LMFDB - Embedded newform 285.10.a.f.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,10,Mod(1,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("285.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	285.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:	$146.785213307$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 5365 x^{12} + 7107 x^{11} + 10970098 x^{10} - 19024208 x^{9} - 10608934432 x^{8} + \cdots - 480881506516992 $ x^14 - x^13 - 5365x^12 + 7107x^11 + 10970098x^10 - 19024208x^9 - 10608934432x^8 + 24552331696x^7 + 4820661863456x^6 - 15731969979520x^5 - 831531966469120x^4 + 3954911489638400x^3 + 12984029397983232x^2 - 9924122935296x - 480881506516992
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{18}\cdot 3^{8}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.198399$ of defining polynomial
Character	$\chi$	$=$	285.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.198399 q^{2} -81.0000 q^{3} -511.961 q^{4} -625.000 q^{5} -16.0704 q^{6} +11709.0 q^{7} -203.153 q^{8} +6561.00 q^{9} -124.000 q^{10} -4212.70 q^{11} +41468.8 q^{12} +187919. q^{13} +2323.06 q^{14} +50625.0 q^{15} +262084. q^{16} +520915. q^{17} +1301.70 q^{18} +130321. q^{19} +319975. q^{20} -948429. q^{21} -835.796 q^{22} +1.17006e6 q^{23} +16455.4 q^{24} +390625. q^{25} +37283.1 q^{26} -531441. q^{27} -5.99455e6 q^{28} +6.20440e6 q^{29} +10044.0 q^{30} -1.27901e6 q^{31} +156012. q^{32} +341228. q^{33} +103349. q^{34} -7.31812e6 q^{35} -3.35897e6 q^{36} +9.41695e6 q^{37} +25855.6 q^{38} -1.52215e7 q^{39} +126971. q^{40} -1.56146e6 q^{41} -188168. q^{42} +3.79485e7 q^{43} +2.15673e6 q^{44} -4.10062e6 q^{45} +232140. q^{46} -4.44554e7 q^{47} -2.12288e7 q^{48} +9.67470e7 q^{49} +77499.8 q^{50} -4.21941e7 q^{51} -9.62073e7 q^{52} -8.77655e7 q^{53} -105438. q^{54} +2.63294e6 q^{55} -2.37872e6 q^{56} -1.05560e7 q^{57} +1.23095e6 q^{58} -1.22719e8 q^{59} -2.59180e7 q^{60} -9.80852e6 q^{61} -253755. q^{62} +7.68227e7 q^{63} -1.34156e8 q^{64} -1.17450e8 q^{65} +67699.5 q^{66} +8.30870e7 q^{67} -2.66688e8 q^{68} -9.47752e7 q^{69} -1.45191e6 q^{70} +1.35563e8 q^{71} -1.33289e6 q^{72} -3.80047e8 q^{73} +1.86832e6 q^{74} -3.16406e7 q^{75} -6.67192e7 q^{76} -4.93265e7 q^{77} -3.01993e6 q^{78} +5.48624e8 q^{79} -1.63802e8 q^{80} +4.30467e7 q^{81} -309793. q^{82} +3.55951e8 q^{83} +4.85558e8 q^{84} -3.25572e8 q^{85} +7.52896e6 q^{86} -5.02556e8 q^{87} +855823. q^{88} +2.07178e8 q^{89} -813562. q^{90} +2.20035e9 q^{91} -5.99027e8 q^{92} +1.03600e8 q^{93} -8.81993e6 q^{94} -8.14506e7 q^{95} -1.26369e7 q^{96} -9.64409e8 q^{97} +1.91945e7 q^{98} -2.76395e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} - 1134 q^{3} + 3563 q^{4} - 8750 q^{5} + 81 q^{6} + 13054 q^{7} + 6249 q^{8} + 91854 q^{9} + 625 q^{10} + 43520 q^{11} - 288603 q^{12} + 256834 q^{13} + 250610 q^{14} + 708750 q^{15} + 866291 q^{16}+ \cdots + 285534720 q^{99}+O(q^{100}) $ 14 * q - q^2 - 1134 * q^3 + 3563 * q^4 - 8750 * q^5 + 81 * q^6 + 13054 * q^7 + 6249 * q^8 + 91854 * q^9 + 625 * q^10 + 43520 * q^11 - 288603 * q^12 + 256834 * q^13 + 250610 * q^14 + 708750 * q^15 + 866291 * q^16 - 91412 * q^17 - 6561 * q^18 + 1824494 * q^19 - 2226875 * q^20 - 1057374 * q^21 + 5028672 * q^22 - 1629286 * q^23 - 506169 * q^24 + 5468750 * q^25 - 5525738 * q^26 - 7440174 * q^27 + 2214066 * q^28 - 3136160 * q^29 - 50625 * q^30 + 216848 * q^31 - 5019923 * q^32 - 3525120 * q^33 + 14499560 * q^34 - 8158750 * q^35 + 23376843 * q^36 + 29450026 * q^37 - 130321 * q^38 - 20803554 * q^39 - 3905625 * q^40 - 18243760 * q^41 - 20299410 * q^42 + 26051662 * q^43 - 66833140 * q^44 - 57408750 * q^45 - 87479176 * q^46 + 15959554 * q^47 - 70169571 * q^48 + 120608310 * q^49 - 390625 * q^50 + 7404372 * q^51 - 76766782 * q^52 + 24009130 * q^53 + 531441 * q^54 - 27200000 * q^55 - 248644798 * q^56 - 147784014 * q^57 - 208603522 * q^58 - 51606384 * q^59 + 180376875 * q^60 - 267404032 * q^61 + 211868546 * q^62 + 85647294 * q^63 - 647618425 * q^64 - 160521250 * q^65 - 407322432 * q^66 + 354061992 * q^67 - 690026380 * q^68 + 131972166 * q^69 - 156631250 * q^70 + 178030792 * q^71 + 40999689 * q^72 + 571450504 * q^73 + 406967766 * q^74 - 442968750 * q^75 + 464333723 * q^76 + 922830092 * q^77 + 447584778 * q^78 + 456688676 * q^79 - 541431875 * q^80 + 602654094 * q^81 + 1477406200 * q^82 + 275098162 * q^83 - 179339346 * q^84 + 57132500 * q^85 - 909539740 * q^86 + 254028960 * q^87 + 1278025456 * q^88 - 2005727664 * q^89 + 4100625 * q^90 - 181709276 * q^91 + 209371504 * q^92 - 17564688 * q^93 - 617421584 * q^94 - 1140308750 * q^95 + 406613763 * q^96 + 1606885598 * q^97 - 3483053209 * q^98 + 285534720 * q^99

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 $

$2$	0.198399	0.00876810	0.00438405	−	0.999990i	$-0.498605\pi$
$2$	0.198399	0.00876810	0.00438405	+	0.999990i	$0.498605\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	−511.961	−0.999923
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	−16.0704	−0.00506226
$7$	11709.0	1.84323	0.921613	−	0.388110i	$-0.126872\pi$
$7$	11709.0	1.84323	0.921613	+	0.388110i	$0.126872\pi$
$8$	−203.153	−0.0175355
$9$	6561.00	0.333333
$10$	−124.000	−0.00392121
$11$	−4212.70	−0.0867547	−0.0433774	−	0.999059i	$-0.513812\pi$
$11$	−4212.70	−0.0867547	−0.0433774	+	0.999059i	$0.513812\pi$
$12$	41468.8	0.577306
$13$	187919.	1.82485	0.912423	−	0.409248i	$-0.134209\pi$
$13$	187919.	1.82485	0.912423	+	0.409248i	$0.134209\pi$
$14$	2323.06	0.0161616
$15$	50625.0	0.258199
$16$	262084.	0.999769
$17$	520915.	1.51268	0.756339	−	0.654180i	$-0.226986\pi$
$17$	520915.	1.51268	0.756339	+	0.654180i	$0.226986\pi$
$18$	1301.70	0.00292270
$19$	130321.	0.229416
$19$	130321.	0.229416
$20$	319975.	0.447179
$21$	−948429.	−1.06419
$22$	−835.796	−0.000760674 0
$23$	1.17006e6	0.871835	0.435918	−	0.899987i	$-0.356424\pi$
$23$	1.17006e6	0.871835	0.435918	+	0.899987i	$0.356424\pi$
$24$	16455.4	0.0101241
$25$	390625.	0.200000
$26$	37283.1	0.0160004
$27$	−531441.	−0.192450
$28$	−5.99455e6	−1.84308
$29$	6.20440e6	1.62895	0.814477	−	0.580197i	$-0.197024\pi$
$29$	6.20440e6	1.62895	0.814477	+	0.580197i	$0.197024\pi$
$30$	10044.0	0.00226391
$31$	−1.27901e6	−0.248740	−0.124370	−	0.992236i	$-0.539691\pi$
$31$	−1.27901e6	−0.248740	−0.124370	+	0.992236i	$0.539691\pi$
$32$	156012.	0.0263016
$33$	341228.	0.0500879
$34$	103349.	0.0132633
$35$	−7.31812e6	−0.824316
$36$	−3.35897e6	−0.333308
$37$	9.41695e6	0.826043	0.413022	−	0.910721i	$-0.364473\pi$
$37$	9.41695e6	0.826043	0.413022	+	0.910721i	$0.364473\pi$
$38$	25855.6	0.00201154
$39$	−1.52215e7	−1.05358
$40$	126971.	0.00784212
