LMFDB - Embedded newform 177.6.a.b.1.8

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:	$1$
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} - 4 x^{11} - 283 x^{10} + 1045 x^{9} + 27968 x^{8} - 94393 x^{7} - 1130486 x^{6} + \cdots - 50564480 $ x^12 - 4x^11 - 283x^10 + 1045x^9 + 27968x^8 - 94393x^7 - 1130486x^6 + 3566264x^5 + 15496192x^4 - 53008480x^3 - 16576192x^2 + 120303168*x - 50564480
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			1.8
Root			$-1.65902$ 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)

$f(q)$	$=$	$q+1.65902 q^{2} -9.00000 q^{3} -29.2477 q^{4} +59.9319 q^{5} -14.9312 q^{6} -87.2478 q^{7} -101.611 q^{8} +81.0000 q^{9} +O(q^{10})$	\(q+1.65902 q^{2} -9.00000 q^{3} -29.2477 q^{4} +59.9319 q^{5} -14.9312 q^{6} -87.2478 q^{7} -101.611 q^{8} +81.0000 q^{9} +99.4282 q^{10} +655.885 q^{11} +263.229 q^{12} +139.966 q^{13} -144.746 q^{14} -539.387 q^{15} +767.351 q^{16} -1518.98 q^{17} +134.380 q^{18} +393.396 q^{19} -1752.87 q^{20} +785.230 q^{21} +1088.12 q^{22} -4746.68 q^{23} +914.499 q^{24} +466.837 q^{25} +232.206 q^{26} -729.000 q^{27} +2551.79 q^{28} +2791.29 q^{29} -894.853 q^{30} -1808.12 q^{31} +4524.60 q^{32} -5902.96 q^{33} -2520.02 q^{34} -5228.93 q^{35} -2369.06 q^{36} +6710.46 q^{37} +652.650 q^{38} -1259.69 q^{39} -6089.74 q^{40} -13926.6 q^{41} +1302.71 q^{42} -19381.1 q^{43} -19183.1 q^{44} +4854.49 q^{45} -7874.82 q^{46} -15752.6 q^{47} -6906.16 q^{48} -9194.83 q^{49} +774.491 q^{50} +13670.8 q^{51} -4093.68 q^{52} -25608.5 q^{53} -1209.42 q^{54} +39308.4 q^{55} +8865.33 q^{56} -3540.56 q^{57} +4630.80 q^{58} -3481.00 q^{59} +15775.8 q^{60} +11066.2 q^{61} -2999.70 q^{62} -7067.07 q^{63} -17048.8 q^{64} +8388.43 q^{65} -9793.12 q^{66} -34547.3 q^{67} +44426.7 q^{68} +42720.1 q^{69} -8674.88 q^{70} +43063.2 q^{71} -8230.49 q^{72} -34956.0 q^{73} +11132.8 q^{74} -4201.53 q^{75} -11505.9 q^{76} -57224.5 q^{77} -2089.85 q^{78} +91122.1 q^{79} +45988.8 q^{80} +6561.00 q^{81} -23104.4 q^{82} -109543. q^{83} -22966.1 q^{84} -91035.5 q^{85} -32153.5 q^{86} -25121.6 q^{87} -66645.1 q^{88} +136931. q^{89} +8053.68 q^{90} -12211.7 q^{91} +138829. q^{92} +16273.0 q^{93} -26133.8 q^{94} +23577.0 q^{95} -40721.4 q^{96} -139282. q^{97} -15254.4 q^{98} +53126.7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9}+O(q^{10}) $ 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9} - 863 q^{10} + 492 q^{11} - 1782 q^{12} - 974 q^{13} - 967 q^{14} - 324 q^{15} + 6370 q^{16} - 1463 q^{17} - 324 q^{18} - 3189 q^{19} - 835 q^{20} + 3699 q^{21} - 2726 q^{22} - 2617 q^{23} + 621 q^{24} + 8642 q^{25} + 2414 q^{26} - 8748 q^{27} - 20458 q^{28} - 1963 q^{29} + 7767 q^{30} - 11929 q^{31} - 14382 q^{32} - 4428 q^{33} - 20744 q^{34} + 1829 q^{35} + 16038 q^{36} - 28105 q^{37} - 23475 q^{38} + 8766 q^{39} - 100576 q^{40} - 7585 q^{41} + 8703 q^{42} - 33146 q^{43} + 26014 q^{44} + 2916 q^{45} - 142851 q^{46} - 79215 q^{47} - 57330 q^{48} - 32569 q^{49} - 136019 q^{50} + 13167 q^{51} - 248218 q^{52} - 12220 q^{53} + 2916 q^{54} - 117770 q^{55} - 186728 q^{56} + 28701 q^{57} - 188072 q^{58} - 41772 q^{59} + 7515 q^{60} - 54195 q^{61} + 36230 q^{62} - 33291 q^{63} + 45197 q^{64} + 42368 q^{65} + 24534 q^{66} + 24224 q^{67} - 209639 q^{68} + 23553 q^{69} - 35684 q^{70} + 60254 q^{71} - 5589 q^{72} - 15385 q^{73} + 214638 q^{74} - 77778 q^{75} - 167504 q^{76} - 17169 q^{77} - 21726 q^{78} - 27054 q^{79} + 216899 q^{80} + 78732 q^{81} + 37917 q^{82} - 117595 q^{83} + 184122 q^{84} - 121585 q^{85} + 306756 q^{86} + 17667 q^{87} - 105799 q^{88} - 36033 q^{89} - 69903 q^{90} - 32217 q^{91} - 30906 q^{92} + 107361 q^{93} + 128392 q^{94} - 50721 q^{95} + 129438 q^{96} - 196914 q^{97} + 574100 q^{98} + 39852 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9 - 863 * q^10 + 492 * q^11 - 1782 * q^12 - 974 * q^13 - 967 * q^14 - 324 * q^15 + 6370 * q^16 - 1463 * q^17 - 324 * q^18 - 3189 * q^19 - 835 * q^20 + 3699 * q^21 - 2726 * q^22 - 2617 * q^23 + 621 * q^24 + 8642 * q^25 + 2414 * q^26 - 8748 * q^27 - 20458 * q^28 - 1963 * q^29 + 7767 * q^30 - 11929 * q^31 - 14382 * q^32 - 4428 * q^33 - 20744 * q^34 + 1829 * q^35 + 16038 * q^36 - 28105 * q^37 - 23475 * q^38 + 8766 * q^39 - 100576 * q^40 - 7585 * q^41 + 8703 * q^42 - 33146 * q^43 + 26014 * q^44 + 2916 * q^45 - 142851 * q^46 - 79215 * q^47 - 57330 * q^48 - 32569 * q^49 - 136019 * q^50 + 13167 * q^51 - 248218 * q^52 - 12220 * q^53 + 2916 * q^54 - 117770 * q^55 - 186728 * q^56 + 28701 * q^57 - 188072 * q^58 - 41772 * q^59 + 7515 * q^60 - 54195 * q^61 + 36230 * q^62 - 33291 * q^63 + 45197 * q^64 + 42368 * q^65 + 24534 * q^66 + 24224 * q^67 - 209639 * q^68 + 23553 * q^69 - 35684 * q^70 + 60254 * q^71 - 5589 * q^72 - 15385 * q^73 + 214638 * q^74 - 77778 * q^75 - 167504 * q^76 - 17169 * q^77 - 21726 * q^78 - 27054 * q^79 + 216899 * q^80 + 78732 * q^81 + 37917 * q^82 - 117595 * q^83 + 184122 * q^84 - 121585 * q^85 + 306756 * q^86 + 17667 * q^87 - 105799 * q^88 - 36033 * q^89 - 69903 * q^90 - 32217 * q^91 - 30906 * q^92 + 107361 * q^93 + 128392 * q^94 - 50721 * q^95 + 129438 * q^96 - 196914 * q^97 + 574100 * q^98 + 39852 * 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 $

$2$	1.65902	0.293276	0.146638	−	0.989190i	$-0.453155\pi$
$2$	1.65902	0.293276	0.146638	+	0.989190i	$0.453155\pi$
$3$	−9.00000	−0.577350
$3$	−9.00000	−0.577350
$4$	−29.2477	−0.913989
$5$	59.9319	1.07210	0.536048	−	0.844188i	$-0.319917\pi$
$5$	59.9319	1.07210	0.536048	+	0.844188i	$0.319917\pi$
$6$	−14.9312	−0.169323
$7$	−87.2478	−0.672991	−0.336495	−	0.941685i	$-0.609242\pi$
$7$	−87.2478	−0.672991	−0.336495	+	0.941685i	$0.609242\pi$
$8$	−101.611	−0.561327
$9$	81.0000	0.333333
$10$	99.4282	0.314419
$11$	655.885	1.63435	0.817176	−	0.576388i	$-0.195538\pi$
$11$	655.885	1.63435	0.817176	+	0.576388i	$0.195538\pi$
$12$	263.229	0.527692
$13$	139.966	0.229702	0.114851	−	0.993383i	$-0.463361\pi$
$13$	139.966	0.229702	0.114851	+	0.993383i	$0.463361\pi$
$14$	−144.746	−0.197372
$15$	−539.387	−0.618974
$16$	767.351	0.749366
$17$	−1518.98	−1.27477	−0.637383	−	0.770548i	$-0.719983\pi$
$17$	−1518.98	−1.27477	−0.637383	+	0.770548i	$0.719983\pi$
$18$	134.380	0.0977586
$19$	393.396	0.250003	0.125002	−	0.992157i	$-0.460106\pi$
$19$	393.396	0.250003	0.125002	+	0.992157i	$0.460106\pi$
$20$	−1752.87	−0.979883
$21$	785.230	0.388551
$22$	1088.12	0.479316
$23$	−4746.68	−1.87098	−0.935492	−	0.353348i	$-0.885043\pi$
$23$	−4746.68	−1.87098	−0.935492	+	0.353348i	$0.885043\pi$
$24$	914.499	0.324082
