LMFDB - Embedded newform 35.10.a.c.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [35,10,Mod(1,35)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("35.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	35.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$18.0262542657$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 648x^{2} + 6926x - 8308 $ x^4 - x^3 - 648x^2 + 6926x - 8308
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 3^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-29.3917$ of defining polynomial
Character	$\chi$	$=$	35.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+15.4436 q^{2} +137.736 q^{3} -273.496 q^{4} -625.000 q^{5} +2127.13 q^{6} -2401.00 q^{7} -12130.9 q^{8} -711.820 q^{9} -9652.23 q^{10} -8060.89 q^{11} -37670.3 q^{12} -137129. q^{13} -37080.0 q^{14} -86084.9 q^{15} -47313.7 q^{16} -23676.1 q^{17} -10993.0 q^{18} +572389. q^{19} +170935. q^{20} -330704. q^{21} -124489. q^{22} -997700. q^{23} -1.67086e6 q^{24} +390625. q^{25} -2.11777e6 q^{26} -2.80910e6 q^{27} +656664. q^{28} +1.97927e6 q^{29} -1.32946e6 q^{30} -8.47740e6 q^{31} +5.48031e6 q^{32} -1.11027e6 q^{33} -365643. q^{34} +1.50062e6 q^{35} +194680. q^{36} -4.33062e6 q^{37} +8.83972e6 q^{38} -1.88876e7 q^{39} +7.58179e6 q^{40} -1.48554e7 q^{41} -5.10725e6 q^{42} +3.14842e7 q^{43} +2.20462e6 q^{44} +444888. q^{45} -1.54081e7 q^{46} +2.31045e7 q^{47} -6.51680e6 q^{48} +5.76480e6 q^{49} +6.03264e6 q^{50} -3.26104e6 q^{51} +3.75044e7 q^{52} -6.79444e6 q^{53} -4.33825e7 q^{54} +5.03805e6 q^{55} +2.91262e7 q^{56} +7.88385e7 q^{57} +3.05671e7 q^{58} +8.85117e7 q^{59} +2.35439e7 q^{60} +1.24823e8 q^{61} -1.30921e8 q^{62} +1.70908e6 q^{63} +1.08860e8 q^{64} +8.57059e7 q^{65} -1.71466e7 q^{66} +9.58712e7 q^{67} +6.47531e6 q^{68} -1.37419e8 q^{69} +2.31750e7 q^{70} -2.16795e8 q^{71} +8.63500e6 q^{72} -1.50701e8 q^{73} -6.68803e7 q^{74} +5.38031e7 q^{75} -1.56546e8 q^{76} +1.93542e7 q^{77} -2.91693e8 q^{78} -3.89487e8 q^{79} +2.95711e7 q^{80} -3.72903e8 q^{81} -2.29420e8 q^{82} -7.43467e8 q^{83} +9.04463e7 q^{84} +1.47975e7 q^{85} +4.86228e8 q^{86} +2.72617e8 q^{87} +9.77855e7 q^{88} +2.64429e8 q^{89} +6.87065e6 q^{90} +3.29248e8 q^{91} +2.72867e8 q^{92} -1.16764e9 q^{93} +3.56816e8 q^{94} -3.57743e8 q^{95} +7.54835e8 q^{96} +1.39343e9 q^{97} +8.90291e7 q^{98} +5.73790e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 19 q^{2} - 18 q^{3} + 1729 q^{4} - 2500 q^{5} - 144 q^{6} - 9604 q^{7} - 30495 q^{8} + 5382 q^{9} + 11875 q^{10} + 82438 q^{11} + 41328 q^{12} - 72962 q^{13} + 45619 q^{14} + 11250 q^{15} + 64257 q^{16}+ \cdots + 1222369524 q^{99}+O(q^{100}) $ 4 * q - 19 * q^2 - 18 * q^3 + 1729 * q^4 - 2500 * q^5 - 144 * q^6 - 9604 * q^7 - 30495 * q^8 + 5382 * q^9 + 11875 * q^10 + 82438 * q^11 + 41328 * q^12 - 72962 * q^13 + 45619 * q^14 + 11250 * q^15 + 64257 * q^16 - 357542 * q^17 - 965367 * q^18 + 300732 * q^19 - 1080625 * q^20 + 43218 * q^21 - 5595068 * q^22 - 2340836 * q^23 - 7636320 * q^24 + 1562500 * q^25 + 1305666 * q^26 - 4240350 * q^27 - 4151329 * q^28 - 1372022 * q^29 + 90000 * q^30 - 4590888 * q^31 - 10529439 * q^32 + 2000034 * q^33 - 7199478 * q^34 + 6002500 * q^35 - 9144243 * q^36 - 38868456 * q^37 - 15477280 * q^38 - 46666242 * q^39 + 19059375 * q^40 + 57287084 * q^41 + 345744 * q^42 - 43403452 * q^43 + 87639348 * q^44 - 3363750 * q^45 + 28892416 * q^46 + 91822222 * q^47 + 156168864 * q^48 + 23059204 * q^49 - 7421875 * q^50 + 86342634 * q^51 + 1953386 * q^52 - 61086884 * q^53 + 187589520 * q^54 - 51523750 * q^55 + 73218495 * q^56 - 79928892 * q^57 + 29615390 * q^58 + 72569680 * q^59 - 25830000 * q^60 - 225681036 * q^61 + 190286472 * q^62 - 12922182 * q^63 + 141443393 * q^64 + 45601250 * q^65 - 119673648 * q^66 - 4429720 * q^67 + 15339698 * q^68 + 348300612 * q^69 - 28511875 * q^70 - 470468984 * q^71 + 298610685 * q^72 - 168326464 * q^73 + 927809502 * q^74 - 7031250 * q^75 - 892265344 * q^76 - 197933638 * q^77 + 281290896 * q^78 - 598805646 * q^79 - 40160625 * q^80 - 847155996 * q^81 - 1821993318 * q^82 - 1159074304 * q^83 - 99228528 * q^84 + 223463750 * q^85 + 706791156 * q^86 - 421480998 * q^87 - 1992103900 * q^88 - 1380153012 * q^89 + 603354375 * q^90 + 175181762 * q^91 + 710319264 * q^92 - 1601969400 * q^93 + 2466744152 * q^94 - 187957500 * q^95 - 799321824 * q^96 + 754874082 * q^97 - 109531219 * q^98 + 1222369524 * 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 $

$2$	15.4436	0.682516	0.341258	−	0.939970i	$-0.389147\pi$
$2$	15.4436	0.682516	0.341258	+	0.939970i	$0.389147\pi$
$3$	137.736	0.981751	0.490876	−	0.871230i	$-0.336677\pi$
$3$	137.736	0.981751	0.490876	+	0.871230i	$0.336677\pi$
$4$	−273.496	−0.534172
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	2127.13	0.670061
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−12130.9	−1.04710
$9$	−711.820	−0.0361642
$10$	−9652.23	−0.305230
$11$	−8060.89	−0.166003	−0.0830015	−	0.996549i	$-0.526451\pi$
$11$	−8060.89	−0.166003	−0.0830015	+	0.996549i	$0.526451\pi$
$12$	−37670.3	−0.524424
$13$	−137129.	−1.33164	−0.665818	−	0.746114i	$-0.731917\pi$
$13$	−137129.	−1.33164	−0.665818	+	0.746114i	$0.731917\pi$
$14$	−37080.0	−0.257967
$15$	−86084.9	−0.439053
$16$	−47313.7	−0.180488
$17$	−23676.1	−0.0687526	−0.0343763	−	0.999409i	$-0.510944\pi$
$17$	−23676.1	−0.0687526	−0.0343763	+	0.999409i	$0.510944\pi$
$18$	−10993.0	−0.0246826
$19$	572389.	1.00763	0.503814	−	0.863812i	$-0.331930\pi$
$19$	572389.	1.00763	0.503814	+	0.863812i	$0.331930\pi$
$20$	170935.	0.238889
$21$	−330704.	−0.371067
$22$	−124489.	−0.113300
$23$	−997700.	−0.743404	−0.371702	−	0.928352i	$-0.621226\pi$
$23$	−997700.	−0.743404	−0.371702	+	0.928352i	$0.621226\pi$
$24$	−1.67086e6	−1.02799
$25$	390625.	0.200000
$26$	−2.11777e6	−0.908862
$27$	−2.80910e6	−1.01726
$28$	656664.	0.201898
$29$	1.97927e6	0.519655	0.259827	−	0.965655i	$-0.416334\pi$
$29$	1.97927e6	0.519655	0.259827	+	0.965655i	$0.416334\pi$
$30$	−1.32946e6	−0.299660
$31$	−8.47740e6	−1.64867	−0.824337	−	0.566099i	$-0.808452\pi$
$31$	−8.47740e6	−1.64867	−0.824337	+	0.566099i	$0.808452\pi$
$32$	5.48031e6	0.923911
$33$	−1.11027e6	−0.162974
$34$	−365643.	−0.0469247
$35$	1.50062e6	0.169031
$36$	194680.	0.0193179
$37$	−4.33062e6	−0.379877	−0.189938	−	0.981796i	$-0.560829\pi$
$37$	−4.33062e6	−0.379877	−0.189938	+	0.981796i	$0.560829\pi$
$38$	8.83972e6	0.687721
$39$	−1.88876e7	−1.30734
$40$	7.58179e6	0.468276
$41$	−1.48554e7	−0.821024	−0.410512	−	0.911855i	$-0.634650\pi$
$41$	−1.48554e7	−0.821024	−0.410512	+	0.911855i	$0.634650\pi$
$42$	−5.10725e6	−0.253259
