LMFDB - Embedded newform 177.6.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,6,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	177.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:	$28.3879361069$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 269 x^{10} + 143 x^{9} + 25384 x^{8} + 8539 x^{7} - 1009736 x^{6} - 720516 x^{5} + \cdots + 49172480 $ x^12 - 2x^11 - 269x^10 + 143x^9 + 25384x^8 + 8539x^7 - 1009736x^6 - 720516x^5 + 15565376x^4 + 6775664x^3 - 75006848x^2 + 21512960*x + 49172480
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$12.3715$ of defining polynomial
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.3715 q^{2} +9.00000 q^{3} +75.5670 q^{4} +33.2592 q^{5} -93.3431 q^{6} -56.9512 q^{7} -451.853 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q-10.3715 q^{2} +9.00000 q^{3} +75.5670 q^{4} +33.2592 q^{5} -93.3431 q^{6} -56.9512 q^{7} -451.853 q^{8} +81.0000 q^{9} -344.946 q^{10} +432.466 q^{11} +680.103 q^{12} +178.063 q^{13} +590.667 q^{14} +299.333 q^{15} +2268.23 q^{16} +1658.66 q^{17} -840.088 q^{18} -168.835 q^{19} +2513.30 q^{20} -512.561 q^{21} -4485.30 q^{22} +143.318 q^{23} -4066.68 q^{24} -2018.83 q^{25} -1846.77 q^{26} +729.000 q^{27} -4303.63 q^{28} +275.265 q^{29} -3104.51 q^{30} -2273.75 q^{31} -9065.52 q^{32} +3892.20 q^{33} -17202.7 q^{34} -1894.15 q^{35} +6120.93 q^{36} -1120.19 q^{37} +1751.06 q^{38} +1602.57 q^{39} -15028.3 q^{40} -2114.42 q^{41} +5316.00 q^{42} +3840.06 q^{43} +32680.2 q^{44} +2693.99 q^{45} -1486.42 q^{46} +14809.7 q^{47} +20414.1 q^{48} -13563.6 q^{49} +20938.2 q^{50} +14927.9 q^{51} +13455.7 q^{52} +9651.99 q^{53} -7560.79 q^{54} +14383.5 q^{55} +25733.6 q^{56} -1519.51 q^{57} -2854.90 q^{58} -3481.00 q^{59} +22619.7 q^{60} +29254.1 q^{61} +23582.1 q^{62} -4613.05 q^{63} +21439.3 q^{64} +5922.23 q^{65} -40367.7 q^{66} +15092.5 q^{67} +125340. q^{68} +1289.86 q^{69} +19645.1 q^{70} +13271.8 q^{71} -36600.1 q^{72} +42497.1 q^{73} +11618.0 q^{74} -18169.4 q^{75} -12758.3 q^{76} -24629.5 q^{77} -16620.9 q^{78} -55585.7 q^{79} +75439.4 q^{80} +6561.00 q^{81} +21929.6 q^{82} +81043.5 q^{83} -38732.7 q^{84} +55165.7 q^{85} -39827.0 q^{86} +2477.39 q^{87} -195411. q^{88} +107408. q^{89} -27940.6 q^{90} -10140.9 q^{91} +10830.1 q^{92} -20463.7 q^{93} -153598. q^{94} -5615.31 q^{95} -81589.7 q^{96} -92436.4 q^{97} +140674. q^{98} +35029.8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9}+O(q^{10}) $ 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9} + 601 q^{10} + 1480 q^{11} + 1782 q^{12} + 472 q^{13} + 1065 q^{14} + 1422 q^{15} + 6370 q^{16} + 1565 q^{17} + 1782 q^{18} + 3939 q^{19} + 8033 q^{20} + 3717 q^{21} - 1738 q^{22} + 7245 q^{23} + 6507 q^{24} + 9690 q^{25} + 3764 q^{26} + 8748 q^{27} + 12154 q^{28} + 10003 q^{29} + 5409 q^{30} + 7295 q^{31} + 11628 q^{32} + 13320 q^{33} - 16344 q^{34} + 11015 q^{35} + 16038 q^{36} + 6741 q^{37} + 3035 q^{38} + 4248 q^{39} + 5572 q^{40} + 34025 q^{41} + 9585 q^{42} - 6336 q^{43} + 41168 q^{44} + 12798 q^{45} + 2345 q^{46} + 66167 q^{47} + 57330 q^{48} + 28319 q^{49} + 31173 q^{50} + 14085 q^{51} + 16440 q^{52} + 62290 q^{53} + 16038 q^{54} + 55764 q^{55} + 107306 q^{56} + 35451 q^{57} + 37952 q^{58} - 41772 q^{59} + 72297 q^{60} + 68469 q^{61} + 99190 q^{62} + 33453 q^{63} + 68525 q^{64} + 80156 q^{65} - 15642 q^{66} + 113310 q^{67} + 33887 q^{68} + 65205 q^{69} + 32034 q^{70} + 84520 q^{71} + 58563 q^{72} + 135895 q^{73} - 31962 q^{74} + 87210 q^{75} - 61848 q^{76} - 3799 q^{77} + 33876 q^{78} + 14122 q^{79} + 77609 q^{80} + 78732 q^{81} - 1501 q^{82} + 114463 q^{83} + 109386 q^{84} - 101097 q^{85} - 203536 q^{86} + 90027 q^{87} - 244967 q^{88} + 189109 q^{89} + 48681 q^{90} - 168249 q^{91} - 71946 q^{92} + 65655 q^{93} - 472284 q^{94} + 21923 q^{95} + 104652 q^{96} - 76192 q^{97} - 17544 q^{98} + 119880 q^{99}+O(q^{100}) \) 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9 + 601 * q^10 + 1480 * q^11 + 1782 * q^12 + 472 * q^13 + 1065 * q^14 + 1422 * q^15 + 6370 * q^16 + 1565 * q^17 + 1782 * q^18 + 3939 * q^19 + 8033 * q^20 + 3717 * q^21 - 1738 * q^22 + 7245 * q^23 + 6507 * q^24 + 9690 * q^25 + 3764 * q^26 + 8748 * q^27 + 12154 * q^28 + 10003 * q^29 + 5409 * q^30 + 7295 * q^31 + 11628 * q^32 + 13320 * q^33 - 16344 * q^34 + 11015 * q^35 + 16038 * q^36 + 6741 * q^37 + 3035 * q^38 + 4248 * q^39 + 5572 * q^40 + 34025 * q^41 + 9585 * q^42 - 6336 * q^43 + 41168 * q^44 + 12798 * q^45 + 2345 * q^46 + 66167 * q^47 + 57330 * q^48 + 28319 * q^49 + 31173 * q^50 + 14085 * q^51 + 16440 * q^52 + 62290 * q^53 + 16038 * q^54 + 55764 * q^55 + 107306 * q^56 + 35451 * q^57 + 37952 * q^58 - 41772 * q^59 + 72297 * q^60 + 68469 * q^61 + 99190 * q^62 + 33453 * q^63 + 68525 * q^64 + 80156 * q^65 - 15642 * q^66 + 113310 * q^67 + 33887 * q^68 + 65205 * q^69 + 32034 * q^70 + 84520 * q^71 + 58563 * q^72 + 135895 * q^73 - 31962 * q^74 + 87210 * q^75 - 61848 * q^76 - 3799 * q^77 + 33876 * q^78 + 14122 * q^79 + 77609 * q^80 + 78732 * q^81 - 1501 * q^82 + 114463 * q^83 + 109386 * q^84 - 101097 * q^85 - 203536 * q^86 + 90027 * q^87 - 244967 * q^88 + 189109 * q^89 + 48681 * q^90 - 168249 * q^91 - 71946 * q^92 + 65655 * q^93 - 472284 * q^94 + 21923 * q^95 + 104652 * q^96 - 76192 * q^97 - 17544 * q^98 + 119880 * 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 $

$2$	−10.3715	−1.83343	−0.916715	−	0.399541i	$-0.869170\pi$
$2$	−10.3715	−1.83343	−0.916715	+	0.399541i	$0.869170\pi$
$3$	9.00000	0.577350
$3$	9.00000	0.577350
$4$	75.5670	2.36147
$5$	33.2592	0.594958	0.297479	−	0.954728i	$-0.403854\pi$
$5$	33.2592	0.594958	0.297479	+	0.954728i	$0.403854\pi$
$6$	−93.3431	−1.05853
$7$	−56.9512	−0.439297	−0.219648	−	0.975579i	$-0.570491\pi$
$7$	−56.9512	−0.439297	−0.219648	+	0.975579i	$0.570491\pi$
$8$	−451.853	−2.49616
$9$	81.0000	0.333333
$10$	−344.946	−1.09081
$11$	432.466	1.07763	0.538816	−	0.842423i	$-0.318872\pi$
$11$	432.466	1.07763	0.538816	+	0.842423i	$0.318872\pi$
$12$	680.103	1.36339
$13$	178.063	0.292224	0.146112	−	0.989268i	$-0.453324\pi$
$13$	178.063	0.292224	0.146112	+	0.989268i	$0.453324\pi$
$14$	590.667	0.805420
$15$	299.333	0.343499
$16$	2268.23	2.21507
$17$	1658.66	1.39199	0.695993	−	0.718048i	$-0.254964\pi$
$17$	1658.66	1.39199	0.695993	+	0.718048i	$0.254964\pi$
$18$	−840.088	−0.611144
$19$	−168.835	−0.107295	−0.0536473	−	0.998560i	$-0.517085\pi$
$19$	−168.835	−0.107295	−0.0536473	+	0.998560i	$0.517085\pi$
$20$	2513.30	1.40498
$21$	−512.561	−0.253628
$22$	−4485.30	−1.97576