$25$	466.837	0.149388
$26$	232.206	0.0673659
$27$	−729.000	−0.192450
$28$	2551.79	0.615106
$29$	2791.29	0.616326	0.308163	−	0.951334i	$-0.400286\pi$
$29$	2791.29	0.616326	0.308163	+	0.951334i	$0.400286\pi$
$30$	−894.853	−0.181530
$31$	−1808.12	−0.337926	−0.168963	−	0.985622i	$-0.554042\pi$
$31$	−1808.12	−0.337926	−0.168963	+	0.985622i	$0.554042\pi$
$32$	4524.60	0.781097
$33$	−5902.96	−0.943594
$34$	−2520.02	−0.373858
$35$	−5228.93	−0.721510
$36$	−2369.06	−0.304663
$37$	6710.46	0.805838	0.402919	−	0.915236i	$-0.367996\pi$
$37$	6710.46	0.805838	0.402919	+	0.915236i	$0.367996\pi$
$38$	652.650	0.0733199
$39$	−1259.69	−0.132618
$40$	−6089.74	−0.601795
$41$	−13926.6	−1.29385	−0.646925	−	0.762553i	$-0.723945\pi$
$41$	−13926.6	−1.29385	−0.646925	+	0.762553i	$0.723945\pi$
$42$	1302.71	0.113953
$43$	−19381.1	−1.59848	−0.799239	−	0.601014i	$-0.794764\pi$
$43$	−19381.1	−1.59848	−0.799239	+	0.601014i	$0.794764\pi$
$44$	−19183.1	−1.49378
$45$	4854.49	0.357365
$46$	−7874.82	−0.548714
$47$	−15752.6	−1.04018	−0.520088	−	0.854113i	$-0.674101\pi$
$47$	−15752.6	−1.04018	−0.520088	+	0.854113i	$0.674101\pi$
$48$	−6906.16	−0.432647
$49$	−9194.83	−0.547083
$50$	774.491	0.0438118
$51$	13670.8	0.735986
$52$	−4093.68	−0.209945
$53$	−25608.5	−1.25226	−0.626131	−	0.779718i	$-0.715363\pi$
$53$	−25608.5	−1.25226	−0.626131	+	0.779718i	$0.715363\pi$
$54$	−1209.42	−0.0564409
$55$	39308.4	1.75218
$56$	8865.33	0.377768
$57$	−3540.56	−0.144339
$58$	4630.80	0.180753
$59$	−3481.00	−0.130189
$59$	−3481.00	−0.130189
$60$	15775.8	0.565736
$61$	11066.2	0.380778	0.190389	−	0.981709i	$-0.439025\pi$
$61$	11066.2	0.380778	0.190389	+	0.981709i	$0.439025\pi$
$62$	−2999.70	−0.0991056
$63$	−7067.07	−0.224330
$64$	−17048.8	−0.520289
$65$	8388.43	0.246262
$66$	−9793.12	−0.276733
$67$	−34547.3	−0.940216	−0.470108	−	0.882609i	$-0.655785\pi$
$67$	−34547.3	−0.940216	−0.470108	+	0.882609i	$0.655785\pi$
$68$	44426.7	1.16512
$69$	42720.1	1.08021
$70$	−8674.88	−0.211601
$71$	43063.2	1.01382	0.506910	−	0.861999i	$-0.330788\pi$
$71$	43063.2	1.01382	0.506910	+	0.861999i	$0.330788\pi$
$72$	−8230.49	−0.187109
$73$	−34956.0	−0.767741	−0.383871	−	0.923387i	$-0.625409\pi$
$73$	−34956.0	−0.767741	−0.383871	+	0.923387i	$0.625409\pi$
$74$	11132.8	0.236333
$75$	−4201.53	−0.0862491
$76$	−11505.9	−0.228500
$77$	−57224.5	−1.09990
$78$	−2089.85	−0.0388937
$79$	91122.1	1.64269	0.821345	−	0.570431i	$-0.193224\pi$
$79$	91122.1	1.64269	0.821345	+	0.570431i	$0.193224\pi$
$80$	45988.8	0.803391
$81$	6561.00	0.111111
$82$	−23104.4	−0.379455
$83$	−109543.	−1.74538	−0.872692	−	0.488271i	$-0.837628\pi$
$83$	−109543.	−1.74538	−0.872692	+	0.488271i	$0.837628\pi$
$84$	−22966.1	−0.355132
$85$	−91035.5	−1.36667
$86$	−32153.5	−0.468795
$87$	−25121.6	−0.355836
$88$	−66645.1	−0.917406
$89$	136931.	1.83243	0.916215	−	0.400687i	$-0.131228\pi$
$89$	136931.	1.83243	0.916215	+	0.400687i	$0.131228\pi$
$90$	8053.68	0.104806
$91$	−12211.7	−0.154587
$92$	138829.	1.71006
$93$	16273.0	0.195102
$94$	−26133.8	−0.305058
$95$	23577.0	0.268027
$96$	−40721.4	−0.450967
$97$	−139282.	−1.50302	−0.751511	−	0.659721i	$-0.770675\pi$
$97$	−139282.	−1.50302	−0.751511	+	0.659721i	$0.770675\pi$
$98$	−15254.4	−0.160446
$99$	53126.7	0.544784
$100$	−13653.9	−0.136539
$101$	−79019.0	−0.770776	−0.385388	−	0.922755i	$-0.625932\pi$
$101$	−79019.0	−0.770776	−0.385388	+	0.922755i	$0.625932\pi$
$102$	22680.2	0.215847
$103$	−8298.49	−0.0770736	−0.0385368	−	0.999257i	$-0.512270\pi$
$103$	−8298.49	−0.0770736	−0.0385368	+	0.999257i	$0.512270\pi$
$104$	−14222.1	−0.128938
$105$	47060.3	0.416564
$106$	−42485.0	−0.367258
$107$	−34725.6	−0.293218	−0.146609	−	0.989195i	$-0.546836\pi$
$107$	−34725.6	−0.293218	−0.146609	+	0.989195i	$0.546836\pi$
$108$	21321.5	0.175897
$109$	211277.	1.70328	0.851639	−	0.524130i	$-0.175609\pi$
$109$	211277.	1.70328	0.851639	+	0.524130i	$0.175609\pi$
$110$	65213.4	0.513872
$111$	−60394.1	−0.465251
$112$	−66949.6	−0.504316
$113$	175697.	1.29440	0.647201	−	0.762319i	$-0.275939\pi$
$113$	175697.	1.29440	0.647201	+	0.762319i	$0.275939\pi$
$114$	−5873.85	−0.0423312
$115$	−284478.	−2.00587
$116$	−81638.8	−0.563315
$117$	11337.2	0.0765672
$118$	−5775.04	−0.0381812
$119$	132528.	0.857905
$120$	54807.7	0.347447
$121$	269134.	1.67111
$122$	18359.0	0.111673
$123$	125339.	0.747005
$124$	52883.2	0.308861
$125$	−159309.	−0.911937
$126$	−11724.4	−0.0657906
$127$	156670.	0.861941	0.430970	−	0.902366i	$-0.358171\pi$
$127$	156670.	0.861941	0.430970	+	0.902366i	$0.358171\pi$
$128$	−173071.	−0.933686
$129$	174430.	0.922881
$130$	13916.6	0.0722226
$131$	21735.5	0.110660	0.0553300	−	0.998468i	$-0.482379\pi$
$131$	21735.5	0.110660	0.0553300	+	0.998468i	$0.482379\pi$
$132$	172648.	0.862435
$133$	−34322.9	−0.168250
$134$	−57314.6	−0.275742
$135$	−43690.4	−0.206325
$136$	154345.	0.715559
$137$	293416.	1.33562	0.667810	−	0.744332i	$-0.267232\pi$
$137$	293416.	1.33562	0.667810	+	0.744332i	$0.267232\pi$
$138$	70873.4	0.316800
$139$	−128147.	−0.562564	−0.281282	−	0.959625i	$-0.590760\pi$
$139$	−128147.	−0.562564	−0.281282	+	0.959625i	$0.590760\pi$
$140$	152934.	0.659453
$141$	141773.	0.600546
$142$	71442.7	0.297329
$143$	91801.5	0.375413
$144$	62155.4	0.249789
$145$	167288.	0.660760
$146$	−57992.7	−0.225160
$147$	82753.5	0.315859
$148$	−196265.	−0.736528
$149$	−217922.	−0.804146	−0.402073	−	0.915608i	$-0.631710\pi$
$149$	−217922.	−0.804146	−0.402073	+	0.915608i	$0.631710\pi$
$150$	−6970.42	−0.0252948
$151$	−394958.	−1.40964	−0.704821	−	0.709385i	$-0.748973\pi$
$151$	−394958.	−1.40964	−0.704821	+	0.709385i	$0.748973\pi$
$152$	−39973.3	−0.140333
$153$	−123037.	−0.424922
$154$	−94936.4	−0.322575
$155$	−108364.	−0.362289
$156$	36843.1	0.121212
$157$	20578.0	0.0666277	0.0333139	−	0.999445i	$-0.489394\pi$
$157$	20578.0	0.0666277	0.0333139	+	0.999445i	$0.489394\pi$
$158$	151173.	0.481761
$159$	230477.	0.722994
$160$	271168.	0.837411
$161$	414137.	1.25916
$162$	10884.8	0.0325862
$163$	−406284.	−1.19773	−0.598867	−	0.800848i	$-0.704382\pi$
$163$	−406284.	−1.19773	−0.598867	+	0.800848i	$0.704382\pi$
$164$	407319.	1.18257
$165$	−353776.	−1.01162
$166$	−181734.	−0.511879
$167$	−439495.	−1.21945	−0.609723	−	0.792614i	$-0.708719\pi$
$167$	−439495.	−1.21945	−0.609723	+	0.792614i	$0.708719\pi$
$168$	−79788.0	−0.218104
$169$	−351703.	−0.947237
$170$	−151030.	−0.400811
$171$	31865.0	0.0833344
$172$	566851.	1.46099
$173$	586270.	1.48930	0.744651	−	0.667454i	$-0.232616\pi$
$173$	586270.	1.48930	0.744651	+	0.667454i	$0.232616\pi$