$43$	3.14842e7	1.40438	0.702189	−	0.711991i	$-0.252206\pi$
$43$	3.14842e7	1.40438	0.702189	+	0.711991i	$0.252206\pi$
$44$	2.20462e6	0.0886742
$45$	444888.	0.0161731
$46$	−1.54081e7	−0.507385
$47$	2.31045e7	0.690647	0.345324	−	0.938484i	$-0.387769\pi$
$47$	2.31045e7	0.690647	0.345324	+	0.938484i	$0.387769\pi$
$48$	−6.51680e6	−0.177194
$49$	5.76480e6	0.142857
$50$	6.03264e6	0.136503
$51$	−3.26104e6	−0.0674980
$52$	3.75044e7	0.711323
$53$	−6.79444e6	−0.118280	−0.0591401	−	0.998250i	$-0.518836\pi$
$53$	−6.79444e6	−0.118280	−0.0591401	+	0.998250i	$0.518836\pi$
$54$	−4.33825e7	−0.694293
$55$	5.03805e6	0.0742388
$56$	2.91262e7	0.395765
$57$	7.88385e7	0.989239
$58$	3.05671e7	0.354673
$59$	8.85117e7	0.950969	0.475485	−	0.879724i	$-0.342273\pi$
$59$	8.85117e7	0.950969	0.475485	+	0.879724i	$0.342273\pi$
$60$	2.35439e7	0.234530
$61$	1.24823e8	1.15428	0.577138	−	0.816647i	$-0.304169\pi$
$61$	1.24823e8	1.15428	0.577138	+	0.816647i	$0.304169\pi$
$62$	−1.30921e8	−1.12525
$63$	1.70908e6	0.0136688
$64$	1.08860e8	0.811071
$65$	8.57059e7	0.595526
$66$	−1.71466e7	−0.111232
$67$	9.58712e7	0.581235	0.290617	−	0.956839i	$-0.406139\pi$
$67$	9.58712e7	0.581235	0.290617	+	0.956839i	$0.406139\pi$
$68$	6.47531e6	0.0367257
$69$	−1.37419e8	−0.729838
$70$	2.31750e7	0.115366
$71$	−2.16795e8	−1.01248	−0.506241	−	0.862392i	$-0.668965\pi$
$71$	−2.16795e8	−1.01248	−0.506241	+	0.862392i	$0.668965\pi$
$72$	8.63500e6	0.0378674
$73$	−1.50701e8	−0.621101	−0.310551	−	0.950557i	$-0.600513\pi$
$73$	−1.50701e8	−0.621101	−0.310551	+	0.950557i	$0.600513\pi$
$74$	−6.68803e7	−0.259272
$75$	5.38031e7	0.196350
$76$	−1.56546e8	−0.538247
$77$	1.93542e7	0.0627432
$78$	−2.91693e8	−0.892277
$79$	−3.89487e8	−1.12505	−0.562523	−	0.826781i	$-0.690169\pi$
$79$	−3.89487e8	−1.12505	−0.562523	+	0.826781i	$0.690169\pi$
$80$	2.95711e7	0.0807165
$81$	−3.72903e8	−0.962528
$82$	−2.29420e8	−0.560362
$83$	−7.43467e8	−1.71953	−0.859766	−	0.510688i	$-0.829391\pi$
$83$	−7.43467e8	−1.71953	−0.859766	+	0.510688i	$0.829391\pi$
$84$	9.04463e7	0.198214
$85$	1.47975e7	0.0307471
$86$	4.86228e8	0.958510
$87$	2.72617e8	0.510172
$88$	9.77855e7	0.173821
$89$	2.64429e8	0.446739	0.223369	−	0.974734i	$-0.428294\pi$
$89$	2.64429e8	0.446739	0.223369	+	0.974734i	$0.428294\pi$
$90$	6.87065e6	0.0110384
$91$	3.29248e8	0.503311
$92$	2.72867e8	0.397106
$93$	−1.16764e9	−1.61859
$94$	3.56816e8	0.471378
$95$	−3.57743e8	−0.450625
$96$	7.54835e8	0.907051
$97$	1.39343e9	1.59813	0.799063	−	0.601248i	$-0.205329\pi$
$97$	1.39343e9	1.59813	0.799063	+	0.601248i	$0.205329\pi$
$98$	8.90291e7	0.0975022
$99$	5.73790e6	0.00600337
$100$	−1.06834e8	−0.106834
$101$	−6.43863e8	−0.615669	−0.307834	−	0.951440i	$-0.599604\pi$
$101$	−6.43863e8	−0.615669	−0.307834	+	0.951440i	$0.599604\pi$
$102$	−5.03621e7	−0.0460684
$103$	−9.64216e8	−0.844125	−0.422063	−	0.906567i	$-0.638694\pi$
$103$	−9.64216e8	−0.844125	−0.422063	+	0.906567i	$0.638694\pi$
$104$	1.66350e9	1.39435
$105$	2.06690e8	0.165946
$106$	−1.04930e8	−0.0807281
$107$	−1.97477e9	−1.45643	−0.728215	−	0.685348i	$-0.759650\pi$
$107$	−1.97477e9	−1.45643	−0.728215	+	0.685348i	$0.759650\pi$
$108$	7.68278e8	0.543390
$109$	1.03957e9	0.705401	0.352701	−	0.935736i	$-0.385263\pi$
$109$	1.03957e9	0.705401	0.352701	+	0.935736i	$0.385263\pi$
$110$	7.78055e7	0.0506691
$111$	−5.96482e8	−0.372944
$112$	1.13600e8	0.0682179
$113$	5.48265e8	0.316328	0.158164	−	0.987413i	$-0.449443\pi$
$113$	5.48265e8	0.316328	0.158164	+	0.987413i	$0.449443\pi$
$114$	1.21755e9	0.675171
$115$	6.23563e8	0.332460
$116$	−5.41324e8	−0.277585
$117$	9.76115e7	0.0481576
$118$	1.36694e9	0.649052
$119$	5.68462e7	0.0259860
$120$	1.04428e9	0.459730
$121$	−2.29297e9	−0.972443
$122$	1.92771e9	0.787811
$123$	−2.04612e9	−0.806042
$124$	2.31854e9	0.880676
$125$	−2.44141e8	−0.0894427
$126$	2.63943e7	0.00932916
$127$	−5.40565e9	−1.84387	−0.921936	−	0.387341i	$-0.873394\pi$
$127$	−5.40565e9	−1.84387	−0.921936	+	0.387341i	$0.873394\pi$
$128$	−1.12473e9	−0.370342
$129$	4.33650e9	1.37875
$130$	1.32360e9	0.406456
$131$	−1.81287e9	−0.537832	−0.268916	−	0.963164i	$-0.586665\pi$
$131$	−1.81287e9	−0.537832	−0.268916	+	0.963164i	$0.586665\pi$
$132$	3.03656e8	0.0870560
$133$	−1.37431e9	−0.380847
$134$	1.48059e9	0.396702
$135$	1.75569e9	0.454931
$136$	2.87211e8	0.0719906
$137$	−7.50191e8	−0.181940	−0.0909702	−	0.995854i	$-0.528997\pi$
$137$	−7.50191e8	−0.181940	−0.0909702	+	0.995854i	$0.528997\pi$
$138$	−2.12224e9	−0.498126
$139$	6.59090e9	1.49754	0.748769	−	0.662831i	$-0.230645\pi$
$139$	6.59090e9	1.49754	0.748769	+	0.662831i	$0.230645\pi$
$140$	−4.10415e8	−0.0902916
$141$	3.18232e9	0.678044
$142$	−3.34809e9	−0.691035
$143$	1.10538e9	0.221055
$144$	3.36789e7	0.00652719
$145$	−1.23705e9	−0.232397
$146$	−2.32736e9	−0.423911
$147$	7.94020e8	0.140250
$148$	1.18441e9	0.202920
$149$	−3.29437e9	−0.547564	−0.273782	−	0.961792i	$-0.588275\pi$
$149$	−3.29437e9	−0.547564	−0.273782	+	0.961792i	$0.588275\pi$
$150$	8.30912e8	0.134012
$151$	−1.04401e10	−1.63421	−0.817103	−	0.576492i	$-0.804421\pi$
$151$	−1.04401e10	−1.63421	−0.817103	+	0.576492i	$0.804421\pi$
$152$	−6.94357e9	−1.05508
$153$	1.68531e7	0.00248638
$154$	2.98898e8	0.0428232
$155$	5.29837e9	0.737310
$156$	5.16570e9	0.698342
$157$	−4.88247e9	−0.641344	−0.320672	−	0.947190i	$-0.603909\pi$
$157$	−4.88247e9	−0.641344	−0.320672	+	0.947190i	$0.603909\pi$
$158$	−6.01506e9	−0.767862
$159$	−9.35838e8	−0.116122
$160$	−3.42519e9	−0.413186
$161$	2.39548e9	0.280980
$162$	−5.75895e9	−0.656940
$163$	−1.00685e10	−1.11717	−0.558584	−	0.829448i	$-0.688655\pi$
$163$	−1.00685e10	−1.11717	−0.558584	+	0.829448i	$0.688655\pi$
$164$	4.06289e9	0.438568
$165$	6.93921e8	0.0728840
$166$	−1.14818e10	−1.17361
$167$	1.11826e10	1.11255	0.556273	−	0.831000i	$-0.312231\pi$
$167$	1.11826e10	1.11255	0.556273	+	0.831000i	$0.312231\pi$
$168$	4.01172e9	0.388543
$169$	8.19997e9	0.773254
$170$	2.28527e8	0.0209854
$171$	−4.07438e8	−0.0364400
$172$	−8.61080e9	−0.750180
$173$	−1.55595e10	−1.32065	−0.660325	−	0.750980i	$-0.729582\pi$
$173$	−1.55595e10	−1.32065	−0.660325	+	0.750980i	$0.729582\pi$
$174$	4.21018e9	0.348200
$175$	−9.37891e8	−0.0755929
$176$	3.81391e8	0.0299615
$177$	1.21912e10	0.933616
$178$	4.08372e9	0.304906
$179$	−1.14811e10	−0.835884	−0.417942	−	0.908474i	$-0.637248\pi$
$179$	−1.14811e10	−0.835884	−0.417942	+	0.908474i	$0.637248\pi$
$180$	−1.21675e8	−0.00863924
$181$	1.64859e10	1.14172	0.570860	−	0.821047i	$-0.306610\pi$
$181$	1.64859e10	1.14172	0.570860	+	0.821047i	$0.306610\pi$
$182$	5.08476e9	0.343518
$183$	1.71926e10	1.13321
$184$	1.21030e10	0.778416
$185$	2.70664e9	0.169886