$23$	143.318	0.0564914	0.0282457	−	0.999601i	$-0.491008\pi$
$23$	143.318	0.0564914	0.0282457	+	0.999601i	$0.491008\pi$
$24$	−4066.68	−1.44116
$25$	−2018.83	−0.646025
$26$	−1846.77	−0.535772
$27$	729.000	0.192450
$28$	−4303.63	−1.03739
$29$	275.265	0.0607794	0.0303897	−	0.999538i	$-0.490325\pi$
$29$	275.265	0.0607794	0.0303897	+	0.999538i	$0.490325\pi$
$30$	−3104.51	−0.629782
$31$	−2273.75	−0.424950	−0.212475	−	0.977166i	$-0.568152\pi$
$31$	−2273.75	−0.424950	−0.212475	+	0.977166i	$0.568152\pi$
$32$	−9065.52	−1.56501
$33$	3892.20	0.622171
$34$	−17202.7	−2.55211
$35$	−1894.15	−0.261363
$36$	6120.93	0.787156
$37$	−1120.19	−0.134520	−0.0672601	−	0.997735i	$-0.521426\pi$
$37$	−1120.19	−0.134520	−0.0672601	+	0.997735i	$0.521426\pi$
$38$	1751.06	0.196717
$39$	1602.57	0.168715
$40$	−15028.3	−1.48511
$41$	−2114.42	−0.196441	−0.0982203	−	0.995165i	$-0.531315\pi$
$41$	−2114.42	−0.196441	−0.0982203	+	0.995165i	$0.531315\pi$
$42$	5316.00	0.465009
$43$	3840.06	0.316714	0.158357	−	0.987382i	$-0.449380\pi$
$43$	3840.06	0.316714	0.158357	+	0.987382i	$0.449380\pi$
$44$	32680.2	2.54479
$45$	2693.99	0.198319
$46$	−1486.42	−0.103573
$47$	14809.7	0.977917	0.488959	−	0.872307i	$-0.337377\pi$
$47$	14809.7	0.977917	0.488959	+	0.872307i	$0.337377\pi$
$48$	20414.1	1.27887
$49$	−13563.6	−0.807019
$50$	20938.2	1.18444
$51$	14927.9	0.803664
$52$	13455.7	0.690077
$53$	9651.99	0.471984	0.235992	−	0.971755i	$-0.424166\pi$
$53$	9651.99	0.471984	0.235992	+	0.971755i	$0.424166\pi$
$54$	−7560.79	−0.352844
$55$	14383.5	0.641146
$56$	25733.6	1.09655
$57$	−1519.51	−0.0619466
$58$	−2854.90	−0.111435
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	22619.7	0.811163
$61$	29254.1	1.00661	0.503307	−	0.864108i	$-0.332117\pi$
$61$	29254.1	1.00661	0.503307	+	0.864108i	$0.332117\pi$
$62$	23582.1	0.779117
$63$	−4613.05	−0.146432
$64$	21439.3	0.654275
$65$	5922.23	0.173861
$66$	−40367.7	−1.14071
$67$	15092.5	0.410747	0.205374	−	0.978684i	$-0.434159\pi$
$67$	15092.5	0.410747	0.205374	+	0.978684i	$0.434159\pi$
$68$	125340.	3.28713
$69$	1289.86	0.0326153
$70$	19645.1	0.479191
$71$	13271.8	0.312453	0.156226	−	0.987721i	$-0.450067\pi$
$71$	13271.8	0.312453	0.156226	+	0.987721i	$0.450067\pi$
$72$	−36600.1	−0.832053
$73$	42497.1	0.933366	0.466683	−	0.884425i	$-0.345449\pi$
$73$	42497.1	0.933366	0.466683	+	0.884425i	$0.345449\pi$
$74$	11618.0	0.246634
$75$	−18169.4	−0.372983
$76$	−12758.3	−0.253373
$77$	−24629.5	−0.473400
$78$	−16620.9	−0.309328
$79$	−55585.7	−1.00206	−0.501032	−	0.865429i	$-0.667046\pi$
$79$	−55585.7	−1.00206	−0.501032	+	0.865429i	$0.667046\pi$
$80$	75439.4	1.31787
$81$	6561.00	0.111111
$82$	21929.6	0.360160
$83$	81043.5	1.29129	0.645643	−	0.763639i	$-0.276589\pi$
$83$	81043.5	1.29129	0.645643	+	0.763639i	$0.276589\pi$
$84$	−38732.7	−0.598935
$85$	55165.7	0.828174
$86$	−39827.0	−0.580673
$87$	2477.39	0.0350910
$88$	−195411.	−2.68994
$89$	107408.	1.43734	0.718672	−	0.695349i	$-0.244750\pi$
$89$	107408.	1.43734	0.718672	+	0.695349i	$0.244750\pi$
$90$	−27940.6	−0.363605
$91$	−10140.9	−0.128373
$92$	10830.1	0.133403
$93$	−20463.7	−0.245345
$94$	−153598.	−1.79294
$95$	−5615.31	−0.0638358
$96$	−81589.7	−0.903560
$97$	−92436.4	−0.997502	−0.498751	−	0.866745i	$-0.666208\pi$
$97$	−92436.4	−0.997502	−0.498751	+	0.866745i	$0.666208\pi$
$98$	140674.	1.47961
$99$	35029.8	0.359211
$100$	−152557.	−1.52557
$101$	−134769.	−1.31458	−0.657291	−	0.753637i	$-0.728298\pi$
$101$	−134769.	−1.31458	−0.657291	+	0.753637i	$0.728298\pi$
$102$	−154824.	−1.47346
$103$	166146.	1.54311	0.771553	−	0.636165i	$-0.219480\pi$
$103$	166146.	1.54311	0.771553	+	0.636165i	$0.219480\pi$
$104$	−80458.3	−0.729437
$105$	−17047.3	−0.150898
$106$	−100105.	−0.865350
$107$	120010.	1.01335	0.506674	−	0.862138i	$-0.330875\pi$
$107$	120010.	1.01335	0.506674	+	0.862138i	$0.330875\pi$
$108$	55088.3	0.454465
$109$	188031.	1.51587	0.757937	−	0.652328i	$-0.226207\pi$
$109$	188031.	1.51587	0.757937	+	0.652328i	$0.226207\pi$
$110$	−149177.	−1.17550
$111$	−10081.7	−0.0776653
$112$	−129178.	−0.973071
$113$	114073.	0.840401	0.420201	−	0.907431i	$-0.361960\pi$
$113$	114073.	0.840401	0.420201	+	0.907431i	$0.361960\pi$
$114$	15759.6	0.113575
$115$	4766.65	0.0336100
$116$	20801.0	0.143529
$117$	14423.1	0.0974079
$118$	36103.0	0.238692
$119$	−94462.7	−0.611495
$120$	−135254.	−0.857429
$121$	25976.1	0.161291
$122$	−303408.	−1.84556
$123$	−19029.8	−0.113415
$124$	−171820.	−1.00351
$125$	−171079.	−0.979316
$126$	47844.0	0.268473
$127$	305300.	1.67964	0.839822	−	0.542861i	$-0.182659\pi$
$127$	305300.	1.67964	0.839822	+	0.542861i	$0.182659\pi$
$128$	67740.1	0.365444
$129$	34560.6	0.182855
$130$	−61422.1	−0.318762
$131$	−152752.	−0.777695	−0.388848	−	0.921302i	$-0.627127\pi$
$131$	−152752.	−0.777695	−0.388848	+	0.921302i	$0.627127\pi$
$132$	294122.	1.46924
$133$	9615.35	0.0471342
$134$	−156531.	−0.753077
$135$	24245.9	0.114500
$136$	−749471.	−3.47462
$137$	−128339.	−0.584196	−0.292098	−	0.956388i	$-0.594353\pi$
$137$	−128339.	−0.584196	−0.292098	+	0.956388i	$0.594353\pi$
$138$	−13377.8	−0.0597979
$139$	155483.	0.682566	0.341283	−	0.939961i	$-0.389139\pi$
$139$	155483.	0.682566	0.341283	+	0.939961i	$0.389139\pi$
$140$	−143135.	−0.617201
$141$	133287.	0.564601
$142$	−137648.	−0.572860
$143$	77006.3	0.314910
$144$	183726.	0.738355
$145$	9155.09	0.0361612
$146$	−440756.	−1.71126
$147$	−122072.	−0.465932
$148$	−84649.5	−0.317665
$149$	444140.	1.63891	0.819454	−	0.573146i	$-0.194277\pi$
$149$	444140.	1.63891	0.819454	+	0.573146i	$0.194277\pi$
$150$	188444.	0.683838
$151$	−68940.1	−0.246054	−0.123027	−	0.992403i	$-0.539260\pi$
$151$	−68940.1	−0.246054	−0.123027	+	0.992403i	$0.539260\pi$
$152$	76288.6	0.267825
$153$	134351.	0.463996
$154$	255443.	0.867946
$155$	−75623.0	−0.252828
$156$	121101.	0.398416
$157$	−69283.9	−0.224328	−0.112164	−	0.993690i	$-0.535778\pi$
$157$	−69283.9	−0.224328	−0.112164	+	0.993690i	$0.535778\pi$
$158$	576504.	1.83721
$159$	86868.0	0.272500
$160$	−301512.	−0.931117
$161$	−8162.15	−0.0248165
$162$	−68047.1	−0.203715
$163$	−267280.	−0.787946	−0.393973	−	0.919122i	$-0.628900\pi$
$163$	−267280.	−0.787946	−0.393973	+	0.919122i	$0.628900\pi$
$164$	−159780.	−0.463888
$165$	129451.	0.370166
$166$	−840538.	−2.36749
$167$	387809.	1.07604	0.538018	−	0.842934i	$-0.319173\pi$
$167$	387809.	1.07604	0.538018	+	0.842934i	$0.319173\pi$
$168$	231602.	0.633096
$169$	−339587.	−0.914605
$170$	−572148.	−1.51840
$171$	−13675.6	−0.0357649
$172$	290182.	0.747910
$173$	−190512.	−0.483958	−0.241979	−	0.970281i	$-0.577797\pi$