$174$	−41677.2	−0.104358
$175$	−40730.5	−0.100537
$176$	503294.	1.22473
$177$	31329.0	0.0751646
$178$	227171.	0.537407
$179$	−548999.	−1.28068	−0.640338	−	0.768093i	$-0.721206\pi$
$179$	−548999.	−1.28068	−0.640338	+	0.768093i	$0.721206\pi$
$180$	−141982.	−0.326628
$181$	−634515.	−1.43961	−0.719806	−	0.694175i	$-0.755769\pi$
$181$	−634515.	−1.43961	−0.719806	+	0.694175i	$0.755769\pi$
$182$	−20259.5	−0.0453366
$183$	−99595.4	−0.219842
$184$	482314.	1.05023
$185$	402171.	0.863935
$186$	26997.3	0.0572186
$187$	−996277.	−2.08342
$188$	460726.	0.950710
$189$	63603.6	0.129517
$190$	39114.6	0.0786059
$191$	−408074.	−0.809385	−0.404692	−	0.914453i	$-0.632621\pi$
$191$	−408074.	−0.809385	−0.404692	+	0.914453i	$0.632621\pi$
$192$	153439.	0.300389
$193$	−29069.5	−0.0561751	−0.0280875	−	0.999605i	$-0.508942\pi$
$193$	−29069.5	−0.0561751	−0.0280875	+	0.999605i	$0.508942\pi$
$194$	−231071.	−0.440800
$195$	−75495.9	−0.142179
$196$	268927.	0.500028
$197$	658204.	1.20836	0.604178	−	0.796849i	$-0.293502\pi$
$197$	658204.	1.20836	0.604178	+	0.796849i	$0.293502\pi$
$198$	88138.1	0.159772
$199$	483961.	0.866319	0.433159	−	0.901317i	$-0.357399\pi$
$199$	483961.	0.866319	0.433159	+	0.901317i	$0.357399\pi$
$200$	−47435.7	−0.0838553
$201$	310926.	0.542834
$202$	−131094.	−0.226050
$203$	−243534.	−0.414782
$204$	−399840.	−0.672683
$205$	−834645.	−1.38713
$206$	−13767.3	−0.0226038
$207$	−384481.	−0.623661
$208$	107403.	0.172131
$209$	258022.	0.408593
$210$	78073.9	0.122168
$211$	167978.	0.259745	0.129872	−	0.991531i	$-0.458543\pi$
$211$	167978.	0.259745	0.129872	+	0.991531i	$0.458543\pi$
$212$	748990.	1.14455
$213$	−387569.	−0.585329
$214$	−57610.4	−0.0859936
$215$	−1.16154e6	−1.71372
$216$	74074.4	0.108027
$217$	157754.	0.227421
$218$	350512.	0.499530
$219$	314604.	0.443256
$220$	−1.14968e6	−1.60148
$221$	−212606.	−0.292816
$222$	−100195.	−0.136447
$223$	−391141.	−0.526709	−0.263355	−	0.964699i	$-0.584829\pi$
$223$	−391141.	−0.526709	−0.263355	+	0.964699i	$0.584829\pi$
$224$	−394761.	−0.525671
$225$	37813.8	0.0497959
$226$	291485.	0.379617
$227$	1.24360e6	1.60183	0.800913	−	0.598780i	$-0.204348\pi$
$227$	1.24360e6	1.60183	0.800913	+	0.598780i	$0.204348\pi$
$228$	103553.	0.131925
$229$	330176.	0.416061	0.208031	−	0.978122i	$-0.433295\pi$
$229$	330176.	0.416061	0.208031	+	0.978122i	$0.433295\pi$
$230$	−471953.	−0.588274
$231$	515020.	0.635030
$232$	−283626.	−0.345960
$233$	−857543.	−1.03482	−0.517412	−	0.855737i	$-0.673104\pi$
$233$	−857543.	−1.03482	−0.517412	+	0.855737i	$0.673104\pi$
$234$	18808.7	0.0224553
$235$	−944082.	−1.11517
$236$	101811.	0.118991
$237$	−820099.	−0.948408
$238$	219866.	0.251603
$239$	−1.03288e6	−1.16965	−0.584825	−	0.811160i	$-0.698837\pi$
$239$	−1.03288e6	−1.16965	−0.584825	+	0.811160i	$0.698837\pi$
$240$	−413899.	−0.463838
$241$	136392.	0.151267	0.0756336	−	0.997136i	$-0.475902\pi$
$241$	136392.	0.151267	0.0756336	+	0.997136i	$0.475902\pi$
$242$	446498.	0.490096
$243$	−59049.0	−0.0641500
$244$	−323659.	−0.348027
$245$	−551064.	−0.586525
$246$	207940.	0.219078
$247$	55062.0	0.0574261
$248$	183724.	0.189687
$249$	985891.	1.00770
$250$	−264296.	−0.267449
$251$	−494314.	−0.495243	−0.247621	−	0.968857i	$-0.579649\pi$
$251$	−494314.	−0.495243	−0.247621	+	0.968857i	$0.579649\pi$
$252$	206695.	0.205035
$253$	−3.11327e6	−3.05785
$254$	259919.	0.252786
$255$	819319.	0.789047
$256$	258434.	0.246462
$257$	259654.	0.245223	0.122612	−	0.992455i	$-0.460873\pi$
$257$	259654.	0.245223	0.122612	+	0.992455i	$0.460873\pi$
$258$	289382.	0.270659
$259$	−585473.	−0.542322
$260$	−245342.	−0.225081
$261$	226095.	0.205442
$262$	36059.6	0.0324539
$263$	−696202.	−0.620649	−0.310324	−	0.950631i	$-0.600438\pi$
$263$	−696202.	−0.620649	−0.310324	+	0.950631i	$0.600438\pi$
$264$	599806.	0.529664
$265$	−1.53477e6	−1.34254
$266$	−56942.3	−0.0493436
$267$	−1.23238e6	−1.05795
$268$	1.01043e6	0.859347
$269$	403193.	0.339729	0.169865	−	0.985467i	$-0.445667\pi$
$269$	403193.	0.339729	0.169865	+	0.985467i	$0.445667\pi$
$270$	−72483.1	−0.0605100
$271$	−83968.2	−0.0694531	−0.0347265	−	0.999397i	$-0.511056\pi$
$271$	−83968.2	−0.0694531	−0.0347265	+	0.999397i	$0.511056\pi$
$272$	−1.16559e6	−0.955265
$273$	109905.	0.0892509
$274$	486783.	0.391705
$275$	306191.	0.244152
$276$	−1.24946e6	−0.987303
$277$	−679016.	−0.531717	−0.265859	−	0.964012i	$-0.585655\pi$
$277$	−679016.	−0.531717	−0.265859	+	0.964012i	$0.585655\pi$
$278$	−212598.	−0.164986
$279$	−146457.	−0.112642
$280$	531316.	0.405003
$281$	1.00480e6	0.759125	0.379563	−	0.925166i	$-0.376074\pi$
$281$	1.00480e6	0.759125	0.379563	+	0.925166i	$0.376074\pi$
$282$	235204.	0.176126
$283$	535938.	0.397785	0.198893	−	0.980021i	$-0.436265\pi$
$283$	535938.	0.397785	0.198893	+	0.980021i	$0.436265\pi$
$284$	−1.25950e6	−0.926621
$285$	−212193.	−0.154746
$286$	152300.	0.110100
$287$	1.21506e6	0.870749
$288$	366493.	0.260366
$289$	887447.	0.625026
$290$	277533.	0.193785
$291$	1.25354e6	0.867770
$292$	1.02238e6	0.701707
$293$	869160.	0.591467	0.295734	−	0.955270i	$-0.404436\pi$
$293$	869160.	0.591467	0.295734	+	0.955270i	$0.404436\pi$
$294$	137289.	0.0926337
$295$	−208623.	−0.139575
$296$	−681856.	−0.452339
$297$	−478140.	−0.314531
$298$	−361536.	−0.235836
$299$	−664373.	−0.429768
$300$	122885.	0.0788307
$301$	1.69095e6	1.07576
$302$	−655243.	−0.413414
$303$	711171.	0.445008
$304$	301872.	0.187344
$305$	663216.	0.408231
$306$	−204121.	−0.124619
$307$	693445.	0.419919	0.209960	−	0.977710i	$-0.432667\pi$
$307$	693445.	0.419919	0.209960	+	0.977710i	$0.432667\pi$
$308$	1.67368e6	1.00530
$309$	74686.4	0.0444985
$310$	−179778.	−0.106251
$311$	1.08592e6	0.636647	0.318324	−	0.947982i	$-0.396880\pi$
$311$	1.08592e6	0.636647	0.318324	+	0.947982i	$0.396880\pi$
$312$	127999.	0.0744422
$313$	2.46914e6	1.42458	0.712288	−	0.701888i	$-0.247659\pi$
$313$	2.46914e6	1.42458	0.712288	+	0.701888i	$0.247659\pi$
$314$	34139.3	0.0195403
$315$	−423543.	−0.240503
$316$	−2.66511e6	−1.50140
$317$	2.16299e6	1.20894	0.604471	−	0.796627i	$-0.293385\pi$
$317$	2.16299e6	1.20894	0.604471	+	0.796627i	$0.293385\pi$
$318$	382365.	0.212037
$319$	1.83077e6	1.00729
$320$	−1.02177e6	−0.557799
$321$	312530.	0.169289
$322$	687061.	0.369280
$323$	−597561.	−0.318695
$324$	−191894.	−0.101554
$325$	65341.2	0.0343146
$326$	−674032.	−0.351266
$327$	−1.90149e6	−0.983387
$328$	1.41509e6	0.726273
$329$	1.37438e6	0.700029
$330$	−586921.	−0.296684
$331$	−1.30386e6	−0.654128	−0.327064	−	0.945002i	$-0.606059\pi$
$331$	−1.30386e6	−0.654128	−0.327064	+	0.945002i	$0.606059\pi$
