LMFDB - Embedded newform 197.10.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,10,Mod(1,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("197.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	197.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:	$101.462059724$
Analytic rank:	$0$
Dimension:	$76$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	197.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-41.6400 q^{2} +9.57611 q^{3} +1221.89 q^{4} +18.3099 q^{5} -398.750 q^{6} +11241.8 q^{7} -29560.0 q^{8} -19591.3 q^{9} +O(q^{10})$	\(q-41.6400 q^{2} +9.57611 q^{3} +1221.89 q^{4} +18.3099 q^{5} -398.750 q^{6} +11241.8 q^{7} -29560.0 q^{8} -19591.3 q^{9} -762.427 q^{10} +79059.0 q^{11} +11701.0 q^{12} -102812. q^{13} -468110. q^{14} +175.338 q^{15} +605269. q^{16} -341756. q^{17} +815782. q^{18} +155870. q^{19} +22372.8 q^{20} +107653. q^{21} -3.29202e6 q^{22} +1.34073e6 q^{23} -283070. q^{24} -1.95279e6 q^{25} +4.28110e6 q^{26} -376095. q^{27} +1.37363e7 q^{28} -1.20356e6 q^{29} -7301.09 q^{30} +8.69177e6 q^{31} -1.00687e7 q^{32} +757078. q^{33} +1.42307e7 q^{34} +205837. q^{35} -2.39385e7 q^{36} +1.00937e7 q^{37} -6.49045e6 q^{38} -984541. q^{39} -541241. q^{40} +1.09113e6 q^{41} -4.48267e6 q^{42} +2.43281e7 q^{43} +9.66016e7 q^{44} -358716. q^{45} -5.58281e7 q^{46} +662485. q^{47} +5.79612e6 q^{48} +8.60248e7 q^{49} +8.13142e7 q^{50} -3.27269e6 q^{51} -1.25625e8 q^{52} +1.65507e7 q^{53} +1.56606e7 q^{54} +1.44757e6 q^{55} -3.32308e8 q^{56} +1.49263e6 q^{57} +5.01164e7 q^{58} -1.42532e8 q^{59} +214244. q^{60} -1.40154e8 q^{61} -3.61926e8 q^{62} -2.20242e8 q^{63} +1.09364e8 q^{64} -1.88249e6 q^{65} -3.15248e7 q^{66} +2.96953e8 q^{67} -4.17589e8 q^{68} +1.28390e7 q^{69} -8.57106e6 q^{70} +1.91980e8 q^{71} +5.79118e8 q^{72} -4.61271e8 q^{73} -4.20302e8 q^{74} -1.87001e7 q^{75} +1.90457e8 q^{76} +8.88767e8 q^{77} +4.09963e7 q^{78} -4.14667e8 q^{79} +1.10824e7 q^{80} +3.82014e8 q^{81} -4.54347e7 q^{82} +1.16968e8 q^{83} +1.31540e8 q^{84} -6.25753e6 q^{85} -1.01302e9 q^{86} -1.15255e7 q^{87} -2.33698e9 q^{88} -4.41361e8 q^{89} +1.49369e7 q^{90} -1.15579e9 q^{91} +1.63823e9 q^{92} +8.32333e7 q^{93} -2.75859e7 q^{94} +2.85398e6 q^{95} -9.64192e7 q^{96} +1.56961e9 q^{97} -3.58207e9 q^{98} -1.54887e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9}+O(q^{10}) $ 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9	\( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9} + 121093 q^{10} + 120464 q^{11} + 415744 q^{12} + 480131 q^{13} + 330849 q^{14} + 544874 q^{15} + 5963776 q^{16} + 942582 q^{17} + 1483945 q^{18} + 3097319 q^{19} + 3237739 q^{20} + 889076 q^{21} + 3791921 q^{22} + 5139200 q^{23} + 1999533 q^{24} + 34080519 q^{25} + 2791454 q^{26} + 24386486 q^{27} + 20891166 q^{28} + 6886818 q^{29} + 14171083 q^{30} + 28002851 q^{31} + 16857332 q^{32} + 30921422 q^{33} + 33506194 q^{34} + 16271736 q^{35} + 151430458 q^{36} + 55950976 q^{37} + 62370882 q^{38} - 11569592 q^{39} + 129854766 q^{40} + 14990859 q^{41} + 82216531 q^{42} + 169867467 q^{43} + 41872434 q^{44} + 205007649 q^{45} + 144032301 q^{46} + 78743342 q^{47} + 156250562 q^{48} + 533861890 q^{49} + 626841163 q^{50} + 477099244 q^{51} + 560784114 q^{52} + 188670216 q^{53} + 525901687 q^{54} + 298497914 q^{55} + 56575048 q^{56} + 213972590 q^{57} + 338315251 q^{58} + 208222151 q^{59} - 615921507 q^{60} - 233556134 q^{61} - 399368105 q^{62} + 329825056 q^{63} + 876517017 q^{64} - 840557006 q^{65} - 2482481592 q^{66} + 1210808414 q^{67} - 1266757099 q^{68} + 327801786 q^{69} - 546384313 q^{70} + 345300221 q^{71} - 1549481681 q^{72} + 1192286460 q^{73} - 1471133595 q^{74} + 761630676 q^{75} - 398699826 q^{76} - 101106252 q^{77} - 2609825943 q^{78} + 955627631 q^{79} + 1059617770 q^{80} + 3387041436 q^{81} + 1062705523 q^{82} + 1538917201 q^{83} + 1394513218 q^{84} + 225481100 q^{85} + 701644810 q^{86} + 1758812842 q^{87} + 3151474875 q^{88} + 855413630 q^{89} + 6070671455 q^{90} + 4652436248 q^{91} + 8082863606 q^{92} + 3462095982 q^{93} + 2660342117 q^{94} + 1036805508 q^{95} + 12370989029 q^{96} + 6393874545 q^{97} + 7510976010 q^{98} + 8731109606 q^{99}+O(q^{100}) \) 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9 + 121093 * q^10 + 120464 * q^11 + 415744 * q^12 + 480131 * q^13 + 330849 * q^14 + 544874 * q^15 + 5963776 * q^16 + 942582 * q^17 + 1483945 * q^18 + 3097319 * q^19 + 3237739 * q^20 + 889076 * q^21 + 3791921 * q^22 + 5139200 * q^23 + 1999533 * q^24 + 34080519 * q^25 + 2791454 * q^26 + 24386486 * q^27 + 20891166 * q^28 + 6886818 * q^29 + 14171083 * q^30 + 28002851 * q^31 + 16857332 * q^32 + 30921422 * q^33 + 33506194 * q^34 + 16271736 * q^35 + 151430458 * q^36 + 55950976 * q^37 + 62370882 * q^38 - 11569592 * q^39 + 129854766 * q^40 + 14990859 * q^41 + 82216531 * q^42 + 169867467 * q^43 + 41872434 * q^44 + 205007649 * q^45 + 144032301 * q^46 + 78743342 * q^47 + 156250562 * q^48 + 533861890 * q^49 + 626841163 * q^50 + 477099244 * q^51 + 560784114 * q^52 + 188670216 * q^53 + 525901687 * q^54 + 298497914 * q^55 + 56575048 * q^56 + 213972590 * q^57 + 338315251 * q^58 + 208222151 * q^59 - 615921507 * q^60 - 233556134 * q^61 - 399368105 * q^62 + 329825056 * q^63 + 876517017 * q^64 - 840557006 * q^65 - 2482481592 * q^66 + 1210808414 * q^67 - 1266757099 * q^68 + 327801786 * q^69 - 546384313 * q^70 + 345300221 * q^71 - 1549481681 * q^72 + 1192286460 * q^73 - 1471133595 * q^74 + 761630676 * q^75 - 398699826 * q^76 - 101106252 * q^77 - 2609825943 * q^78 + 955627631 * q^79 + 1059617770 * q^80 + 3387041436 * q^81 + 1062705523 * q^82 + 1538917201 * q^83 + 1394513218 * q^84 + 225481100 * q^85 + 701644810 * q^86 + 1758812842 * q^87 + 3151474875 * q^88 + 855413630 * q^89 + 6070671455 * q^90 + 4652436248 * q^91 + 8082863606 * q^92 + 3462095982 * q^93 + 2660342117 * q^94 + 1036805508 * q^95 + 12370989029 * q^96 + 6393874545 * q^97 + 7510976010 * q^98 + 8731109606 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−41.6400	−1.84025	−0.920124	−	0.391628i	$-0.871912\pi$
$2$	−41.6400	−1.84025	−0.920124	+	0.391628i	$0.871912\pi$
$3$	9.57611	0.0682564	0.0341282	−	0.999417i	$-0.489135\pi$
$3$	9.57611	0.0682564	0.0341282	+	0.999417i	$0.489135\pi$
$4$	1221.89	2.38651
$5$	18.3099	0.0131015	0.00655077	−	0.999979i	$-0.497915\pi$
$5$	18.3099	0.0131015	0.00655077	+	0.999979i	$0.497915\pi$
$6$	−398.750	−0.125609
$7$	11241.8	1.76968	0.884841	−	0.465893i	$-0.154267\pi$
$7$	11241.8	1.76968	0.884841	+	0.465893i	$0.154267\pi$
$8$	−29560.0	−2.55152
$9$	−19591.3	−0.995341
$10$	−762.427	−0.0241101
$11$	79059.0	1.62811	0.814056	−	0.580786i	$-0.197255\pi$
$11$	79059.0	1.62811	0.814056	+	0.580786i	$0.197255\pi$
$12$	11701.0	0.162895
$13$	−102812.	−0.998388	−0.499194	−	0.866490i	$-0.666370\pi$
$13$	−102812.	−0.998388	−0.499194	+	0.866490i	$0.666370\pi$
$14$	−468110.	−3.25665
$15$	175.338	0.000894264 0
$16$	605269.	2.30892
$17$	−341756.	−0.992420	−0.496210	−	0.868203i	$-0.665275\pi$
$17$	−341756.	−0.992420	−0.496210	+	0.868203i	$0.665275\pi$
$18$	815782.	1.83167
$19$	155870.	0.274393	0.137196	−	0.990544i	$-0.456191\pi$
$19$	155870.	0.274393	0.137196	+	0.990544i	$0.456191\pi$
$20$	22372.8	0.0312669
$21$	107653.	0.120792
$22$	−3.29202e6	−2.99613
$23$	1.34073e6	0.999002	0.499501	−	0.866313i	$-0.333517\pi$
$23$	1.34073e6	0.999002	0.499501	+	0.866313i	$0.333517\pi$
$24$	−283070.	−0.174158
$25$	−1.95279e6	−0.999828
$26$	4.28110e6	1.83728
$27$	−376095.	−0.136195
$28$	1.37363e7	4.22336
$29$	−1.20356e6	−0.315993	−0.157997	−	0.987440i	$-0.550504\pi$
$29$	−1.20356e6	−0.315993	−0.157997	+	0.987440i	$0.550504\pi$
$30$	−7301.09	−0.00164567
$31$	8.69177e6	1.69036	0.845182	−	0.534478i	$-0.179492\pi$
$31$	8.69177e6	1.69036	0.845182	+	0.534478i	$0.179492\pi$
$32$	−1.00687e7	−1.69746
$33$	757078.	0.111129
$34$	1.42307e7	1.82630
$35$	205837.	0.0231855
$36$	−2.39385e7	−2.37539
$37$	1.00937e7	0.885406	0.442703	−	0.896668i	$-0.354020\pi$
$37$	1.00937e7	0.885406	0.442703	+	0.896668i	$0.354020\pi$
$38$	−6.49045e6	−0.504950
$39$	−984541.	−0.0681464
$40$	−541241.	−0.0334288
$41$	1.09113e6	0.0603045	0.0301522	−	0.999545i	$-0.490401\pi$
$41$	1.09113e6	0.0603045	0.0301522	+	0.999545i	$0.490401\pi$
$42$	−4.48267e6	−0.222287
$43$	2.43281e7	1.08518	0.542588	−	0.839999i	$-0.317445\pi$
$43$	2.43281e7	1.08518	0.542588	+	0.839999i	$0.317445\pi$
$44$	9.66016e7	3.88550
$45$	−358716.	−0.0130405
$46$	−5.58281e7	−1.83841
$47$	662485.	0.0198032	0.00990161	−	0.999951i	$-0.496848\pi$
$47$	662485.	0.0198032	0.00990161	+	0.999951i	$0.496848\pi$
$48$	5.79612e6	0.157598
$49$	8.60248e7	2.13177
$50$	8.13142e7	1.83993
$51$	−3.27269e6	−0.0677391
$52$	−1.25625e8	−2.38266
$53$	1.65507e7	0.288122	0.144061	−	0.989569i	$-0.453984\pi$
$53$	1.65507e7	0.288122	0.144061	+	0.989569i	$0.453984\pi$
$54$	1.56606e7	0.250632
$55$	1.44757e6	0.0213308
$56$	−3.32308e8	−4.51538
$57$	1.49263e6	0.0187291
$58$	5.01164e7	0.581506
$59$	−1.42532e8	−1.53137	−0.765683	−	0.643218i	$-0.777599\pi$
$59$	−1.42532e8	−1.53137	−0.765683	+	0.643218i	$0.777599\pi$
$60$	214244.	0.00213417
$61$	−1.40154e8	−1.29605	−0.648024	−	0.761620i	$-0.724404\pi$
$61$	−1.40154e8	−1.29605	−0.648024	+	0.761620i	$0.724404\pi$
$62$	−3.61926e8	−3.11069
$63$	−2.20242e8	−1.76144
$64$	1.09364e8	0.814826
$65$	−1.88249e6	−0.0130804
$66$	−3.15248e7	−0.204505
$67$	2.96953e8	1.80033	0.900164	−	0.435552i	$-0.143447\pi$
$67$	2.96953e8	1.80033	0.900164	+	0.435552i	$0.143447\pi$
$68$	−4.17589e8	−2.36842
$69$	1.28390e7	0.0681883
$70$	−8.57106e6	−0.0426671
$71$	1.91980e8	0.896591	0.448296	−	0.893885i	$-0.352031\pi$
$71$	1.91980e8	0.896591	0.448296	+	0.893885i	$0.352031\pi$
$72$	5.79118e8	2.53963
$73$	−4.61271e8	−1.90109	−0.950546	−	0.310583i	$-0.899476\pi$
$73$	−4.61271e8	−1.90109	−0.950546	+	0.310583i	$0.899476\pi$
$74$	−4.20302e8	−1.62937
$75$	−1.87001e7	−0.0682447
$76$	1.90457e8	0.654841
$77$	8.88767e8	2.88124
$78$	4.09963e7	0.125406
$79$	−4.14667e8	−1.19778	−0.598891	−	0.800831i	$-0.704392\pi$
$79$	−4.14667e8	−1.19778	−0.598891	+	0.800831i	$0.704392\pi$
$80$	1.10824e7	0.0302504
$81$	3.82014e8	0.986045
$82$	−4.54347e7	−0.110975
$83$	1.16968e8	0.270531	0.135266	−	0.990809i	$-0.456811\pi$