$173$	−190512.	−0.483958	−0.241979	+	0.970281i	$0.577797\pi$
$174$	−25694.1	−0.0643369
$175$	114975.	0.283796
$176$	980932.	2.38703
$177$	−31329.0	−0.0751646
$178$	−1.11397e6	−2.63527
$179$	−173534.	−0.404811	−0.202406	−	0.979302i	$-0.564876\pi$
$179$	−173534.	−0.404811	−0.202406	+	0.979302i	$0.564876\pi$
$180$	203577.	0.468325
$181$	717762.	1.62849	0.814243	−	0.580524i	$-0.197152\pi$
$181$	717762.	1.62849	0.814243	+	0.580524i	$0.197152\pi$
$182$	105176.	0.235363
$183$	263287.	0.581168
$184$	−64758.8	−0.141011
$185$	−37256.6	−0.0800339
$186$	212239.	0.449824
$187$	717315.	1.50005
$188$	1.11913e6	2.30932
$189$	−41517.4	−0.0845427
$190$	58238.9	0.117039
$191$	336630.	0.667681	0.333841	−	0.942630i	$-0.391655\pi$
$191$	336630.	0.667681	0.333841	+	0.942630i	$0.391655\pi$
$192$	192954.	0.377746
$193$	293107.	0.566413	0.283206	−	0.959059i	$-0.408602\pi$
$193$	293107.	0.566413	0.283206	+	0.959059i	$0.408602\pi$
$194$	958699.	1.82885
$195$	53300.1	0.100379
$196$	−1.02496e6	−1.90575
$197$	−254135.	−0.466551	−0.233276	−	0.972411i	$-0.574944\pi$
$197$	−254135.	−0.466551	−0.233276	+	0.972411i	$0.574944\pi$
$198$	−363310.	−0.658588
$199$	65290.6	0.116874	0.0584370	−	0.998291i	$-0.481388\pi$
$199$	65290.6	0.116874	0.0584370	+	0.998291i	$0.481388\pi$
$200$	912213.	1.61258
$201$	135833.	0.237145
$202$	1.39775e6	2.41020
$203$	−15676.7	−0.0267002
$204$	1.12806e6	1.89783
$205$	−70323.8	−0.116874
$206$	−1.72317e6	−2.82918
$207$	11608.8	0.0188305
$208$	403888.	0.647295
$209$	−73015.4	−0.115624
$210$	176806.	0.276661
$211$	93142.8	0.144027	0.0720134	−	0.997404i	$-0.477058\pi$
$211$	93142.8	0.144027	0.0720134	+	0.997404i	$0.477058\pi$
$212$	729372.	1.11458
$213$	119446.	0.180395
$214$	−1.24468e6	−1.85790
$215$	127717.	0.188432
$216$	−329401.	−0.480386
$217$	129493.	0.186679
$218$	−1.95015e6	−2.77925
$219$	382474.	0.538879
$220$	1.08692e6	1.51405
$221$	295346.	0.406772
$222$	104562.	0.142394
$223$	30528.4	0.0411095	0.0205548	−	0.999789i	$-0.493457\pi$
$223$	30528.4	0.0411095	0.0205548	+	0.999789i	$0.493457\pi$
$224$	516292.	0.687504
$225$	−163525.	−0.215342
$226$	−1.18310e6	−1.54082
$227$	−777882.	−1.00196	−0.500979	−	0.865460i	$-0.667027\pi$
$227$	−777882.	−1.00196	−0.500979	+	0.865460i	$0.667027\pi$
$228$	−114825.	−0.146285
$229$	−763186.	−0.961705	−0.480852	−	0.876802i	$-0.659673\pi$
$229$	−763186.	−0.961705	−0.480852	+	0.876802i	$0.659673\pi$
$230$	−49437.1	−0.0616216
$231$	−221665.	−0.273318
$232$	−124379.	−0.151715
$233$	−1.27683e6	−1.54079	−0.770393	−	0.637570i	$-0.779940\pi$
$233$	−1.27683e6	−1.54079	−0.770393	+	0.637570i	$0.779940\pi$
$234$	−149589.	−0.178591
$235$	492559.	0.581820
$236$	−263049.	−0.307437
$237$	−500271.	−0.578542
$238$	979715.	1.12113
$239$	71356.0	0.0808045	0.0404023	−	0.999183i	$-0.487136\pi$
$239$	71356.0	0.0808045	0.0404023	+	0.999183i	$0.487136\pi$
$240$	678954.	0.760874
$241$	−1.25147e6	−1.38797	−0.693984	−	0.719991i	$-0.744146\pi$
$241$	−1.25147e6	−1.38797	−0.693984	+	0.719991i	$0.744146\pi$
$242$	−269410.	−0.295716
$243$	59049.0	0.0641500
$244$	2.21065e6	2.37709
$245$	−451113.	−0.480142
$246$	197366.	0.207939
$247$	−30063.3	−0.0313540
$248$	1.02740e6	1.06074
$249$	729391.	0.745525
$250$	1.77434e6	1.79551
$251$	−1.22669e6	−1.22900	−0.614501	−	0.788916i	$-0.710642\pi$
$251$	−1.22669e6	−1.22900	−0.614501	+	0.788916i	$0.710642\pi$
$252$	−348594.	−0.345795
$253$	61980.3	0.0608769
$254$	−3.16640e6	−3.07951
$255$	496491.	0.478146
$256$	−1.38862e6	−1.32429
$257$	−1.22989e6	−1.16154	−0.580770	−	0.814068i	$-0.697248\pi$
$257$	−1.22989e6	−1.16154	−0.580770	+	0.814068i	$0.697248\pi$
$258$	−358443.	−0.335252
$259$	63796.2	0.0590943
$260$	447525.	0.410567
$261$	22296.5	0.0202598
$262$	1.58426e6	1.42585
$263$	−1.03240e6	−0.920364	−0.460182	−	0.887825i	$-0.652216\pi$
$263$	−1.03240e6	−0.920364	−0.460182	+	0.887825i	$0.652216\pi$
$264$	−1.75870e6	−1.55304
$265$	321017.	0.280811
$266$	−99725.1	−0.0864173
$267$	966670.	0.829851
$268$	1.14050e6	0.969967
$269$	−565251.	−0.476278	−0.238139	−	0.971231i	$-0.576537\pi$
$269$	−565251.	−0.476278	−0.238139	+	0.971231i	$0.576537\pi$
$270$	−251466.	−0.209927
$271$	−1.35862e6	−1.12376	−0.561880	−	0.827219i	$-0.689922\pi$
$271$	−1.35862e6	−1.12376	−0.561880	+	0.827219i	$0.689922\pi$
$272$	3.76222e6	3.08334
$273$	−91268.1	−0.0741161
$274$	1.33107e6	1.07108
$275$	−873075.	−0.696177
$276$	97471.2	0.0770200
$277$	219170.	0.171625	0.0858127	−	0.996311i	$-0.472651\pi$
$277$	219170.	0.171625	0.0858127	+	0.996311i	$0.472651\pi$
$278$	−1.61258e6	−1.25144
$279$	−184174.	−0.141650
$280$	855877.	0.652404
$281$	1.54978e6	1.17086	0.585431	−	0.810722i	$-0.300925\pi$
$281$	1.54978e6	1.17086	0.585431	+	0.810722i	$0.300925\pi$
$282$	−1.38238e6	−1.03516
$283$	−1.39782e6	−1.03749	−0.518746	−	0.854928i	$-0.673601\pi$
$283$	−1.39782e6	−1.03749	−0.518746	+	0.854928i	$0.673601\pi$
$284$	1.00291e6	0.737847
$285$	−50537.8	−0.0368556
$286$	−798667.	−0.577365
$287$	120419.	0.0862957
$288$	−734307.	−0.521671
$289$	1.33130e6	0.937628
$290$	−94951.6	−0.0662990
$291$	−831927.	−0.575908
$292$	3.21138e6	2.20411
$293$	2.33918e6	1.59182	0.795910	−	0.605415i	$-0.206993\pi$
$293$	2.33918e6	1.59182	0.795910	+	0.605415i	$0.206993\pi$
$294$	1.26606e6	0.854255
$295$	−115775.	−0.0774569
$296$	506162.	0.335784
$297$	315268.	0.207390
$298$	−4.60638e6	−3.00482
$299$	25519.7	0.0165081
$300$	−1.37301e6	−0.880787
$301$	−218696.	−0.139131
$302$	715009.	0.451122
$303$	−1.21292e6	−0.758975
$304$	−382956.	−0.237665
$305$	972968.	0.598893
$306$	−1.39342e6	−0.850704
$307$	1.73450e6	1.05034	0.525170	−	0.850998i	$-0.324002\pi$
$307$	1.73450e6	1.05034	0.525170	+	0.850998i	$0.324002\pi$
$308$	−1.86118e6	−1.11792
$309$	1.49531e6	0.890913
$310$	784320.	0.463542
$311$	−1.36982e6	−0.803086	−0.401543	−	0.915840i	$-0.631526\pi$
$311$	−1.36982e6	−0.803086	−0.401543	+	0.915840i	$0.631526\pi$
$312$	−724125.	−0.421140
$313$	−2.30372e6	−1.32914	−0.664569	−	0.747227i	$-0.731385\pi$
$313$	−2.30372e6	−1.32914	−0.664569	+	0.747227i	$0.731385\pi$
$314$	718575.	0.411290
$315$	−153426.	−0.0871210
$316$	−4.20045e6	−2.36634
$317$	2.31279e6	1.29267	0.646337	−	0.763052i	$-0.276300\pi$
$317$	2.31279e6	1.29267	0.646337	+	0.763052i	$0.276300\pi$
$318$	−900947.	−0.499610
$319$	119043.	0.0654978
$320$	713053.	0.389266
$321$	1.08009e6	0.585056
$322$	84653.3	0.0454993
$323$	−280040.	−0.149353
$324$	495795.	0.262385
$325$	−359479.	−0.188784
$326$	2.77208e6	1.44465
$327$	1.69228e6	0.875190
$328$	955406.	0.490347
$329$	−843431.	−0.429596