$41$	−1.56146e6	−0.0862987	−0.0431493	−	0.999069i	$-0.513739\pi$
$41$	−1.56146e6	−0.0862987	−0.0431493	+	0.999069i	$0.513739\pi$
$42$	−188168.	−0.00933089
$43$	3.79485e7	1.69273	0.846363	−	0.532606i	$-0.178787\pi$
$43$	3.79485e7	1.69273	0.846363	+	0.532606i	$0.178787\pi$
$44$	2.15673e6	0.0867480
$45$	−4.10062e6	−0.149071
$46$	232140.	0.00764434
$47$	−4.44554e7	−1.32888	−0.664438	−	0.747343i	$-0.731329\pi$
$47$	−4.44554e7	−1.32888	−0.664438	+	0.747343i	$0.731329\pi$
$48$	−2.12288e7	−0.577217
$49$	9.67470e7	2.39748
$50$	77499.8	0.00175362
$51$	−4.21941e7	−0.873345
$52$	−9.62073e7	−1.82471
$53$	−8.77655e7	−1.52786	−0.763928	−	0.645302i	$-0.776732\pi$
$53$	−8.77655e7	−1.52786	−0.763928	+	0.645302i	$0.776732\pi$
$54$	−105438.	−0.00168742
$55$	2.63294e6	0.0387979
$56$	−2.37872e6	−0.0323219
$57$	−1.05560e7	−0.132453
$58$	1.23095e6	0.0142828
$59$	−1.22719e8	−1.31850	−0.659249	−	0.751925i	$-0.729125\pi$
$59$	−1.22719e8	−1.31850	−0.659249	+	0.751925i	$0.729125\pi$
$60$	−2.59180e7	−0.258179
$61$	−9.80852e6	−0.0907025	−0.0453512	−	0.998971i	$-0.514441\pi$
$61$	−9.80852e6	−0.0907025	−0.0453512	+	0.998971i	$0.514441\pi$
$62$	−253755.	−0.00218098
$63$	7.68227e7	0.614409
$64$	−1.34156e8	−0.999539
$65$	−1.17450e8	−0.816096
$66$	67699.5	0.000439175 0
$67$	8.30870e7	0.503729	0.251864	−	0.967763i	$-0.418956\pi$
$67$	8.30870e7	0.503729	0.251864	+	0.967763i	$0.418956\pi$
$68$	−2.66688e8	−1.51256
$69$	−9.47752e7	−0.503354
$70$	−1.45191e6	−0.00722768
$71$	1.35563e8	0.633110	0.316555	−	0.948574i	$-0.397474\pi$
$71$	1.35563e8	0.633110	0.316555	+	0.948574i	$0.397474\pi$
$72$	−1.33289e6	−0.00584517
$73$	−3.80047e8	−1.56633	−0.783167	−	0.621811i	$-0.786397\pi$
$73$	−3.80047e8	−1.56633	−0.783167	+	0.621811i	$0.786397\pi$
$74$	1.86832e6	0.00724283
$75$	−3.16406e7	−0.115470
$76$	−6.67192e7	−0.229398
$77$	−4.93265e7	−0.159909
$78$	−3.01993e6	−0.00923785
$79$	5.48624e8	1.58472	0.792360	−	0.610053i	$-0.208852\pi$
$79$	5.48624e8	1.58472	0.792360	+	0.610053i	$0.208852\pi$
$80$	−1.63802e8	−0.447110
$81$	4.30467e7	0.111111
$82$	−309793.	−0.000756675 0
$83$	3.55951e8	0.823264	0.411632	−	0.911350i	$-0.364959\pi$
$83$	3.55951e8	0.823264	0.411632	+	0.911350i	$0.364959\pi$
$84$	4.85558e8	1.06411
$85$	−3.25572e8	−0.676490
$86$	7.52896e6	0.0148420
$87$	−5.02556e8	−0.940476
$88$	855823.	0.00152129
$89$	2.07178e8	0.350016	0.175008	−	0.984567i	$-0.444005\pi$
$89$	2.07178e8	0.350016	0.175008	+	0.984567i	$0.444005\pi$
$90$	−813562.	−0.00130707
$91$	2.20035e9	3.36360
$92$	−5.99027e8	−0.871768
$93$	1.03600e8	0.143610
$94$	−8.81993e6	−0.0116517
$95$	−8.14506e7	−0.102598
$96$	−1.26369e7	−0.0151852
$97$	−9.64409e8	−1.10608	−0.553042	−	0.833153i	$-0.686533\pi$
$97$	−9.64409e8	−1.10608	−0.553042	+	0.833153i	$0.686533\pi$
$98$	1.91945e7	0.0210213
$99$	−2.76395e7	−0.0289182
$100$	−1.99985e8	−0.199985
$101$	1.57479e9	1.50583	0.752917	−	0.658116i	$-0.228646\pi$
$101$	1.57479e9	1.50583	0.752917	+	0.658116i	$0.228646\pi$
$102$	−8.37128e6	−0.00765758
$103$	1.33405e9	1.16789	0.583947	−	0.811792i	$-0.301508\pi$
$103$	1.33405e9	1.16789	0.583947	+	0.811792i	$0.301508\pi$
$104$	−3.81764e7	−0.0319996
$105$	5.92768e8	0.475919
$106$	−1.74126e7	−0.0133964
$107$	8.58739e7	0.0633336	0.0316668	−	0.999498i	$-0.489918\pi$
$107$	8.58739e7	0.0633336	0.0316668	+	0.999498i	$0.489918\pi$
$108$	2.72077e8	0.192435
$109$	−3.97713e8	−0.269868	−0.134934	−	0.990855i	$-0.543082\pi$
$109$	−3.97713e8	−0.269868	−0.134934	+	0.990855i	$0.543082\pi$
$110$	522373.	0.000340184 0
$111$	−7.62773e8	−0.476916
$112$	3.06874e9	1.84280
$113$	6.62533e8	0.382256	0.191128	−	0.981565i	$-0.438785\pi$
$113$	6.62533e8	0.382256	0.191128	+	0.981565i	$0.438785\pi$
$114$	−2.09430e6	−0.00116136
$115$	−7.31290e8	−0.389897
$116$	−3.17641e9	−1.62883
$117$	1.23294e9	0.608282
$118$	−2.43475e7	−0.0115607
$119$	6.09939e9	2.78821
$120$	−1.02846e7	−0.00452765
$121$	−2.34020e9	−0.992474
$122$	−1.94600e6	−0.000795288 0
$123$	1.26478e8	0.0498246
$124$	6.54803e8	0.248721
$125$	−2.44141e8	−0.0894427
$126$	1.52416e7	0.00538719
$127$	1.40056e8	0.0477733	0.0238867	−	0.999715i	$-0.492396\pi$
$127$	1.40056e8	0.0477733	0.0238867	+	0.999715i	$0.492396\pi$
$128$	−1.06494e8	−0.0350656
$129$	−3.07383e9	−0.977296
$130$	−2.33019e7	−0.00715561
$131$	−4.79459e9	−1.42243	−0.711214	−	0.702976i	$-0.751854\pi$
$131$	−4.79459e9	−1.42243	−0.711214	+	0.702976i	$0.751854\pi$
$132$	−1.74696e8	−0.0500840
$133$	1.52593e9	0.422865
$134$	1.64844e7	0.00441674
$135$	3.32151e8	0.0860663
$136$	−1.05826e8	−0.0265256
$137$	−2.78534e9	−0.675515	−0.337758	−	0.941233i	$-0.609668\pi$
$137$	−2.78534e9	−0.675515	−0.337758	+	0.941233i	$0.609668\pi$
$138$	−1.88033e7	−0.00441346
$139$	−2.29267e9	−0.520924	−0.260462	−	0.965484i	$-0.583875\pi$
$139$	−2.29267e9	−0.520924	−0.260462	+	0.965484i	$0.583875\pi$
$140$	3.74659e9	0.824252
$141$	3.60089e9	0.767227
$142$	2.68957e7	0.00555117
$143$	−7.91647e8	−0.158314
$144$	1.71953e9	0.333256
$145$	−3.87775e9	−0.728490
$146$	−7.54011e7	−0.0137338
$147$	−7.83651e9	−1.38419
$148$	−4.82111e9	−0.825980
$149$	4.32293e9	0.718522	0.359261	−	0.933237i	$-0.383029\pi$
$149$	4.32293e9	0.718522	0.359261	+	0.933237i	$0.383029\pi$
$150$	−6.27748e6	−0.00101245
$151$	9.18962e9	1.43847	0.719236	−	0.694766i	$-0.244492\pi$
$151$	9.18962e9	1.43847	0.719236	+	0.694766i	$0.244492\pi$
$152$	−2.64751e7	−0.00402292
$153$	3.41772e9	0.504226
$154$	−9.78634e6	−0.00140209
$155$	7.99381e8	0.111240
$156$	7.79279e9	1.05349
$157$	3.16561e9	0.415823	0.207912	−	0.978148i	$-0.433333\pi$
$157$	3.16561e9	0.415823	0.207912	+	0.978148i	$0.433333\pi$
$158$	1.08847e8	0.0138950
$159$	7.10900e9	0.882108
$160$	−9.75073e7	−0.0117624
$161$	1.37003e10	1.60699
$162$	8.54044e6	0.000974233 0
$163$	8.59899e9	0.954121	0.477060	−	0.878870i	$-0.341702\pi$
$163$	8.59899e9	0.954121	0.477060	+	0.878870i	$0.341702\pi$
$164$	7.99407e8	0.0862920
$165$	−2.13268e8	−0.0224000
$166$	7.06205e7	0.00721846
$167$	−1.88465e10	−1.87502	−0.937510	−	0.347959i	$-0.886875\pi$
$167$	−1.88465e10	−1.87502	−0.937510	+	0.347959i	$0.886875\pi$
$168$	1.92676e8	0.0186611
$169$	2.47092e10	2.33006
$170$	−6.45932e7	−0.00593153
$171$	8.55036e8	0.0764719
$172$	−1.94281e10	−1.69260
$173$	4.31818e9	0.366516	0.183258	−	0.983065i	$-0.441336\pi$
$173$	4.31818e9	0.366516	0.183258	+	0.983065i	$0.441336\pi$
$174$	−9.97068e7	−0.00824619
$175$	4.57383e9	0.368645
$176$	−1.10408e9	−0.0867347
$177$	9.94027e9	0.761235
$178$	4.11039e7	0.00306897
$179$	7.72961e9	0.562754	0.281377	−	0.959597i	$-0.409209\pi$
$179$	7.72961e9	0.562754	0.281377	+	0.959597i	$0.409209\pi$
$180$	2.09936e9	0.149060
$181$	−2.13864e10	−1.48110	−0.740549	−	0.672002i	$-0.765435\pi$
