978\pi$
$373$	4.92548e6	1.83306	0.916530	+	0.399967i	$0.130978\pi$
$374$	246995.	0.0913082
$375$	254656.	0.0935139
$376$	−8.50911e6	−3.10395
$377$	150674.	0.0545992
$378$	−4.47931e6	−1.61243
$379$	−189213.	−0.0676634	−0.0338317	−	0.999428i	$-0.510771\pi$
$379$	−189213.	−0.0676634	−0.0338317	+	0.999428i	$0.510771\pi$
$380$	1.18776e7	4.21960
$381$	1.38117e6	0.487453
$382$	368506.	0.129207
$383$	−1.15024e6	−0.400674	−0.200337	−	0.979727i	$-0.564204\pi$
$383$	−1.15024e6	−0.400674	−0.200337	+	0.979727i	$0.564204\pi$
$384$	−2.95557e6	−1.02285
$385$	261253.	0.0898276
$386$	−1.90267e6	−0.649974
$387$	890280.	0.302168
$388$	6.78875e6	2.28934
$389$	357281.	0.119711	0.0598557	−	0.998207i	$-0.480936\pi$
$389$	357281.	0.119711	0.0598557	+	0.998207i	$0.480936\pi$
$390$	200771.	0.0668406
$391$	603325.	0.199577
$392$	−1.07538e7	−3.53464
$393$	816432.	0.266648
$394$	8.25402e6	2.67871
$395$	−982376.	−0.316800
$396$	−364116.	−0.116681
$397$	−4.15227e6	−1.32224	−0.661119	−	0.750281i	$-0.729918\pi$
$397$	−4.15227e6	−1.32224	−0.661119	+	0.750281i	$0.729918\pi$
$398$	−974367.	−0.308329
$399$	1.61579e6	0.508105
$400$	9.19613e6	2.87379
$401$	−2.19356e6	−0.681220	−0.340610	−	0.940205i	$-0.610634\pi$
$401$	−2.19356e6	−0.681220	−0.340610	+	0.940205i	$0.610634\pi$
$402$	1.59222e6	0.491403
$403$	81328.3	0.0249448
$404$	−1.39147e7	−4.24152
$405$	−3.20188e6	−0.969992
$406$	5.89627e6	1.77526
$407$	−55800.8	−0.0166976
$408$	3.44768e6	1.02536
$409$	−3.67688e6	−1.08686	−0.543428	−	0.839456i	$-0.682874\pi$
$409$	−3.67688e6	−1.08686	−0.543428	+	0.839456i	$0.682874\pi$
$410$	9.46146e6	2.77970
$411$	−1.38054e6	−0.403130
$412$	−6.07802e6	−1.76408
$413$	−5.14754e6	−1.48499
$414$	−1.21492e6	−0.348374
$415$	−1.68966e6	−0.481592
$416$	−1.16267e6	−0.329399
$417$	1.12099e6	0.315692
$418$	377265.	0.105610
$419$	908635.	0.252845	0.126423	−	0.991976i	$-0.459650\pi$
$419$	908635.	0.252845	0.126423	+	0.991976i	$0.459650\pi$
$420$	5.75169e6	1.59101
$421$	−1.75515e6	−0.482624	−0.241312	−	0.970448i	$-0.577578\pi$
$421$	−1.75515e6	−0.482624	−0.241312	+	0.970448i	$0.577578\pi$
$422$	−1.27579e7	−3.48737
$423$	−3.09490e6	−0.841000
$424$	−1.19615e7	−3.23126
$425$	−2.87661e6	−0.772518
$426$	−843375.	−0.225163
$427$	1.83117e6	0.486025
$428$	−1.03566e7	−2.73281
$429$	4668.47	0.00122471
$430$	−3.28355e6	−0.856391
$431$	−3.51454e6	−0.911330	−0.455665	−	0.890151i	$-0.650598\pi$
$431$	−3.51454e6	−0.911330	−0.455665	+	0.890151i	$0.650598\pi$
$432$	−8.42949e6	−2.17316
$433$	3.07810e6	0.788976	0.394488	−	0.918901i	$-0.370922\pi$
$433$	3.07810e6	0.788976	0.394488	+	0.918901i	$0.370922\pi$
$434$	3.18258e6	0.811065
$435$	−1.02702e6	−0.260228
$436$	−9.39747e6	−2.36753
$437$	921530.	0.230837
$438$	3.21782e6	0.801451
$439$	−1.92920e6	−0.477767	−0.238884	−	0.971048i	$-0.576781\pi$
$439$	−1.92920e6	−0.477767	−0.238884	+	0.971048i	$0.576781\pi$
$440$	851452.	0.209666
$441$	−3.91132e6	−0.957694
$442$	678530.	0.165201
$443$	−4.80846e6	−1.16412	−0.582059	−	0.813147i	$-0.697753\pi$
$443$	−4.80846e6	−1.16412	−0.582059	+	0.813147i	$0.697753\pi$
$444$	−1.22850e6	−0.295745
$445$	−8.18566e6	−1.95954
$446$	5.06650e6	1.20606
$447$	2.05608e6	0.486710
$448$	−2.27553e7	−5.35659
$449$	4.60351e6	1.07764	0.538820	−	0.842421i	$-0.318870\pi$
$449$	4.60351e6	1.07764	0.538820	+	0.842421i	$0.318870\pi$
$450$	5.79264e6	1.34848
$451$	220004.	0.0509319
$452$	1.93017e7	4.44375
$453$	−2.01241e6	−0.460755
$454$	5.83893e6	1.32952
$455$	717698.	0.162522