$186$	−1.80326e10	−1.10471
$187$	1.90850e8	0.0114131
$188$	−6.31900e9	−0.368925
$189$	6.74465e9	0.384486
$190$	−5.52483e9	−0.307558
$191$	1.75186e10	0.952466	0.476233	−	0.879319i	$-0.342002\pi$
$191$	1.75186e10	0.952466	0.476233	+	0.879319i	$0.342002\pi$
$192$	1.49940e10	0.796270
$193$	−2.51278e10	−1.30361	−0.651805	−	0.758387i	$-0.725988\pi$
$193$	−2.51278e10	−1.30361	−0.651805	+	0.758387i	$0.725988\pi$
$194$	2.15195e10	1.09075
$195$	1.18048e10	0.584658
$196$	−1.57665e9	−0.0763103
$197$	3.28481e10	1.55386	0.776930	−	0.629587i	$-0.216776\pi$
$197$	3.28481e10	1.55386	0.776930	+	0.629587i	$0.216776\pi$
$198$	8.86137e7	0.00409739
$199$	−3.56924e9	−0.161338	−0.0806691	−	0.996741i	$-0.525706\pi$
$199$	−3.56924e9	−0.161338	−0.0806691	+	0.996741i	$0.525706\pi$
$200$	−4.73862e9	−0.209419
$201$	1.32049e10	0.570628
$202$	−9.94354e9	−0.420204
$203$	−4.75224e9	−0.196411
$204$	8.91883e8	0.0360556
$205$	9.28460e9	0.367173
$206$	−1.48909e10	−0.576129
$207$	7.10183e8	0.0268846
$208$	6.48810e9	0.240344
$209$	−4.61396e9	−0.167269
$210$	3.19203e9	0.113261
$211$	−8.88255e9	−0.308508	−0.154254	−	0.988031i	$-0.549297\pi$
$211$	−8.88255e9	−0.308508	−0.154254	+	0.988031i	$0.549297\pi$
$212$	1.85825e9	0.0631820
$213$	−2.98605e10	−0.994006
$214$	−3.04975e10	−0.994037
$215$	−1.96776e10	−0.628057
$216$	3.40768e10	1.06517
$217$	2.03542e10	0.623140
$218$	1.60547e10	0.481447
$219$	−2.07569e10	−0.609767
$220$	−1.37789e9	−0.0396563
$221$	3.24668e9	0.0915534
$222$	−9.21182e9	−0.254540
$223$	1.85138e10	0.501330	0.250665	−	0.968074i	$-0.419351\pi$
$223$	1.85138e10	0.501330	0.250665	+	0.968074i	$0.419351\pi$
$224$	−1.31582e10	−0.349206
$225$	−2.78055e8	−0.00723284
$226$	8.46716e9	0.215899
$227$	6.91501e10	1.72853	0.864265	−	0.503037i	$-0.167784\pi$
$227$	6.91501e10	1.72853	0.864265	+	0.503037i	$0.167784\pi$
$228$	−2.15620e10	−0.528424
$229$	−4.14990e10	−0.997190	−0.498595	−	0.866835i	$-0.666150\pi$
$229$	−4.14990e10	−0.997190	−0.498595	+	0.866835i	$0.666150\pi$
$230$	9.63003e9	0.226909
$231$	2.66577e9	0.0615982
$232$	−2.40103e10	−0.544129
$233$	1.06684e10	0.237136	0.118568	−	0.992946i	$-0.462170\pi$
$233$	1.06684e10	0.237136	0.118568	+	0.992946i	$0.462170\pi$
$234$	1.50747e9	0.0328683
$235$	−1.44403e10	−0.308867
$236$	−2.42076e10	−0.507982
$237$	−5.36463e10	−1.10452
$238$	8.77908e8	0.0177359
$239$	6.89311e9	0.136655	0.0683274	−	0.997663i	$-0.478234\pi$
$239$	6.89311e9	0.136655	0.0683274	+	0.997663i	$0.478234\pi$
$240$	4.07300e9	0.0792435
$241$	−2.72593e10	−0.520520	−0.260260	−	0.965539i	$-0.583808\pi$
$241$	−2.72593e10	−0.520520	−0.260260	+	0.965539i	$0.583808\pi$
$242$	−3.54116e10	−0.663708
$243$	3.92936e9	0.0722925
$244$	−3.41386e10	−0.616582
$245$	−3.60300e9	−0.0638877
$246$	−3.15993e10	−0.550136
$247$	−7.84913e10	−1.34179
$248$	1.02838e11	1.72632
$249$	−1.02402e11	−1.68815
$250$	−3.77040e9	−0.0610461
$251$	1.11185e11	1.76812	0.884062	−	0.467370i	$-0.154798\pi$
$251$	1.11185e11	1.76812	0.884062	+	0.467370i	$0.154798\pi$
$252$	−4.67427e8	−0.00730149
$253$	8.04235e9	0.123407
$254$	−8.34825e10	−1.25847
$255$	2.03815e9	0.0301860
$256$	−7.31062e10	−1.06384
$257$	−3.84555e10	−0.549869	−0.274935	−	0.961463i	$-0.588656\pi$
$257$	−3.84555e10	−0.549869	−0.274935	+	0.961463i	$0.588656\pi$
$258$	6.69710e10	0.941018
$259$	1.03978e10	0.143580
$260$	−2.34402e10	−0.318113
$261$	−1.40889e9	−0.0187929
$262$	−2.79972e10	−0.367079
$263$	1.50225e11	1.93616	0.968082	−	0.250634i	$-0.0806390\pi$
$263$	1.50225e11	1.93616	0.968082	+	0.250634i	$0.0806390\pi$
$264$	1.34686e10	0.170649
$265$	4.24653e9	0.0528965
$266$	−2.12242e10	−0.259934
$267$	3.64213e10	0.438587
$268$	−2.62204e10	−0.310479
$269$	9.22583e10	1.07429	0.537143	−	0.843491i	$-0.319503\pi$
$269$	9.22583e10	1.07429	0.537143	+	0.843491i	$0.319503\pi$
$270$	2.71141e10	0.310497
$271$	−1.10392e11	−1.24330	−0.621649	−	0.783296i	$-0.713537\pi$
$271$	−1.10392e11	−1.24330	−0.621649	+	0.783296i	$0.713537\pi$
$272$	1.12020e9	0.0124090
$273$	4.53492e10	0.494126
$274$	−1.15856e10	−0.124177
$275$	−3.14878e9	−0.0332006
$276$	3.75836e10	0.389859
$277$	1.06151e11	1.08334	0.541672	−	0.840590i	$-0.317792\pi$
$277$	1.06151e11	1.08334	0.541672	+	0.840590i	$0.317792\pi$
$278$	1.01787e11	1.02209
$279$	6.03438e9	0.0596230
$280$	−1.82039e10	−0.176992
$281$	1.69943e11	1.62602	0.813008	−	0.582252i	$-0.197828\pi$
$281$	1.69943e11	1.62602	0.813008	+	0.582252i	$0.197828\pi$
$282$	4.91464e10	0.462776
$283$	−6.63477e10	−0.614875	−0.307438	−	0.951568i	$-0.599472\pi$
$283$	−6.63477e10	−0.614875	−0.307438	+	0.951568i	$0.599472\pi$
$284$	5.92927e10	0.540840
$285$	−4.92740e10	−0.442401
$286$	1.70711e10	0.150874
$287$	3.56677e10	0.310318
$288$	−3.90100e9	−0.0334125
$289$	−1.18027e11	−0.995273
$290$	−1.91044e10	−0.158614
$291$	1.91925e11	1.56896
$292$	4.12161e10	0.331775
$293$	7.54377e9	0.0597976	0.0298988	−	0.999553i	$-0.490481\pi$
$293$	7.54377e9	0.0597976	0.0298988	+	0.999553i	$0.490481\pi$
$294$	1.22625e10	0.0957230
$295$	−5.53198e10	−0.425286
$296$	5.25342e10	0.397768
$297$	2.26438e10	0.168867
$298$	−5.08769e10	−0.373721
$299$	1.36814e11	0.989943
$300$	−1.47149e10	−0.104885
$301$	−7.55935e10	−0.530805
$302$	−1.61232e11	−1.11537
$303$	−8.86830e10	−0.604434
$304$	−2.70818e10	−0.181864
$305$	−7.80142e10	−0.516208
$306$	2.60272e8	0.00169700
$307$	−9.90848e10	−0.636626	−0.318313	−	0.947986i	$-0.603116\pi$
$307$	−9.90848e10	−0.636626	−0.318313	+	0.947986i	$0.603116\pi$
$308$	−5.29330e9	−0.0335157
$309$	−1.32807e11	−0.828721
$310$	8.18258e10	0.503225
$311$	−2.78000e10	−0.168509	−0.0842545	−	0.996444i	$-0.526851\pi$
$311$	−2.78000e10	−0.168509	−0.0842545	+	0.996444i	$0.526851\pi$
$312$	2.29123e11	1.36891
$313$	7.09223e10	0.417670	0.208835	−	0.977951i	$-0.433033\pi$
$313$	7.09223e10	0.417670	0.208835	+	0.977951i	$0.433033\pi$
$314$	−7.54027e10	−0.437727
$315$	−1.06818e9	−0.00611287
$316$	1.06523e11	0.600969
$317$	−3.11422e11	−1.73214	−0.866068	−	0.499926i	$-0.833360\pi$
$317$	−3.11422e11	−1.73214	−0.866068	+	0.499926i	$0.833360\pi$
$318$	−1.44527e10	−0.0792550
$319$	−1.59547e10	−0.0862643
$320$	−6.80376e10	−0.362722
$321$	−2.71997e11	−1.42985
$322$	3.69947e10	0.191773
$323$	−1.35519e10	−0.0692770
$324$	1.01988e11	0.514156
$325$	−5.35662e10	−0.266327
$326$	−1.55493e11	−0.762485
$327$	1.43187e11	0.692529
$328$	1.80208e11	0.859692
$329$	−5.54739e10	−0.261040
$330$	1.07166e10	0.0497445
$331$	2.94782e11	1.34982	0.674908	−	0.737902i	$-0.264183\pi$
$331$	2.94782e11	1.34982	0.674908	+	0.737902i	$0.264183\pi$
$332$	2.03336e11	0.918527
$333$	3.08263e9	0.0137379
$334$	1.72699e11	0.759330
$335$	−5.99195e10	−0.259936