$83$	1.16968e8	0.270531	0.135266	+	0.990809i	$0.456811\pi$
$84$	1.31540e8	0.288272
$85$	−6.25753e6	−0.0130022
$86$	−1.01302e9	−1.99699
$87$	−1.15255e7	−0.0215686
$88$	−2.33698e9	−4.15416
$89$	−4.41361e8	−0.745657	−0.372829	−	0.927900i	$-0.621612\pi$
$89$	−4.41361e8	−0.745657	−0.372829	+	0.927900i	$0.621612\pi$
$90$	1.49369e7	0.0239977
$91$	−1.15579e9	−1.76683
$92$	1.63823e9	2.38413
$93$	8.32333e7	0.115378
$94$	−2.75859e7	−0.0364428
$95$	2.85398e6	0.00359497
$96$	−9.64192e7	−0.115862
$97$	1.56961e9	1.80019	0.900095	−	0.435693i	$-0.143497\pi$
$97$	1.56961e9	1.80019	0.900095	+	0.435693i	$0.143497\pi$
$98$	−3.58207e9	−3.92299
$99$	−1.54887e9	−1.62053
$100$	−2.38610e9	−2.38610
$101$	3.88793e6	0.00371768	0.00185884	−	0.999998i	$-0.499408\pi$
$101$	3.88793e6	0.00371768	0.00185884	+	0.999998i	$0.499408\pi$
$102$	1.36275e8	0.124657
$103$	1.29787e9	1.13622	0.568111	−	0.822952i	$-0.307674\pi$
$103$	1.29787e9	1.13622	0.568111	+	0.822952i	$0.307674\pi$
$104$	3.03912e9	2.54741
$105$	1.97112e6	0.00158256
$106$	−6.89173e8	−0.530215
$107$	−2.55046e9	−1.88101	−0.940506	−	0.339776i	$-0.889649\pi$
$107$	−2.55046e9	−1.88101	−0.940506	+	0.339776i	$0.889649\pi$
$108$	−4.59548e8	−0.325030
$109$	1.68336e9	1.14224	0.571119	−	0.820867i	$-0.306509\pi$
$109$	1.68336e9	1.14224	0.571119	+	0.820867i	$0.306509\pi$
$110$	−6.02767e7	−0.0392539
$111$	9.66584e7	0.0604346
$112$	6.80432e9	4.08605
$113$	−1.43842e9	−0.829913	−0.414957	−	0.909841i	$-0.636203\pi$
$113$	−1.43842e9	−0.829913	−0.414957	+	0.909841i	$0.636203\pi$
$114$	−6.21533e7	−0.0344661
$115$	2.45487e7	0.0130885
$116$	−1.47062e9	−0.754121
$117$	2.01422e9	0.993737
$118$	5.93505e9	2.81809
$119$	−3.84195e9	−1.75627
$120$	−5.18299e6	−0.00228173
$121$	3.89238e9	1.65075
$122$	5.83601e9	2.38505
$123$	1.04488e7	0.00411617
$124$	1.06204e10	4.03407
$125$	−7.15171e7	−0.0262008
$126$	9.17087e9	3.24148
$127$	3.33410e9	1.13726	0.568632	−	0.822592i	$-0.307473\pi$
$127$	3.33410e9	1.13726	0.568632	+	0.822592i	$0.307473\pi$
$128$	6.01256e8	0.197977
$129$	2.32969e8	0.0740702
$130$	7.83868e7	0.0240712
$131$	−5.16158e7	−0.0153130	−0.00765652	−	0.999971i	$-0.502437\pi$
$131$	−5.16158e7	−0.0153130	−0.00765652	+	0.999971i	$0.502437\pi$
$132$	9.25068e8	0.265211
$133$	1.75227e9	0.485588
$134$	−1.23651e10	−3.31305
$135$	−6.88628e6	−0.00178436
$136$	1.01023e10	2.53218
$137$	−1.38672e9	−0.336315	−0.168158	−	0.985760i	$-0.553782\pi$
$137$	−1.38672e9	−0.336315	−0.168158	+	0.985760i	$0.553782\pi$
$138$	−5.34616e8	−0.125483
$139$	5.26048e9	1.19525	0.597624	−	0.801776i	$-0.296111\pi$
$139$	5.26048e9	1.19525	0.597624	+	0.801776i	$0.296111\pi$
$140$	2.51511e8	0.0553325
$141$	6.34403e6	0.00135170
$142$	−7.99407e9	−1.64995
$143$	−8.12823e9	−1.62549
$144$	−1.18580e10	−2.29816
$145$	−2.20372e7	−0.00414000
$146$	1.92073e10	3.49848
$147$	8.23783e8	0.145507
$148$	1.23334e10	2.11303
$149$	−2.44267e9	−0.406000	−0.203000	−	0.979179i	$-0.565069\pi$
$149$	−2.44267e9	−0.406000	−0.203000	+	0.979179i	$0.565069\pi$
$150$	7.78674e8	0.125587
$151$	9.21279e9	1.44210	0.721049	−	0.692884i	$-0.243660\pi$
$151$	9.21279e9	1.44210	0.721049	+	0.692884i	$0.243660\pi$
$152$	−4.60752e9	−0.700118
$153$	6.69544e9	0.987796
$154$	−3.70083e10	−5.30219
$155$	1.59146e8	0.0221464
$156$	−1.20300e9	−0.162632
$157$	6.84933e9	0.899704	0.449852	−	0.893103i	$-0.351477\pi$
$157$	6.84933e9	0.899704	0.449852	+	0.893103i	$0.351477\pi$
$158$	1.72668e10	2.20421
$159$	1.58492e8	0.0196662
$160$	−1.84358e8	−0.0222393
$161$	1.50722e10	1.76792
$162$	−1.59071e10	−1.81457
$163$	−6.06337e9	−0.672775	−0.336388	−	0.941724i	$-0.609205\pi$
$163$	−6.06337e9	−0.672775	−0.336388	+	0.941724i	$0.609205\pi$
$164$	1.33324e9	0.143917
$165$	1.38621e7	0.00145596
$166$	−4.87057e9	−0.497844
$167$	1.37419e9	0.136717	0.0683584	−	0.997661i	$-0.478224\pi$
$167$	1.37419e9	0.136717	0.0683584	+	0.997661i	$0.478224\pi$
$168$	−3.18221e9	−0.308204
$169$	−3.41618e7	−0.00322144
$170$	2.60564e8	0.0239273
$171$	−3.05370e9	−0.273114
$172$	2.97263e10	2.58978
$173$	−1.78720e10	−1.51693	−0.758464	−	0.651715i	$-0.774050\pi$
$173$	−1.78720e10	−1.51693	−0.758464	+	0.651715i	$0.774050\pi$
$174$	4.79920e8	0.0396915
$175$	−2.19529e10	−1.76938
$176$	4.78520e10	3.75918
$177$	−1.36491e9	−0.104526
$178$	1.83783e10	1.37219
$179$	9.97519e9	0.726244	0.363122	−	0.931742i	$-0.381711\pi$
$179$	9.97519e9	0.726244	0.363122	+	0.931742i	$0.381711\pi$
$180$	−4.38312e8	−0.0311213
$181$	1.65926e10	1.14911	0.574555	−	0.818466i	$-0.305175\pi$
$181$	1.65926e10	1.14911	0.574555	+	0.818466i	$0.305175\pi$
$182$	4.81273e10	3.25140
$183$	−1.34213e9	−0.0884636
$184$	−3.96320e10	−2.54897
$185$	1.84815e8	0.0116002
$186$	−3.46584e9	−0.212325
$187$	−2.70189e10	−1.61577
$188$	8.09486e8	0.0472606
$189$	−4.22799e9	−0.241022
$190$	−1.18840e8	−0.00661562
$191$	−1.58222e10	−0.860234	−0.430117	−	0.902773i	$-0.641528\pi$
$191$	−1.58222e10	−0.860234	−0.430117	+	0.902773i	$0.641528\pi$
$192$	1.04728e9	0.0556171
$193$	−1.57214e10	−0.815611	−0.407805	−	0.913069i	$-0.633706\pi$
$193$	−1.57214e10	−0.815611	−0.407805	+	0.913069i	$0.633706\pi$