$456$	5.26604e6	1.18597
$457$	−6.67450e6	−1.49496	−0.747478	−	0.664287i	$-0.768735\pi$
$457$	−6.67450e6	−1.49496	−0.747478	+	0.664287i	$0.768735\pi$
$458$	−2.48074e6	−0.552609
$459$	2.63680e6	0.584179
$460$	3.28034e6	0.722811
$461$	−1.11105e6	−0.243489	−0.121745	−	0.992561i	$-0.538849\pi$
$461$	−1.11105e6	−0.243489	−0.121745	+	0.992561i	$0.538849\pi$
$462$	182689.	0.0398206
$463$	4.60438e6	0.998202	0.499101	−	0.866544i	$-0.333664\pi$
$463$	4.60438e6	0.998202	0.499101	+	0.866544i	$0.333664\pi$
$464$	1.10960e7	2.39261
$465$	−554344.	−0.118890
$466$	−6.64021e6	−1.41650
$467$	−3.35465e6	−0.711794	−0.355897	−	0.934525i	$-0.615825\pi$
$467$	−3.35465e6	−0.711794	−0.355897	+	0.934525i	$0.615825\pi$
$468$	−1.00028e6	−0.211108
$469$	5.69171e6	1.19484
$470$	1.14147e7	2.38352
$471$	859862.	0.178598
$472$	−1.67764e7	−3.46612
$473$	−76351.2	−0.0156914
$474$	−686956.	−0.140437
$475$	−4.39379e6	−0.893522
$476$	1.94385e7	3.93229
$477$	−4.35060e6	−0.875494
$478$	1.23814e7	2.47856
$479$	2.15742e6	0.429632	0.214816	−	0.976655i	$-0.431085\pi$
$479$	2.15742e6	0.429632	0.214816	+	0.976655i	$0.431085\pi$
$480$	7.92488e6	1.56996
$481$	−153292.	−0.0302105
$482$	−5.88036e6	−1.15289
$483$	446247.	0.0870377
$484$	−1.40505e7	−2.72634
$485$	−5.77394e6	−1.11460
$486$	−8.09433e6	−1.55450
$487$	−1.02524e7	−1.95886	−0.979432	−	0.201773i	$-0.935330\pi$
$487$	−1.02524e7	−1.95886	−0.979432	+	0.201773i	$0.935330\pi$
$488$	5.96797e6	1.13443
$489$	1.25233e6	0.236836
$490$	1.44258e7	2.71425
$491$	8.31318e6	1.55619	0.778096	−	0.628145i	$-0.216186\pi$
$491$	8.31318e6	1.55619	0.778096	+	0.628145i	$0.216186\pi$
$492$	4.84357e6	0.902095
$493$	−3.47091e6	−0.643171
$494$	1.03640e6	0.191077
$495$	309687.	0.0568081
$496$	5.98922e6	1.09312
$497$	−3.01481e6	−0.547481
$498$	−1.18155e6	−0.213490
$499$	2.56949e6	0.461951	0.230976	−	0.972960i	$-0.425808\pi$
$499$	2.56949e6	0.461951	0.230976	+	0.972960i	$0.425808\pi$
$500$	4.67939e6	0.837074
$501$	−1.83814e6	−0.327179
$502$	−1.74508e7	−3.09070
$503$	934906.	0.164758	0.0823792	−	0.996601i	$-0.473748\pi$
$503$	934906.	0.164758	0.0823792	+	0.996601i	$0.473748\pi$
$504$	−2.48177e7	−4.35196
$505$	1.18347e7	2.06505
$506$	104192.	0.0180909
$507$	−1.75393e6	−0.303034
$508$	2.53793e7	4.36336
$509$	8.59472e6	1.47041	0.735203	−	0.677847i	$-0.237087\pi$
$509$	8.59472e6	1.47041	0.735203	+	0.677847i	$0.237087\pi$
$510$	−4.62494e6	−0.787373
$511$	1.15028e7	1.94872
$512$	−1.15006e7	−1.93885
$513$	4.02750e6	0.675681
$514$	−3.19173e6	−0.532866
$515$	5.16946e6	0.858869
$516$	−1.68093e6	−0.277924
$517$	265422.	0.0436727
$518$	−5.99872e6	−0.982277
$519$	−1.66864e6	−0.271922
$520$	2.33905e6	0.379343
$521$	−2.46099e6	−0.397206	−0.198603	−	0.980080i	$-0.563640\pi$
$521$	−2.46099e6	−0.397206	−0.198603	+	0.980080i	$0.563640\pi$
$522$	6.98938e6	1.12270
$523$	−1.64426e6	−0.262855	−0.131427	−	0.991326i	$-0.541956\pi$
$523$	−1.64426e6	−0.262855	−0.131427	+	0.991326i	$0.541956\pi$
$524$	1.50022e7	2.38686
$525$	−2.12767e6	−0.336904
$526$	−5.12156e6	−0.807119
$527$	−1.87347e6	−0.293846
$528$	343798.	0.0536683
$529$	−6.18184e6	−0.960458
$530$	1.60460e7	2.48128
$531$	−6.10185e6	−0.939128
$532$	2.96907e7	4.54822
$533$	604381.	0.0921495
$534$	−5.72407e6	−0.868664
$535$	8.80850e6	1.33051
$536$	1.85499e7	2.78888
$537$	1.76897e6	0.264718
$538$	1.96198e6	0.292240
$539$	335438.	0.0497326
$540$	1.43366e7	2.11573
$541$	1.75900e6	0.258389	0.129194	−	0.991619i	$-0.458761\pi$