$330$	−1.34260e6	−0.678673
$331$	1.01902e6	0.511224	0.255612	−	0.966779i	$-0.417723\pi$
$331$	1.01902e6	0.511224	0.255612	+	0.966779i	$0.417723\pi$
$332$	6.12421e6	3.04933
$333$	−90735.5	−0.0448401
$334$	−4.02214e6	−1.97284
$335$	501965.	0.244377
$336$	−1.16260e6	−0.561803
$337$	1.96163e6	0.940899	0.470450	−	0.882427i	$-0.344092\pi$
$337$	1.96163e6	0.940899	0.470450	+	0.882427i	$0.344092\pi$
$338$	3.52201e6	1.67687
$339$	1.02666e6	0.485206
$340$	4.16870e6	1.95571
$341$	−983320.	−0.457940
$342$	141836.	0.0655725
$343$	1.72964e6	0.793817
$344$	−1.73514e6	−0.790569
$345$	42899.8	0.0194047
$346$	1.97589e6	0.887304
$347$	567054.	0.252814	0.126407	−	0.991978i	$-0.459656\pi$
$347$	567054.	0.252814	0.126407	+	0.991978i	$0.459656\pi$
$348$	187209.	0.0828663
$349$	2.79317e6	1.22753	0.613767	−	0.789487i	$-0.289653\pi$
$349$	2.79317e6	1.22753	0.613767	+	0.789487i	$0.289653\pi$
$350$	−1.19245e6	−0.520321
$351$	129808.	0.0562385
$352$	−3.92053e6	−1.68651
$353$	2.82854e6	1.20816	0.604081	−	0.796923i	$-0.293540\pi$
$353$	2.82854e6	1.20816	0.604081	+	0.796923i	$0.293540\pi$
$354$	324927.	0.137809
$355$	441409.	0.185896
$356$	8.11648e6	3.39424
$357$	−850164.	−0.353047
$358$	1.79980e6	0.742194
$359$	−200396.	−0.0820641	−0.0410321	−	0.999158i	$-0.513065\pi$
$359$	−200396.	−0.0820641	−0.0410321	+	0.999158i	$0.513065\pi$
$360$	−1.21729e6	−0.495037
$361$	−2.44759e6	−0.988488
$362$	−7.44424e6	−2.98572
$363$	233785.	0.0931214
$364$	−766318.	−0.303148
$365$	1.41342e6	0.555313
$366$	−2.73067e6	−1.06553
$367$	−1.05311e6	−0.408140	−0.204070	−	0.978956i	$-0.565417\pi$
$367$	−1.05311e6	−0.408140	−0.204070	+	0.978956i	$0.565417\pi$
$368$	325079.	0.125132
$369$	−171268.	−0.0654802
$370$	386405.	0.146737
$371$	−549693.	−0.207341
$372$	−1.54638e6	−0.579375
$373$	−1.20089e6	−0.446922	−0.223461	−	0.974713i	$-0.571735\pi$
$373$	−1.20089e6	−0.446922	−0.223461	+	0.974713i	$0.571735\pi$
$374$	−7.43959e6	−2.75024
$375$	−1.53971e6	−0.565408
$376$	−6.69182e6	−2.44104
$377$	49014.5	0.0177612
$378$	430596.	0.155003
$379$	−3.95845e6	−1.41556	−0.707778	−	0.706435i	$-0.750302\pi$
$379$	−3.95845e6	−1.41556	−0.707778	+	0.706435i	$0.750302\pi$
$380$	−424332.	−0.150746
$381$	2.74770e6	0.969743
$382$	−3.49134e6	−1.22415
$383$	−3.58271e6	−1.24800	−0.624000	−	0.781424i	$-0.714494\pi$
$383$	−3.58271e6	−1.24800	−0.624000	+	0.781424i	$0.714494\pi$
$384$	609661.	0.210989
$385$	−819156.	−0.281653
$386$	−3.03994e6	−1.03848
$387$	311045.	0.105571
$388$	−6.98514e6	−2.35557
$389$	−2.75954e6	−0.924619	−0.462309	−	0.886719i	$-0.652979\pi$
$389$	−2.75954e6	−0.924619	−0.462309	+	0.886719i	$0.652979\pi$
$390$	−552799.	−0.184037
$391$	237716.	0.0786352
$392$	6.12874e6	2.01445
$393$	−1.37477e6	−0.449003
$394$	2.63575e6	0.855390
$395$	−1.84873e6	−0.596186
$396$	2.64709e6	0.848265
$397$	4.77985e6	1.52208	0.761041	−	0.648704i	$-0.224689\pi$
$397$	4.77985e6	1.52208	0.761041	+	0.648704i	$0.224689\pi$
$398$	−677158.	−0.214280
$399$	86538.2	0.0272129
$400$	−4.57916e6	−1.43099
$401$	−4.79242e6	−1.48831	−0.744156	−	0.668005i	$-0.767148\pi$
$401$	−4.79242e6	−1.48831	−0.744156	+	0.668005i	$0.767148\pi$
$402$	−1.40878e6	−0.434789
$403$	−404871.	−0.124181
$404$	−1.01841e7	−3.10435
$405$	218213.	0.0661065
$406$	162590.	0.0489529
$407$	−484445.	−0.144963
$408$	−6.74524e6	−2.00607
$409$	804704.	0.237864	0.118932	−	0.992902i	$-0.462053\pi$
$409$	804704.	0.237864	0.118932	+	0.992902i	$0.462053\pi$
$410$	729360.	0.214280
$411$	−1.15505e6	−0.337286
$412$	1.25551e7	3.64400
$413$	198247.	0.0571915
$414$	−120400.	−0.0345243
$415$	2.69544e6	0.768262
$416$	−1.61423e6	−0.457334
$417$	1.39934e6	0.394080
$418$	757276.	0.211989
$419$	5.46503e6	1.52075	0.760374	−	0.649486i	$-0.225016\pi$
$419$	5.46503e6	1.52075	0.760374	+	0.649486i	$0.225016\pi$
$420$	−1.28822e6	−0.356341
$421$	−1.96598e6	−0.540597	−0.270298	−	0.962777i	$-0.587122\pi$
$421$	−1.96598e6	−0.540597	−0.270298	+	0.962777i	$0.587122\pi$
$422$	−966026.	−0.264063
$423$	1.19959e6	0.325972
$424$	−4.36128e6	−1.17815
$425$	−3.34855e6	−0.899258
$426$	−1.23883e6	−0.330741
$427$	−1.66606e6	−0.442202
$428$	9.06880e6	2.39299
$429$	693056.	0.181813
$430$	−1.32461e6	−0.345476
$431$	6.18098e6	1.60274	0.801372	−	0.598167i	$-0.204104\pi$
$431$	6.18098e6	1.60274	0.801372	+	0.598167i	$0.204104\pi$
$432$	1.65354e6	0.426290
$433$	−6.81186e6	−1.74601	−0.873003	−	0.487715i	$-0.837831\pi$
$433$	−6.81186e6	−1.74601	−0.873003	+	0.487715i	$0.837831\pi$
$434$	−1.34303e6	−0.342264
$435$	82395.8	0.0208777
$436$	1.42089e7	3.57969
$437$	−24197.1	−0.00606122
$438$	−3.96681e6	−0.987997
$439$	5.97720e6	1.48026	0.740128	−	0.672466i	$-0.234765\pi$
$439$	5.97720e6	1.48026	0.740128	+	0.672466i	$0.234765\pi$
$440$	−6.49921e6	−1.60040
$441$	−1.09865e6	−0.269006
$442$	−3.06317e6	−0.745787
$443$	−490983.	−0.118866	−0.0594330	−	0.998232i	$-0.518929\pi$
$443$	−490983.	−0.118866	−0.0594330	+	0.998232i	$0.518929\pi$
$444$	−761845.	−0.183404
$445$	3.57229e6	0.855159
$446$	−316624.	−0.0753715
$447$	3.99726e6	0.946223
$448$	−1.22099e6	−0.287421
$449$	7.25924e6	1.69932	0.849660	−	0.527331i	$-0.176807\pi$
$449$	7.25924e6	1.69932	0.849660	+	0.527331i	$0.176807\pi$
$450$	1.69599e6	0.394814
$451$	−914415.	−0.211691
$452$	8.62015e6	1.98458
$453$	−620461.	−0.142059
$454$	8.06777e6	1.83702
$455$	−337278.	−0.0763765
$456$	686597.	0.154629
$457$	−2.78034e6	−0.622740	−0.311370	−	0.950289i	$-0.600788\pi$
$457$	−2.78034e6	−0.622740	−0.311370	+	0.950289i	$0.600788\pi$
$458$	7.91535e6	1.76322
$459$	1.20916e6	0.267888
$460$	360201.	0.0793690
$461$	−6.01371e6	−1.31792	−0.658962	−	0.752176i	$-0.729004\pi$
$461$	−6.01371e6	−1.31792	−0.658962	+	0.752176i	$0.729004\pi$
$462$	2.29899e6	0.501109
$463$	−7.10787e6	−1.54094	−0.770472	−	0.637474i	$-0.779979\pi$
$463$	−7.10787e6	−1.54094	−0.770472	+	0.637474i	$0.779979\pi$
$464$	624364.	0.134630
$465$	−680607.	−0.145970
$466$	1.32425e7	2.82492
$467$	5.51961e6	1.17116	0.585579	−	0.810615i	$-0.300867\pi$
$467$	5.51961e6	1.17116	0.585579	+	0.810615i	$0.300867\pi$
$468$	1.08991e6	0.230026
$469$	−859537.	−0.180440
$470$	−5.10855e6	−1.06673
$471$	−623555.	−0.129516
$472$	1.57290e6	0.324972
$473$	1.66070e6	0.341301
$474$	5.18854e6	1.06072
$475$	340849.	0.0693150
$476$	−7.13826e6	−1.44403
$477$	781812.	0.157328
$478$	−740065.	−0.148150
$479$	−3.18017e6	−0.633304	−0.316652	−	0.948542i	$-0.602559\pi$
$479$	−3.18017e6	−0.633304	−0.316652	+	0.948542i	$0.602559\pi$
$480$	−2.71360e6	−0.537580
$481$	−199465.	−0.0393100
$482$	1.29796e7	2.54474
$483$	−73459.3	−0.0143278
$484$	1.96293e6	0.380884