$332$	3.20389e6	1.59526
$333$	543547.	0.268613
$334$	−729130.	−0.357634
$335$	−2.07049e6	−1.00800
$336$	602547.	0.291167
$337$	3.43860e6	1.64933	0.824664	−	0.565623i	$-0.191364\pi$
$337$	3.43860e6	1.64933	0.824664	+	0.565623i	$0.191364\pi$
$338$	−583481.	−0.277802
$339$	−1.58128e6	−0.747323
$340$	2.66258e6	1.24912
$341$	−1.18592e6	−0.552291
$342$	52864.7	0.0244400
$343$	2.26860e6	1.04117
$344$	1.96933e6	0.897268
$345$	2.56030e6	1.15809
$346$	972633.	0.436776
$347$	−337924.	−0.150659	−0.0753296	−	0.997159i	$-0.524001\pi$
$347$	−337924.	−0.150659	−0.0753296	+	0.997159i	$0.524001\pi$
$348$	734749.	0.325230
$349$	−1.09909e6	−0.483025	−0.241513	−	0.970398i	$-0.577644\pi$
$349$	−1.09909e6	−0.483025	−0.241513	+	0.970398i	$0.577644\pi$
$350$	−67572.6	−0.0294849
$351$	−102035.	−0.0442061
$352$	2.96762e6	1.27659
$353$	−2.32702e6	−0.993945	−0.496973	−	0.867766i	$-0.665555\pi$
$353$	−2.32702e6	−0.993945	−0.496973	+	0.867766i	$0.665555\pi$
$354$	51975.4	0.0220440
$355$	2.58086e6	1.08691
$356$	−4.00492e6	−1.67482
$357$	−1.19275e6	−0.495312
$358$	−910800.	−0.375591
$359$	−2.78944e6	−1.14230	−0.571151	−	0.820845i	$-0.693503\pi$
$359$	−2.78944e6	−1.14230	−0.571151	+	0.820845i	$0.693503\pi$
$360$	−493269.	−0.200598
$361$	−2.32134e6	−0.937498
$362$	−1.05267e6	−0.422203
$363$	−2.42220e6	−0.964816
$364$	357164.	0.141291
$365$	−2.09498e6	−0.823091
$366$	−165231.	−0.0644745
$367$	−1.60366e6	−0.621510	−0.310755	−	0.950490i	$-0.600582\pi$
$367$	−1.60366e6	−0.621510	−0.310755	+	0.950490i	$0.600582\pi$
$368$	−3.64237e6	−1.40205
$369$	−1.12805e6	−0.431283
$370$	667209.	0.253371
$371$	2.23429e6	0.842761
$372$	−475948.	−0.178321
$373$	−1.49956e6	−0.558075	−0.279037	−	0.960280i	$-0.590015\pi$
$373$	−1.49956e6	−0.558075	−0.279037	+	0.960280i	$0.590015\pi$
$374$	−1.65284e6	−0.611015
$375$	1.43378e6	0.526507
$376$	1.60063e6	0.583879
$377$	390686.	0.141571
$378$	105520.	0.0379842
$379$	2.95105e6	1.05531	0.527653	−	0.849460i	$-0.323072\pi$
$379$	2.95105e6	1.05531	0.527653	+	0.849460i	$0.323072\pi$
$380$	−689571.	−0.244974
$381$	−1.41003e6	−0.497642
$382$	−677001.	−0.237373
$383$	1.98411e6	0.691145	0.345572	−	0.938392i	$-0.387685\pi$
$383$	1.98411e6	0.691145	0.345572	+	0.938392i	$0.387685\pi$
$384$	1.55764e6	0.539064
$385$	−3.42957e6	−1.17920
$386$	−48226.8	−0.0164748
$387$	−1.56987e6	−0.532826
$388$	4.07367e6	1.37375
$389$	1.68710e6	0.565284	0.282642	−	0.959225i	$-0.408789\pi$
$389$	1.68710e6	0.565284	0.282642	+	0.959225i	$0.408789\pi$
$390$	−125249.	−0.0416978
$391$	7.21011e6	2.38507
$392$	934295.	0.307092
$393$	−195619.	−0.0638896
$394$	1.09197e6	0.354381
$395$	5.46112e6	1.76112
$396$	−1.55383e6	−0.497927
$397$	233554.	0.0743722	0.0371861	−	0.999308i	$-0.488161\pi$
$397$	233554.	0.0743722	0.0371861	+	0.999308i	$0.488161\pi$
$398$	802900.	0.254070
$399$	308906.	0.0971391
$400$	358228.	0.111946
$401$	−4.29311e6	−1.33325	−0.666625	−	0.745394i	$-0.732262\pi$
$401$	−4.29311e6	−1.33325	−0.666625	+	0.745394i	$0.732262\pi$
$402$	515832.	0.159200
$403$	−253075.	−0.0776222
$404$	2.31112e6	0.704481
$405$	393213.	0.119122
$406$	−404027.	−0.121645
$407$	4.40129e6	1.31702
$408$	−1.38911e6	−0.413128
$409$	1.98371e6	0.586368	0.293184	−	0.956056i	$-0.405285\pi$
$409$	1.98371e6	0.586368	0.293184	+	0.956056i	$0.405285\pi$
$410$	−1.38469e6	−0.406812
$411$	−2.64075e6	−0.771120
$412$	242711.	0.0704445
$413$	303709.	0.0876159
$414$	−637861.	−0.182905
$415$	−6.56515e6	−1.87122
$416$	633290.	0.179419
$417$	1.15332e6	0.324797
$418$	428063.	0.119831
$419$	−76952.5	−0.0214135	−0.0107068	−	0.999943i	$-0.503408\pi$
$419$	−76952.5	−0.0214135	−0.0107068	+	0.999943i	$0.503408\pi$
$420$	−1.37640e6	−0.380735
$421$	1.97318e6	0.542577	0.271288	−	0.962498i	$-0.412550\pi$
$421$	1.97318e6	0.542577	0.271288	+	0.962498i	$0.412550\pi$
$422$	278679.	0.0761769
$423$	−1.27596e6	−0.346725
$424$	2.60211e6	0.702928
$425$	−709116.	−0.190434
$426$	−642984.	−0.171663
$427$	−965497.	−0.256260
$428$	1.01564e6	0.267998
$429$	−826214.	−0.216745
$430$	−1.92702e6	−0.502592
$431$	2.53130e6	0.656372	0.328186	−	0.944613i	$-0.393563\pi$
$431$	2.53130e6	0.656372	0.328186	+	0.944613i	$0.393563\pi$
$432$	−559399.	−0.144216
$433$	896878.	0.229887	0.114943	−	0.993372i	$-0.463331\pi$
$433$	896878.	0.229887	0.114943	+	0.993372i	$0.463331\pi$
$434$	261717.	0.0666972
$435$	−1.50559e6	−0.381490
$436$	−6.17935e6	−1.55678
$437$	−1.86732e6	−0.467752
$438$	521934.	0.129996
$439$	−5.15275e6	−1.27608	−0.638040	−	0.770003i	$-0.720254\pi$
$439$	−5.15275e6	−1.27608	−0.638040	+	0.770003i	$0.720254\pi$
$440$	−3.99417e6	−0.983546
$441$	−744781.	−0.182361
$442$	−352717.	−0.0858757
$443$	1.77270e6	0.429166	0.214583	−	0.976706i	$-0.431161\pi$
$443$	1.77270e6	0.429166	0.214583	+	0.976706i	$0.431161\pi$
$444$	1.76639e6	0.425235
$445$	8.20655e6	1.96454
$446$	−648910.	−0.154471
$447$	1.96130e6	0.464274
$448$	1.48747e6	0.350150
$449$	652208.	0.152676	0.0763379	−	0.997082i	$-0.475677\pi$
$449$	652208.	0.152676	0.0763379	+	0.997082i	$0.475677\pi$
$450$	62733.7	0.0146039
$451$	−9.13422e6	−2.11461
$452$	−5.13874e6	−1.18307
$453$	3.55462e6	0.813857
$454$	2.06315e6	0.469777
$455$	−731872.	−0.165732
$456$	359760.	0.0810215
$457$	6.01636e6	1.34755	0.673773	−	0.738939i	$-0.264673\pi$
$457$	6.01636e6	1.34755	0.673773	+	0.738939i	$0.264673\pi$
$458$	547769.	0.122021
$459$	1.10734e6	0.245329
$460$	8.32030e6	1.83335
$461$	8.80449e6	1.92953	0.964765	−	0.263111i	$-0.0847487\pi$
$461$	8.80449e6	1.92953	0.964765	+	0.263111i	$0.0847487\pi$
$462$	854428.	0.186239
$463$	−6.15435e6	−1.33423	−0.667113	−	0.744956i	$-0.732470\pi$
$463$	−6.15435e6	−1.33423	−0.667113	+	0.744956i	$0.732470\pi$
$464$	2.14190e6	0.461853
$465$	975275.	0.209168
$466$	−1.42268e6	−0.303489
$467$	5.99157e6	1.27130	0.635651	−	0.771977i	$-0.280732\pi$
$467$	5.99157e6	1.27130	0.635651	+	0.771977i	$0.280732\pi$
$468$	−331588.	−0.0699816
$469$	3.01418e6	0.632756
$470$	−1.56625e6	−0.327052
$471$	−185202.	−0.0384675
$472$	353708.	0.0730785
$473$	−1.27117e7	−2.61248
$474$	−1.36056e6	−0.278145
$475$	183652.	0.0373474
$476$	−3.87613e6	−0.784116
$477$	−2.07429e6	−0.417421
$478$	−1.71357e6	−0.343030
$479$	−2.22116e6	−0.442325	−0.221163	−	0.975237i	$-0.570985\pi$
$479$	−2.22116e6	−0.442325	−0.221163	+	0.975237i	$0.570985\pi$
$480$	−2.44051e6	−0.483479
$481$	939236.	0.185102
$482$	226276.	0.0443630
$483$	−3.72723e6	−0.726974
$484$	−7.87154e6	−1.52738
$485$	−8.34743e6	−1.61138
$486$	−97963.3	−0.0188136
$487$	8.07055e6	1.54199	0.770993	−	0.636844i	$-0.219760\pi$