$541$	1.75900e6	0.258389	0.129194	+	0.991619i	$0.458761\pi$
$542$	−7.54960e6	−1.10389
$543$	1.07126e6	0.155917
$544$	2.67830e7	3.88027
$545$	7.99271e6	1.15266
$546$	501872.	0.0720462
$547$	−9.12412e6	−1.30383	−0.651917	−	0.758290i	$-0.726035\pi$
$547$	−9.12412e6	−1.30383	−0.651917	+	0.758290i	$0.726035\pi$
$548$	−2.53679e7	−3.60855
$549$	2.17065e6	0.307368
$550$	−496782.	−0.0700260
$551$	−5.30154e6	−0.743914
$552$	1.45437e6	0.203154
$553$	−2.45566e6	−0.341472
$554$	−1.22144e7	−1.69082
$555$	1.04486e6	0.143988
$556$	2.05986e7	2.82586
$557$	−2.76208e6	−0.377223	−0.188612	−	0.982052i	$-0.560399\pi$
$557$	−2.76208e6	−0.377223	−0.188612	+	0.982052i	$0.560399\pi$
$558$	3.77260e6	0.512927
$559$	−209747.	−0.0283901
$560$	5.28530e7	7.12196
$561$	−107542.	−0.0144269
$562$	1.91051e6	0.255158
$563$	−1.00081e7	−1.33071	−0.665353	−	0.746529i	$-0.731719\pi$
$563$	−1.00081e7	−1.33071	−0.665353	+	0.746529i	$0.731719\pi$
$564$	5.84347e6	0.773522
$565$	−1.64164e7	−2.16351
$566$	−1.55900e6	−0.204552
$567$	−8.00380e6	−1.04553
$568$	−9.82559e6	−1.27787
$569$	1.08203e7	1.40106	0.700532	−	0.713621i	$-0.252946\pi$
$569$	1.08203e7	1.40106	0.700532	+	0.713621i	$0.252946\pi$
$570$	−7.06422e6	−0.910703
$571$	2.23335e6	0.286660	0.143330	−	0.989675i	$-0.454219\pi$
$571$	2.23335e6	0.286660	0.143330	+	0.989675i	$0.454219\pi$
$572$	85784.6	0.0109627
$573$	−160448.	−0.0204149
$574$	2.36510e7	2.99619
$575$	−1.21347e6	−0.153059
$576$	−2.69740e7	−3.38757
$577$	595575.	0.0744727	0.0372363	−	0.999306i	$-0.488145\pi$
$577$	595575.	0.0744727	0.0372363	+	0.999306i	$0.488145\pi$
$578$	−113299.	−0.0141060
$579$	828427.	0.102697
$580$	−1.88717e7	−2.32939
$581$	−4.22367e6	−0.519099
$582$	−4.03760e6	−0.494102
$583$	373111.	0.0454639
$584$	3.74887e7	4.54850
$585$	850752.	0.102781
$586$	−1.25677e7	−1.51186
$587$	−1.00823e7	−1.20772	−0.603860	−	0.797091i	$-0.706371\pi$
$587$	−1.00823e7	−1.20772	−0.603860	+	0.797091i	$0.706371\pi$
$588$	7.38494e6	0.880854
$589$	−2.86157e6	−0.339872
$590$	2.25049e7	2.66163
$591$	−3.59381e6	−0.423240
$592$	−1.12888e7	−1.32387
$593$	−1.22549e6	−0.143111	−0.0715554	−	0.997437i	$-0.522796\pi$
$593$	−1.22549e6	−0.143111	−0.0715554	+	0.997437i	$0.522796\pi$
$594$	455368.	0.0529537
$595$	−1.65328e7	−1.91449
$596$	3.77810e7	4.35671
$597$	424241.	0.0487166
$598$	286231.	0.0327313
$599$	1.16014e7	1.32112	0.660560	−	0.750773i	$-0.270319\pi$
$599$	1.16014e7	1.32112	0.660560	+	0.750773i	$0.270319\pi$
$600$	−6.93431e6	−0.786367
$601$	1.25845e7	1.42118	0.710590	−	0.703607i	$-0.248428\pi$
$601$	1.25845e7	1.42118	0.710590	+	0.703607i	$0.248428\pi$
$602$	−8.20793e6	−0.923087
$603$	6.74690e6	0.755633
$604$	−3.69786e7	−4.12437
$605$	1.19502e7	1.32736
$606$	8.27578e6	0.915435
$607$	−1.58815e7	−1.74952	−0.874760	−	0.484557i	$-0.838981\pi$
$607$	−1.58815e7	−1.74952	−0.874760	+	0.484557i	$0.838981\pi$
$608$	4.09089e7	4.48806
$609$	−2.56725e6	−0.280494
$610$	−8.00583e6	−0.871128
$611$	729149.	0.0790157
$612$	2.30422e7	2.48683
$613$	−2.70884e6	−0.291160	−0.145580	−	0.989346i	$-0.546505\pi$
$613$	−2.70884e6	−0.291160	−0.145580	+	0.989346i	$0.546505\pi$
$614$	−4.90383e6	−0.524946
$615$	−4.11954e6	−0.439198
$616$	2.12839e6	0.225995
$617$	1.43995e7	1.52278	0.761388	−	0.648297i	$-0.224518\pi$
$617$	1.43995e7	1.52278	0.761388	+	0.648297i	$0.224518\pi$
$618$	3.61490e6	0.380737
$619$	−1.12592e7	−1.18108	−0.590541	−	0.807008i	$-0.701085\pi$
$619$	−1.12592e7	−1.18108	−0.590541	+	0.807008i	$0.701085\pi$
$620$	−1.01862e7	−1.06423