$485$	−3.07436e6	−0.593472
$486$	−612424.	−0.117615
$487$	−4.01718e6	−0.767537	−0.383768	−	0.923429i	$-0.625374\pi$
$487$	−4.01718e6	−0.767537	−0.383768	+	0.923429i	$0.625374\pi$
$488$	−1.32186e7	−2.51267
$489$	−2.40552e6	−0.454921
$490$	4.67869e6	0.880308
$491$	2.25211e6	0.421585	0.210793	−	0.977531i	$-0.432396\pi$
$491$	2.25211e6	0.421585	0.210793	+	0.977531i	$0.432396\pi$
$492$	−1.43802e6	−0.267826
$493$	456571.	0.0846041
$494$	311800.	0.0574855
$495$	1.16506e6	0.213715
$496$	−5.15738e6	−0.941293
$497$	−755845.	−0.137259
$498$	−7.56484e6	−1.36687
$499$	4.87566e6	0.876561	0.438281	−	0.898838i	$-0.355588\pi$
$499$	4.87566e6	0.876561	0.438281	+	0.898838i	$0.355588\pi$
$500$	−1.29280e7	−2.31262
$501$	3.49028e6	0.621249
$502$	1.27226e7	2.25329
$503$	−3.03011e6	−0.533996	−0.266998	−	0.963697i	$-0.586032\pi$
$503$	−3.03011e6	−0.533996	−0.266998	+	0.963697i	$0.586032\pi$
$504$	2.08442e6	0.365518
$505$	−4.48232e6	−0.782122
$506$	−642826.	−0.111614
$507$	−3.05628e6	−0.528048
$508$	2.30706e7	3.96643
$509$	−6.31223e6	−1.07991	−0.539956	−	0.841693i	$-0.681559\pi$
$509$	−6.31223e6	−1.07991	−0.539956	+	0.841693i	$0.681559\pi$
$510$	−5.14933e6	−0.876648
$511$	−2.42026e6	−0.410024
$512$	1.22343e7	2.06255
$513$	−123081.	−0.0206489
$514$	1.27558e7	2.12960
$515$	5.52586e6	0.918083
$516$	2.61164e6	0.431806
$517$	6.40470e6	1.05384
$518$	−661659.	−0.108345
$519$	−1.71461e6	−0.279414
$520$	−2.67598e6	−0.433984
$521$	−1.00384e7	−1.62021	−0.810106	−	0.586283i	$-0.800591\pi$
$521$	−1.00384e7	−1.62021	−0.810106	+	0.586283i	$0.800591\pi$
$522$	−231247.	−0.0371449
$523$	4.29564e6	0.686710	0.343355	−	0.939206i	$-0.388437\pi$
$523$	4.29564e6	0.686710	0.343355	+	0.939206i	$0.388437\pi$
$524$	−1.15430e7	−1.83650
$525$	1.03477e6	0.163850
$526$	1.07075e7	1.68742
$527$	−3.77138e6	−0.591525
$528$	8.82839e6	1.37815
$529$	−6.41580e6	−0.996809
$530$	−3.32942e6	−0.514847
$531$	−281961.	−0.0433963
$532$	726603.	0.111306
$533$	−376500.	−0.0574046
$534$	−1.00258e7	−1.52147
$535$	3.99144e6	0.602899
$536$	−6.81960e6	−1.02529
$537$	−1.56181e6	−0.233718
$538$	5.86247e6	0.873223
$539$	−5.86578e6	−0.869669
$540$	1.83219e6	0.270388
$541$	−6.40724e6	−0.941190	−0.470595	−	0.882349i	$-0.655961\pi$
$541$	−6.40724e6	−0.941190	−0.470595	+	0.882349i	$0.655961\pi$
$542$	1.40908e7	2.06033
$543$	6.45986e6	0.940207
$544$	−1.50366e7	−2.17848
$545$	6.25375e6	0.901882
$546$	946583.	0.135887
$547$	2.87214e6	0.410429	0.205214	−	0.978717i	$-0.434211\pi$
$547$	2.87214e6	0.410429	0.205214	+	0.978717i	$0.434211\pi$
$548$	−9.69822e6	−1.37956
$549$	2.36958e6	0.335538
$550$	9.05505e6	1.27639
$551$	−46474.4	−0.00652130
$552$	−582829.	−0.0814130
$553$	3.16567e6	0.440203
$554$	−2.27311e6	−0.314663
$555$	−335310.	−0.0462076
$556$	1.17494e7	1.61186
$557$	−1.93992e6	−0.264939	−0.132470	−	0.991187i	$-0.542291\pi$
$557$	−1.93992e6	−0.264939	−0.132470	+	0.991187i	$0.542291\pi$
$558$	1.91015e6	0.259706
$559$	683774.	0.0925514
$560$	−4.29636e6	−0.578937
$561$	6.45583e6	0.866054
$562$	−1.60735e7	−2.14669
$563$	2.17438e6	0.289110	0.144555	−	0.989497i	$-0.453825\pi$
$563$	2.17438e6	0.289110	0.144555	+	0.989497i	$0.453825\pi$
$564$	1.00721e7	1.33329
$565$	3.79397e6	0.500004
$566$	1.44974e7	1.90217
$567$	−373657.	−0.0488107
$568$	−5.99690e6	−0.779931
$569$	−4.07789e6	−0.528025	−0.264012	−	0.964519i	$-0.585046\pi$
$569$	−4.07789e6	−0.528025	−0.264012	+	0.964519i	$0.585046\pi$
$570$	524150.	0.0675723
$571$	7.41602e6	0.951876	0.475938	−	0.879479i	$-0.342109\pi$
$571$	7.41602e6	0.951876	0.475938	+	0.879479i	$0.342109\pi$
$572$	5.81913e6	0.743649
$573$	3.02967e6	0.385486
$574$	−1.24892e6	−0.158217
$575$	−289335.	−0.0364948
$576$	1.73658e6	0.218092
$577$	1.29497e6	0.161927	0.0809636	−	0.996717i	$-0.474200\pi$
$577$	1.29497e6	0.161927	0.0809636	+	0.996717i	$0.474200\pi$
$578$	−1.38075e7	−1.71908
$579$	2.63796e6	0.327018
$580$	691823.	0.0853935
$581$	−4.61552e6	−0.567258
$582$	8.62829e6	1.05589
$583$	4.17416e6	0.508625
$584$	−1.92024e7	−2.32983
$585$	479701.	0.0579536
$586$	−2.42607e7	−2.91849
$587$	9.79730e6	1.17358	0.586788	−	0.809741i	$-0.300392\pi$
$587$	9.79730e6	1.17358	0.586788	+	0.809741i	$0.300392\pi$
$588$	−9.22462e6	−1.10028
$589$	383888.	0.0455949
$590$	1.20076e6	0.142012
$591$	−2.28722e6	−0.269364
$592$	−2.54085e6	−0.297971
$593$	2.89314e6	0.337857	0.168929	−	0.985628i	$-0.445969\pi$
$593$	2.89314e6	0.337857	0.168929	+	0.985628i	$0.445969\pi$
$594$	−3.26979e6	−0.380236
$595$	−3.14175e6	−0.363814
$596$	3.35623e7	3.87023
$597$	587615.	0.0674772
$598$	−264676.	−0.0302665
$599$	1.07146e6	0.122013	0.0610066	−	0.998137i	$-0.480569\pi$
$599$	1.07146e6	0.122013	0.0610066	+	0.998137i	$0.480569\pi$
$600$	8.20992e6	0.931024
$601$	−8.77640e6	−0.991129	−0.495564	−	0.868571i	$-0.665039\pi$
$601$	−8.77640e6	−0.991129	−0.495564	+	0.868571i	$0.665039\pi$
$602$	2.26820e6	0.255088
$603$	1.22249e6	0.136916
$604$	−5.20960e6	−0.581048
$605$	863943.	0.0959614
$606$	1.25798e7	1.39153
$607$	−1.38832e7	−1.52939	−0.764696	−	0.644391i	$-0.777111\pi$
$607$	−1.38832e7	−1.52939	−0.764696	+	0.644391i	$0.777111\pi$
$608$	1.53058e6	0.167917
$609$	−141090.	−0.0154153
$610$	−1.00911e7	−1.09803
$611$	2.63706e6	0.285771
$612$	1.01525e7	1.09571
$613$	−2.96162e6	−0.318330	−0.159165	−	0.987252i	$-0.550880\pi$
$613$	−2.96162e6	−0.318330	−0.159165	+	0.987252i	$0.550880\pi$
$614$	−1.79893e7	−1.92572
$615$	−632914.	−0.0674772
$616$	1.11289e7	1.18168
$617$	−1.63962e7	−1.73393	−0.866964	−	0.498370i	$-0.833932\pi$
$617$	−1.63962e7	−1.73393	−0.866964	+	0.498370i	$0.833932\pi$
$618$	−1.55085e7	−1.63343
$619$	−1.35257e7	−1.41884	−0.709418	−	0.704788i	$-0.751042\pi$
$619$	−1.35257e7	−1.41884	−0.709418	+	0.704788i	$0.751042\pi$
$620$	−5.71460e6	−0.597045
$621$	104479.	0.0108718
$622$	1.42070e7	1.47240
$623$	−6.11700e6	−0.631420
$624$	3.63499e6	0.373716
$625$	618876.	0.0633729
$626$	2.38930e7	2.43688
$627$	−657139.	−0.0667557
$628$	−5.23558e6	−0.529743
$629$	−1.85802e6	−0.187250
$630$	1.59125e6	0.159730
$631$	−1.19825e7	−1.19805	−0.599025	−	0.800731i	$-0.704445\pi$
$631$	−1.19825e7	−1.19805	−0.599025	+	0.800731i	$0.704445\pi$
$632$	2.51166e7	2.50131
$633$	838285.	0.0831539
$634$	−2.39870e7	−2.37003
$635$	1.01540e7	0.999318
$636$	6.56435e6	0.643501
$637$	−2.41517e6	−0.235830
$638$	−1.23465e6	−0.120086
$639$	1.07502e6	0.104151
$640$	2.25298e6	0.217424
$641$	−7.00957e6	−0.673823	−0.336912	−	0.941536i	$-0.609382\pi$
$641$	−7.00957e6	−0.673823	−0.336912	+	0.941536i	$0.609382\pi$
$642$	−1.12021e7	−1.07266