$336$	1.56468e10	0.0669730
$337$	−2.02609e11	−0.855705	−0.427852	−	0.903849i	$-0.640730\pi$
$337$	−2.02609e11	−0.855705	−0.427852	+	0.903849i	$0.640730\pi$
$338$	1.26637e11	0.527758
$339$	7.55158e10	0.310555
$340$	−4.04707e9	−0.0164243
$341$	6.83353e10	0.273685
$342$	−6.29229e9	−0.0248709
$343$	−1.38413e10	−0.0539949
$344$	−3.81930e11	−1.47052
$345$	8.58870e10	0.326393
$346$	−2.40294e11	−0.901365
$347$	−1.52000e11	−0.562810	−0.281405	−	0.959589i	$-0.590800\pi$
$347$	−1.52000e11	−0.562810	−0.281405	+	0.959589i	$0.590800\pi$
$348$	−7.45598e10	−0.272520
$349$	−2.82049e11	−1.01768	−0.508840	−	0.860861i	$-0.669925\pi$
$349$	−2.82049e11	−1.01768	−0.508840	+	0.860861i	$0.669925\pi$
$350$	−1.44844e10	−0.0515933
$351$	3.85210e11	1.35461
$352$	−4.41762e10	−0.153372
$353$	−4.32937e11	−1.48402	−0.742008	−	0.670391i	$-0.766126\pi$
$353$	−4.32937e11	−1.48402	−0.742008	+	0.670391i	$0.766126\pi$
$354$	1.88276e11	0.637207
$355$	1.35497e11	0.452796
$356$	−7.23203e10	−0.238636
$357$	7.82976e9	0.0255118
$358$	−1.77310e11	−0.570504
$359$	1.35500e10	0.0430542	0.0215271	−	0.999768i	$-0.493147\pi$
$359$	1.35500e10	0.0430542	0.0215271	+	0.999768i	$0.493147\pi$
$360$	−5.39687e9	−0.0169348
$361$	4.94112e9	0.0153124
$362$	2.54601e11	0.779242
$363$	−3.15824e11	−0.954697
$364$	−9.00480e10	−0.268855
$365$	9.41879e10	0.277765
$366$	2.65515e11	0.773435
$367$	−1.26149e11	−0.362984	−0.181492	−	0.983392i	$-0.558093\pi$
$367$	−1.26149e11	−0.362984	−0.181492	+	0.983392i	$0.558093\pi$
$368$	4.72049e10	0.134175
$369$	1.05744e10	0.0296917
$370$	4.18002e10	0.115950
$371$	1.63135e10	0.0447057
$372$	3.19346e11	0.864605
$373$	−2.45212e11	−0.655923	−0.327961	−	0.944691i	$-0.606362\pi$
$373$	−2.45212e11	−0.655923	−0.327961	+	0.944691i	$0.606362\pi$
$374$	2.94741e9	0.00778964
$375$	−3.36269e10	−0.0878105
$376$	−2.80278e11	−0.723175
$377$	−2.71417e11	−0.691991
$378$	1.04161e11	0.262418
$379$	3.62591e11	0.902694	0.451347	−	0.892348i	$-0.350944\pi$
$379$	3.62591e11	0.902694	0.451347	+	0.892348i	$0.350944\pi$
$380$	9.78413e10	0.240711
$381$	−7.44552e11	−1.81022
$382$	2.70550e11	0.650073
$383$	7.23039e10	0.171699	0.0858494	−	0.996308i	$-0.472640\pi$
$383$	7.23039e10	0.171699	0.0858494	+	0.996308i	$0.472640\pi$
$384$	−1.54916e11	−0.363584
$385$	−1.20964e10	−0.0280596
$386$	−3.88064e11	−0.889734
$387$	−2.24111e10	−0.0507882
$388$	−3.81097e11	−0.853674
$389$	3.00609e11	0.665624	0.332812	−	0.942993i	$-0.392002\pi$
$389$	3.00609e11	0.665624	0.332812	+	0.942993i	$0.392002\pi$
$390$	1.82308e11	0.399038
$391$	2.36216e10	0.0511110
$392$	−6.99320e10	−0.149585
$393$	−2.49698e11	−0.528017
$394$	5.07291e11	1.06053
$395$	2.43429e11	0.503136
$396$	−1.56930e9	−0.00320683
$397$	−2.86335e11	−0.578518	−0.289259	−	0.957251i	$-0.593409\pi$
$397$	−2.86335e11	−0.578518	−0.289259	+	0.957251i	$0.593409\pi$
$398$	−5.51219e10	−0.110116
$399$	−1.89291e11	−0.373897
$400$	−1.84819e10	−0.0360975
$401$	8.19964e11	1.58360	0.791800	−	0.610781i	$-0.209144\pi$
$401$	8.19964e11	1.58360	0.791800	+	0.610781i	$0.209144\pi$
$402$	2.03931e11	0.389462
$403$	1.16250e12	2.19543
$404$	1.76094e11	0.328873
$405$	2.33064e11	0.430456
$406$	−7.33915e10	−0.134054
$407$	3.49087e10	0.0630607
$408$	3.95593e10	0.0706769
$409$	9.67528e11	1.70966	0.854828	−	0.518911i	$-0.173663\pi$
$409$	9.67528e11	1.70966	0.854828	+	0.518911i	$0.173663\pi$
$410$	1.43387e11	0.250601
$411$	−1.03328e11	−0.178620
$412$	2.63710e11	0.450908
$413$	−2.12517e11	−0.359433
$414$	1.09678e10	0.0183492
$415$	4.64667e11	0.768998
$416$	−7.51511e11	−1.23031
$417$	9.07803e11	1.47021
$418$	−7.12560e10	−0.114164
$419$	−8.51357e10	−0.134942	−0.0674712	−	0.997721i	$-0.521493\pi$
$419$	−8.51357e10	−0.134942	−0.0674712	+	0.997721i	$0.521493\pi$
$420$	−5.65289e10	−0.0886439
$421$	5.61043e10	0.0870415	0.0435207	−	0.999053i	$-0.486143\pi$
$421$	5.61043e10	0.0870415	0.0435207	+	0.999053i	$0.486143\pi$
$422$	−1.37178e11	−0.210562
$423$	−1.64463e10	−0.0249767
$424$	8.24224e10	0.123851
$425$	−9.24846e9	−0.0137505
$426$	−4.61153e11	−0.678425
$427$	−2.99700e11	−0.436275
$428$	5.40093e11	0.777985
$429$	1.52251e11	0.217022
$430$	−3.03892e11	−0.428659
$431$	−1.36440e11	−0.190456	−0.0952278	−	0.995456i	$-0.530358\pi$
$431$	−1.36440e11	−0.190456	−0.0952278	+	0.995456i	$0.530358\pi$
$432$	1.32909e11	0.183602
$433$	3.25710e11	0.445282	0.222641	−	0.974900i	$-0.428532\pi$
$433$	3.25710e11	0.445282	0.222641	+	0.974900i	$0.428532\pi$
$434$	3.14342e11	0.425303
$435$	−1.70386e11	−0.228156
$436$	−2.84320e11	−0.376806
$437$	−5.71072e11	−0.749074
$438$	−3.20560e11	−0.416175
$439$	1.44336e11	0.185474	0.0927372	−	0.995691i	$-0.470438\pi$
$439$	1.44336e11	0.185474	0.0927372	+	0.995691i	$0.470438\pi$
$440$	−6.11160e10	−0.0777352
$441$	−4.10350e9	−0.00516632
$442$	5.01404e10	0.0624867
$443$	−9.59823e11	−1.18406	−0.592031	−	0.805915i	$-0.701674\pi$
$443$	−9.59823e11	−1.18406	−0.592031	+	0.805915i	$0.701674\pi$
$444$	1.63136e11	0.199217
$445$	−1.65268e11	−0.199788
$446$	2.85919e11	0.342166
$447$	−4.53754e11	−0.537572
$448$	−2.61373e11	−0.306556
$449$	−1.02004e12	−1.18443	−0.592215	−	0.805780i	$-0.701747\pi$
$449$	−1.02004e12	−1.18443	−0.592215	+	0.805780i	$0.701747\pi$
$450$	−4.29416e9	−0.00493653
$451$	1.19747e11	0.136292
$452$	−1.49948e11	−0.168974
$453$	−1.43797e12	−1.60438
$454$	1.06792e12	1.17975
$455$	−2.05780e11	−0.225088
$456$	−9.56379e11	−1.03583
$457$	−6.45199e11	−0.691944	−0.345972	−	0.938245i	$-0.612451\pi$
$457$	−6.45199e11	−0.691944	−0.345972	+	0.938245i	$0.612451\pi$
$458$	−6.40892e11	−0.680598
$459$	6.65084e10	0.0699390
$460$	−1.70542e11	−0.177591
$461$	1.04575e12	1.07838	0.539192	−	0.842183i	$-0.318730\pi$
$461$	1.04575e12	1.07838	0.539192	+	0.842183i	$0.318730\pi$
$462$	4.11690e10	0.0420418
$463$	6.01465e11	0.608269	0.304134	−	0.952629i	$-0.401633\pi$
$463$	6.01465e11	0.608269	0.304134	+	0.952629i	$0.401633\pi$
$464$	−9.36469e10	−0.0937913
$465$	7.29776e11	0.723855
$466$	1.64758e11	0.161849
$467$	9.53000e11	0.927186	0.463593	−	0.886048i	$-0.346560\pi$
$467$	9.53000e11	0.927186	0.463593	+	0.886048i	$0.346560\pi$
$468$	−2.66964e10	−0.0257244
$469$	−2.30187e11	−0.219686
$470$	−2.23010e11	−0.210806
$471$	−6.72491e11	−0.629640
$472$	−1.07372e12	−0.995757
$473$	−2.53790e11	−0.233131
$474$	−8.28490e11	−0.753850
$475$	2.23589e11	0.201525
$476$	−1.55472e10	−0.0138810
$477$	4.83642e9	0.00427751
$478$	1.06454e11	0.0932690
$479$	1.99157e12	1.72857	0.864283	−	0.503005i	$-0.167772\pi$
$479$	1.99157e12	1.72857	0.864283	+	0.503005i	$0.167772\pi$
$480$	−4.71772e11	−0.405646
$481$	5.93856e11	0.505857
$482$	−4.20981e11	−0.355263