$181$	−2.13864e10	−1.48110	−0.740549	+	0.672002i	$0.765435\pi$
$182$	4.36547e8	0.0294924
$183$	7.94490e8	0.0523671
$184$	−2.37702e8	−0.0152881
$185$	−5.88560e9	−0.369418
$186$	2.05541e7	0.00125919
$187$	−2.19446e9	−0.131232
$188$	2.27594e10	1.32877
$189$	−6.22264e9	−0.354729
$190$	−1.61598e7	−0.000899588 0
$191$	3.22208e10	1.75181	0.875904	−	0.482485i	$-0.160266\pi$
$191$	3.22208e10	1.75181	0.875904	+	0.482485i	$0.160266\pi$
$192$	1.08666e10	0.577084
$193$	4.80908e8	0.0249490	0.0124745	−	0.999922i	$-0.496029\pi$
$193$	4.80908e8	0.0249490	0.0124745	+	0.999922i	$0.496029\pi$
$194$	−1.91338e8	−0.00969826
$195$	9.51341e9	0.471173
$196$	−4.95307e10	−2.39730
$197$	−3.24478e10	−1.53493	−0.767463	−	0.641093i	$-0.778481\pi$
$197$	−3.24478e10	−1.53493	−0.767463	+	0.641093i	$0.778481\pi$
$198$	−5.48366e6	−0.000253558 0
$199$	−2.30836e10	−1.04344	−0.521718	−	0.853118i	$-0.674709\pi$
$199$	−2.30836e10	−1.04344	−0.521718	+	0.853118i	$0.674709\pi$
$200$	−7.93567e7	−0.00350710
$201$	−6.73005e9	−0.290828
$202$	3.12438e8	0.0132033
$203$	7.26473e10	3.00253
$204$	2.16017e10	0.873278
$205$	9.75914e8	0.0385939
$206$	2.64674e8	0.0102402
$207$	7.67679e9	0.290612
$208$	4.92506e10	1.82443
$209$	−5.49003e8	−0.0199029
$210$	1.17605e8	0.00417290
$211$	−1.11400e10	−0.386913	−0.193456	−	0.981109i	$-0.561970\pi$
$211$	−1.11400e10	−0.386913	−0.193456	+	0.981109i	$0.561970\pi$
$212$	4.49325e10	1.52774
$213$	−1.09806e10	−0.365526
$214$	1.70373e7	0.000555315 0
$215$	−2.37178e10	−0.757010
$216$	1.07964e8	0.00337471
$217$	−1.49759e10	−0.458485
$218$	−7.89061e7	−0.00236623
$219$	3.07838e10	0.904324
$220$	−1.34796e9	−0.0387949
$221$	9.78899e10	2.76041
$222$	−1.51334e8	−0.00418165
$223$	−4.67023e10	−1.26464	−0.632320	−	0.774707i	$-0.717897\pi$
$223$	−4.67023e10	−1.26464	−0.632320	+	0.774707i	$0.717897\pi$
$224$	1.82674e9	0.0484798
$225$	2.56289e9	0.0666667
$226$	1.31446e8	0.00335166
$227$	−3.90534e10	−0.976209	−0.488105	−	0.872785i	$-0.662312\pi$
$227$	−3.90534e10	−0.976209	−0.488105	+	0.872785i	$0.662312\pi$
$228$	5.40426e9	0.132443
$229$	−1.46881e10	−0.352943	−0.176472	−	0.984306i	$-0.556468\pi$
$229$	−1.46881e10	−0.352943	−0.176472	+	0.984306i	$0.556468\pi$
$230$	−1.45088e8	−0.00341865
$231$	3.99544e9	0.0923232
$232$	−1.26044e9	−0.0285645
$233$	−2.16981e10	−0.482304	−0.241152	−	0.970487i	$-0.577525\pi$
$233$	−2.16981e10	−0.482304	−0.241152	+	0.970487i	$0.577525\pi$
$234$	2.44614e8	0.00533348
$235$	2.77847e10	0.594292
$236$	6.28275e10	1.31840
$237$	−4.44385e10	−0.914939
$238$	1.21012e9	0.0244473
$239$	−6.95602e10	−1.37902	−0.689510	−	0.724277i	$-0.742174\pi$
$239$	−6.95602e10	−1.37902	−0.689510	+	0.724277i	$0.742174\pi$
$240$	1.32680e10	0.258139
$241$	1.03001e11	1.96682	0.983412	−	0.181387i	$-0.0580586\pi$
$241$	1.03001e11	1.96682	0.983412	+	0.181387i	$0.0580586\pi$
$242$	−4.64294e8	−0.00870211
$243$	−3.48678e9	−0.0641500
$244$	5.02158e9	0.0906955
$245$	−6.04669e10	−1.07219
$246$	2.50932e7	0.000436867 0
$247$	2.44898e10	0.418648
$248$	2.59835e8	0.00436179
$249$	−2.88321e10	−0.475312
$250$	−4.84374e7	−0.000784242 0
$251$	−6.24095e10	−0.992474	−0.496237	−	0.868187i	$-0.665285\pi$
$251$	−6.24095e10	−0.992474	−0.496237	+	0.868187i	$0.665285\pi$
$252$	−3.93302e10	−0.614361
$253$	−4.92912e9	−0.0756358
$254$	2.77871e7	0.000418881 0
$255$	2.63713e10	0.390572
$256$	6.86667e10	0.999231
$257$	2.96210e10	0.423545	0.211773	−	0.977319i	$-0.432076\pi$
$257$	2.96210e10	0.423545	0.211773	+	0.977319i	$0.432076\pi$
$258$	−6.09846e8	−0.00856903
$259$	1.10263e11	1.52258
$260$	6.01295e10	0.816033
$261$	4.07070e10	0.542984
$262$	−9.51243e8	−0.0124720
$263$	1.18888e11	1.53228	0.766138	−	0.642676i	$-0.222176\pi$
$263$	1.18888e11	1.53228	0.766138	+	0.642676i	$0.222176\pi$
$264$	−6.93216e7	−0.000878317 0
$265$	5.48534e10	0.683278
$266$	3.02743e8	0.00370772
$267$	−1.67814e10	−0.202082
$268$	−4.25373e10	−0.503690
$269$	−1.41085e11	−1.64284	−0.821418	−	0.570326i	$-0.806817\pi$
$269$	−1.41085e11	−1.64284	−0.821418	+	0.570326i	$0.806817\pi$
$270$	6.58985e7	0.000754638 0
$271$	−1.42296e10	−0.160263	−0.0801313	−	0.996784i	$-0.525534\pi$
$271$	−1.42296e10	−0.160263	−0.0801313	+	0.996784i	$0.525534\pi$
$272$	1.36523e11	1.51233
$273$	−1.78228e11	−1.94198
$274$	−5.52609e8	−0.00592298
$275$	−1.64558e9	−0.0173509
$276$	4.85212e10	0.503316
$277$	−3.22456e10	−0.329088	−0.164544	−	0.986370i	$-0.552615\pi$
$277$	−3.22456e10	−0.329088	−0.164544	+	0.986370i	$0.552615\pi$
$278$	−4.54864e8	−0.00456751
$279$	−8.39158e9	−0.0829134
$280$	1.48670e9	0.0144548
$281$	8.86186e9	0.0847904	0.0423952	−	0.999101i	$-0.486501\pi$
$281$	8.86186e9	0.0847904	0.0423952	+	0.999101i	$0.486501\pi$
$282$	7.14415e8	0.00672712
$283$	9.33181e9	0.0864822	0.0432411	−	0.999065i	$-0.486232\pi$
$283$	9.33181e9	0.0864822	0.0432411	+	0.999065i	$0.486232\pi$
$284$	−6.94031e10	−0.633062
$285$	6.59750e9	0.0592349
$286$	−1.57062e8	−0.00138811
$287$	−1.82832e10	−0.159068
$288$	1.02359e9	0.00876720
$289$	1.52764e11	1.28820
$290$	−7.69343e8	−0.00638747
$291$	7.81171e10	0.638598
$292$	1.94569e11	1.56621
$293$	2.58184e10	0.204656	0.102328	−	0.994751i	$-0.467371\pi$
$293$	2.58184e10	0.204656	0.102328	+	0.994751i	$0.467371\pi$
$294$	−1.55476e9	−0.0121367
$295$	7.66996e10	0.589650
$296$	−1.91308e9	−0.0144851
$297$	2.23880e9	0.0166960
$298$	8.57667e8	0.00630007
$299$	2.19878e11	1.59097
$300$	1.61988e10	0.115461
$301$	4.44339e11	3.12008
$302$	1.82321e9	0.0126127
$303$	−1.27558e11	−0.869393
$304$	3.41550e10	0.229363
$305$	6.13032e9	0.0405634
$306$	6.78074e8	0.00442110
$307$	2.19877e11	1.41273	0.706363	−	0.707850i	$-0.250335\pi$
$307$	2.19877e11	1.41273	0.706363	+	0.707850i	$0.250335\pi$
$308$	2.52532e10	0.159896
$309$	−1.08058e11	−0.674283
$310$	1.58597e8	0.000975364 0
$311$	−2.84889e11	−1.72685	−0.863423	−	0.504481i	$-0.831684\pi$
$311$	−2.84889e11	−1.72685	−0.863423	+	0.504481i	$0.831684\pi$
$312$	3.09229e9	0.0184750
$313$	−2.56198e11	−1.50878	−0.754391	−	0.656425i	$-0.772068\pi$
$313$	−2.56198e11	−1.50878	−0.754391	+	0.656425i	$0.772068\pi$
$314$	6.28055e8	0.00364598
$315$	−4.80142e10	−0.274772
$316$	−2.80874e11	−1.58460
$317$	6.04838e10	0.336413	0.168206	−	0.985752i	$-0.446203\pi$
$317$	6.04838e10	0.336413	0.168206	+	0.985752i	$0.446203\pi$
$318$	1.41042e9	0.00773441
$319$	−2.61372e10	−0.141319
$320$	8.38474e10	0.447007
$321$	−6.95579e9	−0.0365657
$322$	2.71813e9	0.0140902
$323$	6.78861e10	0.347032
$324$	−2.20382e10	−0.111103
$325$	7.34060e10	0.364969
$326$	1.70604e9	0.00836582
$327$	3.22148e10	0.155808
$328$	3.17216e8	0.00151329
$329$	−5.20529e11	−2.44942
$330$	−4.23122e7	−0.000196405 0