$643$	605033.	0.0577101	0.0288550	−	0.999584i	$-0.490814\pi$
$643$	605033.	0.0577101	0.0288550	+	0.999584i	$0.490814\pi$
$644$	−616789.	−0.0586033
$645$	1.14946e6	0.108791
$646$	2.90442e6	0.273828
$647$	1.46414e7	1.37506	0.687531	−	0.726155i	$-0.258695\pi$
$647$	1.46414e7	1.37506	0.687531	+	0.726155i	$0.258695\pi$
$648$	−2.96461e6	−0.277351
$649$	−1.50542e6	−0.140296
$650$	3.72831e6	0.346122
$651$	1.16543e6	0.107779
$652$	−2.01975e7	−1.86071
$653$	3.99497e6	0.366632	0.183316	−	0.983054i	$-0.441317\pi$
$653$	3.99497e6	0.366632	0.183316	+	0.983054i	$0.441317\pi$
$654$	−1.75514e7	−1.60460
$655$	−5.08041e6	−0.462696
$656$	−4.79598e6	−0.435129
$657$	3.44226e6	0.311122
$658$	8.74761e6	0.787634
$659$	274018.	0.0245791	0.0122895	−	0.999924i	$-0.496088\pi$
$659$	274018.	0.0245791	0.0122895	+	0.999924i	$0.496088\pi$
$660$	9.78224e6	0.874135
$661$	−1.92782e7	−1.71618	−0.858091	−	0.513497i	$-0.828350\pi$
$661$	−1.92782e7	−1.71618	−0.858091	+	0.513497i	$0.828350\pi$
$662$	−1.05687e7	−0.937294
$663$	2.65811e6	0.234850
$664$	−3.66197e7	−3.22326
$665$	319799.	0.0280429
$666$	941058.	0.0822112
$667$	39450.5	0.00343351
$668$	2.93056e7	2.54102
$669$	274756.	0.0237346
$670$	−5.20610e6	−0.448049
$671$	1.26514e7	1.08476
$672$	4.64663e6	0.396931
$673$	−1.19222e7	−1.01466	−0.507329	−	0.861753i	$-0.669367\pi$
$673$	−1.19222e7	−1.01466	−0.507329	+	0.861753i	$0.669367\pi$
$674$	−2.03450e7	−1.72507
$675$	−1.47173e6	−0.124328
$676$	−2.56615e7	−2.15981
$677$	−3.81809e6	−0.320166	−0.160083	−	0.987104i	$-0.551176\pi$
$677$	−3.81809e6	−0.320166	−0.160083	+	0.987104i	$0.551176\pi$
$678$	−1.06479e7	−0.889591
$679$	5.26436e6	0.438199
$680$	−2.49268e7	−2.06725
$681$	−7.00094e6	−0.578480
$682$	1.01985e7	0.839602
$683$	1.71086e7	1.40334	0.701672	−	0.712500i	$-0.252437\pi$
$683$	1.71086e7	1.40334	0.701672	+	0.712500i	$0.252437\pi$
$684$	−1.03343e6	−0.0844577
$685$	−4.26846e6	−0.347572
$686$	−1.79389e7	−1.45541
$687$	−6.86867e6	−0.555240
$688$	8.71014e6	0.701543
$689$	1.71866e6	0.137925
$690$	−444933.	−0.0355772
$691$	1.16432e6	0.0927639	0.0463820	−	0.998924i	$-0.485231\pi$
$691$	1.16432e6	0.0927639	0.0463820	+	0.998924i	$0.485231\pi$
$692$	−1.43965e7	−1.14285
$693$	−1.99499e6	−0.157800
$694$	−5.88117e6	−0.463516
$695$	5.17122e6	0.406098
$696$	−1.11941e6	−0.0875927
$697$	−3.50710e6	−0.273443
$698$	−2.89692e7	−2.25060
$699$	−1.14914e7	−0.889573
$700$	8.68829e6	0.670177
$701$	−2.35243e6	−0.180810	−0.0904050	−	0.995905i	$-0.528816\pi$
$701$	−2.35243e6	−0.180810	−0.0904050	+	0.995905i	$0.528816\pi$
$702$	−1.34630e6	−0.103109
$703$	189127.	0.0144333
$704$	9.27177e6	0.705068
$705$	4.43303e6	0.335914
$706$	−2.93360e7	−2.21508
$707$	7.67528e6	0.577492
$708$	−2.36744e6	−0.177499
$709$	−2.37540e7	−1.77468	−0.887342	−	0.461112i	$-0.847451\pi$
$709$	−2.37540e7	−1.77468	−0.887342	+	0.461112i	$0.847451\pi$
$710$	−4.57805e6	−0.340828
$711$	−4.50244e6	−0.334021
$712$	−4.85325e7	−3.58784
$713$	−325870.	−0.0240060
$714$	8.81744e6	0.647287
$715$	2.56116e6	0.187358
$716$	−1.31135e7	−0.955949
$717$	642204.	0.0466525
$718$	2.07840e6	0.150459
$719$	7.28156e6	0.525294	0.262647	−	0.964892i	$-0.415405\pi$
$719$	7.28156e6	0.525294	0.262647	+	0.964892i	$0.415405\pi$
$720$	6.11059e6	0.439291
$721$	−9.46219e6	−0.677881
$722$	2.53851e7	1.81232
$723$	−1.12633e7	−0.801344
$724$	5.42392e7	3.84562
$725$	−555713.	−0.0392650
$726$	−2.42469e6	−0.170732
$727$	400663.	0.0281153	0.0140577	−	0.999901i	$-0.495525\pi$
$727$	400663.	0.0281153	0.0140577	+	0.999901i	$0.495525\pi$
$728$	4.58220e6	0.320439
$729$	531441.	0.0370370
$730$	−1.46592e7	−1.01813
$731$	6.36936e6	0.440862
$732$	1.98958e7	1.37241
$733$	2.06252e7	1.41787	0.708937	−	0.705272i	$-0.249175\pi$
$733$	2.06252e7	1.41787	0.708937	+	0.705272i	$0.249175\pi$
$734$	1.09223e7	0.748297
$735$	−4.06001e6	−0.277210
$736$	−1.29925e6	−0.0884097
$737$	6.52701e6	0.442634
$738$	1.77630e6	0.120053
$739$	−1.36694e7	−0.920744	−0.460372	−	0.887726i	$-0.652284\pi$
$739$	−1.36694e7	−0.920744	−0.460372	+	0.887726i	$0.652284\pi$
$740$	−2.81537e6	−0.188998
$741$	−270569.	−0.0181023
$742$	5.70111e6	0.380145
$743$	1.13736e7	0.755833	0.377917	−	0.925840i	$-0.376641\pi$
$743$	1.13736e7	0.755833	0.377917	+	0.925840i	$0.376641\pi$
$744$	9.24660e6	0.612421
$745$	1.47717e7	0.975081
$746$	1.24550e7	0.819400
$747$	6.56452e6	0.430429
$748$	5.42053e7	3.54232
$749$	−6.83472e6	−0.445160
$750$	1.59691e7	1.03664
$751$	−1.25684e6	−0.0813171	−0.0406585	−	0.999173i	$-0.512946\pi$
$751$	−1.25684e6	−0.0813171	−0.0406585	+	0.999173i	$0.512946\pi$
$752$	3.35918e7	2.16615
$753$	−1.10403e7	−0.709564
$754$	−508352.	−0.0325639
$755$	−2.29289e6	−0.146392
$756$	−3.13735e6	−0.199645
$757$	−1.34819e7	−0.855087	−0.427544	−	0.903995i	$-0.640621\pi$
$757$	−1.34819e7	−0.855087	−0.427544	+	0.903995i	$0.640621\pi$
$758$	4.10549e7	2.59533
$759$	557823.	0.0351473
$760$	2.53729e6	0.159344
$761$	−865364.	−0.0541673	−0.0270837	−	0.999633i	$-0.508622\pi$
$761$	−865364.	−0.0541673	−0.0270837	+	0.999633i	$0.508622\pi$
$762$	−2.84976e7	−1.77796
$763$	−1.07086e7	−0.665918
$764$	2.54381e7	1.57671
$765$	4.46842e6	0.276058
$766$	3.71579e7	2.28812
$767$	−619837.	−0.0380443
$768$	−1.24976e7	−0.764580
$769$	−2.08760e7	−1.27301	−0.636503	−	0.771274i	$-0.719620\pi$
$769$	−2.08760e7	−1.27301	−0.636503	+	0.771274i	$0.719620\pi$
$770$	8.49584e6	0.516392
$771$	−1.10690e7	−0.670615
$772$	2.21492e7	1.33757
$773$	2.75458e7	1.65809	0.829043	−	0.559185i	$-0.188886\pi$
$773$	2.75458e7	1.65809	0.829043	+	0.559185i	$0.188886\pi$
$774$	−3.22599e6	−0.193558
$775$	4.59031e6	0.274529
$776$	4.17677e7	2.48992
$777$	574166.	0.0341181
$778$	2.86204e7	1.69522
$779$	356988.	0.0210770
$780$	4.02773e6	0.237041
$781$	5.73961e6	0.336709
$782$	−2.46546e6	−0.144172
$783$	200668.	0.0116970
$784$	−3.07652e7	−1.78760
$785$	−2.30433e6	−0.133466
$786$	1.42584e7	0.823215
$787$	1.86224e7	1.07176	0.535881	−	0.844293i	$-0.319979\pi$
$787$	1.86224e7	1.07176	0.535881	+	0.844293i	$0.319979\pi$
$788$	−1.92042e7	−1.10175
$789$	−9.29162e6	−0.531373
$790$	1.91741e7	1.09307
$791$	−6.49659e6	−0.369185
$792$	−1.58283e7	−0.896647
$793$	5.20908e6	0.294156
$794$	−4.95740e7	−2.79063
$795$	2.88916e6	0.162126
$796$	4.93381e6	0.275994
$797$	−1.01313e7	−0.564965	−0.282482	−	0.959272i	$-0.591158\pi$
$797$	−1.01313e7	−0.564965	−0.282482	+	0.959272i	$0.591158\pi$
$798$	−897526.	−0.0498930
$799$	2.45643e7	1.36125
$800$	1.83017e7	1.01104
$801$	8.70003e6	0.479115
$802$	4.97044e7	2.72872
$803$	1.83785e7	1.00582
$804$	1.02645e7	0.560011
$805$	−271466.	−0.0147648
$806$	4.19910e6	0.227677