$483$	3.29943e11	0.275853
$484$	6.27119e11	0.519452
$485$	−8.70891e11	−0.714703
$486$	6.06833e10	0.0493408
$487$	−2.40847e12	−1.94027	−0.970134	−	0.242570i	$-0.922010\pi$
$487$	−2.40847e12	−1.94027	−0.970134	+	0.242570i	$0.922010\pi$
$488$	−1.51421e12	−1.20864
$489$	−1.38679e12	−1.09678
$490$	−5.56432e10	−0.0436043
$491$	2.85374e11	0.221589	0.110794	−	0.993843i	$-0.464661\pi$
$491$	2.85374e11	0.221589	0.110794	+	0.993843i	$0.464661\pi$
$492$	5.59605e11	0.430565
$493$	−4.68614e10	−0.0357276
$494$	−1.21219e12	−0.915794
$495$	−3.58619e9	−0.00268479
$496$	4.01097e11	0.297565
$497$	5.20526e11	0.382682
$498$	−1.58145e12	−1.15219
$499$	2.11594e12	1.52775	0.763873	−	0.645367i	$-0.223296\pi$
$499$	2.11594e12	1.52775	0.763873	+	0.645367i	$0.223296\pi$
$500$	6.67715e10	0.0477778
$501$	1.54024e12	1.09224
$502$	1.71709e12	1.20677
$503$	7.41865e11	0.516736	0.258368	−	0.966047i	$-0.416815\pi$
$503$	7.41865e11	0.516736	0.258368	+	0.966047i	$0.416815\pi$
$504$	−2.07326e10	−0.0143125
$505$	4.02414e11	0.275335
$506$	1.24203e11	0.0842274
$507$	1.12943e12	0.759143
$508$	1.47842e12	0.984946
$509$	1.62377e12	1.07225	0.536124	−	0.844140i	$-0.319888\pi$
$509$	1.62377e12	1.07225	0.536124	+	0.844140i	$0.319888\pi$
$510$	3.14763e10	0.0206024
$511$	3.61832e11	0.234754
$512$	−5.53160e11	−0.355742
$513$	−1.60790e12	−1.02501
$514$	−5.93890e11	−0.375294
$515$	6.02635e11	0.377504
$516$	−1.18602e12	−0.736490
$517$	−1.86243e11	−0.114649
$518$	1.60580e11	0.0979955
$519$	−2.14310e12	−1.29655
$520$	−1.03969e12	−0.623573
$521$	1.48817e12	0.884877	0.442439	−	0.896799i	$-0.354113\pi$
$521$	1.48817e12	0.884877	0.442439	+	0.896799i	$0.354113\pi$
$522$	−2.17583e10	−0.0128265
$523$	2.41360e12	1.41061	0.705306	−	0.708903i	$-0.250810\pi$
$523$	2.41360e12	1.41061	0.705306	+	0.708903i	$0.250810\pi$
$524$	4.95814e11	0.287295
$525$	−1.29181e11	−0.0742134
$526$	2.32001e12	1.32146
$527$	2.00711e11	0.113351
$528$	5.25312e10	0.0294147
$529$	−8.05747e11	−0.447351
$530$	6.55815e10	0.0361027
$531$	−6.30044e10	−0.0343911
$532$	3.75867e11	0.203438
$533$	2.03711e12	1.09331
$534$	5.62475e11	0.299342
$535$	1.23423e12	0.651336
$536$	−1.16300e12	−0.608609
$537$	−1.58136e12	−0.820630
$538$	1.42480e12	0.733218
$539$	−4.64694e10	−0.0237147
$540$	−4.80174e11	−0.243011
$541$	−2.14334e12	−1.07573	−0.537864	−	0.843032i	$-0.680769\pi$
$541$	−2.14334e12	−1.07573	−0.537864	+	0.843032i	$0.680769\pi$
$542$	−1.70484e12	−0.848570
$543$	2.27070e12	1.12089
$544$	−1.29752e11	−0.0635213
$545$	−6.49734e11	−0.315465
$546$	7.00354e11	0.337249
$547$	1.02462e12	0.489349	0.244675	−	0.969605i	$-0.421319\pi$
$547$	1.02462e12	0.489349	0.244675	+	0.969605i	$0.421319\pi$
$548$	2.05174e11	0.0971875
$549$	−8.88514e10	−0.0417435
$550$	−4.86285e10	−0.0226599
$551$	1.13291e12	0.523618
$552$	1.66701e12	0.764211
$553$	9.35157e11	0.425228
$554$	1.63935e12	0.739399
$555$	3.72801e11	0.166786
$556$	−1.80259e12	−0.799944
$557$	−3.18977e12	−1.40414	−0.702070	−	0.712108i	$-0.747741\pi$
$557$	−3.18977e12	−1.40414	−0.702070	+	0.712108i	$0.747741\pi$
$558$	9.31924e10	0.0406936
$559$	−4.31740e12	−1.87012
$560$	−7.10002e10	−0.0305080
$561$	2.62869e10	0.0112049
$562$	2.62453e12	1.10978
$563$	1.08826e12	0.456503	0.228252	−	0.973602i	$-0.426699\pi$
$563$	1.08826e12	0.456503	0.228252	+	0.973602i	$0.426699\pi$
$564$	−8.70353e11	−0.362192
$565$	−3.42666e11	−0.141466
$566$	−1.02465e12	−0.419662
$567$	8.95340e11	0.363801
$568$	2.62992e12	1.06017
$569$	−3.28834e12	−1.31514	−0.657569	−	0.753394i	$-0.728415\pi$
$569$	−3.28834e12	−1.31514	−0.657569	+	0.753394i	$0.728415\pi$
$570$	−7.60967e11	−0.301946
$571$	−1.88806e12	−0.743283	−0.371641	−	0.928376i	$-0.621205\pi$
$571$	−1.88806e12	−0.743283	−0.371641	+	0.928376i	$0.621205\pi$
$572$	−3.02319e11	−0.118082
$573$	2.41294e12	0.935084
$574$	5.50837e11	0.211797
$575$	−3.89727e11	−0.148681
$576$	−7.74889e10	−0.0293318
$577$	1.12881e12	0.423963	0.211982	−	0.977274i	$-0.432008\pi$
$577$	1.12881e12	0.423963	0.211982	+	0.977274i	$0.432008\pi$
$578$	−1.82276e12	−0.679289
$579$	−3.46101e12	−1.27982
$580$	3.38328e11	0.124140
$581$	1.78506e12	0.649922
$582$	2.96400e12	1.07084
$583$	5.47692e10	0.0196349
$584$	1.82813e12	0.650353
$585$	−6.10072e10	−0.0215367
$586$	1.16503e11	0.0408128
$587$	6.31776e11	0.219630	0.109815	−	0.993952i	$-0.464974\pi$
$587$	6.31776e11	0.219630	0.109815	+	0.993952i	$0.464974\pi$
$588$	−2.17162e11	−0.0749178
$589$	−4.85237e12	−1.66125
$590$	−8.54335e11	−0.290265
$591$	4.52436e12	1.52550
$592$	2.04898e11	0.0685630
$593$	−4.97504e12	−1.65215	−0.826077	−	0.563557i	$-0.809432\pi$
$593$	−4.97504e12	−1.65215	−0.826077	+	0.563557i	$0.809432\pi$
$594$	3.49702e11	0.115255
$595$	−3.55289e10	−0.0116213
$596$	9.00999e11	0.292493
$597$	−4.91613e11	−0.158394
$598$	2.11290e12	0.675652
$599$	−4.55686e12	−1.44626	−0.723128	−	0.690714i	$-0.757296\pi$
$599$	−4.55686e12	−1.44626	−0.723128	+	0.690714i	$0.757296\pi$
$600$	−6.52678e11	−0.205598
$601$	−5.78188e12	−1.80773	−0.903866	−	0.427815i	$-0.859283\pi$
$601$	−5.78188e12	−1.80773	−0.903866	+	0.427815i	$0.859283\pi$
$602$	−1.16743e12	−0.362283
$603$	−6.82431e10	−0.0210199
$604$	2.85532e12	0.872948
$605$	1.43311e12	0.434890
$606$	−1.36958e12	−0.412536
$607$	−7.37332e11	−0.220452	−0.110226	−	0.993907i	$-0.535157\pi$
$607$	−7.37332e11	−0.220452	−0.110226	+	0.993907i	$0.535157\pi$
$608$	3.13687e12	0.930958
$609$	−6.54554e11	−0.192827
$610$	−1.20482e12	−0.352320
$611$	−3.16831e12	−0.919691
$612$	−4.60926e9	−0.00132816
$613$	−3.50587e12	−1.00282	−0.501410	−	0.865210i	$-0.667185\pi$
$613$	−3.50587e12	−1.00282	−0.501410	+	0.865210i	$0.667185\pi$
$614$	−1.53022e12	−0.434507
$615$	1.27882e12	0.360473
$616$	−2.34783e11	−0.0656982
$617$	2.47222e12	0.686759	0.343380	−	0.939197i	$-0.388428\pi$
$617$	2.47222e12	0.686759	0.343380	+	0.939197i	$0.388428\pi$
$618$	−2.05102e12	−0.565615
$619$	−1.57589e12	−0.431436	−0.215718	−	0.976456i	$-0.569209\pi$
$619$	−1.57589e12	−0.431436	−0.215718	+	0.976456i	$0.569209\pi$
$620$	−1.44908e12	−0.393850
$621$	2.80264e12	0.756232
$622$	−4.29331e11	−0.115010
$623$	−6.34894e11	−0.168851
$624$	8.93645e11	0.235958
$625$	1.52588e11	0.0400000
$626$	1.09529e12	0.285066
$627$	−6.35508e11	−0.164217
$628$	1.33534e12	0.342588
$629$	1.02532e11	0.0261175
$630$	−1.64964e10	−0.00417213
$631$	4.95895e11	0.124525	0.0622627	−	0.998060i	$-0.480168\pi$
$631$	4.95895e11	0.124525	0.0622627	+	0.998060i	$0.480168\pi$
$632$	4.72481e12	1.17803
$633$	−1.22345e12	−0.302878
$634$	−4.80946e12	−1.18221
$635$	3.37853e12	0.824605
$636$	2.55948e11	0.0620291
$637$	−7.90524e11	−0.190234
$638$	−2.46398e11	−0.0588767