$621$	1.11231e6	0.115743
$622$	1.26636e7	1.31244
$623$	−2.04618e7	−2.11215
$624$	944459.	0.0971005
$625$	−1.14966e7	−1.17725
$626$	1.54472e7	1.57548
$627$	−164262.	−0.0166866
$628$	1.58002e7	1.59869
$629$	3.53122e6	0.355875
$630$	3.32921e7	3.34187
$631$	1.63264e7	1.63237	0.816184	−	0.577793i	$-0.196086\pi$
$631$	1.63264e7	1.63237	0.816184	+	0.577793i	$0.196086\pi$
$632$	−8.00326e6	−0.797029
$633$	5.55482e6	0.551011
$634$	−8.82099e6	−0.871554
$635$	−2.15856e7	−2.12436
$636$	8.21434e6	0.805248
$637$	921494.	0.0899796
$638$	−599416.	−0.0583011
$639$	−3.57373e6	−0.346234
$640$	4.61912e7	4.45768
$641$	5.84821e6	0.562183	0.281092	−	0.959681i	$-0.409303\pi$
$641$	5.84821e6	0.562183	0.281092	+	0.959681i	$0.409303\pi$
$642$	6.15961e6	0.589815
$643$	7.26858e6	0.693301	0.346651	−	0.937994i	$-0.387319\pi$
$643$	7.26858e6	0.693301	0.346651	+	0.937994i	$0.387319\pi$
$644$	8.19992e6	0.779103
$645$	1.42966e6	0.135311
$646$	−2.38743e7	−2.25087
$647$	1.44885e7	1.36070	0.680349	−	0.732888i	$-0.261828\pi$
$647$	1.44885e7	1.36070	0.680349	+	0.732888i	$0.261828\pi$
$648$	−2.60852e7	−2.44038
$649$	523300.	0.0487684
$650$	−1.36473e6	−0.126696
$651$	−1.38570e6	−0.128150
$652$	2.30120e7	2.12000
$653$	195119.	0.0179067	0.00895335	−	0.999960i	$-0.497150\pi$
$653$	195119.	0.0179067	0.00895335	+	0.999960i	$0.497150\pi$
$654$	5.58914e6	0.510976
$655$	−1.27596e7	−1.16208
$656$	4.45081e7	4.03812
$657$	1.36353e7	1.23239
$658$	2.85334e7	2.56915
$659$	1.56954e7	1.40786	0.703929	−	0.710271i	$-0.251427\pi$
$659$	1.56954e7	1.40786	0.703929	+	0.710271i	$0.251427\pi$
$660$	−584718.	−0.0522501
$661$	−1.83337e6	−0.163209	−0.0816047	−	0.996665i	$-0.526005\pi$
$661$	−1.83337e6	−0.163209	−0.0816047	+	0.996665i	$0.526005\pi$
$662$	1.25099e7	1.10945
$663$	−295433.	−0.0261021
$664$	−1.37654e7	−1.21163
$665$	−2.52525e7	−2.21437
$666$	−7.11082e6	−0.621204
$667$	−1.46417e6	−0.127431
$668$	−3.37764e7	−2.92869
$669$	−2.20596e6	−0.190560
$670$	−2.48840e7	−2.14158
$671$	−186157.	−0.0159615
$672$	1.98099e7	1.69223
$673$	−1.56431e7	−1.33133	−0.665663	−	0.746253i	$-0.731851\pi$
$673$	−1.56431e7	−1.33133	−0.665663	+	0.746253i	$0.731851\pi$
$674$	−3.34134e7	−2.83315
$675$	−5.30340e6	−0.448017
$676$	−3.22289e7	−2.71256
$677$	−16458.7	−0.00138014	−0.000690070	−	1.00000i	$-0.500220\pi$
$677$	−16458.7	−0.00138014	−0.000690070		1.00000i	$0.500220\pi$
$678$	−1.14797e7	−0.959083
$679$	−1.44332e7	−1.20140
$680$	−5.38820e7	−4.46860
$681$	−2.54228e6	−0.210066
$682$	−323542.	−0.0266360
$683$	−2.42120e7	−1.98600	−0.992998	−	0.118132i	$-0.962310\pi$
$683$	−2.42120e7	−1.98600	−0.992998	+	0.118132i	$0.962310\pi$
$684$	3.51951e7	2.87635
$685$	2.15758e7	1.75688
$686$	1.91549e6	0.155407
$687$	1.08012e6	0.0873131
$688$	−1.54463e7	−1.24409
$689$	1.02499e6	0.0822565
$690$	−1.95098e6	−0.156002
$691$	−1.72925e7	−1.37772	−0.688862	−	0.724893i	$-0.741889\pi$
$691$	−1.72925e7	−1.37772	−0.688862	+	0.724893i	$0.741889\pi$
$692$	−3.06618e7	−2.43407
$693$	774129.	0.0612323
$694$	1.27839e7	1.00755
$695$	−1.75195e7	−1.37581
$696$	−8.36693e6	−0.654701
$697$	−1.39224e7	−1.08551
$698$	4.68393e7	3.63891
$699$	2.89116e6	0.223810
$700$	−3.90966e7	−3.01574
$701$	8.46470e6	0.650604	0.325302	−	0.945610i	$-0.394534\pi$
$701$	8.46470e6	0.650604	0.325302	+	0.945610i	$0.394534\pi$
$702$	1.25096e6	0.0958075
$703$	5.39365e6	0.411618
$704$	2.31331e6	0.175915
$705$	−4.96997e6	−0.376601
$706$	818247.	0.0617835
$707$	2.95834e7	2.22587
$708$	1.15209e7	0.863777