$487$	8.07055e6	1.54199	0.770993	+	0.636844i	$0.219760\pi$
$488$	−1.12444e6	−0.213741
$489$	3.65655e6	0.691512
$490$	−914225.	−0.172014
$491$	−4.90913e6	−0.918968	−0.459484	−	0.888186i	$-0.651966\pi$
$491$	−4.90913e6	−0.918968	−0.459484	+	0.888186i	$0.651966\pi$
$492$	−3.66587e6	−0.682754
$493$	−4.23992e6	−0.785670
$494$	91348.8	0.0168417
$495$	3.18398e6	0.584061
$496$	−1.38746e6	−0.253230
$497$	−3.75717e6	−0.682292
$498$	1.63561e6	0.295533
$499$	−6.59947e6	−1.18647	−0.593236	−	0.805029i	$-0.702150\pi$
$499$	−6.59947e6	−1.18647	−0.593236	+	0.805029i	$0.702150\pi$
$500$	4.65941e6	0.833501
$501$	3.95546e6	0.704048
$502$	−820075.	−0.145243
$503$	1.46824e6	0.258749	0.129374	−	0.991596i	$-0.458703\pi$
$503$	1.46824e6	0.258749	0.129374	+	0.991596i	$0.458703\pi$
$504$	718092.	0.125923
$505$	−4.73576e6	−0.826345
$506$	−5.16498e6	−0.896793
$507$	3.16532e6	0.546888
$508$	−4.58224e6	−0.787805
$509$	−6.43314e6	−1.10060	−0.550299	−	0.834968i	$-0.685486\pi$
$509$	−6.43314e6	−1.10060	−0.550299	+	0.834968i	$0.685486\pi$
$510$	1.35927e6	0.231408
$511$	3.04983e6	0.516683
$512$	5.96703e6	1.00597
$513$	−286785.	−0.0481131
$514$	430770.	0.0719181
$515$	−497344.	−0.0826302
$516$	−5.10166e6	−0.843504
$517$	−1.03319e7	−1.70002
$518$	−971309.	−0.159050
$519$	−5.27643e6	−0.859849
$520$	−852356.	−0.138233
$521$	−508460.	−0.0820658	−0.0410329	−	0.999158i	$-0.513065\pi$
$521$	−508460.	−0.0820658	−0.0410329	+	0.999158i	$0.513065\pi$
$522$	375095.	0.0602511
$523$	1.57290e6	0.251447	0.125723	−	0.992065i	$-0.459875\pi$
$523$	1.57290e6	0.251447	0.125723	+	0.992065i	$0.459875\pi$
$524$	−635712.	−0.101142
$525$	366574.	0.0580448
$526$	−1.15501e6	−0.182021
$527$	2.74649e6	0.430777
$528$	−4.52964e6	−0.707097
$529$	1.60946e7	2.50058
$530$	−2.54621e6	−0.393736
$531$	−281961.	−0.0433963
$532$	1.00386e6	0.153779
$533$	−1.94924e6	−0.297199
$534$	−2.04454e6	−0.310272
$535$	−2.08117e6	−0.314357
$536$	3.51039e6	0.527768
$537$	4.94099e6	0.739399
$538$	668905.	0.0996343
$539$	−6.03075e6	−0.894127
$540$	1.27784e6	0.188579
$541$	−2.60509e6	−0.382675	−0.191337	−	0.981524i	$-0.561282\pi$
$541$	−2.60509e6	−0.382675	−0.191337	+	0.981524i	$0.561282\pi$
$542$	−139305.	−0.0203689
$543$	5.71064e6	0.831161
$544$	−6.87278e6	−0.995716
$545$	1.26622e7	1.82607
$546$	182335.	0.0261751
$547$	6.69896e6	0.957281	0.478640	−	0.878011i	$-0.341130\pi$
$547$	6.69896e6	0.957281	0.478640	+	0.878011i	$0.341130\pi$
$548$	−8.58174e6	−1.22074
$549$	896359.	0.126926
$550$	507977.	0.0716039
$551$	1.09808e6	0.154083
$552$	−4.34083e6	−0.606352
$553$	−7.95020e6	−1.10552
$554$	−1.12650e6	−0.155940
$555$	−3.61954e6	−0.498793
$556$	3.74800e6	0.514178
$557$	7.81333e6	1.06708	0.533541	−	0.845774i	$-0.320861\pi$
$557$	7.81333e6	1.06708	0.533541	+	0.845774i	$0.320861\pi$
$558$	−242975.	−0.0330352
$559$	−2.71269e6	−0.367173
$560$	−4.01242e6	−0.540675
$561$	8.96649e6	1.20286
$562$	1.66698e6	0.222633
$563$	−4.79892e6	−0.638076	−0.319038	−	0.947742i	$-0.603360\pi$
$563$	−4.79892e6	−0.638076	−0.319038	+	0.947742i	$0.603360\pi$
$564$	−4.14653e6	−0.548893
$565$	1.05299e7	1.38772
$566$	889131.	0.116661
$567$	−572433.	−0.0747768
$568$	−4.37570e6	−0.569084
$569$	1.34812e7	1.74561	0.872807	−	0.488065i	$-0.162297\pi$
$569$	1.34812e7	1.74561	0.872807	+	0.488065i	$0.162297\pi$
$570$	−352031.	−0.0453831
$571$	−2.16268e6	−0.277589	−0.138795	−	0.990321i	$-0.544323\pi$
$571$	−2.16268e6	−0.277589	−0.138795	+	0.990321i	$0.544323\pi$
$572$	−2.68498e6	−0.343124
$573$	3.67266e6	0.467299
$574$	2.01581e6	0.255370
$575$	−2.21592e6	−0.279502
$576$	−1.38096e6	−0.173430
$577$	1.07356e7	1.34241	0.671207	−	0.741270i	$-0.265776\pi$
$577$	1.07356e7	1.34241	0.671207	+	0.741270i	$0.265776\pi$
$578$	1.47229e6	0.183305
$579$	261625.	0.0324327
$580$	−4.89277e6	−0.603927
$581$	9.55742e6	1.17463
$582$	2.07964e6	0.254496
$583$	−1.67963e7	−2.04664
$584$	3.55191e6	0.430954
$585$	679463.	0.0820873
$586$	1.44195e6	0.173463
$587$	1.12328e7	1.34553	0.672766	−	0.739855i	$-0.265106\pi$
$587$	1.12328e7	1.34553	0.672766	+	0.739855i	$0.265106\pi$
$588$	−2.42035e6	−0.288691
$589$	−711305.	−0.0844827
$590$	−346109.	−0.0409339
$591$	−5.92384e6	−0.697645
$592$	5.14928e6	0.603868
$593$	3.19409e6	0.373001	0.186501	−	0.982455i	$-0.440285\pi$
$593$	3.19409e6	0.373001	0.186501	+	0.982455i	$0.440285\pi$
$594$	−793243.	−0.0922444
$595$	7.94264e6	0.919756
$596$	6.37370e6	0.734981
$597$	−4.35565e6	−0.500169
$598$	−1.10221e6	−0.126041
$599$	−2.10973e6	−0.240248	−0.120124	−	0.992759i	$-0.538329\pi$
$599$	−2.10973e6	−0.240248	−0.120124	+	0.992759i	$0.538329\pi$
$600$	426922.	0.0484139
$601$	−1.29771e6	−0.146552	−0.0732758	−	0.997312i	$-0.523345\pi$
$601$	−1.29771e6	−0.146552	−0.0732758	+	0.997312i	$0.523345\pi$
$602$	2.80532e6	0.315494
$603$	−2.79833e6	−0.313405
$604$	1.15516e7	1.28840
$605$	1.61297e7	1.79159
$606$	1.17985e6	0.130510
$607$	−1.34730e7	−1.48420	−0.742101	−	0.670288i	$-0.766171\pi$
$607$	−1.34730e7	−1.48420	−0.742101	+	0.670288i	$0.766171\pi$
$608$	1.77996e6	0.195277
$609$	2.19181e6	0.239474
$610$	1.10029e6	0.119724
$611$	−2.20482e6	−0.238930
$612$	3.59856e6	0.388374
$613$	−4.89540e6	−0.526183	−0.263092	−	0.964771i	$-0.584742\pi$
$613$	−4.89540e6	−0.526183	−0.263092	+	0.964771i	$0.584742\pi$
$614$	1.15044e6	0.123152
$615$	7.51181e6	0.800860
$616$	5.81463e6	0.617406
$617$	−1.41804e7	−1.49960	−0.749798	−	0.661666i	$-0.769849\pi$
$617$	−1.41804e7	−1.49960	−0.749798	+	0.661666i	$0.769849\pi$
$618$	123906.	0.0130503
$619$	1.40027e7	1.46887	0.734436	−	0.678678i	$-0.237447\pi$
$619$	1.40027e7	1.46887	0.734436	+	0.678678i	$0.237447\pi$
$620$	3.16939e6	0.331128
$621$	3.46033e6	0.360071
$622$	1.80157e6	0.186713
$623$	−1.19469e7	−1.23321
$624$	−966627.	−0.0993796
$625$	−1.10066e7	−1.12707
$626$	4.09635e6	0.417793
$627$	−2.32220e6	−0.235902
$628$	−601860.	−0.0608970
$629$	−1.01931e7	−1.02725
$630$	−702666.	−0.0705338
$631$	−131565.	−0.0131543	−0.00657714	−	0.999978i	$-0.502094\pi$
$631$	−131565.	−0.0131543	−0.00657714	+	0.999978i	$0.502094\pi$
$632$	−9.25900e6	−0.922086
$633$	−1.51180e6	−0.149964
$634$	3.58843e6	0.354553
$635$	9.38956e6	0.924083
$636$	−6.74091e6	−0.660809
$637$	−1.28696e6	−0.125666
$638$	3.03727e6	0.295415
$639$	3.48812e6	0.337940
$640$	−1.03725e7	−1.00100
$641$	1.53623e7	1.47676	0.738382	−	0.674383i	$-0.235590\pi$
$641$	1.53623e7	1.47676	0.738382	+	0.674383i	$0.235590\pi$
$642$	518493.	0.0496484
$643$	−1.11320e7	−1.06181	−0.530904	−	0.847432i	$-0.678148\pi$
$643$	−1.11320e7	−1.06181	−0.530904	+	0.847432i	$0.678148\pi$