$194$	−6.53585e10	−3.31280
$195$	−1.80269e7	−0.000892822 0
$196$	1.05113e11	5.08750
$197$	1.50614e9	0.0712470
$197$	1.50614e9	0.0712470
$198$	6.44949e10	2.98217
$199$	1.56293e10	0.706480	0.353240	−	0.935533i	$-0.385080\pi$
$199$	1.56293e10	0.706480	0.353240	+	0.935533i	$0.385080\pi$
$200$	5.77244e10	2.55108
$201$	2.84366e9	0.122884
$202$	−1.61893e8	−0.00684145
$203$	−1.35302e10	−0.559207
$204$	−3.99888e9	−0.161660
$205$	1.99785e7	0.000790081 0
$206$	−5.40433e10	−2.09093
$207$	−2.62667e10	−0.994348
$208$	−6.22290e10	−2.30520
$209$	1.23230e10	0.446742
$210$	−8.20775e7	−0.00291231
$211$	−2.63294e10	−0.914471	−0.457235	−	0.889346i	$-0.651160\pi$
$211$	−2.63294e10	−0.914471	−0.457235	+	0.889346i	$0.651160\pi$
$212$	2.02232e10	0.687605
$213$	1.83843e9	0.0611981
$214$	1.06201e11	3.46153
$215$	4.45446e8	0.0142175
$216$	1.11174e10	0.347504
$217$	9.77112e10	2.99141
$218$	−7.00950e10	−2.10200
$219$	−4.41718e9	−0.129762
$220$	1.76877e9	0.0509061
$221$	3.51366e10	0.990820
$222$	−4.02486e9	−0.111215
$223$	−4.91890e10	−1.33198	−0.665988	−	0.745963i	$-0.731990\pi$
$223$	−4.91890e10	−1.33198	−0.665988	+	0.745963i	$0.731990\pi$
$224$	−1.13191e11	−3.00396
$225$	3.82577e10	0.995170
$226$	5.98959e10	1.52725
$227$	4.05034e10	1.01245	0.506227	−	0.862401i	$-0.331040\pi$
$227$	4.05034e10	1.01245	0.506227	+	0.862401i	$0.331040\pi$
$228$	1.82384e9	0.0446971
$229$	−1.16797e10	−0.280653	−0.140327	−	0.990105i	$-0.544815\pi$
$229$	−1.16797e10	−0.280653	−0.140327	+	0.990105i	$0.544815\pi$
$230$	−1.02221e9	−0.0240860
$231$	8.51093e9	0.196663
$232$	3.55773e10	0.806263
$233$	4.04904e9	0.0900016	0.0450008	−	0.998987i	$-0.485671\pi$
$233$	4.04904e9	0.0900016	0.0450008	+	0.998987i	$0.485671\pi$
$234$	−8.38723e10	−1.82872
$235$	1.21301e7	0.000259453 0
$236$	−1.74159e11	−3.65462
$237$	−3.97090e9	−0.0817563
$238$	1.59979e11	3.23197
$239$	−4.91622e10	−0.974632	−0.487316	−	0.873226i	$-0.662024\pi$
$239$	−4.91622e10	−0.974632	−0.487316	+	0.873226i	$0.662024\pi$
$240$	1.06127e8	0.00206478
$241$	−1.54268e10	−0.294577	−0.147288	−	0.989094i	$-0.547055\pi$
$241$	−1.54268e10	−0.294577	−0.147288	+	0.989094i	$0.547055\pi$
$242$	−1.62079e11	−3.03779
$243$	1.10609e10	0.203499
$244$	−1.71253e11	−3.09303
$245$	1.57511e9	0.0279295
$246$	−4.35088e8	−0.00757476
$247$	−1.60254e10	−0.273950
$248$	−2.56928e11	−4.31300
$249$	1.12010e9	0.0184655
$250$	2.97797e9	0.0482160
$251$	8.61152e10	1.36946	0.684728	−	0.728798i	$-0.259921\pi$
$251$	8.61152e10	1.36946	0.684728	+	0.728798i	$0.259921\pi$
$252$	−2.69112e11	−4.20369
$253$	1.05997e11	1.62649
$254$	−1.38832e11	−2.09285
$255$	−5.99228e7	−0.000887485 0
$256$	−8.10308e10	−1.17915
$257$	6.63025e10	0.948049	0.474025	−	0.880512i	$-0.342801\pi$
$257$	6.63025e10	0.948049	0.474025	+	0.880512i	$0.342801\pi$
$258$	−9.70082e9	−0.136307
$259$	1.13471e11	1.56689
$260$	−2.30020e9	−0.0312165
$261$	2.35794e10	0.314521
$262$	2.14928e9	0.0281798
$263$	1.08526e11	1.39873	0.699364	−	0.714766i	$-0.253467\pi$
$263$	1.08526e11	1.39873	0.699364	+	0.714766i	$0.253467\pi$
$264$	−2.23792e10	−0.283548
$265$	3.03043e8	0.00377484
$266$	−7.29644e10	−0.893601
$267$	−4.22653e9	−0.0508959
$268$	3.62845e11	4.29650
$269$	1.43596e11	1.67207	0.836037	−	0.548672i	$-0.184867\pi$
$269$	1.43596e11	1.67207	0.836037	+	0.548672i	$0.184867\pi$
$270$	2.86745e8	0.00328367
$271$	9.17668e10	1.03353	0.516766	−	0.856127i	$-0.327136\pi$
$271$	9.17668e10	1.03353	0.516766	+	0.856127i	$0.327136\pi$
$272$	−2.06854e11	−2.29142
$273$	−1.10680e10	−0.120597
$274$	5.77431e10	0.618903
$275$	−1.54386e11	−1.62783
$276$	1.56879e10	0.162732
$277$	1.64024e11	1.67397	0.836986	−	0.547224i	$-0.184315\pi$
$277$	1.64024e11	1.67397	0.836986	+	0.547224i	$0.184315\pi$
$278$	−2.19046e11	−2.19955
$279$	−1.70283e11	−1.68249
$280$	−6.08454e9	−0.0591584
$281$	−1.58923e11	−1.52058	−0.760288	−	0.649586i	$-0.774942\pi$
$281$	−1.58923e11	−1.52058	−0.760288	+	0.649586i	$0.774942\pi$
$282$	−2.64166e8	−0.00248746
$283$	−1.04623e11	−0.969593	−0.484797	−	0.874627i	$-0.661106\pi$
$283$	−1.04623e11	−0.969593	−0.484797	+	0.874627i	$0.661106\pi$
$284$	2.34580e11	2.13972
$285$	2.73300e7	0.000245379 0
$286$	3.38460e11	2.99130
$287$	1.22663e10	0.106720
$288$	1.97259e11	1.68955
$289$	−1.79096e9	−0.0151024
$290$	9.17629e8	0.00761861
$291$	1.50307e10	0.122875
$292$	−5.63624e11	−4.53698
$293$	1.18366e11	0.938259	0.469129	−	0.883129i	$-0.344568\pi$
$293$	1.18366e11	0.938259	0.469129	+	0.883129i	$0.344568\pi$
$294$	−3.43023e10	−0.267769
$295$	−2.60976e9	−0.0200633
$296$	−2.98369e11	−2.25913
$297$	−2.97337e10	−0.221740
$298$	1.01713e11	0.747141
$299$	−1.37843e11	−0.997392
$300$	−2.28496e10	−0.162867
$301$	2.73492e11	1.92042
$302$	−3.83621e11	−2.65382
$303$	3.72312e7	0.000253755 0
$304$	9.43435e10	0.633550
$305$	−2.56621e9	−0.0169802
$306$	−2.78798e11	−1.81779
$307$	−6.01218e9	−0.0386287	−0.0193143	−	0.999813i	$-0.506148\pi$
$307$	−6.01218e9	−0.0386287	−0.0193143	+	0.999813i	$0.506148\pi$
$308$	1.08598e12	6.87611
$309$	1.24285e10	0.0775545
$310$	−6.62684e9	−0.0407548
$311$	2.24310e10	0.135965	0.0679824	−	0.997687i	$-0.478344\pi$