$709$	−2.27672e7	−1.70096	−0.850480	−	0.526008i	$-0.823688\pi$
$709$	−2.27672e7	−1.70096	−0.850480	+	0.526008i	$0.823688\pi$
$710$	1.31807e7	0.981279
$711$	−2.91092e6	−0.215951
$712$	−6.66873e7	−4.92996
$713$	−790302.	−0.0582196
$714$	−1.15610e7	−0.848694
$715$	−72961.3	−0.00533737
$716$	3.25053e7	2.36958
$717$	−5.39088e6	−0.391617
$718$	−1.03343e7	−0.748119
$719$	9.55645e6	0.689405	0.344702	−	0.938712i	$-0.387980\pi$
$719$	9.55645e6	0.689405	0.344702	+	0.938712i	$0.387980\pi$
$720$	6.26514e7	4.50402
$721$	1.29222e7	0.925758
$722$	−9.40550e6	−0.671489
$723$	2.56032e6	0.182158
$724$	1.96847e7	1.39567
$725$	6.98105e6	0.493260
$726$	8.35655e6	0.588417
$727$	1.46289e7	1.02654	0.513269	−	0.858228i	$-0.328434\pi$
$727$	1.46289e7	1.02654	0.513269	+	0.858228i	$0.328434\pi$
$728$	5.84697e6	0.408886
$729$	−6.93821e6	−0.483536
$730$	−5.02898e7	−3.49279
$731$	4.83170e6	0.334431
$732$	−4.09839e6	−0.282707
$733$	−4.48853e6	−0.308563	−0.154281	−	0.988027i	$-0.549306\pi$
$733$	−4.48853e6	−0.308563	−0.154281	+	0.988027i	$0.549306\pi$
$734$	−3.42112e6	−0.234384
$735$	−6.28102e6	−0.428856
$736$	1.12981e7	0.768798
$737$	−578620.	−0.0392396
$738$	2.80356e7	1.89483
$739$	−4.73663e6	−0.319050	−0.159525	−	0.987194i	$-0.550996\pi$
$739$	−4.73663e6	−0.319050	−0.159525	+	0.987194i	$0.550996\pi$
$740$	1.91996e7	1.28888
$741$	−451250.	−0.0301906
$742$	4.01103e7	2.67452
$743$	5.36451e6	0.356498	0.178249	−	0.983985i	$-0.442957\pi$
$743$	5.36451e6	0.356498	0.178249	+	0.983985i	$0.442957\pi$
$744$	−4.51615e6	−0.299114
$745$	−3.21334e7	−2.12112
$746$	−5.38291e7	−3.54136
$747$	−5.00670e6	−0.328284
$748$	−1.97612e6	−0.129140
$749$	2.20188e7	1.43413
$750$	−2.78306e6	−0.180663
$751$	−8.02694e6	−0.519338	−0.259669	−	0.965698i	$-0.583613\pi$
$751$	−8.02694e6	−0.519338	−0.259669	+	0.965698i	$0.583613\pi$
$752$	5.36963e7	3.46258
$753$	7.59813e6	0.488336
$754$	−1.64668e6	−0.105482
$755$	3.14509e7	2.00801
$756$	3.58373e7	2.28051
$757$	−2.59961e7	−1.64880	−0.824402	−	0.566005i	$-0.808488\pi$
$757$	−2.59961e7	−1.64880	−0.824402	+	0.566005i	$0.808488\pi$
$758$	2.06786e6	0.130722
$759$	−45365.5	−0.00285839
$760$	−8.23004e7	−5.16854
$761$	−2.53208e7	−1.58495	−0.792474	−	0.609906i	$-0.791207\pi$
$761$	−2.53208e7	−1.58495	−0.792474	+	0.609906i	$0.791207\pi$
$762$	−1.50943e7	−0.941731
$763$	1.99795e7	1.24243
$764$	−2.94828e6	−0.182741
$765$	−1.95978e7	−1.21075
$766$	1.25706e7	0.774078
$767$	1.43758e6	0.0882353
$768$	1.36615e7	0.835785
$769$	2.01646e7	1.22963	0.614815	−	0.788672i	$-0.289231\pi$
$769$	2.01646e7	1.22963	0.614815	+	0.788672i	$0.289231\pi$
$770$	−2.85516e6	−0.173542
$771$	1.38968e6	0.0841938
$772$	1.52226e7	0.919275
$773$	−4.05825e6	−0.244281	−0.122141	−	0.992513i	$-0.538976\pi$
$773$	−4.05825e6	−0.244281	−0.122141	+	0.992513i	$0.538976\pi$
$774$	−9.72960e6	−0.583771
$775$	3.76810e6	0.225356
$776$	−4.70394e7	−2.80419
$777$	2.61185e6	0.155201
$778$	−3.90461e6	−0.231275
$779$	−2.12654e7	−1.25554
$780$	−1.60630e6	−0.0945345
$781$	306486.	0.0179797
$782$	−6.59356e6	−0.385570
$783$	−6.39907e6	−0.373003
$784$	6.78611e7	3.94304
$785$	−1.34384e7	−0.778345
$786$	−8.92255e6	−0.515149
$787$	−2.91195e7	−1.67589	−0.837947	−	0.545752i	$-0.816244\pi$
$787$	−2.91195e7	−1.67589	−0.837947	+	0.545752i	$0.816244\pi$
$788$	−6.60374e7	−3.78856
$789$	2.22993e6	0.127526
$790$	1.07361e7	0.612038
$791$	−4.10365e7	−2.33200
$792$	2.52297e6	0.142922
$793$	−511398.	−0.0288786
$794$	4.53790e7	2.55449