$639$	1.54319e11	0.0366156
$640$	7.02956e11	0.165622
$641$	1.72054e12	0.402535	0.201268	−	0.979536i	$-0.435494\pi$
$641$	1.72054e12	0.402535	0.201268	+	0.979536i	$0.435494\pi$
$642$	−4.20060e12	−0.975897
$643$	8.19457e12	1.89050	0.945250	−	0.326346i	$-0.105818\pi$
$643$	8.19457e12	1.89050	0.945250	+	0.326346i	$0.105818\pi$
$644$	−6.55154e11	−0.150092
$645$	−2.71031e12	−0.616596
$646$	−2.09290e11	−0.0472826
$647$	−2.56336e12	−0.575097	−0.287549	−	0.957766i	$-0.592840\pi$
$647$	−2.56336e12	−0.575097	−0.287549	+	0.957766i	$0.592840\pi$
$648$	4.52364e12	1.00786
$649$	−7.13483e11	−0.157864
$650$	−8.27253e11	−0.181772
$651$	2.80351e12	0.611769
$652$	2.75368e12	0.596760
$653$	−2.23256e12	−0.480499	−0.240250	−	0.970711i	$-0.577229\pi$
$653$	−2.23256e12	−0.480499	−0.240250	+	0.970711i	$0.577229\pi$
$654$	2.21131e12	0.472662
$655$	1.13305e12	0.240526
$656$	7.02863e11	0.148185
$657$	1.07272e11	0.0224616
$658$	−8.56715e11	−0.178164
$659$	6.47077e12	1.33651	0.668254	−	0.743933i	$-0.267042\pi$
$659$	6.47077e12	1.33651	0.668254	+	0.743933i	$0.267042\pi$
$660$	−1.89785e11	−0.0389326
$661$	−2.35514e12	−0.479856	−0.239928	−	0.970791i	$-0.577124\pi$
$661$	−2.35514e12	−0.479856	−0.239928	+	0.970791i	$0.577124\pi$
$662$	4.55248e12	0.921270
$663$	4.47185e11	0.0898827
$664$	9.01890e12	1.80052
$665$	8.58941e11	0.170320
$666$	4.76067e10	0.00937636
$667$	−1.97472e12	−0.386314
$668$	−3.05839e12	−0.594291
$669$	2.55002e12	0.492182
$670$	−9.25371e11	−0.177410
$671$	−1.00618e12	−0.191613
$672$	−1.81236e12	−0.342833
$673$	−1.00068e13	−1.88030	−0.940149	−	0.340764i	$-0.889314\pi$
$673$	−1.00068e13	−1.88030	−0.940149	+	0.340764i	$0.889314\pi$
$674$	−3.12900e12	−0.584032
$675$	−1.09730e12	−0.203451
$676$	−2.24266e12	−0.413051
$677$	−4.75925e12	−0.870742	−0.435371	−	0.900251i	$-0.643383\pi$
$677$	−4.75925e12	−0.870742	−0.435371	+	0.900251i	$0.643383\pi$
$678$	1.16623e12	0.211959
$679$	−3.34561e12	−0.604035
$680$	−1.79507e11	−0.0321952
$681$	9.52446e12	1.69699
$682$	1.05534e12	0.186794
$683$	5.44016e11	0.0956575	0.0478287	−	0.998856i	$-0.484770\pi$
$683$	5.44016e11	0.0956575	0.0478287	+	0.998856i	$0.484770\pi$
$684$	1.11433e11	0.0194653
$685$	4.68869e11	0.0813662
$686$	−2.13759e11	−0.0368524
$687$	−5.71590e12	−0.978992
$688$	−1.48963e12	−0.253473
$689$	9.31717e11	0.157506
$690$	1.32640e12	0.222769
$691$	8.57339e12	1.43054	0.715272	−	0.698846i	$-0.246303\pi$
$691$	8.57339e12	1.43054	0.715272	+	0.698846i	$0.246303\pi$
$692$	4.25546e12	0.705455
$693$	−1.37767e10	−0.00226906
$694$	−2.34743e12	−0.384127
$695$	−4.11931e12	−0.669720
$696$	−3.30708e12	−0.534199
$697$	3.51716e11	0.0564476
$698$	−4.35585e12	−0.694582
$699$	1.46942e12	0.232809
$700$	2.56510e11	0.0403796
$701$	1.25396e13	1.96133	0.980666	−	0.195687i	$-0.0626935\pi$
$701$	1.25396e13	1.96133	0.980666	+	0.195687i	$0.0626935\pi$
$702$	5.94902e12	0.924545
$703$	−2.47880e12	−0.382774
$704$	−8.77510e11	−0.134640
$705$	−1.98895e12	−0.303230
$706$	−6.68609e12	−1.01286
$707$	1.54591e12	0.232701
$708$	−3.33426e12	−0.498712
$709$	4.37869e12	0.650782	0.325391	−	0.945580i	$-0.394504\pi$
$709$	4.37869e12	0.650782	0.325391	+	0.945580i	$0.394504\pi$
$710$	2.09256e12	0.309040
$711$	2.77244e11	0.0406864
$712$	−3.20775e12	−0.467779
$713$	8.45790e12	1.22563
$714$	1.20919e11	0.0174122
$715$	−6.90865e11	−0.0988590
$716$	3.14004e12	0.446506
$717$	9.49429e11	0.134161
$718$	2.09261e11	0.0293852
$719$	7.76448e12	1.08351	0.541754	−	0.840537i	$-0.317760\pi$
$719$	7.76448e12	1.08351	0.541754	+	0.840537i	$0.317760\pi$
$720$	−2.10493e10	−0.00291905
$721$	2.31508e12	0.319049
$722$	7.63086e10	0.0104510
$723$	−3.75458e12	−0.511022
$724$	−4.50884e12	−0.609875
$725$	7.73154e11	0.103931
$726$	−4.87745e12	−0.651596
$727$	7.08318e11	0.0940423	0.0470211	−	0.998894i	$-0.485027\pi$
$727$	7.08318e11	0.0940423	0.0470211	+	0.998894i	$0.485027\pi$
$728$	−3.99406e12	−0.527015
$729$	7.88106e12	1.03350
$730$	1.45460e12	0.189579
$731$	−7.45421e11	−0.0965547
$732$	−4.70211e12	−0.605331
$733$	6.81304e12	0.871712	0.435856	−	0.900017i	$-0.356446\pi$
$733$	6.81304e12	0.871712	0.435856	+	0.900017i	$0.356446\pi$
$734$	−1.94820e12	−0.247743
$735$	−4.96263e11	−0.0627218
$736$	−5.46771e12	−0.686839
$737$	−7.72807e11	−0.0964866
$738$	1.63306e11	0.0202651
$739$	9.20369e12	1.13517	0.567586	−	0.823314i	$-0.307877\pi$
$739$	9.20369e12	1.13517	0.567586	+	0.823314i	$0.307877\pi$
$740$	−7.40256e11	−0.0907484
$741$	−1.08111e13	−1.31731
$742$	2.51938e11	0.0305124
$743$	−8.72196e12	−1.04994	−0.524970	−	0.851121i	$-0.675923\pi$
$743$	−8.72196e12	−1.04994	−0.524970	+	0.851121i	$0.675923\pi$
$744$	1.41645e13	1.69482
$745$	2.05898e12	0.244878
$746$	−3.78695e12	−0.447678
$747$	5.29215e11	0.0621856
$748$	−5.21968e10	−0.00609658
$749$	4.74143e12	0.550479
$750$	−5.19320e11	−0.0599321
$751$	−1.63201e13	−1.87216	−0.936078	−	0.351793i	$-0.885572\pi$
$751$	−1.63201e13	−1.87216	−0.936078	+	0.351793i	$0.885572\pi$
$752$	−1.09316e12	−0.124653
$753$	1.53141e13	1.73586
$754$	−4.19164e12	−0.472295
$755$	6.52504e12	0.730839
$756$	−1.84464e12	−0.205382
$757$	−3.23287e12	−0.357813	−0.178907	−	0.983866i	$-0.557256\pi$
$757$	−3.23287e12	−0.357813	−0.178907	+	0.983866i	$0.557256\pi$
$758$	5.59970e12	0.616103
$759$	1.10772e12	0.121155
$760$	4.33973e12	0.471847
$761$	−6.46766e11	−0.0699063	−0.0349531	−	0.999389i	$-0.511128\pi$
$761$	−6.46766e11	−0.0699063	−0.0349531	+	0.999389i	$0.511128\pi$
$762$	−1.14985e13	−1.23551
$763$	−2.49602e12	−0.266617
$764$	−4.79127e12	−0.508781
$765$	−1.05332e10	−0.00111195
$766$	1.11663e12	0.117187
$767$	−1.21376e13	−1.26634
$768$	−1.00694e13	−1.04442
$769$	−2.42101e12	−0.249648	−0.124824	−	0.992179i	$-0.539837\pi$
$769$	−2.42101e12	−0.249648	−0.124824	+	0.992179i	$0.539837\pi$
$770$	−1.86811e11	−0.0191511
$771$	−5.29670e12	−0.539835
$772$	6.87237e12	0.696352
$773$	−4.43910e12	−0.447185	−0.223592	−	0.974683i	$-0.571778\pi$
$773$	−4.43910e12	−0.447185	−0.223592	+	0.974683i	$0.571778\pi$
$774$	−3.46107e11	−0.0346638
$775$	−3.31148e12	−0.329735
$776$	−1.69035e13	−1.67339
$777$	1.43215e12	0.140960
$778$	4.64248e12	0.454299
$779$	−8.50304e12	−0.827286
$780$	−3.22856e12	−0.312308
$781$	1.74756e12	0.168075
$782$	3.64802e11	0.0348840
$783$	−5.55998e12	−0.528622
$784$	−2.72754e11	−0.0257839
$785$	3.05154e12	0.286818
$786$	−3.85622e12	−0.360380
$787$	−1.72989e13	−1.60744	−0.803718	−	0.595011i	$-0.797148\pi$
$787$	−1.72989e13	−1.60744	−0.803718	+	0.595011i	$0.797148\pi$
$788$	−8.98382e12	−0.830029
$789$	2.06914e13	1.90083
$790$	3.75941e12	0.343398
$791$	−1.31638e12	−0.119561
$792$	−6.96057e10	−0.00628611