$311$	2.24310e10	0.135965	0.0679824	+	0.997687i	$0.478344\pi$
$312$	2.91030e10	0.173877
$313$	1.00030e11	0.589090	0.294545	−	0.955638i	$-0.404832\pi$
$313$	1.00030e11	0.589090	0.294545	+	0.955638i	$0.404832\pi$
$314$	−2.85206e11	−1.65568
$315$	−4.03261e9	−0.0230775
$316$	−5.06679e11	−2.85852
$317$	4.25898e10	0.236886	0.118443	−	0.992961i	$-0.462210\pi$
$317$	4.25898e10	0.236886	0.118443	+	0.992961i	$0.462210\pi$
$318$	−6.59960e9	−0.0361906
$319$	−9.51525e10	−0.514472
$320$	2.00245e9	0.0106755
$321$	−2.44235e10	−0.128391
$322$	−6.27609e11	−3.25340
$323$	−5.32696e10	−0.272313
$324$	4.66780e11	2.35321
$325$	2.00771e11	0.998217
$326$	2.52479e11	1.23807
$327$	1.61200e10	0.0779651
$328$	−3.22538e10	−0.153868
$329$	7.44754e9	0.0350454
$330$	−5.77217e8	−0.00267933
$331$	−8.08377e10	−0.370159	−0.185079	−	0.982724i	$-0.559254\pi$
$331$	−8.08377e10	−0.370159	−0.185079	+	0.982724i	$0.559254\pi$
$332$	1.42923e11	0.645625
$333$	−1.97749e11	−0.881281
$334$	−5.72212e10	−0.251593
$335$	5.43720e9	0.0235871
$336$	6.51589e10	0.278899
$337$	3.44413e11	1.45461	0.727303	−	0.686317i	$-0.240774\pi$
$337$	3.44413e11	1.45461	0.727303	+	0.686317i	$0.240774\pi$
$338$	1.42250e9	0.00592825
$339$	−1.37745e10	−0.0566469
$340$	−7.64603e9	−0.0310299
$341$	6.87162e11	2.75210
$342$	1.27156e11	0.502598
$343$	5.13427e11	2.00288
$344$	−7.19138e11	−2.76885
$345$	2.35081e8	0.000893371 0
$346$	7.44190e11	2.79152
$347$	9.48993e10	0.351383	0.175691	−	0.984445i	$-0.443784\pi$
$347$	9.48993e10	0.351383	0.175691	+	0.984445i	$0.443784\pi$
$348$	−1.40829e10	−0.0514736
$349$	1.32442e11	0.477873	0.238936	−	0.971035i	$-0.423201\pi$
$349$	1.32442e11	0.477873	0.238936	+	0.971035i	$0.423201\pi$
$350$	9.14120e11	3.25609
$351$	3.86671e10	0.135975
$352$	−7.96023e11	−2.76365
$353$	2.92730e11	1.00342	0.501709	−	0.865037i	$-0.332705\pi$
$353$	2.92730e11	1.00342	0.501709	+	0.865037i	$0.332705\pi$
$354$	5.68347e10	0.192353
$355$	3.51515e9	0.0117467
$356$	−5.39296e11	−1.77952
$357$	−3.67910e10	−0.119877
$358$	−4.15367e11	−1.33647
$359$	4.62584e11	1.46982	0.734912	−	0.678163i	$-0.237224\pi$
$359$	4.62584e11	1.46982	0.734912	+	0.678163i	$0.237224\pi$
$360$	1.06036e10	0.0332731
$361$	−2.98392e11	−0.924709
$362$	−6.90918e11	−2.11465
$363$	3.72739e10	0.112674
$364$	−1.41226e12	−4.21655
$365$	−8.44585e9	−0.0249072
$366$	5.58863e10	0.162795
$367$	−1.04700e11	−0.301265	−0.150633	−	0.988590i	$-0.548131\pi$
$367$	−1.04700e11	−0.301265	−0.150633	+	0.988590i	$0.548131\pi$
$368$	8.11503e11	2.30661
$369$	−2.13767e10	−0.0600235
$370$	−7.69571e9	−0.0213472
$371$	1.86060e11	0.509884
$372$	1.01702e11	0.275351
$373$	−1.12070e11	−0.299778	−0.149889	−	0.988703i	$-0.547892\pi$
$373$	−1.12070e11	−0.299778	−0.149889	+	0.988703i	$0.547892\pi$
$374$	1.12507e12	2.97342
$375$	−6.84856e8	−0.00178837
$376$	−1.95830e10	−0.0505283
$377$	1.23741e11	0.315484
$378$	1.76054e11	0.443539
$379$	4.61565e11	1.14910	0.574549	−	0.818470i	$-0.305178\pi$
$379$	4.61565e11	1.14910	0.574549	+	0.818470i	$0.305178\pi$
$380$	3.48726e9	0.00857942
$381$	3.19277e10	0.0776256
$382$	6.58837e11	1.58304
$383$	3.67316e11	0.872260	0.436130	−	0.899884i	$-0.356349\pi$
$383$	3.67316e11	0.872260	0.436130	+	0.899884i	$0.356349\pi$
$384$	5.75770e9	0.0135132
$385$	1.62733e10	0.0377487
$386$	6.54639e11	1.50093
$387$	−4.76619e11	−1.08012
$388$	1.91789e12	4.29617
$389$	9.77460e9	0.0216434	0.0108217	−	0.999941i	$-0.496555\pi$
$389$	9.77460e9	0.0216434	0.0108217	+	0.999941i	$0.496555\pi$
$390$	7.50640e8	0.00164301
$391$	−4.58202e11	−0.991430
$392$	−2.54289e12	−5.43926
$393$	−4.94278e8	−0.00104521
$394$	−6.27157e10	−0.131112
$395$	−7.59253e9	−0.0156928
$396$	−1.89255e12	−3.86740
$397$	−4.48800e11	−0.906767	−0.453384	−	0.891315i	$-0.649783\pi$
$397$	−4.48800e11	−0.906767	−0.453384	+	0.891315i	$0.649783\pi$
$398$	−6.50804e11	−1.30010
$399$	1.67799e10	0.0331445
$400$	−1.18196e12	−2.30852
$401$	−5.86253e11	−1.13223	−0.566116	−	0.824326i	$-0.691554\pi$
$401$	−5.86253e11	−1.13223	−0.566116	+	0.824326i	$0.691554\pi$
$402$	−1.18410e11	−0.226137
$403$	−8.93619e11	−1.68764
$404$	4.75063e9	0.00887227
$405$	6.99466e9	0.0129187
$406$	5.63399e11	1.02908
$407$	7.97997e11	1.44154
$408$	9.67406e10	0.172838
$409$	1.36487e11	0.241178	0.120589	−	0.992703i	$-0.461522\pi$
$409$	1.36487e11	0.241178	0.120589	+	0.992703i	$0.461522\pi$
$410$	−8.31908e8	−0.00145394
$411$	−1.32794e10	−0.0229557
$412$	1.58586e12	2.71161
$413$	−1.60232e12	−2.71003
$414$	1.09374e12	1.82985
$415$	2.14169e9	0.00354437
$416$	1.03519e12	1.69472
$417$	5.03749e10	0.0815834
$418$	−5.13129e11	−0.822116
$419$	−2.49774e11	−0.395899	−0.197949	−	0.980212i	$-0.563428\pi$
$419$	−2.49774e11	−0.395899	−0.197949	+	0.980212i	$0.563428\pi$
$420$	2.40850e9	0.00377680
$421$	2.33264e10	0.0361892	0.0180946	−	0.999836i	$-0.494240\pi$
$421$	2.33264e10	0.0361892	0.0180946	+	0.999836i	$0.494240\pi$
$422$	1.09636e12	1.68285
$423$	−1.29789e10	−0.0197110
$424$	−4.89239e11	−0.735148
$425$	6.67377e11	0.992250
$426$	−7.65522e10	−0.112620
$427$	−1.57558e12	−2.29359
$428$	−3.11639e12	−4.48906