$807$	−5.08726e6	−0.274979
$808$	6.08960e7	3.28141
$809$	1.76196e7	0.946507	0.473254	−	0.880926i	$-0.343079\pi$
$809$	1.76196e7	0.946507	0.473254	+	0.880926i	$0.343079\pi$
$810$	−2.26319e6	−0.121202
$811$	−1.37418e6	−0.0733654	−0.0366827	−	0.999327i	$-0.511679\pi$
$811$	−1.37418e6	−0.0733654	−0.0366827	+	0.999327i	$0.511679\pi$
$812$	−1.18464e6	−0.0630516
$813$	−1.22275e7	−0.648803
$814$	5.02440e6	0.265780
$815$	−8.88950e6	−0.468795
$816$	3.38600e7	1.78017
$817$	−648337.	−0.0339817
$818$	−8.34595e6	−0.436107
$819$	−821413.	−0.0427909
$820$	−5.31416e6	−0.275994
$821$	−1.13057e7	−0.585382	−0.292691	−	0.956207i	$-0.594551\pi$
$821$	−1.13057e7	−0.585382	−0.292691	+	0.956207i	$0.594551\pi$
$822$	1.19796e7	0.618390
$823$	2.63250e7	1.35478	0.677389	−	0.735625i	$-0.263111\pi$
$823$	2.63250e7	1.35478	0.677389	+	0.735625i	$0.263111\pi$
$824$	−7.50734e7	−3.85184
$825$	−7.85767e6	−0.401938
$826$	−2.05611e6	−0.104857
$827$	2.02274e6	0.102843	0.0514217	−	0.998677i	$-0.483625\pi$
$827$	2.02274e6	0.102843	0.0514217	+	0.998677i	$0.483625\pi$
$828$	877241.	0.0444675
$829$	−1.96942e7	−0.995297	−0.497649	−	0.867379i	$-0.665803\pi$
$829$	−1.96942e7	−0.995297	−0.497649	+	0.867379i	$0.665803\pi$
$830$	−2.79556e7	−1.40855
$831$	1.97253e6	0.0990880
$832$	3.81754e6	0.191195
$833$	−2.24973e7	−1.12336
$834$	−1.45132e7	−0.722518
$835$	1.28982e7	0.640196
$836$	−5.51756e6	−0.273043
$837$	−1.65756e6	−0.0817818
$838$	−5.66803e7	−2.78819
$839$	−3.39690e6	−0.166601	−0.0833006	−	0.996524i	$-0.526546\pi$
$839$	−3.39690e6	−0.166601	−0.0833006	+	0.996524i	$0.526546\pi$
$840$	7.70290e6	0.376665
$841$	−2.04354e7	−0.996306
$842$	2.03900e7	0.991147
$843$	1.39481e7	0.675997
$844$	7.03852e6	0.340115
$845$	−1.12944e7	−0.544152
$846$	−1.24415e7	−0.597648
$847$	−1.47937e6	−0.0708546
$848$	2.18929e7	1.04548
$849$	−1.25804e7	−0.598997
$850$	3.47293e7	1.64873
$851$	−160544.	−0.00759923
$852$	9.02619e6	0.425996
$853$	−8.12673e6	−0.382422	−0.191211	−	0.981549i	$-0.561242\pi$
$853$	−8.12673e6	−0.382422	−0.191211	+	0.981549i	$0.561242\pi$
$854$	1.72794e7	0.810746
$855$	−454840.	−0.0212786
$856$	−5.42269e7	−2.52948
$857$	2.17376e7	1.01102	0.505509	−	0.862821i	$-0.331305\pi$
$857$	2.17376e7	1.01102	0.505509	+	0.862821i	$0.331305\pi$
$858$	−7.18800e6	−0.333342
$859$	180961.	0.00836764	0.00418382	−	0.999991i	$-0.498668\pi$
$859$	180961.	0.00836764	0.00418382	+	0.999991i	$0.498668\pi$
$860$	9.65122e6	0.444975
$861$	1.08377e6	0.0498228
$862$	−6.41057e7	−2.93852
$863$	3.07976e7	1.40764	0.703818	−	0.710381i	$-0.251477\pi$
$863$	3.07976e7	1.40764	0.703818	+	0.710381i	$0.251477\pi$
$864$	−6.60876e6	−0.301187
$865$	−6.33629e6	−0.287935
$866$	7.06488e7	3.20118
$867$	1.19817e7	0.541340
$868$	9.78538e6	0.440837
$869$	−2.40389e7	−1.07986
$870$	−854564.	−0.0382778
$871$	2.68742e6	0.120030
$872$	−8.49624e7	−3.78386
$873$	−7.48735e6	−0.332501
$874$	250959.	0.0111128
$875$	9.74318e6	0.430210
$876$	2.89024e7	1.27255
$877$	1.10924e7	0.486998	0.243499	−	0.969901i	$-0.421705\pi$
$877$	1.10924e7	0.486998	0.243499	+	0.969901i	$0.421705\pi$
$878$	−6.19923e7	−2.71395
$879$	2.10526e7	0.919038
$880$	3.26250e7	1.42018
$881$	3.34548e7	1.45217	0.726086	−	0.687603i	$-0.241337\pi$
$881$	3.34548e7	1.45217	0.726086	+	0.687603i	$0.241337\pi$
$882$	1.13946e7	0.493204
$883$	−2.73782e7	−1.18169	−0.590844	−	0.806786i	$-0.701205\pi$
$883$	−2.73782e7	−1.18169	−0.590844	+	0.806786i	$0.701205\pi$
$884$	2.23184e7	0.960578
$885$	−1.04198e6	−0.0447198
$886$	5.09221e6	0.217932
$887$	−2.42168e7	−1.03350	−0.516748	−	0.856138i	$-0.672857\pi$
$887$	−2.42168e7	−1.03350	−0.516748	+	0.856138i	$0.672857\pi$
$888$	4.55546e6	0.193865
$889$	−1.73872e7	−0.737862
$890$	−3.70499e7	−1.56788
$891$	2.83741e6	0.119737
$892$	2.30694e6	0.0970788
$893$	−2.50040e6	−0.104925
$894$	−4.14574e7	−1.73484
$895$	−5.77161e6	−0.240846
$896$	−3.85788e6	−0.160538
$897$	229677.	0.00953096
$898$	−7.52888e7	−3.11559
$899$	−625884.	−0.0258282
$900$	−1.23571e7	−0.508523
$901$	1.60094e7	0.656996
$902$	9.48381e6	0.388120
$903$	−1.96827e6	−0.0803276
$904$	−5.15442e7	−2.09778
$905$	2.38722e7	0.968881
$906$	6.43508e6	0.260455
$907$	−2.31796e7	−0.935595	−0.467797	−	0.883836i	$-0.654952\pi$
$907$	−2.31796e7	−0.935595	−0.467797	+	0.883836i	$0.654952\pi$
$908$	−5.87822e7	−2.36609
$909$	−1.09163e7	−0.438194
$910$	3.49806e6	0.140031
$911$	1.41080e7	0.563209	0.281605	−	0.959531i	$-0.409133\pi$
$911$	1.41080e7	0.563209	0.281605	+	0.959531i	$0.409133\pi$
$912$	−3.44660e6	−0.137216
$913$	3.50486e7	1.39153
$914$	2.88361e7	1.14175
$915$	8.75671e6	0.345771
$916$	−5.76717e7	−2.27104
$917$	8.69943e6	0.341639
$918$	−1.25408e7	−0.491154
$919$	3.48252e7	1.36020	0.680102	−	0.733117i	$-0.261935\pi$
$919$	3.48252e7	1.36020	0.680102	+	0.733117i	$0.261935\pi$
$920$	−2.15382e6	−0.0838959
$921$	1.56105e7	0.606414
$922$	6.23709e7	2.41632
$923$	2.36322e6	0.0913060
$924$	−1.67506e7	−0.645431
$925$	2.26147e6	0.0869034
$926$	7.37189e7	2.82521
$927$	1.34578e7	0.514369
$928$	−2.49542e6	−0.0951204
$929$	8.18223e6	0.311052	0.155526	−	0.987832i	$-0.450293\pi$
$929$	8.18223e6	0.311052	0.155526	+	0.987832i	$0.450293\pi$
$930$	7.05888e6	0.267626
$931$	2.29000e6	0.0865888
$932$	−9.64860e7	−3.63852
$933$	−1.23284e7	−0.463662
$934$	−5.72463e7	−2.14724
$935$	2.38573e7	0.892467
$936$	−6.51712e6	−0.243146
$937$	−3.29144e7	−1.22472	−0.612361	−	0.790578i	$-0.709780\pi$
$937$	−3.29144e7	−1.22472	−0.612361	+	0.790578i	$0.709780\pi$
$938$	8.91465e6	0.330824
$939$	−2.07335e7	−0.767378
$940$	3.72212e7	1.37395
$941$	2.12414e7	0.782004	0.391002	−	0.920390i	$-0.372128\pi$
$941$	2.12414e7	0.782004	0.391002	+	0.920390i	$0.372128\pi$
$942$	6.46717e6	0.237458
$943$	−303035.	−0.0110972
$944$	−7.89570e6	−0.288377
$945$	−1.38084e6	−0.0502993
$946$	−1.72239e7	−0.625752
$947$	4.07231e7	1.47559	0.737795	−	0.675025i	$-0.235867\pi$
$947$	4.07231e7	1.47559	0.737795	+	0.675025i	$0.235867\pi$
$948$	−3.78040e7	−1.36621
$949$	7.56716e6	0.272752
$950$	−3.53509e6	−0.127084
$951$	2.08151e7	0.746325
$952$	4.26833e7	1.52639
$953$	−3.41302e7	−1.21733	−0.608663	−	0.793429i	$-0.708294\pi$
$953$	−3.41302e7	−1.21733	−0.608663	+	0.793429i	$0.708294\pi$
$954$	−8.10852e6	−0.288450
$955$	1.11960e7	0.397242
$956$	5.39216e6	0.190817
$957$	1.07139e6	0.0378152
$958$	3.29830e7	1.16112
$959$	7.30908e6	0.256635
$960$	6.41748e6	0.224743
$961$	−2.34592e7	−0.819417
$962$	2.06874e6	0.0720722
$963$	9.72082e6	0.337782
$964$	−9.45702e7	−3.27764
$965$	9.74849e6	0.336992
$966$	761880.	0.0262690
$967$	5.84049e6	0.200855	0.100428	−	0.994944i	$-0.467979\pi$