$793$	−1.71169e13	−1.53708
$794$	−4.42203e12	−0.394848
$795$	5.84899e11	0.0519313
$796$	9.76175e11	0.0861825
$797$	−1.37776e13	−1.20951	−0.604756	−	0.796410i	$-0.706730\pi$
$797$	−1.37776e13	−1.20951	−0.604756	+	0.796410i	$0.706730\pi$
$798$	−2.92333e12	−0.255191
$799$	−5.47024e11	−0.0474838
$800$	2.14075e12	0.184782
$801$	−1.88226e11	−0.0161560
$802$	1.26632e13	1.08083
$803$	1.21478e12	0.103105
$804$	−3.61149e12	−0.304814
$805$	−1.49717e12	−0.125658
$806$	1.79531e13	1.49842
$807$	1.27073e13	1.05468
$808$	7.81061e12	0.644665
$809$	1.38369e13	1.13572	0.567860	−	0.823125i	$-0.307772\pi$
$809$	1.38369e13	1.13572	0.567860	+	0.823125i	$0.307772\pi$
$810$	3.59935e12	0.293793
$811$	−1.96078e13	−1.59161	−0.795804	−	0.605555i	$-0.792951\pi$
$811$	−1.96078e13	−1.59161	−0.795804	+	0.605555i	$0.792951\pi$
$812$	1.29972e12	0.104917
$813$	−1.52049e13	−1.22061
$814$	5.39114e11	0.0430399
$815$	6.29278e12	0.499613
$816$	1.54292e11	0.0121825
$817$	1.80212e13	1.41509
$818$	1.49421e13	1.16687
$819$	−2.34365e11	−0.0182019
$820$	−2.53930e12	−0.196134
$821$	2.41017e13	1.85142	0.925708	−	0.378239i	$-0.123470\pi$
$821$	2.41017e13	1.85142	0.925708	+	0.378239i	$0.123470\pi$
$822$	−1.59576e12	−0.121911
$823$	8.20762e12	0.623617	0.311809	−	0.950145i	$-0.399065\pi$
$823$	8.20762e12	0.623617	0.311809	+	0.950145i	$0.399065\pi$
$824$	1.16968e13	0.883881
$825$	−4.33701e11	−0.0325947
$826$	−3.28201e12	−0.245318
$827$	2.84612e12	0.211582	0.105791	−	0.994388i	$-0.466263\pi$
$827$	2.84612e12	0.211582	0.105791	+	0.994388i	$0.466263\pi$
$828$	−1.94233e11	−0.0143610
$829$	−5.88562e12	−0.432809	−0.216405	−	0.976304i	$-0.569433\pi$
$829$	−5.88562e12	−0.432809	−0.216405	+	0.976304i	$0.569433\pi$
$830$	7.17612e12	0.524853
$831$	1.46208e13	1.06357
$832$	−1.49279e13	−1.08005
$833$	−1.36488e11	−0.00982180
$834$	1.40197e13	1.00344
$835$	−6.98911e12	−0.497546
$836$	1.26190e12	0.0893505
$837$	2.38138e13	1.67712
$838$	−1.31480e12	−0.0921003
$839$	−8.44799e12	−0.588606	−0.294303	−	0.955712i	$-0.595087\pi$
$839$	−8.44799e12	−0.588606	−0.294303	+	0.955712i	$0.595087\pi$
$840$	−2.50733e12	−0.173762
$841$	−1.05896e13	−0.729959
$842$	8.66450e11	0.0594072
$843$	2.34073e13	1.59634
$844$	2.42934e12	0.164796
$845$	−5.12498e12	−0.345810
$846$	−2.53989e11	−0.0170470
$847$	5.50542e12	0.367549
$848$	3.21470e11	0.0213481
$849$	−9.13847e12	−0.603655
$850$	−1.42829e11	−0.00938495
$851$	4.32066e12	0.282402
$852$	8.16674e12	0.530970
$853$	−7.17311e12	−0.463913	−0.231957	−	0.972726i	$-0.574513\pi$
$853$	−7.17311e12	−0.463913	−0.231957	+	0.972726i	$0.574513\pi$
$854$	−4.62843e12	−0.297765
$855$	2.54649e11	0.0162965
$856$	2.39557e13	1.52502
$857$	2.17636e13	1.37821	0.689107	−	0.724660i	$-0.258003\pi$
$857$	2.17636e13	1.37821	0.689107	+	0.724660i	$0.258003\pi$
$858$	2.35130e12	0.148121
$859$	−9.02945e12	−0.565838	−0.282919	−	0.959144i	$-0.591303\pi$
$859$	−9.02945e12	−0.565838	−0.282919	+	0.959144i	$0.591303\pi$
$860$	5.38175e12	0.335491
$861$	4.91273e12	0.304655
$862$	−2.10712e12	−0.129989
$863$	−1.84428e13	−1.13182	−0.565910	−	0.824467i	$-0.691475\pi$
$863$	−1.84428e13	−1.13182	−0.565910	+	0.824467i	$0.691475\pi$
$864$	−1.53947e13	−0.939854
$865$	9.72468e12	0.590613
$866$	5.03012e12	0.303912
$867$	−1.62566e13	−0.977111
$868$	−5.56680e12	−0.332864
$869$	3.13961e12	0.186761
$870$	−2.63136e12	−0.155720
$871$	−1.31468e13	−0.773993
$872$	−1.26109e13	−0.738623
$873$	−9.91868e11	−0.0577950
$874$	−8.81940e12	−0.511255
$875$	5.86182e11	0.0338062
$876$	5.67693e12	0.325721
$877$	−1.12140e13	−0.640120	−0.320060	−	0.947397i	$-0.603703\pi$
$877$	−1.12140e13	−0.640120	−0.320060	+	0.947397i	$0.603703\pi$
$878$	2.22906e12	0.126589
$879$	1.03905e12	0.0587064
$880$	−2.38369e11	−0.0133992
$881$	3.00664e13	1.68147	0.840735	−	0.541446i	$-0.182123\pi$
$881$	3.00664e13	1.68147	0.840735	+	0.541446i	$0.182123\pi$
$882$	−6.33727e10	−0.00352609
$883$	−1.58968e13	−0.880007	−0.440004	−	0.897996i	$-0.645023\pi$
$883$	−1.58968e13	−0.880007	−0.440004	+	0.897996i	$0.645023\pi$
$884$	−8.87956e11	−0.0489053
$885$	−7.61952e12	−0.417526
$886$	−1.48231e13	−0.808141
$887$	1.46131e13	0.792658	0.396329	−	0.918109i	$-0.370284\pi$
$887$	1.46131e13	0.792658	0.396329	+	0.918109i	$0.370284\pi$
$888$	7.23585e12	0.390509
$889$	1.29790e13	0.696918
$890$	−2.55233e12	−0.136358
$891$	3.00593e12	0.159782
$892$	−5.06346e12	−0.267797
$893$	1.32248e13	0.695915
$894$	−7.00758e12	−0.366901
$895$	7.17570e12	0.373819
$896$	2.70047e12	0.139976
$897$	1.88442e13	0.971878
$898$	−1.57531e13	−0.808393
$899$	−1.67791e13	−0.856742
$900$	7.60469e10	0.00386359
$901$	1.60866e11	0.00813208
$902$	1.84933e12	0.0930217
$903$	−1.04119e13	−0.521118
$904$	−6.65093e12	−0.331226
$905$	−1.03037e13	−0.510593
$906$	−2.22074e13	−1.09502
$907$	1.41504e12	0.0694281	0.0347141	−	0.999397i	$-0.488948\pi$
$907$	1.41504e12	0.0694281	0.0347141	+	0.999397i	$0.488948\pi$
$908$	−1.89123e13	−0.923333
$909$	4.58315e11	0.0222652
$910$	−3.17797e12	−0.153626
$911$	−1.61901e13	−0.778784	−0.389392	−	0.921072i	$-0.627315\pi$
$911$	−1.61901e13	−0.778784	−0.389392	+	0.921072i	$0.627315\pi$
$912$	−3.73014e12	−0.178545
$913$	5.99301e12	0.285447
$914$	−9.96417e12	−0.472262
$915$	−1.07454e13	−0.506788
$916$	1.13498e13	0.532671
$917$	4.35271e12	0.203281
$918$	1.02713e12	0.0477345
$919$	−1.60413e13	−0.741858	−0.370929	−	0.928661i	$-0.620961\pi$
$919$	−1.60413e13	−0.741858	−0.370929	+	0.928661i	$0.620961\pi$
$920$	−7.56435e12	−0.348118
$921$	−1.36475e13	−0.625008
$922$	1.61501e13	0.736014
$923$	2.97290e13	1.34826
$924$	−7.29077e11	−0.0329041
$925$	−1.69165e12	−0.0759753
$926$	9.28876e12	0.415153
$927$	6.86349e11	0.0305271
$928$	1.08470e13	0.480115
$929$	−3.98759e13	−1.75647	−0.878233	−	0.478233i	$-0.841277\pi$
$929$	−3.98759e13	−1.75647	−0.878233	+	0.478233i	$0.841277\pi$
$930$	1.12703e13	0.494042
$931$	3.29971e12	0.143947
$932$	−2.91777e12	−0.126672
$933$	−3.82906e12	−0.165434
$934$	1.47177e13	0.632819
$935$	−1.19281e11	−0.00510411
$936$	−1.18411e12	−0.0504256
$937$	−5.95427e12	−0.252348	−0.126174	−	0.992008i	$-0.540270\pi$
$937$	−5.95427e12	−0.252348	−0.126174	+	0.992008i	$0.540270\pi$
$938$	−3.55490e12	−0.149939
$939$	9.76855e12	0.410048
$940$	3.94937e12	0.164988
$941$	9.86055e12	0.409966	0.204983	−	0.978766i	$-0.434286\pi$
$941$	9.86055e12	0.409966	0.204983	+	0.978766i	$0.434286\pi$
$942$	−1.03857e13	−0.429739
$943$	1.48212e13	0.610353
$944$	−4.18782e12	−0.171638
$945$	−4.21540e12	−0.171948
$946$	−3.91943e12	−0.159115
$947$	−2.10061e13	−0.848732	−0.424366	−	0.905491i	$-0.639503\pi$
$947$	−2.10061e13	−0.848732	−0.424366	+	0.905491i	$0.639503\pi$