$331$	4.07305e10	0.186506	0.0932531	−	0.995642i	$-0.470273\pi$
$331$	4.07305e10	0.186506	0.0932531	+	0.995642i	$0.470273\pi$
$332$	−1.82233e11	−0.823201
$333$	6.17846e10	0.275348
$334$	−3.73913e9	−0.0164404
$335$	−5.19294e10	−0.225274
$336$	−2.48568e11	−1.06394
$337$	−3.54053e11	−1.49532	−0.747659	−	0.664083i	$-0.768822\pi$
$337$	−3.54053e11	−1.49532	−0.747659	+	0.664083i	$0.768822\pi$
$338$	4.90228e9	0.0204302
$339$	−5.36652e10	−0.220696
$340$	1.66680e11	0.676438
$341$	5.38808e9	0.0215794
$342$	1.69639e8	0.000670513 0
$343$	6.60310e11	2.57587
$344$	−7.70936e9	−0.0296828
$345$	5.92345e10	0.225107
$346$	8.56725e8	0.00321365
$347$	−2.95295e11	−1.09338	−0.546692	−	0.837334i	$-0.684113\pi$
$347$	−2.95295e11	−1.09338	−0.546692	+	0.837334i	$0.684113\pi$
$348$	2.57289e11	0.940404
$349$	−8.30547e10	−0.299675	−0.149837	−	0.988711i	$-0.547875\pi$
$349$	−8.30547e10	−0.299675	−0.149837	+	0.988711i	$0.547875\pi$
$350$	9.07445e8	0.00323232
$351$	−9.98680e10	−0.351192
$352$	−6.57230e8	−0.00228179
$353$	−1.34581e11	−0.461316	−0.230658	−	0.973035i	$-0.574088\pi$
$353$	−1.34581e11	−0.461316	−0.230658	+	0.973035i	$0.574088\pi$
$354$	1.97214e9	0.00667458
$355$	−8.47270e10	−0.283136
$356$	−1.06067e11	−0.349989
$357$	−4.94051e11	−1.60977
$358$	1.53355e9	0.00493428
$359$	2.46014e11	0.781690	0.390845	−	0.920457i	$-0.372183\pi$
$359$	2.46014e11	0.781690	0.390845	+	0.920457i	$0.372183\pi$
$360$	8.33055e8	0.00261404
$361$	1.69836e10	0.0526316
$362$	−4.24305e9	−0.0129864
$363$	1.89556e11	0.573005
$364$	−1.12649e12	−3.36335
$365$	2.37529e11	0.700486
$366$	1.57626e8	0.000459160 0
$367$	−5.51687e10	−0.158743	−0.0793717	−	0.996845i	$-0.525291\pi$
$367$	−5.51687e10	−0.158743	−0.0793717	+	0.996845i	$0.525291\pi$
$368$	3.06655e11	0.871634
$369$	−1.02448e10	−0.0287662
$370$	−1.16770e9	−0.00323909
$371$	−1.02765e12	−2.81618
$372$	−5.30390e10	−0.143599
$373$	−1.31990e11	−0.353061	−0.176531	−	0.984295i	$-0.556487\pi$
$373$	−1.31990e11	−0.353061	−0.176531	+	0.984295i	$0.556487\pi$
$374$	−4.35379e8	−0.00115065
$375$	1.97754e10	0.0516398
$376$	9.03126e9	0.0233025
$377$	1.16593e12	2.97259
$378$	−1.23457e9	−0.00311030
$379$	5.27113e11	1.31228	0.656141	−	0.754638i	$-0.272188\pi$
$379$	5.27113e11	1.31228	0.656141	+	0.754638i	$0.272188\pi$
$380$	4.16995e10	0.102590
$381$	−1.13446e10	−0.0275819
$382$	6.39260e9	0.0153600
$383$	4.41475e11	1.04836	0.524182	−	0.851606i	$-0.324371\pi$
$383$	4.41475e11	1.04836	0.524182	+	0.851606i	$0.324371\pi$
$384$	8.62605e9	0.0202452
$385$	3.08290e10	0.0715133
$386$	9.54118e7	0.000218756 0
$387$	2.48980e11	0.564242
$388$	4.93739e11	1.10600
$389$	6.32902e11	1.40140	0.700702	−	0.713454i	$-0.252870\pi$
$389$	6.32902e11	1.40140	0.700702	+	0.713454i	$0.252870\pi$
$390$	1.88746e9	0.00413129
$391$	6.09504e11	1.31881
$392$	−1.96545e10	−0.0420411
$393$	3.88361e11	0.821239
$394$	−6.43763e9	−0.0134584
$395$	−3.42890e11	−0.708709
$396$	1.41503e10	0.0289160
$397$	−8.85133e11	−1.78834	−0.894172	−	0.447723i	$-0.852235\pi$
$397$	−8.85133e11	−1.78834	−0.894172	+	0.447723i	$0.852235\pi$
$398$	−4.57978e9	−0.00914894
$399$	−1.23600e11	−0.244141
$400$	1.02376e11	0.199954
$401$	1.92148e11	0.371096	0.185548	−	0.982635i	$-0.440594\pi$
$401$	1.92148e11	0.371096	0.185548	+	0.982635i	$0.440594\pi$
$402$	−1.33524e9	−0.00255001
$403$	−2.40351e11	−0.453913
$404$	−8.06231e11	−1.50572
$405$	−2.69042e10	−0.0496904
$406$	1.44132e10	0.0263265
$407$	−3.96708e10	−0.0716631
$408$	8.57187e9	0.0153146
$409$	1.12406e11	0.198626	0.0993128	−	0.995056i	$-0.468336\pi$
$409$	1.12406e11	0.198626	0.0993128	+	0.995056i	$0.468336\pi$
$410$	1.93621e8	0.000338395 0
$411$	2.25612e11	0.390009
$412$	−6.82979e11	−1.16780
$413$	−1.43692e12	−2.43029
$414$	1.52307e9	0.00254811
$415$	−2.22470e11	−0.368175
$416$	2.93176e10	0.0479964
$417$	1.85706e11	0.300756
$418$	−1.08922e8	−0.000174511 0
$419$	−6.23205e11	−0.987797	−0.493898	−	0.869520i	$-0.664429\pi$
$419$	−6.23205e11	−0.987797	−0.493898	+	0.869520i	$0.664429\pi$
$420$	−3.03474e11	−0.475882
$421$	5.66694e11	0.879183	0.439592	−	0.898198i	$-0.355123\pi$
$421$	5.66694e11	0.879183	0.439592	+	0.898198i	$0.355123\pi$
$422$	−2.21016e9	−0.00339249
$423$	−2.91672e11	−0.442959
$424$	1.78298e10	0.0267917
$425$	2.03482e11	0.302536
$426$	−2.17855e9	−0.00320497
$427$	−1.14848e11	−0.167185
$428$	−4.39641e10	−0.0633288
$429$	6.41234e10	0.0914026
$430$	−4.70560e9	−0.00663754
$431$	−1.03318e12	−1.44220	−0.721102	−	0.692829i	$-0.756364\pi$
$431$	−1.03318e12	−1.44220	−0.721102	+	0.692829i	$0.756364\pi$
$432$	−1.39282e11	−0.192406
$433$	7.21062e11	0.985773	0.492887	−	0.870094i	$-0.335942\pi$
$433$	7.21062e11	0.985773	0.492887	+	0.870094i	$0.335942\pi$
$434$	−2.97121e9	−0.00402004
$435$	3.14098e11	0.420594
$436$	2.03614e11	0.269847
$437$	1.52484e11	0.200013
$438$	6.10749e9	0.00792920
$439$	−1.46512e12	−1.88270	−0.941352	−	0.337427i	$-0.890444\pi$
$439$	−1.46512e12	−1.88270	−0.941352	+	0.337427i	$0.890444\pi$
$440$	−5.34889e8	−0.000680341 0
$441$	6.34757e11	0.799160
$442$	1.94213e10	0.0242035
$443$	7.55273e11	0.931724	0.465862	−	0.884857i	$-0.345744\pi$
$443$	7.55273e11	0.931724	0.465862	+	0.884857i	$0.345744\pi$
$444$	3.90510e11	0.476880
$445$	−1.29486e11	−0.156532
$446$	−9.26572e9	−0.0110885
$447$	−3.50157e11	−0.414839
$448$	−1.57083e12	−1.84238
$449$	−3.45981e10	−0.0401739	−0.0200869	−	0.999798i	$-0.506394\pi$
$449$	−3.45981e10	−0.0401739	−0.0200869	+	0.999798i	$0.506394\pi$
$450$	5.08476e8	0.000584540 0
$451$	6.57796e9	0.00748681
$452$	−3.39191e11	−0.382227
$453$	−7.44359e11	−0.830502
$454$	−7.74818e9	−0.00855950
$455$	−1.37522e12	−1.50425
$456$	2.14449e9	0.00232264
$457$	1.17296e11	0.125794	0.0628968	−	0.998020i	$-0.479966\pi$
$457$	1.17296e11	0.125794	0.0628968	+	0.998020i	$0.479966\pi$
$458$	−2.91410e9	−0.00309464
$459$	−2.76836e11	−0.291115
$460$	3.74392e11	0.389867
$461$	−1.51534e12	−1.56263	−0.781317	−	0.624135i	$-0.785452\pi$
$461$	−1.51534e12	−1.56263	−0.781317	+	0.624135i	$0.785452\pi$
$462$	7.92693e8	0.000809499 0
$463$	−8.39331e11	−0.848826	−0.424413	−	0.905469i	$-0.639520\pi$
$463$	−8.39331e11	−0.848826	−0.424413	+	0.905469i	$0.639520\pi$
$464$	1.62607e12	1.62858
$465$	−6.47499e10	−0.0642245
$466$	−4.30489e9	−0.00422889
$467$	−5.02642e11	−0.489027	−0.244513	−	0.969646i	$-0.578628\pi$
$467$	−5.02642e11	−0.489027	−0.244513	+	0.969646i	$0.578628\pi$
$468$	−6.31216e11	−0.608235
$469$	9.72866e11	0.928485
$470$	5.51246e9	0.00521081
$471$	−2.56414e11	−0.240076
$472$	2.49308e10	0.0231205
$473$	−1.59866e11	−0.146852
$474$	−8.81658e9	−0.00802227
$475$	5.09066e10	0.0458831
$476$	−3.12265e12	−2.78799
$477$	−5.75829e11	−0.509285