$429$	−7.78368e10	−0.110950
$430$	−1.85484e10	−0.0261636
$431$	−9.46176e10	−0.132076	−0.0660380	−	0.997817i	$-0.521036\pi$
$431$	−9.46176e10	−0.132076	−0.0660380	+	0.997817i	$0.521036\pi$
$432$	−2.27639e11	−0.314463
$433$	6.50019e11	0.888650	0.444325	−	0.895866i	$-0.353444\pi$
$433$	6.50019e11	0.888650	0.444325	+	0.895866i	$0.353444\pi$
$434$	−4.06870e12	−5.50493
$435$	−2.11030e8	−0.000282581 0
$436$	2.05688e12	2.72596
$437$	2.08980e11	0.274119
$438$	1.83932e11	0.238794
$439$	−3.84913e10	−0.0494621	−0.0247310	−	0.999694i	$-0.507873\pi$
$439$	−3.84913e10	−0.0494621	−0.0247310	+	0.999694i	$0.507873\pi$
$440$	−4.27900e10	−0.0544259
$441$	−1.68534e12	−2.12184
$442$	−1.46309e12	−1.82335
$443$	8.19656e11	1.01115	0.505574	−	0.862783i	$-0.331281\pi$
$443$	8.19656e11	1.01115	0.505574	+	0.862783i	$0.331281\pi$
$444$	1.18106e11	0.144228
$445$	−8.08130e9	−0.00976925
$446$	2.04823e12	2.45116
$447$	−2.33913e10	−0.0277121
$448$	1.22945e12	1.44198
$449$	4.54198e11	0.527395	0.263698	−	0.964605i	$-0.415058\pi$
$449$	4.54198e11	0.527395	0.263698	+	0.964605i	$0.415058\pi$
$450$	−1.59305e12	−1.83136
$451$	8.62637e10	0.0981824
$452$	−1.75759e12	−1.98060
$453$	8.82227e10	0.0984324
$454$	−1.68656e12	−1.86316
$455$	−2.11625e10	−0.0231482
$456$	−4.41222e10	−0.0477876
$457$	−2.51971e11	−0.270227	−0.135113	−	0.990830i	$-0.543140\pi$
$457$	−2.51971e11	−0.270227	−0.135113	+	0.990830i	$0.543140\pi$
$458$	4.86341e11	0.516471
$459$	1.28533e11	0.135163
$460$	2.99959e10	0.0312357
$461$	6.49296e11	0.669558	0.334779	−	0.942297i	$-0.391338\pi$
$461$	6.49296e11	0.669558	0.334779	+	0.942297i	$0.391338\pi$
$462$	−3.54395e11	−0.361909
$463$	1.74357e12	1.76329	0.881646	−	0.471911i	$-0.156435\pi$
$463$	1.74357e12	1.76329	0.881646	+	0.471911i	$0.156435\pi$
$464$	−7.28479e11	−0.729602
$465$	1.52400e9	0.00151163
$466$	−1.68602e11	−0.165625
$467$	−9.48810e11	−0.923109	−0.461555	−	0.887112i	$-0.652708\pi$
$467$	−9.48810e11	−0.923109	−0.461555	+	0.887112i	$0.652708\pi$
$468$	2.46117e12	2.37156
$469$	3.33829e12	3.18601
$470$	−5.05097e8	−0.000477457 0
$471$	6.55899e10	0.0614106
$472$	4.21325e12	3.90731
$473$	1.92335e12	1.76679
$474$	1.65348e11	0.150452
$475$	−3.04382e11	−0.274346
$476$	−4.69445e12	−4.19135
$477$	−3.24250e11	−0.286779
$478$	2.04711e12	1.79356
$479$	1.55616e12	1.35065	0.675327	−	0.737519i	$-0.264003\pi$
$479$	1.55616e12	1.35065	0.675327	+	0.737519i	$0.264003\pi$
$480$	−1.76543e9	−0.00151798
$481$	−1.03775e12	−0.883979
$482$	6.42372e11	0.542094
$483$	1.44334e11	0.120672
$484$	4.75607e12	3.93953
$485$	2.87394e10	0.0235853
$486$	−4.60576e11	−0.374488
$487$	1.98792e12	1.60147	0.800734	−	0.599019i	$-0.204443\pi$
$487$	1.98792e12	1.60147	0.800734	+	0.599019i	$0.204443\pi$
$488$	4.14294e12	3.30689
$489$	−5.80635e10	−0.0459212
$490$	−6.55876e10	−0.0513972
$491$	−2.01335e11	−0.156334	−0.0781669	−	0.996940i	$-0.524907\pi$
$491$	−2.01335e11	−0.156334	−0.0781669	+	0.996940i	$0.524907\pi$
$492$	1.27673e10	0.00982327
$493$	4.11324e11	0.313598
$494$	6.67297e11	0.504136
$495$	−2.83597e10	−0.0212314
$496$	5.26086e12	3.90291
$497$	2.15821e12	1.58668
$498$	−4.66411e10	−0.0339811
$499$	−2.37825e11	−0.171714	−0.0858568	−	0.996307i	$-0.527363\pi$
$499$	−2.37825e11	−0.171714	−0.0858568	+	0.996307i	$0.527363\pi$
$500$	−8.73862e10	−0.0625285
$501$	1.31594e10	0.00933180
$502$	−3.58584e12	−2.52014
$503$	1.70034e12	1.18435	0.592174	−	0.805810i	$-0.298270\pi$
$503$	1.70034e12	1.18435	0.592174	+	0.805810i	$0.298270\pi$
$504$	6.51034e12	4.49434
$505$	7.11877e7	4.87073e−5 0
$506$	−4.41371e12	−2.99314
$507$	−3.27137e8	−0.000219884 0
$508$	4.07391e12	2.71409
$509$	−2.38839e12	−1.57716	−0.788579	−	0.614933i	$-0.789183\pi$
$509$	−2.38839e12	−1.57716	−0.788579	+	0.614933i	$0.789183\pi$
$510$	2.49519e9	0.00163319
$511$	−5.18552e12	−3.36433
$512$	3.06628e12	1.97196
$513$	−5.86221e10	−0.0373709
$514$	−2.76084e12	−1.74464
$515$	2.37639e10	0.0148863
$516$	2.84663e11	0.176769
$517$	5.23754e10	0.0322419
$518$	−4.72495e12	−2.88346
$519$	−1.71144e11	−0.103540
$520$	5.56462e10	0.0333749
$521$	5.23422e10	0.0311230	0.0155615	−	0.999879i	$-0.495046\pi$
$521$	5.23422e10	0.0311230	0.0155615	+	0.999879i	$0.495046\pi$
$522$	−9.81845e11	−0.578796
$523$	1.80904e12	1.05728	0.528640	−	0.848846i	$-0.322702\pi$
$523$	1.80904e12	1.05728	0.528640	+	0.848846i	$0.322702\pi$
$524$	−6.30689e10	−0.0365447
$525$	−2.10223e11	−0.120771
$526$	−4.51903e12	−2.57401
$527$	−2.97046e12	−1.67755
$528$	4.58236e11	0.256588
$529$	−3.59352e9	−0.00199512
$530$	−1.26187e10	−0.00694663
$531$	2.79239e12	1.52423
$532$	2.14108e12	1.15886
$533$	−1.12181e11	−0.0602072
$534$	1.75993e11	0.0936610
$535$	−4.66988e10	−0.0246442
$536$	−8.77793e12	−4.59357
$537$	9.55235e10	0.0495708
$538$	−5.97932e12	−3.07703
$539$	6.80103e12	3.47077
$540$	−8.41430e9	−0.00425840
$541$	−4.40577e11	−0.221123	−0.110561	−	0.993869i	$-0.535265\pi$
$541$	−4.40577e11	−0.221123	−0.110561	+	0.993869i	$0.535265\pi$
$542$	−3.82117e12	−1.90195
$543$	1.58893e11	0.0784342
$544$	3.44104e12	1.68459
$545$	3.08222e10	0.0149651
$546$	4.60873e11	0.221929