$967$	5.84049e6	0.200855	0.100428	+	0.994944i	$0.467979\pi$
$968$	−1.17374e7	−0.402608
$969$	−2.52036e6	−0.0862289
$970$	3.18855e7	1.08809
$971$	−3.95959e7	−1.34773	−0.673864	−	0.738856i	$-0.735367\pi$
$971$	−3.95959e7	−1.34773	−0.673864	+	0.738856i	$0.735367\pi$
$972$	4.46216e6	0.151488
$973$	−8.85492e6	−0.299849
$974$	4.16640e7	1.40723
$975$	−3.23531e6	−0.108994
$976$	6.63550e7	2.22971
$977$	2.78950e7	0.934955	0.467477	−	0.884005i	$-0.345163\pi$
$977$	2.78950e7	0.934955	0.467477	+	0.884005i	$0.345163\pi$
$978$	2.49487e7	0.834066
$979$	4.64502e7	1.54893
$980$	−3.40892e7	−1.13384
$981$	1.52305e7	0.505291
$982$	−2.33576e7	−0.772948
$983$	−2.02573e7	−0.668650	−0.334325	−	0.942458i	$-0.608508\pi$
$983$	−2.02573e7	−0.668650	−0.334325	+	0.942458i	$0.608508\pi$
$984$	8.59866e6	0.283102
$985$	−8.45233e6	−0.277579
$986$	−4.73531e6	−0.155116
$987$	−7.59088e6	−0.248027
$988$	−2.27179e6	−0.0740416
$989$	550352.	0.0178916
$990$	−1.20834e7	−0.391832
$991$	4.46979e6	0.144578	0.0722891	−	0.997384i	$-0.476970\pi$
$991$	4.46979e6	0.144578	0.0722891	+	0.997384i	$0.476970\pi$
$992$	2.06127e7	0.665053
$993$	9.17115e6	0.295155
$994$	7.83921e6	0.251655
$995$	2.17151e6	0.0695351
$996$	5.51179e7	1.76053
$997$	−482842.	−0.0153839	−0.00769196	−	0.999970i	$-0.502448\pi$
$997$	−482842.	−0.0153839	−0.00769196	+	0.999970i	$0.502448\pi$
$998$	−5.05677e7	−1.60711
$999$	−816619.	−0.0258884

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.c.1.1	✓	12
3.2	odd	2		531.6.a.c.1.12		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.c.1.1	✓	12	1.1	even	1	trivial
531.6.a.c.1.12		12	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-10.3715 q^{2} +9.00000 q^{3} +75.5670 q^{4} +33.2592 q^{5} -93.3431 q^{6} -56.9512 q^{7} -451.853 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q-10.3715 q^{2} +9.00000 q^{3} +75.5670 q^{4} +33.2592 q^{5} -93.3431 q^{6} -56.9512 q^{7} -451.853 q^{8} +81.0000 q^{9} -344.946 q^{10} +432.466 q^{11} +680.103 q^{12} +178.063 q^{13} +590.667 q^{14} +299.333 q^{15} +2268.23 q^{16} +1658.66 q^{17} -840.088 q^{18} -168.835 q^{19} +2513.30 q^{20} -512.561 q^{21} -4485.30 q^{22} +143.318 q^{23} -4066.68 q^{24} -2018.83 q^{25} -1846.77 q^{26} +729.000 q^{27} -4303.63 q^{28} +275.265 q^{29} -3104.51 q^{30} -2273.75 q^{31} -9065.52 q^{32} +3892.20 q^{33} -17202.7 q^{34} -1894.15 q^{35} +6120.93 q^{36} -1120.19 q^{37} +1751.06 q^{38} +1602.57 q^{39} -15028.3 q^{40} -2114.42 q^{41} +5316.00 q^{42} +3840.06 q^{43} +32680.2 q^{44} +2693.99 q^{45} -1486.42 q^{46} +14809.7 q^{47} +20414.1 q^{48} -13563.6 q^{49} +20938.2 q^{50} +14927.9 q^{51} +13455.7 q^{52} +9651.99 q^{53} -7560.79 q^{54} +14383.5 q^{55} +25733.6 q^{56} -1519.51 q^{57} -2854.90 q^{58} -3481.00 q^{59} +22619.7 q^{60} +29254.1 q^{61} +23582.1 q^{62} -4613.05 q^{63} +21439.3 q^{64} +5922.23 q^{65} -40367.7 q^{66} +15092.5 q^{67} +125340. q^{68} +1289.86 q^{69} +19645.1 q^{70} +13271.8 q^{71} -36600.1 q^{72} +42497.1 q^{73} +11618.0 q^{74} -18169.4 q^{75} -12758.3 q^{76} -24629.5 q^{77} -16620.9 q^{78} -55585.7 q^{79} +75439.4 q^{80} +6561.00 q^{81} +21929.6 q^{82} +81043.5 q^{83} -38732.7 q^{84} +55165.7 q^{85} -39827.0 q^{86} +2477.39 q^{87} -195411. q^{88} +107408. q^{89} -27940.6 q^{90} -10140.9 q^{91} +10830.1 q^{92} -20463.7 q^{93} -153598. q^{94} -5615.31 q^{95} -81589.7 q^{96} -92436.4 q^{97} +140674. q^{98} +35029.8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9}+O(q^{10}) \) 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9	\( 12 q + 22 q^{2} + 108 q^{3} + 198 q^{4} + 158 q^{5} + 198 q^{6} + 413 q^{7} + 723 q^{8} + 972 q^{9} + 601 q^{10} + 1480 q^{11} + 1782 q^{12} + 472 q^{13} + 1065 q^{14} + 1422 q^{15} + 6370 q^{16} + 1565 q^{17} + 1782 q^{18} + 3939 q^{19} + 8033 q^{20} + 3717 q^{21} - 1738 q^{22} + 7245 q^{23} + 6507 q^{24} + 9690 q^{25} + 3764 q^{26} + 8748 q^{27} + 12154 q^{28} + 10003 q^{29} + 5409 q^{30} + 7295 q^{31} + 11628 q^{32} + 13320 q^{33} - 16344 q^{34} + 11015 q^{35} + 16038 q^{36} + 6741 q^{37} + 3035 q^{38} + 4248 q^{39} + 5572 q^{40} + 34025 q^{41} + 9585 q^{42} - 6336 q^{43} + 41168 q^{44} + 12798 q^{45} + 2345 q^{46} + 66167 q^{47} + 57330 q^{48} + 28319 q^{49} + 31173 q^{50} + 14085 q^{51} + 16440 q^{52} + 62290 q^{53} + 16038 q^{54} + 55764 q^{55} + 107306 q^{56} + 35451 q^{57} + 37952 q^{58} - 41772 q^{59} + 72297 q^{60} + 68469 q^{61} + 99190 q^{62} + 33453 q^{63} + 68525 q^{64} + 80156 q^{65} - 15642 q^{66} + 113310 q^{67} + 33887 q^{68} + 65205 q^{69} + 32034 q^{70} + 84520 q^{71} + 58563 q^{72} + 135895 q^{73} - 31962 q^{74} + 87210 q^{75} - 61848 q^{76} - 3799 q^{77} + 33876 q^{78} + 14122 q^{79} + 77609 q^{80} + 78732 q^{81} - 1501 q^{82} + 114463 q^{83} + 109386 q^{84} - 101097 q^{85} - 203536 q^{86} + 90027 q^{87} - 244967 q^{88} + 189109 q^{89} + 48681 q^{90} - 168249 q^{91} - 71946 q^{92} + 65655 q^{93} - 472284 q^{94} + 21923 q^{95} + 104652 q^{96} - 76192 q^{97} - 17544 q^{98} + 119880 q^{99}+O(q^{100}) \) 12 * q + 22 * q^2 + 108 * q^3 + 198 * q^4 + 158 * q^5 + 198 * q^6 + 413 * q^7 + 723 * q^8 + 972 * q^9 + 601 * q^10 + 1480 * q^11 + 1782 * q^12 + 472 * q^13 + 1065 * q^14 + 1422 * q^15 + 6370 * q^16 + 1565 * q^17 + 1782 * q^18 + 3939 * q^19 + 8033 * q^20 + 3717 * q^21 - 1738 * q^22 + 7245 * q^23 + 6507 * q^24 + 9690 * q^25 + 3764 * q^26 + 8748 * q^27 + 12154 * q^28 + 10003 * q^29 + 5409 * q^30 + 7295 * q^31 + 11628 * q^32 + 13320 * q^33 - 16344 * q^34 + 11015 * q^35 + 16038 * q^36 + 6741 * q^37 + 3035 * q^38 + 4248 * q^39 + 5572 * q^40 + 34025 * q^41 + 9585 * q^42 - 6336 * q^43 + 41168 * q^44 + 12798 * q^45 + 2345 * q^46 + 66167 * q^47 + 57330 * q^48 + 28319 * q^49 + 31173 * q^50 + 14085 * q^51 + 16440 * q^52 + 62290 * q^53 + 16038 * q^54 + 55764 * q^55 + 107306 * q^56 + 35451 * q^57 + 37952 * q^58 - 41772 * q^59 + 72297 * q^60 + 68469 * q^61 + 99190 * q^62 + 33453 * q^63 + 68525 * q^64 + 80156 * q^65 - 15642 * q^66 + 113310 * q^67 + 33887 * q^68 + 65205 * q^69 + 32034 * q^70 + 84520 * q^71 + 58563 * q^72 + 135895 * q^73 - 31962 * q^74 + 87210 * q^75 - 61848 * q^76 - 3799 * q^77 + 33876 * q^78 + 14122 * q^79 + 77609 * q^80 + 78732 * q^81 - 1501 * q^82 + 114463 * q^83 + 109386 * q^84 - 101097 * q^85 - 203536 * q^86 + 90027 * q^87 - 244967 * q^88 + 189109 * q^89 + 48681 * q^90 - 168249 * q^91 - 71946 * q^92 + 65655 * q^93 - 472284 * q^94 + 21923 * q^95 + 104652 * q^96 - 76192 * q^97 - 17544 * q^98 + 119880 * q^99

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