$478$	−1.38007e10	−0.0120914
$479$	7.33267e11	0.636432	0.318216	−	0.948018i	$-0.396916\pi$
$479$	7.33267e11	0.636432	0.318216	+	0.948018i	$0.396916\pi$
$480$	7.89809e9	0.00679104
$481$	1.76963e12	1.50740
$482$	2.04354e10	0.0172453
$483$	−1.10972e12	−0.927796
$484$	1.19809e12	0.992397
$485$	6.02755e11	0.494656
$486$	−6.91776e8	−0.000562474 0
$487$	−7.07522e11	−0.569980	−0.284990	−	0.958530i	$-0.591990\pi$
$487$	−7.07522e11	−0.569980	−0.284990	+	0.958530i	$0.591990\pi$
$488$	1.99263e9	0.00159052
$489$	−6.96518e11	−0.550862
$490$	−1.19966e10	−0.00940103
$491$	−1.53203e12	−1.18960	−0.594798	−	0.803875i	$-0.702768\pi$
$491$	−1.53203e12	−1.18960	−0.594798	+	0.803875i	$0.702768\pi$
$492$	−6.47520e10	−0.0498207
$493$	3.23196e12	2.46408
$494$	4.85877e9	0.00367075
$495$	1.72747e10	0.0129326
$496$	−3.35207e11	−0.248683
$497$	1.58731e12	1.16697
$498$	−5.72026e9	−0.00416758
$499$	−1.83326e12	−1.32364	−0.661822	−	0.749661i	$-0.730216\pi$
$499$	−1.83326e12	−1.32364	−0.661822	+	0.749661i	$0.730216\pi$
$500$	1.24990e11	0.0894358
$501$	1.52656e12	1.08254
$502$	−1.23820e10	−0.00870211
$503$	8.92347e11	0.621552	0.310776	−	0.950483i	$-0.399411\pi$
$503$	8.92347e11	0.621552	0.310776	+	0.950483i	$0.399411\pi$
$504$	−1.56068e10	−0.0107740
$505$	−9.84245e11	−0.673429
$506$	−9.77935e8	−0.000663182 0
$507$	−2.00144e12	−1.34526
$508$	−7.17033e10	−0.0477697
$509$	6.00406e11	0.396475	0.198237	−	0.980154i	$-0.436478\pi$
$509$	6.00406e11	0.396475	0.198237	+	0.980154i	$0.436478\pi$
$510$	5.23205e9	0.00342457
$511$	−4.44997e12	−2.88711
$512$	6.81486e10	0.0438270
$513$	−6.92579e10	−0.0441511
$514$	5.87678e9	0.00371369
$515$	−8.33778e11	−0.522298
$516$	1.57368e12	0.977221
$517$	1.87277e11	0.115286
$518$	2.18761e10	0.0133502
$519$	−3.49773e11	−0.211608
$520$	2.38602e10	0.0143107
$521$	1.44615e11	0.0859891	0.0429946	−	0.999075i	$-0.486310\pi$
$521$	1.44615e11	0.0859891	0.0429946	+	0.999075i	$0.486310\pi$
$522$	8.07625e9	0.00476094
$523$	−1.60979e11	−0.0940833	−0.0470416	−	0.998893i	$-0.514979\pi$
$523$	−1.60979e11	−0.0940833	−0.0470416	+	0.998893i	$0.514979\pi$
$524$	2.45464e12	1.42232
$525$	−3.70480e11	−0.212837
$526$	2.35873e10	0.0134351
$527$	−6.66255e11	−0.376264
$528$	8.94303e10	0.0500763
$529$	−4.32103e11	−0.239903
$530$	1.08829e10	0.00599105
$531$	−8.05162e11	−0.439499
$532$	−7.81215e11	−0.422832
$533$	−2.93429e11	−0.157482
$534$	−3.32942e9	−0.00177187
$535$	−5.36712e10	−0.0283237
$536$	−1.68794e10	−0.00883314
$537$	−6.26098e11	−0.324906
$538$	−2.79911e10	−0.0144046
$539$	−4.07566e11	−0.207993
$540$	−1.70048e11	−0.0860597
$541$	1.72068e12	0.863601	0.431800	−	0.901969i	$-0.357878\pi$
$541$	1.72068e12	0.863601	0.431800	+	0.901969i	$0.357878\pi$
$542$	−2.82315e9	−0.00140520
$543$	1.73230e12	0.855113
$544$	8.12688e10	0.0397859
$545$	2.48571e11	0.120689
$546$	−3.53603e10	−0.0170274
$547$	8.30514e11	0.396647	0.198323	−	0.980137i	$-0.436450\pi$
$547$	8.30514e11	0.396647	0.198323	+	0.980137i	$0.436450\pi$
$548$	1.42598e12	0.675463
$549$	−6.43537e10	−0.0302342
$550$	−3.26483e8	−0.000152135 0
$551$	8.08563e11	0.373707
$552$	1.92539e10	0.00882658
$553$	6.42384e12	2.92100
$554$	−6.39751e9	−0.00288547
$555$	4.76733e11	0.213283
$556$	1.17376e12	0.520884
$557$	−4.54143e10	−0.0199914	−0.00999572	−	0.999950i	$-0.503182\pi$
$557$	−4.54143e10	−0.0199914	−0.00999572	+	0.999950i	$0.503182\pi$
$558$	−1.66489e9	−0.000726993 0
$559$	7.13126e12	3.08897
$560$	−1.91796e12	−0.824126
$561$	1.77751e11	0.0757668
$562$	1.75819e9	0.000743450 0
$563$	−3.59000e12	−1.50594	−0.752968	−	0.658057i	$-0.771379\pi$
$563$	−3.59000e12	−1.50594	−0.752968	+	0.658057i	$0.771379\pi$
$564$	−1.84351e12	−0.767168
$565$	−4.14083e11	−0.170950
$566$	1.85143e9	0.000758285 0
$567$	5.04034e11	0.204803
$568$	−2.75401e10	−0.0111019
$569$	−2.40627e12	−0.962364	−0.481182	−	0.876621i	$-0.659792\pi$
$569$	−2.40627e12	−0.962364	−0.481182	+	0.876621i	$0.659792\pi$
$570$	1.30894e9	0.000519377 0
$571$	2.46069e12	0.968711	0.484355	−	0.874871i	$-0.339054\pi$
$571$	2.46069e12	0.968711	0.484355	+	0.874871i	$0.339054\pi$
$572$	4.05292e11	0.158302
$573$	−2.60989e12	−1.01141
$574$	−3.62737e9	−0.00139472
$575$	4.57056e11	0.174367
$576$	−8.80196e11	−0.333180
$577$	3.71890e11	0.139676	0.0698382	−	0.997558i	$-0.477752\pi$
$577$	3.71890e11	0.139676	0.0698382	+	0.997558i	$0.477752\pi$
$578$	3.03084e10	0.0112950
$579$	−3.89535e10	−0.0144043
$580$	1.98525e12	0.728434
$581$	4.16783e12	1.51746
$582$	1.54984e10	0.00559929
$583$	3.69729e11	0.132549
$584$	7.72078e10	0.0274665
$585$	−7.70587e11	−0.272032
$586$	5.12235e9	0.00179445
$587$	−1.61101e11	−0.0560050	−0.0280025	−	0.999608i	$-0.508915\pi$
$587$	−1.61101e11	−0.0560050	−0.0280025	+	0.999608i	$0.508915\pi$
$588$	4.01198e12	1.38408
$589$	−1.66682e11	−0.0570649
$590$	1.52172e10	0.00517011
$591$	2.62827e12	0.886190
$592$	2.46803e12	0.825853
$593$	2.16316e12	0.718360	0.359180	−	0.933268i	$-0.383056\pi$
$593$	2.16316e12	0.718360	0.359180	+	0.933268i	$0.383056\pi$
$594$	4.44176e8	0.000146392 0
$595$	−3.81212e12	−1.24692
$596$	−2.21317e12	−0.718467
$597$	1.86978e12	0.602428
$598$	4.36236e10	0.0139497
$599$	9.32906e11	0.296085	0.148043	−	0.988981i	$-0.452703\pi$
$599$	9.32906e11	0.296085	0.148043	+	0.988981i	$0.452703\pi$
$600$	6.42789e9	0.00202483
$601$	7.04332e11	0.220213	0.110106	−	0.993920i	$-0.464881\pi$
$601$	7.04332e11	0.220213	0.110106	+	0.993920i	$0.464881\pi$
$602$	8.81566e10	0.0273571
$603$	5.45134e11	0.167910
$604$	−4.70472e12	−1.43836
$605$	1.46263e12	0.443848
$606$	−2.53075e10	−0.00762293
$607$	2.31940e11	0.0693469	0.0346735	−	0.999399i	$-0.488961\pi$
$607$	2.31940e11	0.0693469	0.0346735	+	0.999399i	$0.488961\pi$
$608$	2.03316e10	0.00603400
$609$	−5.88443e12	−1.73351
$610$	1.21625e9	0.000355664 0
$611$	−8.35404e12	−2.42500
$612$	−1.74974e12	−0.504187
$613$	−6.30752e12	−1.80421	−0.902103	−	0.431520i	$-0.857977\pi$
$613$	−6.30752e12	−1.80421	−0.902103	+	0.431520i	$0.857977\pi$
$614$	4.36235e10	0.0123869
$615$	−7.90490e10	−0.0222822
$616$	1.00208e10	0.00280408
$617$	−2.00719e11	−0.0557578	−0.0278789	−	0.999611i	$-0.508875\pi$
$617$	−2.00719e11	−0.0557578	−0.0278789	+	0.999611i	$0.508875\pi$
$618$	−2.14386e10	−0.00591218
$619$	1.51444e12	0.414613	0.207307	−	0.978276i	$-0.433530\pi$
$619$	1.51444e12	0.414613	0.207307	+	0.978276i	$0.433530\pi$
$620$	−4.09252e11	−0.111232
$621$	−6.21820e11	−0.167785
$622$	−5.65218e10	−0.0151412
$623$	2.42584e12	0.645158
$624$	−3.98929e12	−1.05333
$625$	1.52588e11	0.0400000
$626$	−5.08296e10	−0.0132291
$627$	4.44692e10	0.0114909
$628$	−1.62067e12	−0.415791
$629$	4.90543e12	1.24954
$630$	−9.52599e9	−0.00240923