$644$	−1.21125e7	−1.15085
$645$	1.04539e7	0.989417
$646$	−991364.	−0.0934656
$647$	584009.	0.0548477	0.0274239	−	0.999624i	$-0.491270\pi$
$647$	584009.	0.0548477	0.0274239	+	0.999624i	$0.491270\pi$
$648$	−666670.	−0.0623696
$649$	−2.28313e6	−0.212775
$650$	108402.	0.0100636
$651$	−1.41979e6	−0.131302
$652$	1.18829e7	1.09472
$653$	1.13214e7	1.03900	0.519502	−	0.854469i	$-0.326117\pi$
$653$	1.13214e7	1.03900	0.519502	+	0.854469i	$0.326117\pi$
$654$	−3.15461e6	−0.288404
$655$	1.30265e6	0.118638
$656$	−1.06866e7	−0.969567
$657$	−2.83144e6	−0.255914
$658$	2.28012e6	0.205302
$659$	−4.47059e6	−0.401007	−0.200503	−	0.979693i	$-0.564258\pi$
$659$	−4.47059e6	−0.401007	−0.200503	+	0.979693i	$0.564258\pi$
$660$	1.03471e7	0.924612
$661$	−7.44213e6	−0.662512	−0.331256	−	0.943541i	$-0.607472\pi$
$661$	−7.44213e6	−0.662512	−0.331256	+	0.943541i	$0.607472\pi$
$662$	−2.16314e6	−0.191840
$663$	1.91345e6	0.169057
$664$	1.11308e7	0.979730
$665$	−2.05704e6	−0.180380
$666$	901755.	0.0787776
$667$	−1.32494e7	−1.15314
$668$	1.28542e7	1.11456
$669$	3.52027e6	0.304096
$670$	−3.43498e6	−0.295622
$671$	7.25812e6	0.622326
$672$	3.55285e6	0.303497
$673$	−5.93148e6	−0.504807	−0.252404	−	0.967622i	$-0.581221\pi$
$673$	−5.93148e6	−0.504807	−0.252404	+	0.967622i	$0.581221\pi$
$674$	5.70470e6	0.483708
$675$	−340324.	−0.0287497
$676$	1.02865e7	0.865765
$677$	−4.33126e6	−0.363197	−0.181599	−	0.983373i	$-0.558127\pi$
$677$	−4.33126e6	−0.363197	−0.181599	+	0.983373i	$0.558127\pi$
$678$	−2.62337e6	−0.219172
$679$	1.21520e7	1.01152
$680$	9.25020e6	0.767148
$681$	−1.11924e7	−0.924815
$682$	−1.96746e6	−0.161974
$683$	2.27665e7	1.86743	0.933715	−	0.358016i	$-0.116547\pi$
$683$	2.27665e7	1.86743	0.933715	+	0.358016i	$0.116547\pi$
$684$	−931978.	−0.0761667
$685$	1.75850e7	1.43191
$686$	3.76365e6	0.305351
$687$	−2.97159e6	−0.240213
$688$	−1.48721e7	−1.19784
$689$	−3.58432e6	−0.287647
$690$	4.24758e6	0.339640
$691$	−2.18683e7	−1.74229	−0.871145	−	0.491026i	$-0.836622\pi$
$691$	−2.18683e7	−1.74229	−0.871145	+	0.491026i	$0.836622\pi$
$692$	−1.71470e7	−1.36121
$693$	−4.63518e6	−0.366635
$694$	−560623.	−0.0441847
$695$	−7.68011e6	−0.603122
$696$	2.55263e6	0.199740
$697$	2.11542e7	1.64936
$698$	−1.82341e6	−0.141660
$699$	7.71789e6	0.597456
$700$	1.19127e6	0.0918894
$701$	−4.41044e6	−0.338990	−0.169495	−	0.985531i	$-0.554214\pi$
$701$	−4.41044e6	−0.338990	−0.169495	+	0.985531i	$0.554214\pi$
$702$	−169278.	−0.0129646
$703$	2.63987e6	0.201462
$704$	−1.11821e7	−0.850336
$705$	8.49674e6	0.643842
$706$	−3.86056e6	−0.291500
$707$	6.89423e6	0.518725
$708$	−916300.	−0.0686996
$709$	−4.71774e6	−0.352467	−0.176233	−	0.984348i	$-0.556391\pi$
$709$	−4.71774e6	−0.352467	−0.176233	+	0.984348i	$0.556391\pi$
$710$	4.28170e6	0.318765
$711$	7.38089e6	0.547564
$712$	−1.39137e7	−1.02859
$713$	8.58254e6	0.632255
$714$	−1.97879e6	−0.145263
$715$	5.50184e6	0.402479
$716$	1.60569e7	1.17052
$717$	9.29594e6	0.675298
$718$	−4.62773e6	−0.335009
$719$	3.92428e6	0.283098	0.141549	−	0.989931i	$-0.454792\pi$
$719$	3.92428e6	0.283098	0.141549	+	0.989931i	$0.454792\pi$
$720$	3.72509e6	0.267797
$721$	724024.	0.0518698
$722$	−3.85114e6	−0.274946
$723$	−1.22752e6	−0.0873342
$724$	1.85581e7	1.31579
$725$	1.30308e6	0.0920715
$726$	−4.01848e6	−0.282957
$727$	−1.54526e7	−1.08434	−0.542170	−	0.840269i	$-0.682397\pi$
$727$	−1.54526e7	−1.08434	−0.542170	+	0.840269i	$0.682397\pi$
$728$	1.24084e6	0.0867738
$729$	531441.	0.0370370
$730$	−3.47561e6	−0.241393
$731$	2.94395e7	2.03768
$732$	2.91293e6	0.200934
$733$	−2.46334e7	−1.69342	−0.846711	−	0.532053i	$-0.821421\pi$
$733$	−2.46334e7	−1.69342	−0.846711	+	0.532053i	$0.821421\pi$
$734$	−2.66051e6	−0.182274
$735$	4.95958e6	0.338631
$736$	−2.14768e7	−1.46142
$737$	−2.26591e7	−1.53664
$738$	−1.87146e6	−0.126485
$739$	−1.82294e7	−1.22789	−0.613946	−	0.789348i	$-0.710419\pi$
$739$	−1.82294e7	−1.22789	−0.613946	+	0.789348i	$0.710419\pi$
$740$	−1.17626e7	−0.789628
$741$	−495558.	−0.0331550
$742$	3.70672e6	0.247161
$743$	2.17675e7	1.44656	0.723281	−	0.690553i	$-0.242633\pi$
$743$	2.17675e7	1.44656	0.723281	+	0.690553i	$0.242633\pi$
$744$	−1.65352e6	−0.109516
$745$	−1.30605e7	−0.862121
$746$	−2.48780e6	−0.163670
$747$	−8.87302e6	−0.581795
$748$	2.91388e7	1.90422
$749$	3.02973e6	0.197333
$750$	2.37867e6	0.154412
$751$	2.75126e7	1.78005	0.890024	−	0.455915i	$-0.150688\pi$
$751$	2.75126e7	1.78005	0.890024	+	0.455915i	$0.150688\pi$
$752$	−1.20877e7	−0.779473
$753$	4.44882e6	0.285929
$754$	648155.	0.0415193
$755$	−2.36706e7	−1.51127
$756$	−1.86026e6	−0.118377
$757$	−1.19675e7	−0.759039	−0.379519	−	0.925184i	$-0.623911\pi$
$757$	−1.19675e7	−0.759039	−0.379519	+	0.925184i	$0.623911\pi$
$758$	4.89585e6	0.309496
$759$	2.80195e7	1.76545
$760$	−2.39568e6	−0.150451
$761$	−1.99524e7	−1.24892	−0.624460	−	0.781057i	$-0.714681\pi$
$761$	−1.99524e7	−1.24892	−0.624460	+	0.781057i	$0.714681\pi$
$762$	−2.33927e6	−0.145946
$763$	−1.84334e7	−1.14629
$764$	1.19352e7	0.739769
$765$	−7.37387e6	−0.455556
$766$	3.29168e6	0.202696
$767$	−487221.	−0.0299046
$768$	−2.32590e6	−0.142295
$769$	−2.53565e7	−1.54623	−0.773113	−	0.634268i	$-0.781302\pi$
$769$	−2.53565e7	−1.54623	−0.773113	+	0.634268i	$0.781302\pi$
$770$	−5.68972e6	−0.345831
$771$	−2.33688e6	−0.141580
$772$	850214.	0.0513434
$773$	1.62164e7	0.976123	0.488062	−	0.872809i	$-0.337704\pi$
$773$	1.62164e7	0.976123	0.488062	+	0.872809i	$0.337704\pi$
$774$	−2.60444e6	−0.156265
$775$	−844095.	−0.0504821
$776$	1.41526e7	0.843686
$777$	5.26925e6	0.313110
$778$	2.79893e6	0.165784
$779$	−5.47865e6	−0.323467
$780$	2.20808e6	0.129950
$781$	2.82445e7	1.65694
$782$	1.19617e7	0.699482
$783$	−2.03485e6	−0.118612
$784$	−7.05566e6	−0.409966
$785$	1.23328e6	0.0714312
$786$	−324536.	−0.0187373
$787$	−1.75632e7	−1.01080	−0.505401	−	0.862885i	$-0.668655\pi$
$787$	−1.75632e7	−1.01080	−0.505401	+	0.862885i	$0.668655\pi$
$788$	−1.92509e7	−1.10442
$789$	6.26582e6	0.358332
$790$	9.06010e6	0.516494
$791$	−1.53292e7	−0.871121
$792$	−5.39825e6	−0.305802
$793$	1.54888e6	0.0874654
$794$	387470.	0.0218115
$795$	1.38129e7	0.775118
$796$	−1.41547e7	−0.791806
$797$	2.00493e7	1.11803	0.559015	−	0.829158i	$-0.311179\pi$
$797$	2.00493e7	1.11803	0.559015	+	0.829158i	$0.311179\pi$
$798$	512481.	0.0284885
$799$	2.39279e7	1.32598
$800$	2.11225e6	0.116686
$801$	1.10914e7	0.610810
$802$	−7.12235e6	−0.391010
$803$	−2.29271e7	−1.25476
$804$	−9.09386e6	−0.496144
$805$	2.48200e7	1.34993
$806$	−419855.	−0.0227647
$807$	−3.62874e6	−0.196143
$808$	8.02920e6	0.432657