$795$	−6.98644e6	−0.392047
$796$	7.79555e6	0.436078
$797$	1.43107e7	0.798020	0.399010	−	0.916947i	$-0.369354\pi$
$797$	1.43107e7	0.798020	0.399010	+	0.916947i	$0.369354\pi$
$798$	−1.76585e7	−0.981629
$799$	−1.67966e7	−0.930794
$800$	−5.38687e7	−2.97585
$801$	−2.42553e7	−1.33575
$802$	2.39727e7	1.31608
$803$	−1.16937e6	−0.0639976
$804$	−1.27388e7	−0.695004
$805$	−6.97417e6	−0.379318
$806$	−888814.	−0.0481918
$807$	−854251.	−0.0461744
$808$	9.64156e7	5.19540
$809$	−3.00137e7	−1.61231	−0.806154	−	0.591705i	$-0.798455\pi$
$809$	−3.00137e7	−1.61231	−0.806154	+	0.591705i	$0.798455\pi$
$810$	3.49924e7	1.87397
$811$	1.24114e7	0.662624	0.331312	−	0.943521i	$-0.392509\pi$
$811$	1.24114e7	0.662624	0.331312	+	0.943521i	$0.392509\pi$
$812$	−4.71739e7	−2.51080
$813$	3.28711e6	0.174416
$814$	609831.	0.0322588
$815$	−1.95721e7	−1.03215
$816$	−2.17564e7	−1.14383
$817$	7.38003e6	0.386815
$818$	4.01836e7	2.09974
$819$	2.12664e6	0.110786
$820$	−7.56977e7	−3.93141
$821$	1.34744e7	0.697670	0.348835	−	0.937184i	$-0.386577\pi$
$821$	1.34744e7	0.697670	0.348835	+	0.937184i	$0.386577\pi$
$822$	1.50876e7	0.778824
$823$	−1.10990e7	−0.571197	−0.285599	−	0.958349i	$-0.592192\pi$
$823$	−1.10990e7	−0.571197	−0.285599	+	0.958349i	$0.592192\pi$
$824$	4.21148e7	2.16081
$825$	216300.	0.0110642
$826$	5.62560e7	2.86892
$827$	−2.77248e7	−1.40963	−0.704813	−	0.709393i	$-0.748969\pi$
$827$	−2.77248e7	−1.40963	−0.704813	+	0.709393i	$0.748969\pi$
$828$	9.72011e6	0.492715
$829$	1.24604e7	0.629716	0.314858	−	0.949139i	$-0.398043\pi$
$829$	1.24604e7	0.629716	0.314858	+	0.949139i	$0.398043\pi$
$830$	1.84658e7	0.930407
$831$	5.31816e6	0.267152
$832$	6.35498e6	0.318277
$833$	−2.12274e7	−1.05995
$834$	−1.22510e7	−0.609898
$835$	2.87274e7	1.42587
$836$	−3.01836e6	−0.149367
$837$	−3.45398e6	−0.170414
$838$	−9.93021e6	−0.488482
$839$	−5.58957e6	−0.274141	−0.137070	−	0.990561i	$-0.543769\pi$
$839$	−5.58957e6	−0.274141	−0.137070	+	0.990561i	$0.543769\pi$
$840$	−3.98536e7	−1.94881
$841$	−1.20878e7	−0.589330
$842$	1.91815e7	0.932401
$843$	−831840.	−0.0403154
$844$	1.02071e8	4.93228
$845$	2.74113e7	1.32065
$846$	3.38233e7	1.62476
$847$	2.98721e7	1.43073
$848$	7.54825e7	3.60460
$849$	678790.	0.0323196
$850$	3.14376e7	1.49246
$851$	1.48961e6	0.0705095
$852$	6.74754e6	0.318454
$853$	2.41509e7	1.13648	0.568239	−	0.822864i	$-0.307625\pi$
$853$	2.41509e7	1.13648	0.568239	+	0.822864i	$0.307625\pi$
$854$	−2.00123e7	−0.938972
$855$	−2.99340e7	−1.40039
$856$	7.17615e7	3.34739
$857$	2.57828e7	1.19916	0.599581	−	0.800314i	$-0.295334\pi$
$857$	2.57828e7	1.19916	0.599581	+	0.800314i	$0.295334\pi$
$858$	−51020.4	−0.00236606
$859$	1.45019e7	0.670567	0.335284	−	0.942117i	$-0.391168\pi$
$859$	1.45019e7	0.670567	0.335284	+	0.942117i	$0.391168\pi$
$860$	2.62705e7	1.21122
$861$	−1.02977e7	−0.473403
$862$	3.84094e7	1.76063
$863$	2.63498e7	1.20434	0.602171	−	0.798367i	$-0.294303\pi$
$863$	2.63498e7	1.20434	0.602171	+	0.798367i	$0.294303\pi$
$864$	4.93779e7	2.25034
$865$	2.60784e7	1.18506
$866$	−3.36397e7	−1.52425
$867$	49330.4	0.00222878
$868$	−2.54627e7	−1.14711
$869$	249643.	0.0112142
$870$	1.12239e7	0.502745
$871$	−1.58955e6	−0.0709950
$872$	6.51153e7	2.89996
$873$	−1.71090e7	−0.759782
$874$	−1.00711e7	−0.445964
$875$	−9.94861e6	−0.439281
$876$	−2.57446e7	−1.13351
$877$	2.30198e7	1.01066	0.505328	−	0.862927i	$-0.331372\pi$
$877$	2.30198e7	1.01066	0.505328	+	0.862927i	$0.331372\pi$
$878$	2.10837e7	0.923018
$879$	5.47201e6	0.238877