$631$	3.85957e12	0.969185	0.484593	−	0.874740i	$-0.338968\pi$
$631$	3.85957e12	0.969185	0.484593	+	0.874740i	$0.338968\pi$
$632$	−1.11455e11	−0.0277889
$633$	9.02337e11	0.223384
$634$	1.19999e10	0.00294970
$635$	−8.75351e10	−0.0213649
$636$	−3.63953e12	−0.882040
$637$	1.81806e13	4.37503
$638$	−5.18561e9	−0.00123910
$639$	8.89431e11	0.211037
$640$	6.65590e10	0.0156818
$641$	−4.97143e12	−1.16311	−0.581555	−	0.813507i	$-0.697555\pi$
$641$	−4.97143e12	−1.16311	−0.581555	+	0.813507i	$0.697555\pi$
$642$	−1.38002e9	−0.000320612 0
$643$	2.94228e12	0.678788	0.339394	−	0.940644i	$-0.389778\pi$
$643$	2.94228e12	0.678788	0.339394	+	0.940644i	$0.389778\pi$
$644$	−7.01400e12	−1.60687
$645$	1.92114e12	0.437060
$646$	1.34686e10	0.00304281
$647$	3.64144e11	0.0816966	0.0408483	−	0.999165i	$-0.486994\pi$
$647$	3.64144e11	0.0816966	0.0408483	+	0.999165i	$0.486994\pi$
$648$	−8.74508e9	−0.00194839
$649$	5.16980e11	0.114386
$650$	1.45637e10	0.00320009
$651$	1.21305e12	0.264706
$652$	−4.40235e12	−0.954048
$653$	7.65121e12	1.64672	0.823362	−	0.567516i	$-0.192096\pi$
$653$	7.65121e12	1.64672	0.823362	+	0.567516i	$0.192096\pi$
$654$	6.39139e9	0.00136614
$655$	2.99662e12	0.636129
$656$	−4.09233e11	−0.0862788
$657$	−2.49349e12	−0.522112
$658$	−1.03273e11	−0.0214767
$659$	7.78898e12	1.60878	0.804389	−	0.594103i	$-0.202493\pi$
$659$	7.78898e12	1.60878	0.804389	+	0.594103i	$0.202493\pi$
$660$	1.09185e11	0.0223982
$661$	6.26276e12	1.27603	0.638013	−	0.770026i	$-0.279757\pi$
$661$	6.26276e12	1.27603	0.638013	+	0.770026i	$0.279757\pi$
$662$	8.08090e9	0.00163530
$663$	−7.92909e12	−1.59372
$664$	−7.23127e10	−0.0144364
$665$	−9.53705e11	−0.189111
$666$	1.22580e10	0.00241428
$667$	7.25954e12	1.42018
$668$	9.64865e12	1.87488
$669$	3.78289e12	0.730140
$670$	−1.03028e10	−0.00197523
$671$	4.13203e10	0.00786887
$672$	−1.47966e11	−0.0279898
$673$	−5.07344e12	−0.953310	−0.476655	−	0.879090i	$-0.658151\pi$
$673$	−5.07344e12	−0.953310	−0.476655	+	0.879090i	$0.658151\pi$
$674$	−7.02439e10	−0.0131111
$675$	−2.07594e11	−0.0384900
$676$	−1.26501e13	−2.32988
$677$	4.66052e12	0.852678	0.426339	−	0.904563i	$-0.359803\pi$
$677$	4.66052e12	0.852678	0.426339	+	0.904563i	$0.359803\pi$
$678$	−1.06471e10	−0.00193508
$679$	−1.12923e13	−2.03876
$680$	6.61409e10	0.0118626
$681$	3.16333e12	0.563615
$682$	1.06899e9	0.000189210 0
$683$	−5.67652e12	−0.998134	−0.499067	−	0.866563i	$-0.666324\pi$
$683$	−5.67652e12	−0.998134	−0.499067	+	0.866563i	$0.666324\pi$
$684$	−4.37745e11	−0.0764660
$685$	1.74084e12	0.302100
$686$	1.31005e11	0.0225855
$687$	1.18973e12	0.203772
$688$	9.94568e12	1.69234
$689$	−1.64928e13	−2.78810
$690$	1.17521e10	0.00197376
$691$	9.53629e12	1.59121	0.795606	−	0.605814i	$-0.207152\pi$
$691$	9.53629e12	1.59121	0.795606	+	0.605814i	$0.207152\pi$
$692$	−2.21074e12	−0.366488
$693$	−3.23631e11	−0.0533028
$694$	−5.85863e10	−0.00958690
$695$	1.43292e12	0.232964
$696$	1.02096e11	0.0164917
$697$	−8.13389e11	−0.130542
$698$	−1.64780e10	−0.00262758
$699$	1.75755e12	0.278458
$700$	−2.34162e12	−0.368617
$701$	−9.20594e12	−1.43992	−0.719958	−	0.694018i	$-0.755839\pi$
$701$	−9.20594e12	−1.43992	−0.719958	+	0.694018i	$0.755839\pi$
$702$	−1.98138e10	−0.00307928
$703$	1.22723e12	0.189507
$704$	5.65158e11	0.0867147
$705$	−2.25056e12	−0.343114
$706$	−2.67009e10	−0.00404487
$707$	1.84392e13	2.77559
$708$	−5.08903e12	−0.761176
$709$	5.21615e12	0.775251	0.387625	−	0.921817i	$-0.373295\pi$
$709$	5.21615e12	0.775251	0.387625	+	0.921817i	$0.373295\pi$
$710$	−1.68098e10	−0.00248256
$711$	3.59952e12	0.528240
$712$	−4.20888e10	−0.00613771
$713$	−1.49652e12	−0.216861
$714$	−9.80194e10	−0.0141146
$715$	4.94779e11	0.0708002
$716$	−3.95726e12	−0.562711
$717$	5.63438e12	0.796177
$718$	4.88090e10	0.00685393
$719$	−1.01367e13	−1.41454	−0.707270	−	0.706943i	$-0.750074\pi$
$719$	−1.01367e13	−1.41454	−0.707270	+	0.706943i	$0.750074\pi$
$720$	−1.07471e12	−0.149037
$721$	1.56203e13	2.15269
$722$	3.36953e9	0.000461479 0
$723$	−8.34309e12	−1.13555
$724$	1.09490e13	1.48099
$725$	2.42359e12	0.325791
$726$	3.76079e10	0.00502416
$727$	1.19606e13	1.58799	0.793993	−	0.607927i	$-0.207999\pi$
$727$	1.19606e13	1.58799	0.793993	+	0.607927i	$0.207999\pi$
$728$	−4.47007e11	−0.0589825
$729$	2.82430e11	0.0370370
$730$	4.71257e10	0.00614193
$731$	1.97679e13	2.56055
$732$	−4.06748e11	−0.0523631
$733$	−4.21815e12	−0.539703	−0.269851	−	0.962902i	$-0.586975\pi$
$733$	−4.21815e12	−0.539703	−0.269851	+	0.962902i	$0.586975\pi$
$734$	−1.09454e10	−0.00139188
$735$	4.89782e12	0.619027
$736$	1.82544e11	0.0229307
$737$	−3.50020e11	−0.0437008
$738$	−2.03255e9	−0.000252225 0
$739$	6.57570e11	0.0811040	0.0405520	−	0.999177i	$-0.487088\pi$
$739$	6.57570e11	0.0811040	0.0405520	+	0.999177i	$0.487088\pi$
$740$	3.01319e12	0.369389
$741$	−1.98368e12	−0.241707
$742$	−2.03884e11	−0.0246926
$743$	−2.89571e12	−0.348582	−0.174291	−	0.984694i	$-0.555763\pi$
$743$	−2.89571e12	−0.348582	−0.174291	+	0.984694i	$0.555763\pi$
$744$	−2.10466e10	−0.00251828
$745$	−2.70183e12	−0.321333
$746$	−2.61866e10	−0.00309567
$747$	2.33540e12	0.274421
$748$	1.12348e12	0.131222
$749$	1.00550e12	0.116738
$750$	3.92343e9	0.000452783 0
$751$	7.73714e12	0.887566	0.443783	−	0.896134i	$-0.353636\pi$
$751$	7.73714e12	0.887566	0.443783	+	0.896134i	$0.353636\pi$
$752$	−1.16510e13	−1.32857
$753$	5.05517e12	0.573005
$754$	2.31319e11	0.0260639
$755$	−5.74351e12	−0.643304
$756$	3.18575e12	0.354702
$757$	8.85032e12	0.979552	0.489776	−	0.871848i	$-0.337079\pi$
$757$	8.85032e12	0.979552	0.489776	+	0.871848i	$0.337079\pi$
$758$	1.04579e11	0.0115062
$759$	3.99259e11	0.0436684
$760$	1.65470e10	0.00179911
$761$	6.94957e12	0.751150	0.375575	−	0.926792i	$-0.377445\pi$
$761$	6.94957e12	0.751150	0.375575	+	0.926792i	$0.377445\pi$
$762$	−2.25075e9	−0.000241841 0
$763$	−4.65682e12	−0.497427
$764$	−1.64958e13	−1.75167
$765$	−2.13608e12	−0.225497
$766$	8.75885e10	0.00919216
$767$	−2.30613e13	−2.40605
$768$	−5.56200e12	−0.576906
$769$	−9.18717e12	−0.947356	−0.473678	−	0.880698i	$-0.657074\pi$
$769$	−9.18717e12	−0.947356	−0.473678	+	0.880698i	$0.657074\pi$
$770$	6.11646e9	0.000627035 0
$771$	−2.39930e12	−0.244534
$772$	−2.46206e11	−0.0249471
$773$	−1.15670e13	−1.16523	−0.582615	−	0.812748i	$-0.697970\pi$
$773$	−1.15670e13	−1.16523	−0.582615	+	0.812748i	$0.697970\pi$
$774$	4.93975e10	0.00494733
$775$	−4.99613e11	−0.0497481
$776$	1.95923e11	0.0193958
$777$	−8.93131e12	−0.879064
$778$	1.25567e11	0.0122877
$779$	−2.03491e11	−0.0197983
$780$	−4.87049e12	−0.471137
$781$	−5.71087e11	−0.0549253
$782$	1.20925e11	0.0115634
$783$	−3.29727e12	−0.313492
$784$	2.53558e13	2.39693