$547$	1.26833e12	0.605746	0.302873	−	0.953031i	$-0.402054\pi$
$547$	1.26833e12	0.605746	0.302873	+	0.953031i	$0.402054\pi$
$548$	−1.69443e12	−0.802620
$549$	2.74580e12	1.29001
$550$	6.42862e12	2.99561
$551$	−1.87600e11	−0.0867062
$552$	−3.79520e11	−0.173984
$553$	−4.66161e12	−2.11969
$554$	−6.82996e12	−3.08052
$555$	1.76981e9	0.000791787 0
$556$	6.42774e12	2.85247
$557$	−8.45744e11	−0.372298	−0.186149	−	0.982522i	$-0.559601\pi$
$557$	−8.45744e11	−0.372298	−0.186149	+	0.982522i	$0.559601\pi$
$558$	7.09059e12	3.09620
$559$	−2.50122e12	−1.08343
$560$	1.24587e11	0.0535335
$561$	−2.58736e11	−0.110287
$562$	6.61756e12	2.79824
$563$	1.00197e10	0.00420307	0.00210154	−	0.999998i	$-0.499331\pi$
$563$	1.00197e10	0.00420307	0.00210154	+	0.999998i	$0.499331\pi$
$564$	7.75173e9	0.00322584
$565$	−2.63374e10	−0.0108731
$566$	4.35652e12	1.78429
$567$	4.29453e12	1.74499
$568$	−5.67494e12	−2.28767
$569$	−2.50624e12	−1.00234	−0.501172	−	0.865348i	$-0.667098\pi$
$569$	−2.50624e12	−1.00234	−0.501172	+	0.865348i	$0.667098\pi$
$570$	−1.13802e9	−0.000451559 0
$571$	−2.66132e12	−1.04769	−0.523847	−	0.851813i	$-0.675504\pi$
$571$	−2.66132e12	−1.04769	−0.523847	+	0.851813i	$0.675504\pi$
$572$	−9.93182e12	−3.87924
$573$	−1.51515e11	−0.0587165
$574$	−5.10769e11	−0.196391
$575$	−2.61817e12	−0.998830
$576$	−2.14259e12	−0.811030
$577$	−1.96260e12	−0.737124	−0.368562	−	0.929603i	$-0.620150\pi$
$577$	−1.96260e12	−0.737124	−0.368562	+	0.929603i	$0.620150\pi$
$578$	7.45757e10	0.0277922
$579$	−1.50550e11	−0.0556707
$580$	−2.69271e10	−0.00988014
$581$	1.31494e12	0.478754
$582$	−6.25881e11	−0.226120
$583$	1.30849e12	0.469094
$584$	1.36352e13	4.85068
$585$	3.68803e10	0.0130195
$586$	−4.92877e12	−1.72663
$587$	5.04870e11	0.175512	0.0877562	−	0.996142i	$-0.472030\pi$
$587$	5.04870e11	0.175512	0.0877562	+	0.996142i	$0.472030\pi$
$588$	1.00657e12	0.347254
$589$	1.35479e12	0.463824
$590$	1.08670e11	0.0369213
$591$	1.44230e10	0.00486307
$592$	6.10940e12	2.04433
$593$	−3.55790e12	−1.18154	−0.590769	−	0.806841i	$-0.701175\pi$
$593$	−3.55790e12	−1.18154	−0.590769	+	0.806841i	$0.701175\pi$
$594$	1.23811e12	0.408057
$595$	−7.03460e10	−0.0230098
$596$	−2.98468e12	−0.968924
$597$	1.49668e11	0.0482218
$598$	5.73981e12	1.83545
$599$	−4.62502e12	−1.46789	−0.733944	−	0.679210i	$-0.762322\pi$
$599$	−4.62502e12	−1.46789	−0.733944	+	0.679210i	$0.762322\pi$
$600$	5.52775e11	0.174128
$601$	5.31850e12	1.66285	0.831426	−	0.555635i	$-0.187525\pi$
$601$	5.31850e12	1.66285	0.831426	+	0.555635i	$0.187525\pi$
$602$	−1.13882e13	−3.53404
$603$	−5.81770e12	−1.79194
$604$	1.12570e13	3.44158
$605$	7.12693e10	0.0216273
$606$	−1.55031e9	−0.000466973 0
$607$	5.95088e12	1.77923	0.889616	−	0.456710i	$-0.150972\pi$
$607$	5.95088e12	1.77923	0.889616	+	0.456710i	$0.150972\pi$
$608$	−1.56942e12	−0.465770
$609$	−1.29567e11	−0.0381695
$610$	1.06857e11	0.0312478
$611$	−6.81115e10	−0.0197713
$612$	8.18111e12	2.35739
$613$	−2.14687e12	−0.614094	−0.307047	−	0.951694i	$-0.599341\pi$
$613$	−2.14687e12	−0.614094	−0.307047	+	0.951694i	$0.599341\pi$
$614$	2.50348e11	0.0710863
$615$	1.91317e8	5.39281e−5 0
$616$	−2.62719e13	−7.35154
$617$	−1.73802e12	−0.482803	−0.241402	−	0.970425i	$-0.577607\pi$
$617$	−1.73802e12	−0.482803	−0.241402	+	0.970425i	$0.577607\pi$
$618$	−5.17525e11	−0.142719
$619$	−1.75267e12	−0.479835	−0.239917	−	0.970793i	$-0.577120\pi$
$619$	−1.75267e12	−0.479835	−0.239917	+	0.970793i	$0.577120\pi$
$620$	1.94459e11	0.0528525
$621$	−5.04242e11	−0.136059
$622$	−9.34027e11	−0.250209
$623$	−4.96170e12	−1.31958
$624$	−5.95912e11	−0.157344
$625$	3.81273e12	0.999485
$626$	−4.16526e12	−1.08407
$627$	1.18006e11	0.0304930
$628$	8.36914e12	2.14715
$629$	−3.44958e12	−0.878695
$630$	1.67918e11	0.0424684
$631$	−2.82107e12	−0.708405	−0.354203	−	0.935169i	$-0.615248\pi$
$631$	−2.82107e12	−0.708405	−0.354203	+	0.935169i	$0.615248\pi$
$632$	1.22575e13	3.05616
$633$	−2.52133e11	−0.0624185
$634$	−1.77344e12	−0.435929
$635$	6.10471e10	0.0148999
$636$	1.93660e11	0.0469335
$637$	−8.84439e12	−2.12834
$638$	3.96215e12	0.946756
$639$	−3.76115e12	−0.892414
$640$	1.10090e10	0.00259380
$641$	6.58329e12	1.54022	0.770109	−	0.637913i	$-0.220202\pi$
$641$	6.58329e12	1.54022	0.770109	+	0.637913i	$0.220202\pi$
$642$	1.01700e12	0.236272
$643$	6.63337e12	1.53033	0.765164	−	0.643835i	$-0.222658\pi$
$643$	6.63337e12	1.53033	0.765164	+	0.643835i	$0.222658\pi$
$644$	1.84167e13	4.21915
$645$	4.26564e9	0.000970433 0
$646$	2.21815e12	0.501123
$647$	7.05174e12	1.58208	0.791038	−	0.611767i	$-0.209541\pi$
$647$	7.05174e12	1.58208	0.791038	+	0.611767i	$0.209541\pi$
$648$	−1.12923e13	−2.51591
$649$	−1.12685e13	−2.49324
$650$	−8.36009e12	−1.83697
$651$	9.35694e11	0.204183
$652$	−7.40879e12	−1.60558
$653$	−1.25730e12	−0.270601	−0.135300	−	0.990805i	$-0.543200\pi$
$653$	−1.25730e12	−0.270601	−0.135300	+	0.990805i	$0.543200\pi$
$654$	−6.71238e11	−0.143475
$655$	−9.45082e8	−0.000200624 0
$656$	6.60427e11	0.139238
$657$	9.03690e12	1.89224
$658$	−3.10116e11	−0.0644922
$659$	−4.90612e12	−1.01334	−0.506668	−	0.862141i	$-0.669123\pi$