$880$	−5.37305e6	−0.233891
$881$	−3.85668e7	−1.67407	−0.837035	−	0.547149i	$-0.815713\pi$
$881$	−3.85668e7	−1.67407	−0.837035	+	0.547149i	$0.815713\pi$
$882$	4.27457e7	1.85021
$883$	4.48222e7	1.93460	0.967300	−	0.253636i	$-0.0816264\pi$
$883$	4.48222e7	1.93460	0.967300	+	0.253636i	$0.0816264\pi$
$884$	−5.42867e6	−0.233648
$885$	−9.79869e6	−0.420542
$886$	5.25503e7	2.24901
$887$	−3.13962e7	−1.33989	−0.669944	−	0.742412i	$-0.733682\pi$
$887$	−3.13962e7	−1.33989	−0.669944	+	0.742412i	$0.733682\pi$
$888$	8.51230e6	0.362255
$889$	−5.39578e7	−2.28981
$890$	8.94587e7	3.78571
$891$	813668.	0.0343362
$892$	−4.05352e7	−1.70577
$893$	−2.56554e7	−1.07659
$894$	−2.24703e7	−0.940295
$895$	−2.76463e7	−1.15366
$896$	1.15465e8	4.80485
$897$	−124625.	−0.00517160
$898$	−5.03105e7	−2.08194
$899$	4.54659e6	0.187623
$900$	−4.63448e7	−1.90719
$901$	−2.36114e7	−0.968970
$902$	−2.40436e6	−0.0983973
$903$	3.57375e6	0.145849
$904$	−1.33742e8	−5.44311
$905$	−1.67422e7	−0.679501
$906$	2.19930e7	0.890151
$907$	7.46481e6	0.301301	0.150650	−	0.988587i	$-0.451863\pi$
$907$	7.46481e6	0.301301	0.150650	+	0.988587i	$0.451863\pi$
$908$	−4.67152e7	−1.88037
$909$	3.50679e7	1.40767
$910$	−7.84351e6	−0.313983
$911$	8.05203e6	0.321447	0.160724	−	0.986999i	$-0.448617\pi$
$911$	8.05203e6	0.321447	0.160724	+	0.986999i	$0.448617\pi$
$912$	−3.32311e7	−1.32299
$913$	429379.	0.0170476
$914$	7.29437e7	2.88817
$915$	3.48575e6	0.137640
$916$	1.98475e7	0.781569
$917$	−3.18954e7	−1.25258
$918$	−2.88168e7	−1.12860
$919$	3.62909e7	1.41745	0.708726	−	0.705484i	$-0.249270\pi$
$919$	3.62909e7	1.41745	0.708726	+	0.705484i	$0.249270\pi$
$920$	−2.27296e7	−0.885364
$921$	2.13513e6	0.0829423
$922$	1.21423e7	0.470407
$923$	841959.	0.0325302
$924$	−1.46163e6	−0.0563193
$925$	−7.10234e6	−0.272927
$926$	−5.03199e7	−1.92847
$927$	1.53178e7	0.585461
$928$	−6.49978e7	−2.47759
$929$	4.85255e7	1.84472	0.922360	−	0.386331i	$-0.126258\pi$
$929$	4.85255e7	1.84472	0.922360	+	0.386331i	$0.126258\pi$
$930$	6.05826e6	0.229689
$931$	−3.24231e7	−1.22597
$932$	5.31259e7	2.00339
$933$	−5.51374e6	−0.207368
$934$	3.66619e7	1.37514
$935$	1.68072e6	0.0628735
$936$	6.93094e6	0.258584
$937$	1.45620e7	0.541839	0.270920	−	0.962602i	$-0.412672\pi$
$937$	1.45620e7	0.541839	0.270920	+	0.962602i	$0.412672\pi$
$938$	−6.22030e7	−2.30836
$939$	−6.72573e6	−0.248929
$940$	−9.13247e7	−3.37108
$941$	3.47602e6	0.127970	0.0639850	−	0.997951i	$-0.479619\pi$
$941$	3.47602e6	0.127970	0.0639850	+	0.997951i	$0.479619\pi$
$942$	−9.39718e6	−0.345041
$943$	−5.87303e6	−0.215072
$944$	1.05867e8	3.86660
$945$	−3.04803e7	−1.11030
$946$	834420.	0.0303149
$947$	3.00257e6	0.108797	0.0543987	−	0.998519i	$-0.482676\pi$
$947$	3.00257e6	0.108797	0.0543987	+	0.998519i	$0.482676\pi$
$948$	5.49608e6	0.198624
$949$	−3.21242e6	−0.115789
$950$	4.80184e7	1.72623
$951$	3.84068e6	0.137707
$952$	−1.34690e8	−4.81662
$953$	−1.36418e7	−0.486563	−0.243282	−	0.969956i	$-0.578224\pi$
$953$	−1.36418e7	−0.486563	−0.243282	+	0.969956i	$0.578224\pi$
$954$	4.75464e7	1.69140
$955$	2.50756e6	0.0889700
$956$	−9.90590e7	−3.50550
$957$	260987.	0.00921168
$958$	−2.35779e7	−0.830024
$959$	5.39335e7	1.89370
$960$	−4.33163e7	−1.51696
$961$	−2.61751e7	−0.914281
$962$	1.67529e6	0.0583649
$963$	2.61008e7	0.906961
$964$	4.70466e7	1.63056
$965$	−1.29471e7	−0.447562
$966$	−4.87690e6	−0.168152
$967$	−1.49342e7	−0.513589	−0.256794	−	0.966466i	$-0.582666\pi$
$967$	−1.49342e7	−0.513589	−0.256794	+	0.966466i	$0.582666\pi$