$785$	−1.97850e12	−0.185962
$786$	7.70507e10	0.00720071
$787$	−3.62687e11	−0.0337012	−0.0168506	−	0.999858i	$-0.505364\pi$
$787$	−3.62687e11	−0.0337012	−0.0168506	+	0.999858i	$0.505364\pi$
$788$	1.66120e13	1.53481
$789$	−9.62993e12	−0.884660
$790$	−6.80292e10	−0.00621403
$791$	7.75760e12	0.704585
$792$	5.61505e9	0.000507096 0
$793$	−1.84321e12	−0.165518
$794$	−1.75610e11	−0.0156804
$795$	−4.44313e12	−0.394491
$796$	1.18179e13	1.04336
$797$	1.80915e13	1.58823	0.794114	−	0.607769i	$-0.207935\pi$
$797$	1.80915e13	1.58823	0.794114	+	0.607769i	$0.207935\pi$
$798$	−2.45222e10	−0.00214065
$799$	−2.31575e13	−2.01016
$800$	6.09420e10	0.00526032
$801$	1.35929e12	0.116672
$802$	3.81221e10	0.00325381
$803$	1.60102e12	0.135887
$804$	3.44552e12	0.290805
$805$	−8.56267e12	−0.718667
$806$	−4.76854e10	−0.00397995
$807$	1.14279e13	0.948492
$808$	−3.19924e11	−0.0264056
$809$	−2.43786e12	−0.200097	−0.100049	−	0.994983i	$-0.531900\pi$
$809$	−2.43786e12	−0.200097	−0.100049	+	0.994983i	$0.531900\pi$
$810$	−5.33778e9	−0.000435690 0
$811$	1.21471e13	0.986002	0.493001	−	0.870029i	$-0.335900\pi$
$811$	1.21471e13	0.986002	0.493001	+	0.870029i	$0.335900\pi$
$812$	−3.71925e13	−3.00230
$813$	1.15260e12	0.0925277
$814$	−7.87066e9	−0.000628349 0
$815$	−5.37437e12	−0.426696
$816$	−1.10584e13	−0.873144
$817$	4.94549e12	0.388338
$818$	2.23013e10	0.00174157
$819$	1.44365e13	1.12120
$820$	−4.99629e11	−0.0385910
$821$	5.24507e12	0.402909	0.201455	−	0.979498i	$-0.435433\pi$
$821$	5.24507e12	0.402909	0.201455	+	0.979498i	$0.435433\pi$
$822$	4.47613e10	0.00341964
$823$	1.17862e13	0.895515	0.447758	−	0.894155i	$-0.352223\pi$
$823$	1.17862e13	0.895515	0.447758	+	0.894155i	$0.352223\pi$
$824$	−2.71016e11	−0.0204796
$825$	1.33292e11	0.0100176
$826$	−2.85084e11	−0.0213090
$827$	2.88395e12	0.214394	0.107197	−	0.994238i	$-0.465812\pi$
$827$	2.88395e12	0.214394	0.107197	+	0.994238i	$0.465812\pi$
$828$	−3.93021e12	−0.290589
$829$	3.09584e12	0.227658	0.113829	−	0.993500i	$-0.463688\pi$
$829$	3.09584e12	0.227658	0.113829	+	0.993500i	$0.463688\pi$
$830$	−4.41378e10	−0.00322819
$831$	2.61189e12	0.189999
$832$	−2.52105e13	−1.82400
$833$	5.03970e13	3.62662
$834$	3.68440e10	0.00263706
$835$	1.17790e13	0.838534
$836$	2.81068e11	0.0199014
$837$	6.79718e11	0.0478701
$838$	−1.23643e11	−0.00866110
$839$	−1.83575e11	−0.0127904	−0.00639519	−	0.999980i	$-0.502036\pi$
$839$	−1.83575e11	−0.0127904	−0.00639519	+	0.999980i	$0.502036\pi$
$840$	−1.20423e11	−0.00834548
$841$	2.39874e13	1.65349
$842$	1.12432e11	0.00770876
$843$	−7.17811e11	−0.0489537
$844$	5.70323e12	0.386883
$845$	−1.54432e13	−1.04204
$846$	−5.78676e10	−0.00388391
$847$	−2.74014e13	−1.82935
$848$	−2.30019e13	−1.52750
$849$	−7.55876e11	−0.0499305
$850$	4.03708e10	0.00265266
$851$	1.10184e13	0.720173
$852$	5.62165e12	0.365498
$853$	1.47458e13	0.953672	0.476836	−	0.878992i	$-0.341784\pi$
$853$	1.47458e13	0.953672	0.476836	+	0.878992i	$0.341784\pi$
$854$	−2.27858e10	−0.00146590
$855$	−5.34398e11	−0.0341993
$856$	−1.74456e10	−0.00111059
$857$	−1.52592e13	−0.966315	−0.483157	−	0.875534i	$-0.660510\pi$
$857$	−1.52592e13	−0.966315	−0.483157	+	0.875534i	$0.660510\pi$
$858$	1.27220e10	0.000801427 0
$859$	2.05951e13	1.29061	0.645305	−	0.763925i	$-0.276730\pi$
$859$	2.05951e13	1.29061	0.645305	+	0.763925i	$0.276730\pi$
$860$	1.21426e13	0.756952
$861$	1.48094e12	0.0918379
$862$	−2.04981e11	−0.0126454
$863$	1.60640e13	0.985840	0.492920	−	0.870075i	$-0.335930\pi$
$863$	1.60640e13	0.985840	0.492920	+	0.870075i	$0.335930\pi$
$864$	−8.29110e10	−0.00506174
$865$	−2.69886e12	−0.163911
$866$	1.43058e11	0.00864336
$867$	−1.23739e13	−0.743740
$868$	7.66708e12	0.458449
$869$	−2.31119e12	−0.137482
$870$	6.23168e10	0.00368781
$871$	1.56137e13	0.919227
$872$	8.07967e10	0.00473227
$873$	−6.32748e12	−0.368695
$874$	3.02527e10	0.00175373
$875$	−2.85864e12	−0.164863
$876$	−1.57601e13	−0.904254
$877$	4.60084e12	0.262627	0.131313	−	0.991341i	$-0.458081\pi$
$877$	4.60084e12	0.262627	0.131313	+	0.991341i	$0.458081\pi$
$878$	−2.90678e11	−0.0165077
$879$	−2.09129e12	−0.118158
$880$	6.90049e11	0.0387889
$881$	3.34648e12	0.187153	0.0935766	−	0.995612i	$-0.470170\pi$
$881$	3.34648e12	0.187153	0.0935766	+	0.995612i	$0.470170\pi$
$882$	1.25935e11	0.00700712
$883$	2.94374e13	1.62958	0.814792	−	0.579753i	$-0.196851\pi$
$883$	2.94374e13	1.62958	0.814792	+	0.579753i	$0.196851\pi$
$884$	−5.01158e13	−2.76019
$885$	−6.21267e12	−0.340434
$886$	1.49846e11	0.00816944
$887$	1.42855e13	0.774886	0.387443	−	0.921894i	$-0.373358\pi$
$887$	1.42855e13	0.774886	0.387443	+	0.921894i	$0.373358\pi$
$888$	1.54960e11	0.00836297
$889$	1.63992e12	0.0880570
$890$	−2.56899e10	−0.00137249
$891$	−1.81343e11	−0.00963941
$892$	2.39098e13	1.26454
$893$	−5.79348e12	−0.304865
$894$	−6.94710e10	−0.00363735
$895$	−4.83101e12	−0.251671
$896$	−1.24694e12	−0.0646339
$897$	−1.78101e13	−0.918544
$898$	−6.86424e9	−0.000352249 0
$899$	−7.93548e12	−0.405186
$900$	−1.31210e12	−0.0666615
$901$	−4.57183e13	−2.31115
$902$	1.30506e9	6.56451e−5 0
$903$	−3.59915e13	−1.80138
$904$	−1.34596e11	−0.00670306
$905$	1.33665e13	0.662368
$906$	−1.47680e11	−0.00728192
$907$	−2.35557e13	−1.15575	−0.577875	−	0.816125i	$-0.696118\pi$
$907$	−2.35557e13	−1.15575	−0.577875	+	0.816125i	$0.696118\pi$
$908$	1.99938e13	0.976134
$909$	1.03322e13	0.501944
$910$	−2.72842e11	−0.0131894
$911$	−1.41444e13	−0.680381	−0.340191	−	0.940357i	$-0.610492\pi$
$911$	−1.41444e13	−0.680381	−0.340191	+	0.940357i	$0.610492\pi$
$912$	−2.76655e12	−0.132423
$913$	−1.49952e12	−0.0714221
$914$	2.32714e10	0.00110297
$915$	−4.96556e11	−0.0234193
$916$	7.51971e12	0.352916
$917$	−5.61398e13	−2.62186
$918$	−5.49240e10	−0.00255253
$919$	−2.13484e12	−0.0987290	−0.0493645	−	0.998781i	$-0.515720\pi$
$919$	−2.13484e12	−0.0987290	−0.0493645	+	0.998781i	$0.515720\pi$
$920$	1.48564e11	0.00683704
$921$	−1.78101e13	−0.815638
$922$	−3.00643e11	−0.0137013
$923$	2.54750e13	1.15533
$924$	−2.04551e12	−0.0923161
$925$	3.67850e12	0.165209
$926$	−1.66523e11	−0.00744259
$927$	8.75267e12	0.389298
$928$	9.67958e11	0.0428441
$929$	−1.73687e13	−0.765064	−0.382532	−	0.923942i	$-0.624948\pi$
$929$	−1.73687e13	−0.765064	−0.382532	+	0.923942i	$0.624948\pi$
$930$	−1.28463e10	−0.000563127 0
$931$	1.26082e13	0.550020
$932$	1.11086e13	0.482267
$933$	2.30760e13	0.996995
$934$	−9.97239e10	−0.00428784
$935$	1.37154e12	0.0586887
$936$	−2.50475e11	−0.0106665
$937$	−1.06545e13	−0.451548	−0.225774	−	0.974180i	$-0.572491\pi$
$937$	−1.06545e13	−0.451548	−0.225774	+	0.974180i	$0.572491\pi$
$938$	1.93016e11	0.00814105
$939$	2.07520e13	0.871096
$940$	−1.42246e13	−0.594246