$809$	−6.09192e6	−0.327253	−0.163626	−	0.986522i	$-0.552319\pi$
$809$	−6.09192e6	−0.327253	−0.163626	+	0.986522i	$0.552319\pi$
$810$	652348.	0.0349355
$811$	3.13530e6	0.167389	0.0836945	−	0.996491i	$-0.473328\pi$
$811$	3.13530e6	0.167389	0.0836945	+	0.996491i	$0.473328\pi$
$812$	7.12280e6	0.379106
$813$	755713.	0.0400987
$814$	7.30182e6	0.386251
$815$	−2.43494e7	−1.28409
$816$	1.04903e7	0.551523
$817$	−7.62443e6	−0.399624
$818$	3.29101e6	0.171967
$819$	−989149.	−0.0515290
$820$	2.44114e7	1.26782
$821$	−1.57429e7	−0.815128	−0.407564	−	0.913177i	$-0.633622\pi$
$821$	−1.57429e7	−0.815128	−0.407564	+	0.913177i	$0.633622\pi$
$822$	−4.38105e6	−0.226151
$823$	1.59042e7	0.818486	0.409243	−	0.912425i	$-0.365793\pi$
$823$	1.59042e7	0.818486	0.409243	+	0.912425i	$0.365793\pi$
$824$	843217.	0.0432635
$825$	−2.75572e6	−0.140961
$826$	503859.	0.0256956
$827$	−1.65484e7	−0.841378	−0.420689	−	0.907205i	$-0.638212\pi$
$827$	−1.65484e7	−0.841378	−0.420689	+	0.907205i	$0.638212\pi$
$828$	1.12452e7	0.570020
$829$	−1.93567e7	−0.978240	−0.489120	−	0.872217i	$-0.662682\pi$
$829$	−1.93567e7	−0.978240	−0.489120	+	0.872217i	$0.662682\pi$
$830$	−1.08917e7	−0.548783
$831$	6.11115e6	0.306987
$832$	−2.38626e6	−0.119511
$833$	1.39668e7	0.697403
$834$	1.91339e6	0.0952549
$835$	−2.63398e7	−1.30736
$836$	−7.54655e6	−0.373450
$837$	1.31812e6	0.0650340
$838$	−127666.	−0.00628006
$839$	1.52692e7	0.748878	0.374439	−	0.927252i	$-0.377835\pi$
$839$	1.52692e7	0.748878	0.374439	+	0.927252i	$0.377835\pi$
$840$	−4.78185e6	−0.233828
$841$	−1.27198e7	−0.620143
$842$	3.27354e6	0.159125
$843$	−9.04319e6	−0.438281
$844$	−4.91297e6	−0.237404
$845$	−2.10782e7	−1.01553
$846$	−2.11684e6	−0.101686
$847$	−2.34813e7	−1.12464
$848$	−1.96507e7	−0.938403
$849$	−4.82345e6	−0.229661
$850$	−1.17644e6	−0.0558498
$851$	−3.18524e7	−1.50771
$852$	1.13355e7	0.534985
$853$	−1.98871e7	−0.935836	−0.467918	−	0.883772i	$-0.654996\pi$
$853$	−1.98871e7	−0.935836	−0.467918	+	0.883772i	$0.654996\pi$
$854$	−1.60178e6	−0.0751549
$855$	1.90973e6	0.0893424
$856$	3.52850e6	0.164591
$857$	3.45630e6	0.160753	0.0803765	−	0.996765i	$-0.474388\pi$
$857$	3.45630e6	0.160753	0.0803765	+	0.996765i	$0.474388\pi$
$858$	−1.37070e6	−0.0635661
$859$	−3.93767e7	−1.82077	−0.910387	−	0.413758i	$-0.864216\pi$
$859$	−3.93767e7	−1.82077	−0.910387	+	0.413758i	$0.864216\pi$
$860$	3.39725e7	1.56632
$861$	−1.09355e7	−0.502727
$862$	4.19947e6	0.192498
$863$	9.80271e6	0.448043	0.224021	−	0.974584i	$-0.428081\pi$
$863$	9.80271e6	0.448043	0.224021	+	0.974584i	$0.428081\pi$
$864$	−3.29843e6	−0.150322
$865$	3.51363e7	1.59667
$866$	1.48794e6	0.0674202
$867$	−7.98703e6	−0.360859
$868$	−4.61394e6	−0.207861
$869$	5.97656e7	2.68474
$870$	−2.49780e6	−0.111882
$871$	−4.83545e6	−0.215969
$872$	−2.14680e7	−0.956095
$873$	−1.12818e7	−0.501007
$874$	−3.09792e6	−0.137180
$875$	1.38993e7	0.613725
$876$	−9.20144e6	−0.405131
$877$	8.26623e6	0.362918	0.181459	−	0.983399i	$-0.441918\pi$
$877$	8.26623e6	0.362918	0.181459	+	0.983399i	$0.441918\pi$
$878$	−8.54850e6	−0.374243
$879$	−7.82244e6	−0.341484
$880$	3.01634e7	1.31303
$881$	1.37572e7	0.597160	0.298580	−	0.954385i	$-0.403487\pi$
$881$	1.37572e7	0.597160	0.298580	+	0.954385i	$0.403487\pi$
$882$	−1.23561e6	−0.0534821
$883$	−1.63401e7	−0.705267	−0.352634	−	0.935762i	$-0.614714\pi$
$883$	−1.63401e7	−0.705267	−0.352634	+	0.935762i	$0.614714\pi$
$884$	6.21822e6	0.267630
$885$	1.87761e6	0.0805836
$886$	2.94094e6	0.125864
$887$	−5.51374e6	−0.235308	−0.117654	−	0.993055i	$-0.537537\pi$
$887$	−5.51374e6	−0.235308	−0.117654	+	0.993055i	$0.537537\pi$
$888$	6.13671e6	0.261158
$889$	−1.36691e7	−0.580078
$890$	1.36148e7	0.576152
$891$	4.30326e6	0.181595
$892$	1.14400e7	0.481407
$893$	−6.19699e6	−0.260047
$894$	3.25382e6	0.136160
$895$	−3.29026e7	−1.37301
$896$	1.51001e7	0.628362
$897$	5.97936e6	0.248127
$898$	1.08202e6	0.0447761
$899$	−5.04698e6	−0.208273
$900$	−1.10596e6	−0.0455129
$901$	3.88989e7	1.59634
$902$	−1.51538e7	−0.620163
$903$	−1.52186e7	−0.621091
$904$	−1.78528e7	−0.726582
$905$	−3.80277e7	−1.54340
$906$	5.89718e6	0.238684
$907$	−1.18836e7	−0.479655	−0.239828	−	0.970816i	$-0.577091\pi$
$907$	−1.18836e7	−0.479655	−0.239828	+	0.970816i	$0.577091\pi$
$908$	−3.63723e7	−1.46405
$909$	−6.40054e6	−0.256925
$910$	−1.21419e6	−0.0486052
$911$	425792.	0.0169981	0.00849907	−	0.999964i	$-0.497295\pi$
$911$	425792.	0.0169981	0.00849907	+	0.999964i	$0.497295\pi$
$912$	−2.71685e6	−0.108163
$913$	−7.18479e7	−2.85257
$914$	9.98125e6	0.395202
$915$	−5.96895e6	−0.235692
$916$	−9.65689e6	−0.380276
$917$	−1.89637e6	−0.0744732
$918$	1.83709e6	0.0719489
$919$	−3.84199e7	−1.50061	−0.750304	−	0.661093i	$-0.770093\pi$
$919$	−3.84199e7	−1.50061	−0.750304	+	0.661093i	$0.770093\pi$
$920$	2.89060e7	1.12595
$921$	−6.24100e6	−0.242440
$922$	1.46068e7	0.565885
$923$	6.02739e6	0.232876
$924$	−1.50631e7	−0.580411
$925$	3.13269e6	0.120382
$926$	−1.02102e7	−0.391296
$927$	−672177.	−0.0256912
$928$	1.26295e7	0.481410
$929$	3.79880e7	1.44413	0.722066	−	0.691824i	$-0.243193\pi$
$929$	3.79880e7	1.44413	0.722066	+	0.691824i	$0.243193\pi$
$930$	1.61800e6	0.0613438
$931$	−3.61721e6	−0.136773
$932$	2.50811e7	0.945818
$933$	−9.77332e6	−0.367568
$934$	9.94012e6	0.372842
$935$	−5.97088e7	−2.23362
$936$	−1.15199e6	−0.0429792
$937$	2.79681e7	1.04067	0.520337	−	0.853961i	$-0.325806\pi$
$937$	2.79681e7	1.04067	0.520337	+	0.853961i	$0.325806\pi$
$938$	5.00057e6	0.185572
$939$	−2.22223e7	−0.822479
$940$	2.76122e7	1.01925
$941$	−6.99862e6	−0.257655	−0.128827	−	0.991667i	$-0.541121\pi$
$941$	−6.99862e6	−0.257655	−0.128827	+	0.991667i	$0.541121\pi$
$942$	−307254.	−0.0112816
$943$	6.61049e7	2.42077
$944$	−2.67115e6	−0.0975591
$945$	3.81189e6	0.138855
$946$	−2.10890e7	−0.766176
$947$	−1.69519e7	−0.614248	−0.307124	−	0.951670i	$-0.599367\pi$
$947$	−1.69519e7	−0.614248	−0.307124	+	0.951670i	$0.599367\pi$
$948$	2.39860e7	0.866835
$949$	−4.89265e6	−0.176351
$950$	304681.	0.0109531
$951$	−1.94669e7	−0.697983
$952$	−1.34663e7	−0.481565
$953$	−2.60411e7	−0.928810	−0.464405	−	0.885623i	$-0.653732\pi$
$953$	−2.60411e7	−0.928810	−0.464405	+	0.885623i	$0.653732\pi$
$954$	−3.44129e6	−0.122419
$955$	−2.44566e7	−0.867737
$956$	3.02094e7	1.06905
$957$	−1.64769e7	−0.581561
$958$	−3.68495e6	−0.129723
$959$	−2.55999e7	−0.898860
$960$	9.19592e6	0.322046
$961$	−2.53599e7	−0.885806
$962$	1.55821e6	0.0542860
$963$	−2.81277e6	−0.0977392
$964$	−3.98913e6	−0.138257
$965$	−1.74219e6	−0.0602250
$966$	−6.18355e6	−0.213204
$967$	3.96216e7	1.36259	0.681296	−	0.732008i	$-0.261417\pi$