$968$	9.73565e7	3.33946
$969$	1.03949e7	0.355641
$970$	6.31017e7	2.15334
$971$	−6.12959e6	−0.208633	−0.104317	−	0.994544i	$-0.533266\pi$
$971$	−6.12959e6	−0.208633	−0.104317	+	0.994544i	$0.533266\pi$
$972$	6.47598e7	2.19857
$973$	−4.37937e7	−1.48296
$974$	1.12046e8	3.78441
$975$	594204.	0.0200182
$976$	−3.76606e7	−1.26550
$977$	−3.09811e7	−1.03839	−0.519194	−	0.854656i	$-0.673768\pi$
$977$	−3.09811e7	−1.03839	−0.519194	+	0.854656i	$0.673768\pi$
$978$	−1.36864e7	−0.457554
$979$	2.08015e6	0.0693647
$980$	−1.15416e8	−3.83883
$981$	2.36835e7	0.785730
$982$	−9.08523e7	−3.00647
$983$	−966289.	−0.0318950
$983$	−966289.	−0.0318950
$984$	−3.35612e7	−1.10497
$985$	5.61660e7	1.84452
$986$	3.79326e7	1.24257
$987$	−1.24235e7	−0.405930
$988$	−8.29185e6	−0.270246
$989$	2.03820e6	0.0662608
$990$	−3.38448e6	−0.109750
$991$	5.06652e7	1.63880	0.819399	−	0.573224i	$-0.194308\pi$
$991$	5.06652e7	1.63880	0.819399	+	0.573224i	$0.194308\pi$
$992$	−3.50834e7	−1.13194
$993$	−5.44684e6	−0.175296
$994$	3.29480e7	1.05770
$995$	−6.63025e6	−0.212311
$996$	9.45312e6	0.301944
$997$	3.00934e7	0.958812	0.479406	−	0.877593i	$-0.340852\pi$
$997$	3.00934e7	0.958812	0.479406	+	0.877593i	$0.340852\pi$
$998$	−2.80812e7	−0.892463
$999$	6.51025e6	0.206388

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.6.a.a.1.3	✓	191

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.6.a.a.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-10.9287 q^{2} +4.75838 q^{3} +87.4366 q^{4} -74.3663 q^{5} -52.0029 q^{6} -185.895 q^{7} -605.851 q^{8} -220.358 q^{9} +O(q^{10})\)	\(q-10.9287 q^{2} +4.75838 q^{3} +87.4366 q^{4} -74.3663 q^{5} -52.0029 q^{6} -185.895 q^{7} -605.851 q^{8} -220.358 q^{9} +812.728 q^{10} +18.8981 q^{11} +416.056 q^{12} +51.9156 q^{13} +2031.59 q^{14} -353.863 q^{15} +3823.19 q^{16} -1195.92 q^{17} +2408.23 q^{18} -1826.67 q^{19} -6502.34 q^{20} -884.557 q^{21} -206.532 q^{22} -504.486 q^{23} -2882.87 q^{24} +2405.35 q^{25} -567.370 q^{26} -2204.83 q^{27} -16254.0 q^{28} +2902.30 q^{29} +3867.27 q^{30} +1566.55 q^{31} -22395.3 q^{32} +89.9243 q^{33} +13069.9 q^{34} +13824.3 q^{35} -19267.3 q^{36} -2952.72 q^{37} +19963.1 q^{38} +247.034 q^{39} +45054.9 q^{40} +11641.6 q^{41} +9667.07 q^{42} -4040.15 q^{43} +1652.39 q^{44} +16387.2 q^{45} +5513.38 q^{46} +14044.9 q^{47} +18192.2 q^{48} +17749.9 q^{49} -26287.4 q^{50} -5690.64 q^{51} +4539.33 q^{52} +19743.3 q^{53} +24096.0 q^{54} -1405.38 q^{55} +112624. q^{56} -8691.98 q^{57} -31718.3 q^{58} +27690.6 q^{59} -30940.6 q^{60} -9850.57 q^{61} -17120.4 q^{62} +40963.4 q^{63} +122410. q^{64} -3860.77 q^{65} -982.756 q^{66} -30617.9 q^{67} -104567. q^{68} -2400.54 q^{69} -151082. q^{70} +16217.8 q^{71} +133504. q^{72} -61877.8 q^{73} +32269.4 q^{74} +11445.6 q^{75} -159718. q^{76} -3513.06 q^{77} -2699.76 q^{78} +13209.9 q^{79} -284317. q^{80} +43055.5 q^{81} -127228. q^{82} +22720.8 q^{83} -77342.7 q^{84} +88936.2 q^{85} +44153.7 q^{86} +13810.2 q^{87} -11449.4 q^{88} +110072. q^{89} -179091. q^{90} -9650.84 q^{91} -44110.6 q^{92} +7454.23 q^{93} -153493. q^{94} +135843. q^{95} -106565. q^{96} +77641.9 q^{97} -193983. q^{98} -4164.34 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 191 q - 37 q^{2} - 74 q^{3} + 2821 q^{4} - 247 q^{5} - 335 q^{6} - 1569 q^{7} - 1761 q^{8} + 13251 q^{9}+O(q^{10}) \) 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

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