$941$	1.57584e13	0.655178	0.327589	−	0.944820i	$-0.393764\pi$
$941$	1.57584e13	0.655178	0.327589	+	0.944820i	$0.393764\pi$
$942$	−5.08724e10	−0.00210501
$943$	−1.82701e12	−0.0752382
$944$	−3.21627e13	−1.31819
$945$	3.88915e12	0.158640
$946$	−3.17172e10	−0.00128761
$947$	−2.86027e13	−1.15566	−0.577832	−	0.816156i	$-0.696101\pi$
$947$	−2.86027e13	−1.15566	−0.577832	+	0.816156i	$0.696101\pi$
$948$	2.27508e13	0.914869
$949$	−7.14182e13	−2.85832
$950$	1.00998e10	0.000402308 0
$951$	−4.89919e12	−0.194228
$952$	−1.23911e12	−0.0488927
$953$	−3.75406e13	−1.47429	−0.737145	−	0.675734i	$-0.763827\pi$
$953$	−3.75406e13	−1.47429	−0.737145	+	0.675734i	$0.763827\pi$
$954$	−1.14244e11	−0.00446546
$955$	−2.01380e13	−0.783433
$956$	3.56121e13	1.37891
$957$	2.11712e12	0.0815908
$958$	1.45480e11	0.00558030
$959$	−3.26135e13	−1.24513
$960$	−6.79164e12	−0.258080
$961$	−2.48038e13	−0.938128
$962$	3.51093e11	0.0132170
$963$	5.63419e11	0.0211112
$964$	−5.27325e13	−1.96667
$965$	−3.00567e11	−0.0111575
$966$	−2.20168e11	−0.00813500
$967$	−3.29746e13	−1.21272	−0.606359	−	0.795191i	$-0.707371\pi$
$967$	−3.29746e13	−1.21272	−0.606359	+	0.795191i	$0.707371\pi$
$968$	4.75419e11	0.0174035
$969$	−5.49878e12	−0.200359
$970$	1.19586e11	0.00433719
$971$	−3.79455e13	−1.36985	−0.684925	−	0.728613i	$-0.740165\pi$
$971$	−3.79455e13	−1.36985	−0.684925	+	0.728613i	$0.740165\pi$
$972$	1.78510e12	0.0641451
$973$	−2.68448e13	−0.960181
$974$	−1.40372e11	−0.00499764
$975$	−5.94588e12	−0.210715
$976$	−2.57065e12	−0.0906816
$977$	1.08658e13	0.381536	0.190768	−	0.981635i	$-0.438902\pi$
$977$	1.08658e13	0.381536	0.190768	+	0.981635i	$0.438902\pi$
$978$	−1.38189e11	−0.00483001
$979$	−8.72776e11	−0.0303655
$980$	3.09567e13	1.07210
$981$	−2.60940e12	−0.0899559
$982$	−3.03953e11	−0.0104305
$983$	3.71055e13	1.26750	0.633749	−	0.773539i	$-0.281515\pi$
$983$	3.71055e13	1.26750	0.633749	+	0.773539i	$0.281515\pi$
$984$	−2.56945e10	−0.000873699 0
$985$	2.02799e13	0.686440
$986$	6.41219e11	0.0216053
$987$	4.21628e13	1.41417
$988$	−1.25378e13	−0.418616
$989$	4.44022e13	1.47578
$990$	3.42729e9	0.000113395 0
$991$	−2.68561e13	−0.884527	−0.442264	−	0.896885i	$-0.645824\pi$
$991$	−2.68561e13	−0.884527	−0.442264	+	0.896885i	$0.645824\pi$
$992$	−1.99540e11	−0.00654227
$993$	−3.29917e12	−0.107679
$994$	3.14921e11	0.0102321
$995$	1.44273e13	0.466639
$996$	1.47609e13	0.475275
$997$	−4.67453e13	−1.49834	−0.749168	−	0.662380i	$-0.769547\pi$
$997$	−4.67453e13	−1.49834	−0.749168	+	0.662380i	$0.769547\pi$
$998$	−3.63717e11	−0.0116058
$999$	−5.00456e12	−0.158972

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	285.10.a.f.1.8	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.10.a.f.1.8	✓	14	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	285.a (trivial)

\(f(q)\)	\(=\)	\(q+0.198399 q^{2} -81.0000 q^{3} -511.961 q^{4} -625.000 q^{5} -16.0704 q^{6} +11709.0 q^{7} -203.153 q^{8} +6561.00 q^{9} -124.000 q^{10} -4212.70 q^{11} +41468.8 q^{12} +187919. q^{13} +2323.06 q^{14} +50625.0 q^{15} +262084. q^{16} +520915. q^{17} +1301.70 q^{18} +130321. q^{19} +319975. q^{20} -948429. q^{21} -835.796 q^{22} +1.17006e6 q^{23} +16455.4 q^{24} +390625. q^{25} +37283.1 q^{26} -531441. q^{27} -5.99455e6 q^{28} +6.20440e6 q^{29} +10044.0 q^{30} -1.27901e6 q^{31} +156012. q^{32} +341228. q^{33} +103349. q^{34} -7.31812e6 q^{35} -3.35897e6 q^{36} +9.41695e6 q^{37} +25855.6 q^{38} -1.52215e7 q^{39} +126971. q^{40} -1.56146e6 q^{41} -188168. q^{42} +3.79485e7 q^{43} +2.15673e6 q^{44} -4.10062e6 q^{45} +232140. q^{46} -4.44554e7 q^{47} -2.12288e7 q^{48} +9.67470e7 q^{49} +77499.8 q^{50} -4.21941e7 q^{51} -9.62073e7 q^{52} -8.77655e7 q^{53} -105438. q^{54} +2.63294e6 q^{55} -2.37872e6 q^{56} -1.05560e7 q^{57} +1.23095e6 q^{58} -1.22719e8 q^{59} -2.59180e7 q^{60} -9.80852e6 q^{61} -253755. q^{62} +7.68227e7 q^{63} -1.34156e8 q^{64} -1.17450e8 q^{65} +67699.5 q^{66} +8.30870e7 q^{67} -2.66688e8 q^{68} -9.47752e7 q^{69} -1.45191e6 q^{70} +1.35563e8 q^{71} -1.33289e6 q^{72} -3.80047e8 q^{73} +1.86832e6 q^{74} -3.16406e7 q^{75} -6.67192e7 q^{76} -4.93265e7 q^{77} -3.01993e6 q^{78} +5.48624e8 q^{79} -1.63802e8 q^{80} +4.30467e7 q^{81} -309793. q^{82} +3.55951e8 q^{83} +4.85558e8 q^{84} -3.25572e8 q^{85} +7.52896e6 q^{86} -5.02556e8 q^{87} +855823. q^{88} +2.07178e8 q^{89} -813562. q^{90} +2.20035e9 q^{91} -5.99027e8 q^{92} +1.03600e8 q^{93} -8.81993e6 q^{94} -8.14506e7 q^{95} -1.26369e7 q^{96} -9.64409e8 q^{97} +1.91945e7 q^{98} -2.76395e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} - 1134 q^{3} + 3563 q^{4} - 8750 q^{5} + 81 q^{6} + 13054 q^{7} + 6249 q^{8} + 91854 q^{9} + 625 q^{10} + 43520 q^{11} - 288603 q^{12} + 256834 q^{13} + 250610 q^{14} + 708750 q^{15} + 866291 q^{16}+ \cdots + 285534720 q^{99}+O(q^{100}) \) 14 * q - q^2 - 1134 * q^3 + 3563 * q^4 - 8750 * q^5 + 81 * q^6 + 13054 * q^7 + 6249 * q^8 + 91854 * q^9 + 625 * q^10 + 43520 * q^11 - 288603 * q^12 + 256834 * q^13 + 250610 * q^14 + 708750 * q^15 + 866291 * q^16 - 91412 * q^17 - 6561 * q^18 + 1824494 * q^19 - 2226875 * q^20 - 1057374 * q^21 + 5028672 * q^22 - 1629286 * q^23 - 506169 * q^24 + 5468750 * q^25 - 5525738 * q^26 - 7440174 * q^27 + 2214066 * q^28 - 3136160 * q^29 - 50625 * q^30 + 216848 * q^31 - 5019923 * q^32 - 3525120 * q^33 + 14499560 * q^34 - 8158750 * q^35 + 23376843 * q^36 + 29450026 * q^37 - 130321 * q^38 - 20803554 * q^39 - 3905625 * q^40 - 18243760 * q^41 - 20299410 * q^42 + 26051662 * q^43 - 66833140 * q^44 - 57408750 * q^45 - 87479176 * q^46 + 15959554 * q^47 - 70169571 * q^48 + 120608310 * q^49 - 390625 * q^50 + 7404372 * q^51 - 76766782 * q^52 + 24009130 * q^53 + 531441 * q^54 - 27200000 * q^55 - 248644798 * q^56 - 147784014 * q^57 - 208603522 * q^58 - 51606384 * q^59 + 180376875 * q^60 - 267404032 * q^61 + 211868546 * q^62 + 85647294 * q^63 - 647618425 * q^64 - 160521250 * q^65 - 407322432 * q^66 + 354061992 * q^67 - 690026380 * q^68 + 131972166 * q^69 - 156631250 * q^70 + 178030792 * q^71 + 40999689 * q^72 + 571450504 * q^73 + 406967766 * q^74 - 442968750 * q^75 + 464333723 * q^76 + 922830092 * q^77 + 447584778 * q^78 + 456688676 * q^79 - 541431875 * q^80 + 602654094 * q^81 + 1477406200 * q^82 + 275098162 * q^83 - 179339346 * q^84 + 57132500 * q^85 - 909539740 * q^86 + 254028960 * q^87 + 1278025456 * q^88 - 2005727664 * q^89 + 4100625 * q^90 - 181709276 * q^91 + 209371504 * q^92 - 17564688 * q^93 - 617421584 * q^94 - 1140308750 * q^95 + 406613763 * q^96 + 1606885598 * q^97 - 3483053209 * q^98 + 285534720 * q^99

Introduction

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