$948$	1.46721e13	0.590002
$949$	2.06655e13	0.827080
$950$	3.45302e12	0.137544
$951$	−4.28939e13	−1.70053
$952$	−6.89594e11	−0.0272099
$953$	−4.25218e13	−1.66991	−0.834955	−	0.550318i	$-0.814506\pi$
$953$	−4.25218e13	−1.66991	−0.834955	+	0.550318i	$0.814506\pi$
$954$	7.46916e10	0.00291947
$955$	−1.09491e13	−0.425956
$956$	−1.88524e12	−0.0729972
$957$	−2.19754e12	−0.0846901
$958$	3.07570e13	1.17977
$959$	1.80121e12	0.0687670
$960$	−9.37122e12	−0.356103
$961$	4.54266e13	1.71813
$962$	9.17125e12	0.345256
$963$	1.40568e12	0.0526707
$964$	7.45531e12	0.278048
$965$	1.57049e13	0.582992
$966$	5.09550e12	0.188274
$967$	−1.21906e13	−0.448338	−0.224169	−	0.974550i	$-0.571967\pi$
$967$	−1.21906e13	−0.448338	−0.224169	+	0.974550i	$0.571967\pi$
$968$	2.78157e13	1.01824
$969$	−1.86658e12	−0.0680128
$970$	−1.34497e13	−0.487796
$971$	5.38639e12	0.194452	0.0972258	−	0.995262i	$-0.469003\pi$
$971$	5.38639e12	0.194452	0.0972258	+	0.995262i	$0.469003\pi$
$972$	−1.07466e12	−0.0386167
$973$	−1.58247e13	−0.566016
$974$	−3.71954e13	−1.32426
$975$	−7.37798e12	−0.261467
$976$	−5.90583e12	−0.208332
$977$	−1.89284e13	−0.664643	−0.332321	−	0.943166i	$-0.607832\pi$
$977$	−1.89284e13	−0.664643	−0.332321	+	0.943166i	$0.607832\pi$
$978$	−2.14169e13	−0.748570
$979$	−2.13153e12	−0.0741600
$980$	9.85407e11	0.0341270
$981$	−7.39990e11	−0.0255103
$982$	4.40719e12	0.151238
$983$	3.98513e13	1.36129	0.680647	−	0.732612i	$-0.261699\pi$
$983$	3.98513e13	1.36129	0.680647	+	0.732612i	$0.261699\pi$
$984$	2.48212e13	0.844004
$985$	−2.05300e13	−0.694907
$986$	−7.23708e11	−0.0243847
$987$	−7.64075e12	−0.256277
$988$	2.14671e13	0.716748
$989$	−3.14118e13	−1.04402
$990$	−5.53836e10	−0.00183241
$991$	−3.44424e13	−1.13439	−0.567194	−	0.823584i	$-0.691971\pi$
$991$	−3.44424e13	−1.13439	−0.567194	+	0.823584i	$0.691971\pi$
$992$	−4.64588e13	−1.52323
$993$	4.06020e13	1.32518
$994$	8.03877e12	0.261187
$995$	2.23078e12	0.0721527
$996$	2.80066e13	0.901765
$997$	4.12406e13	1.32189	0.660947	−	0.750433i	$-0.270155\pi$
$997$	4.12406e13	1.32189	0.660947	+	0.750433i	$0.270155\pi$
$998$	3.26777e13	1.04271
$999$	1.21652e13	0.386432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.10.a.c.1.3	✓	4
3.2	odd	2		315.10.a.g.1.2		4
5.2	odd	4		175.10.b.e.99.5		8
5.3	odd	4		175.10.b.e.99.4		8
5.4	even	2		175.10.a.e.1.2		4
7.6	odd	2		245.10.a.e.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.c.1.3	✓	4	1.1	even	1	trivial
175.10.a.e.1.2		4	5.4	even	2
175.10.b.e.99.4		8	5.3	odd	4
175.10.b.e.99.5		8	5.2	odd	4
245.10.a.e.1.3		4	7.6	odd	2
315.10.a.g.1.2		4	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	35.a (trivial)

\(f(q)\)	\(=\)	\(q+15.4436 q^{2} +137.736 q^{3} -273.496 q^{4} -625.000 q^{5} +2127.13 q^{6} -2401.00 q^{7} -12130.9 q^{8} -711.820 q^{9} -9652.23 q^{10} -8060.89 q^{11} -37670.3 q^{12} -137129. q^{13} -37080.0 q^{14} -86084.9 q^{15} -47313.7 q^{16} -23676.1 q^{17} -10993.0 q^{18} +572389. q^{19} +170935. q^{20} -330704. q^{21} -124489. q^{22} -997700. q^{23} -1.67086e6 q^{24} +390625. q^{25} -2.11777e6 q^{26} -2.80910e6 q^{27} +656664. q^{28} +1.97927e6 q^{29} -1.32946e6 q^{30} -8.47740e6 q^{31} +5.48031e6 q^{32} -1.11027e6 q^{33} -365643. q^{34} +1.50062e6 q^{35} +194680. q^{36} -4.33062e6 q^{37} +8.83972e6 q^{38} -1.88876e7 q^{39} +7.58179e6 q^{40} -1.48554e7 q^{41} -5.10725e6 q^{42} +3.14842e7 q^{43} +2.20462e6 q^{44} +444888. q^{45} -1.54081e7 q^{46} +2.31045e7 q^{47} -6.51680e6 q^{48} +5.76480e6 q^{49} +6.03264e6 q^{50} -3.26104e6 q^{51} +3.75044e7 q^{52} -6.79444e6 q^{53} -4.33825e7 q^{54} +5.03805e6 q^{55} +2.91262e7 q^{56} +7.88385e7 q^{57} +3.05671e7 q^{58} +8.85117e7 q^{59} +2.35439e7 q^{60} +1.24823e8 q^{61} -1.30921e8 q^{62} +1.70908e6 q^{63} +1.08860e8 q^{64} +8.57059e7 q^{65} -1.71466e7 q^{66} +9.58712e7 q^{67} +6.47531e6 q^{68} -1.37419e8 q^{69} +2.31750e7 q^{70} -2.16795e8 q^{71} +8.63500e6 q^{72} -1.50701e8 q^{73} -6.68803e7 q^{74} +5.38031e7 q^{75} -1.56546e8 q^{76} +1.93542e7 q^{77} -2.91693e8 q^{78} -3.89487e8 q^{79} +2.95711e7 q^{80} -3.72903e8 q^{81} -2.29420e8 q^{82} -7.43467e8 q^{83} +9.04463e7 q^{84} +1.47975e7 q^{85} +4.86228e8 q^{86} +2.72617e8 q^{87} +9.77855e7 q^{88} +2.64429e8 q^{89} +6.87065e6 q^{90} +3.29248e8 q^{91} +2.72867e8 q^{92} -1.16764e9 q^{93} +3.56816e8 q^{94} -3.57743e8 q^{95} +7.54835e8 q^{96} +1.39343e9 q^{97} +8.90291e7 q^{98} +5.73790e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 19 q^{2} - 18 q^{3} + 1729 q^{4} - 2500 q^{5} - 144 q^{6} - 9604 q^{7} - 30495 q^{8} + 5382 q^{9} + 11875 q^{10} + 82438 q^{11} + 41328 q^{12} - 72962 q^{13} + 45619 q^{14} + 11250 q^{15} + 64257 q^{16}+ \cdots + 1222369524 q^{99}+O(q^{100}) \) 4 * q - 19 * q^2 - 18 * q^3 + 1729 * q^4 - 2500 * q^5 - 144 * q^6 - 9604 * q^7 - 30495 * q^8 + 5382 * q^9 + 11875 * q^10 + 82438 * q^11 + 41328 * q^12 - 72962 * q^13 + 45619 * q^14 + 11250 * q^15 + 64257 * q^16 - 357542 * q^17 - 965367 * q^18 + 300732 * q^19 - 1080625 * q^20 + 43218 * q^21 - 5595068 * q^22 - 2340836 * q^23 - 7636320 * q^24 + 1562500 * q^25 + 1305666 * q^26 - 4240350 * q^27 - 4151329 * q^28 - 1372022 * q^29 + 90000 * q^30 - 4590888 * q^31 - 10529439 * q^32 + 2000034 * q^33 - 7199478 * q^34 + 6002500 * q^35 - 9144243 * q^36 - 38868456 * q^37 - 15477280 * q^38 - 46666242 * q^39 + 19059375 * q^40 + 57287084 * q^41 + 345744 * q^42 - 43403452 * q^43 + 87639348 * q^44 - 3363750 * q^45 + 28892416 * q^46 + 91822222 * q^47 + 156168864 * q^48 + 23059204 * q^49 - 7421875 * q^50 + 86342634 * q^51 + 1953386 * q^52 - 61086884 * q^53 + 187589520 * q^54 - 51523750 * q^55 + 73218495 * q^56 - 79928892 * q^57 + 29615390 * q^58 + 72569680 * q^59 - 25830000 * q^60 - 225681036 * q^61 + 190286472 * q^62 - 12922182 * q^63 + 141443393 * q^64 + 45601250 * q^65 - 119673648 * q^66 - 4429720 * q^67 + 15339698 * q^68 + 348300612 * q^69 - 28511875 * q^70 - 470468984 * q^71 + 298610685 * q^72 - 168326464 * q^73 + 927809502 * q^74 - 7031250 * q^75 - 892265344 * q^76 - 197933638 * q^77 + 281290896 * q^78 - 598805646 * q^79 - 40160625 * q^80 - 847155996 * q^81 - 1821993318 * q^82 - 1159074304 * q^83 - 99228528 * q^84 + 223463750 * q^85 + 706791156 * q^86 - 421480998 * q^87 - 1992103900 * q^88 - 1380153012 * q^89 + 603354375 * q^90 + 175181762 * q^91 + 710319264 * q^92 - 1601969400 * q^93 + 2466744152 * q^94 - 187957500 * q^95 - 799321824 * q^96 + 754874082 * q^97 - 109531219 * q^98 + 1222369524 * q^99

Introduction

L-functions

Modular forms

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Database

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