$967$	3.96216e7	1.36259	0.681296	+	0.732008i	$0.261417\pi$
$968$	−2.73470e7	−0.938038
$969$	5.37805e6	0.183999
$970$	−1.38485e7	−0.472579
$971$	1.53561e7	0.522675	0.261338	−	0.965247i	$-0.415836\pi$
$971$	1.53561e7	0.522675	0.261338	+	0.965247i	$0.415836\pi$
$972$	1.72705e6	0.0586324
$973$	1.11806e7	0.378600
$974$	1.33892e7	0.452227
$975$	−588071.	−0.0198115
$976$	8.49162e6	0.285342
$977$	1.61769e7	0.542200	0.271100	−	0.962551i	$-0.412613\pi$
$977$	1.61769e7	0.542200	0.271100	+	0.962551i	$0.412613\pi$
$978$	6.06629e6	0.202804
$979$	8.98111e7	2.99484
$980$	1.61173e7	0.536078
$981$	1.71134e7	0.567759
$982$	−8.14433e6	−0.269511
$983$	−2.91065e7	−0.960739	−0.480370	−	0.877066i	$-0.659497\pi$
$983$	−2.91065e7	−0.960739	−0.480370	+	0.877066i	$0.659497\pi$
$984$	−1.27358e7	−0.419314
$985$	3.94474e7	1.29547
$986$	−7.03410e6	−0.230418
$987$	−1.23694e7	−0.404162
$988$	−1.61043e6	−0.0524869
$989$	9.19957e7	2.99073
$990$	5.28229e6	0.171291
$991$	423539.	0.0136996	0.00684982	−	0.999977i	$-0.497820\pi$
$991$	423539.	0.0136996	0.00684982	+	0.999977i	$0.497820\pi$
$992$	−8.18100e6	−0.263953
$993$	1.17348e7	0.377661
$994$	−6.23322e6	−0.200100
$995$	2.90047e7	0.928776
$996$	−2.88350e7	−0.921025
$997$	4.48353e7	1.42851	0.714254	−	0.699887i	$-0.246766\pi$
$997$	4.48353e7	1.42851	0.714254	+	0.699887i	$0.246766\pi$
$998$	−1.09486e7	−0.347963
$999$	−4.89193e6	−0.155084

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.6.a.b.1.8	✓	12
3.2	odd	2		531.6.a.d.1.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.6.a.b.1.8	✓	12	1.1	even	1	trivial
531.6.a.d.1.5		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)

\(f(q)\)	\(=\)	\(q+1.65902 q^{2} -9.00000 q^{3} -29.2477 q^{4} +59.9319 q^{5} -14.9312 q^{6} -87.2478 q^{7} -101.611 q^{8} +81.0000 q^{9} +O(q^{10})\)	\(q+1.65902 q^{2} -9.00000 q^{3} -29.2477 q^{4} +59.9319 q^{5} -14.9312 q^{6} -87.2478 q^{7} -101.611 q^{8} +81.0000 q^{9} +99.4282 q^{10} +655.885 q^{11} +263.229 q^{12} +139.966 q^{13} -144.746 q^{14} -539.387 q^{15} +767.351 q^{16} -1518.98 q^{17} +134.380 q^{18} +393.396 q^{19} -1752.87 q^{20} +785.230 q^{21} +1088.12 q^{22} -4746.68 q^{23} +914.499 q^{24} +466.837 q^{25} +232.206 q^{26} -729.000 q^{27} +2551.79 q^{28} +2791.29 q^{29} -894.853 q^{30} -1808.12 q^{31} +4524.60 q^{32} -5902.96 q^{33} -2520.02 q^{34} -5228.93 q^{35} -2369.06 q^{36} +6710.46 q^{37} +652.650 q^{38} -1259.69 q^{39} -6089.74 q^{40} -13926.6 q^{41} +1302.71 q^{42} -19381.1 q^{43} -19183.1 q^{44} +4854.49 q^{45} -7874.82 q^{46} -15752.6 q^{47} -6906.16 q^{48} -9194.83 q^{49} +774.491 q^{50} +13670.8 q^{51} -4093.68 q^{52} -25608.5 q^{53} -1209.42 q^{54} +39308.4 q^{55} +8865.33 q^{56} -3540.56 q^{57} +4630.80 q^{58} -3481.00 q^{59} +15775.8 q^{60} +11066.2 q^{61} -2999.70 q^{62} -7067.07 q^{63} -17048.8 q^{64} +8388.43 q^{65} -9793.12 q^{66} -34547.3 q^{67} +44426.7 q^{68} +42720.1 q^{69} -8674.88 q^{70} +43063.2 q^{71} -8230.49 q^{72} -34956.0 q^{73} +11132.8 q^{74} -4201.53 q^{75} -11505.9 q^{76} -57224.5 q^{77} -2089.85 q^{78} +91122.1 q^{79} +45988.8 q^{80} +6561.00 q^{81} -23104.4 q^{82} -109543. q^{83} -22966.1 q^{84} -91035.5 q^{85} -32153.5 q^{86} -25121.6 q^{87} -66645.1 q^{88} +136931. q^{89} +8053.68 q^{90} -12211.7 q^{91} +138829. q^{92} +16273.0 q^{93} -26133.8 q^{94} +23577.0 q^{95} -40721.4 q^{96} -139282. q^{97} -15254.4 q^{98} +53126.7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9}+O(q^{10}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9	\( 12 q - 4 q^{2} - 108 q^{3} + 198 q^{4} + 36 q^{5} + 36 q^{6} - 411 q^{7} - 69 q^{8} + 972 q^{9} - 863 q^{10} + 492 q^{11} - 1782 q^{12} - 974 q^{13} - 967 q^{14} - 324 q^{15} + 6370 q^{16} - 1463 q^{17} - 324 q^{18} - 3189 q^{19} - 835 q^{20} + 3699 q^{21} - 2726 q^{22} - 2617 q^{23} + 621 q^{24} + 8642 q^{25} + 2414 q^{26} - 8748 q^{27} - 20458 q^{28} - 1963 q^{29} + 7767 q^{30} - 11929 q^{31} - 14382 q^{32} - 4428 q^{33} - 20744 q^{34} + 1829 q^{35} + 16038 q^{36} - 28105 q^{37} - 23475 q^{38} + 8766 q^{39} - 100576 q^{40} - 7585 q^{41} + 8703 q^{42} - 33146 q^{43} + 26014 q^{44} + 2916 q^{45} - 142851 q^{46} - 79215 q^{47} - 57330 q^{48} - 32569 q^{49} - 136019 q^{50} + 13167 q^{51} - 248218 q^{52} - 12220 q^{53} + 2916 q^{54} - 117770 q^{55} - 186728 q^{56} + 28701 q^{57} - 188072 q^{58} - 41772 q^{59} + 7515 q^{60} - 54195 q^{61} + 36230 q^{62} - 33291 q^{63} + 45197 q^{64} + 42368 q^{65} + 24534 q^{66} + 24224 q^{67} - 209639 q^{68} + 23553 q^{69} - 35684 q^{70} + 60254 q^{71} - 5589 q^{72} - 15385 q^{73} + 214638 q^{74} - 77778 q^{75} - 167504 q^{76} - 17169 q^{77} - 21726 q^{78} - 27054 q^{79} + 216899 q^{80} + 78732 q^{81} + 37917 q^{82} - 117595 q^{83} + 184122 q^{84} - 121585 q^{85} + 306756 q^{86} + 17667 q^{87} - 105799 q^{88} - 36033 q^{89} - 69903 q^{90} - 32217 q^{91} - 30906 q^{92} + 107361 q^{93} + 128392 q^{94} - 50721 q^{95} + 129438 q^{96} - 196914 q^{97} + 574100 q^{98} + 39852 q^{99}+O(q^{100}) \) 12 * q - 4 * q^2 - 108 * q^3 + 198 * q^4 + 36 * q^5 + 36 * q^6 - 411 * q^7 - 69 * q^8 + 972 * q^9 - 863 * q^10 + 492 * q^11 - 1782 * q^12 - 974 * q^13 - 967 * q^14 - 324 * q^15 + 6370 * q^16 - 1463 * q^17 - 324 * q^18 - 3189 * q^19 - 835 * q^20 + 3699 * q^21 - 2726 * q^22 - 2617 * q^23 + 621 * q^24 + 8642 * q^25 + 2414 * q^26 - 8748 * q^27 - 20458 * q^28 - 1963 * q^29 + 7767 * q^30 - 11929 * q^31 - 14382 * q^32 - 4428 * q^33 - 20744 * q^34 + 1829 * q^35 + 16038 * q^36 - 28105 * q^37 - 23475 * q^38 + 8766 * q^39 - 100576 * q^40 - 7585 * q^41 + 8703 * q^42 - 33146 * q^43 + 26014 * q^44 + 2916 * q^45 - 142851 * q^46 - 79215 * q^47 - 57330 * q^48 - 32569 * q^49 - 136019 * q^50 + 13167 * q^51 - 248218 * q^52 - 12220 * q^53 + 2916 * q^54 - 117770 * q^55 - 186728 * q^56 + 28701 * q^57 - 188072 * q^58 - 41772 * q^59 + 7515 * q^60 - 54195 * q^61 + 36230 * q^62 - 33291 * q^63 + 45197 * q^64 + 42368 * q^65 + 24534 * q^66 + 24224 * q^67 - 209639 * q^68 + 23553 * q^69 - 35684 * q^70 + 60254 * q^71 - 5589 * q^72 - 15385 * q^73 + 214638 * q^74 - 77778 * q^75 - 167504 * q^76 - 17169 * q^77 - 21726 * q^78 - 27054 * q^79 + 216899 * q^80 + 78732 * q^81 + 37917 * q^82 - 117595 * q^83 + 184122 * q^84 - 121585 * q^85 + 306756 * q^86 + 17667 * q^87 - 105799 * q^88 - 36033 * q^89 - 69903 * q^90 - 32217 * q^91 - 30906 * q^92 + 107361 * q^93 + 128392 * q^94 - 50721 * q^95 + 129438 * q^96 - 196914 * q^97 + 574100 * q^98 + 39852 * q^99

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