$659$	−4.90612e12	−1.01334	−0.506668	+	0.862141i	$0.669123\pi$
$660$	1.69379e10	0.00347467
$661$	−3.67929e12	−0.749648	−0.374824	−	0.927096i	$-0.622297\pi$
$661$	−3.67929e12	−0.749648	−0.374824	+	0.927096i	$0.622297\pi$
$662$	3.36608e12	0.681183
$663$	3.36472e11	0.0676299
$664$	−3.45758e12	−0.690266
$665$	3.20839e10	0.00636194
$666$	8.23426e12	1.62177
$667$	−1.61365e12	−0.315678
$668$	1.67911e12	0.326276
$669$	−4.71039e11	−0.0909159
$670$	−2.26405e11	−0.0434060
$671$	−1.10804e13	−2.11011
$672$	−1.08393e12	−0.205040
$673$	2.99155e12	0.562119	0.281059	−	0.959690i	$-0.409314\pi$
$673$	2.99155e12	0.562119	0.281059	+	0.959690i	$0.409314\pi$
$674$	−1.43414e13	−2.67683
$675$	7.34435e11	0.136171
$676$	−4.17421e10	−0.00768801
$677$	6.62303e12	1.21174	0.605868	−	0.795565i	$-0.292826\pi$
$677$	6.62303e12	1.21174	0.605868	+	0.795565i	$0.292826\pi$
$678$	5.73570e11	0.104244
$679$	1.76452e13	3.18576
$680$	1.84972e11	0.0331754
$681$	3.87865e11	0.0691064
$682$	−2.86135e13	−5.06455
$683$	−3.50547e12	−0.616387	−0.308193	−	0.951324i	$-0.599724\pi$
$683$	−3.50547e12	−0.616387	−0.308193	+	0.951324i	$0.599724\pi$
$684$	−3.73130e12	−0.651790
$685$	−2.53908e10	−0.00440625
$686$	−2.13791e13	−3.68579
$687$	−1.11846e11	−0.0191564
$688$	1.47250e13	2.50558
$689$	−1.70162e12	−0.287657
$690$	−9.78879e9	−0.00164402
$691$	8.32278e12	1.38873	0.694364	−	0.719624i	$-0.255686\pi$
$691$	8.32278e12	1.38873	0.694364	+	0.719624i	$0.255686\pi$
$692$	−2.18376e13	−3.62016
$693$	−1.74121e13	−2.86782
$694$	−3.95161e12	−0.646631
$695$	9.63190e10	0.0156596
$696$	3.40692e11	0.0550326
$697$	−3.72900e11	−0.0598474
$698$	−5.51490e12	−0.879403
$699$	3.87740e10	0.00614319
$700$	−2.68241e13	−4.22264
$701$	5.34082e11	0.0835366	0.0417683	−	0.999127i	$-0.486701\pi$
$701$	5.34082e11	0.0835366	0.0417683	+	0.999127i	$0.486701\pi$
$702$	−1.61010e12	−0.250228
$703$	1.57331e12	0.242949
$704$	8.64622e12	1.32663
$705$	1.16159e8	1.77093e−5 0
$706$	−1.21893e13	−1.84654
$707$	4.37073e10	0.00657911
$708$	−1.66777e12	−0.249451
$709$	9.42279e11	0.140046	0.0700232	−	0.997545i	$-0.477693\pi$
$709$	9.42279e11	0.140046	0.0700232	+	0.997545i	$0.477693\pi$
$710$	−1.46371e11	−0.0216169
$711$	8.12387e12	1.19220
$712$	1.30466e13	1.90256
$713$	1.16533e13	1.68868
$714$	1.53198e12	0.220603
$715$	−1.48827e11	−0.0212964
$716$	1.21886e13	1.73319
$717$	−4.70782e11	−0.0665249
$718$	−1.92620e13	−2.70484
$719$	5.63560e12	0.786430	0.393215	−	0.919447i	$-0.371363\pi$
$719$	5.63560e12	0.786430	0.393215	+	0.919447i	$0.371363\pi$
$720$	−2.17119e11	−0.0301094
$721$	1.45904e13	2.01075
$722$	1.24251e13	1.70169
$723$	−1.47729e11	−0.0201068
$724$	2.02744e13	2.74236
$725$	2.35030e12	0.315939
$726$	−1.55208e12	−0.207348
$727$	−2.34395e12	−0.311203	−0.155601	−	0.987820i	$-0.549732\pi$
$727$	−2.34395e12	−0.311203	−0.155601	+	0.987820i	$0.549732\pi$
$728$	3.41653e13	4.50810
$729$	−7.41326e12	−0.972155
$730$	3.51685e11	0.0458355
$731$	−8.31426e12	−1.07695
$732$	−1.63994e12	−0.211119
$733$	3.13413e12	0.401004	0.200502	−	0.979693i	$-0.435743\pi$
$733$	3.13413e12	0.401004	0.200502	+	0.979693i	$0.435743\pi$
$734$	4.35971e12	0.554402
$735$	1.50834e10	0.00190637
$736$	−1.34994e13	−1.69576
$737$	2.34768e13	2.93113
$738$	8.90125e11	0.110458
$739$	−9.79933e12	−1.20864	−0.604319	−	0.796742i	$-0.706555\pi$
$739$	−9.79933e12	−1.20864	−0.604319	+	0.796742i	$0.706555\pi$
$740$	2.25824e11	0.0276839
$741$	−1.53461e11	−0.0186989
$742$	−7.74756e12	−0.938312
$743$	1.38593e13	1.66837	0.834186	−	0.551484i	$-0.185938\pi$
$743$	1.38593e13	1.66837	0.834186	+	0.551484i	$0.185938\pi$
$744$	−2.46037e12	−0.294390
$745$	−4.47251e10	−0.00531923
$746$	4.66660e12	0.551665
$747$	−2.29156e12	−0.269271
$748$	−3.30142e13	−3.85605
$749$	−2.86718e13	−3.32879
$750$	2.85174e10	0.00329105
$751$	−3.36991e12	−0.386579	−0.193289	−	0.981142i	$-0.561916\pi$
$751$	−3.36991e12	−0.386579	−0.193289	+	0.981142i	$0.561916\pi$
$752$	4.00982e11	0.0457240
$753$	8.24649e11	0.0934742
$754$	−5.15257e12	−0.580568
$755$	1.68686e11	0.0188937
$756$	−5.16615e12	−0.575200
$757$	3.82296e12	0.423125	0.211562	−	0.977364i	$-0.432145\pi$
$757$	3.82296e12	0.423125	0.211562	+	0.977364i	$0.432145\pi$
$758$	−1.92196e13	−2.11462
$759$	1.01504e12	0.111018
$760$	−8.43635e10	−0.00917262
$761$	4.96673e12	0.536834	0.268417	−	0.963303i	$-0.413500\pi$
$761$	4.96673e12	0.536834	0.268417	+	0.963303i	$0.413500\pi$
$762$	−1.32947e12	−0.142850
$763$	1.89240e13	2.02140
$764$	−1.93330e13	−2.05296
$765$	1.22593e11	0.0129416
$766$	−1.52951e13	−1.60517
$767$	1.46540e13	1.52890
$768$	−7.75960e11	−0.0804848
$769$	−5.52575e12	−0.569801	−0.284900	−	0.958557i	$-0.591961\pi$
$769$	−5.52575e12	−0.569801	−0.284900	+	0.958557i	$0.591961\pi$
$770$	−6.77620e11	−0.0694669
$771$	6.34920e11	0.0647104
$772$	−1.92098e13	−1.94646
$773$	7.16384e12	0.721670	0.360835	−	0.932630i	$-0.382492\pi$
$773$	7.16384e12	0.721670	0.360835	+	0.932630i	$0.382492\pi$
$774$	1.98464e13	1.98769
$775$	−1.69732e13	−1.69007
$776$	−4.63976e13	−4.59322
$777$	1.08662e12	0.106950
$778$	−4.07015e11	−0.0398292
$779$	1.70075e11	0.0165471
$780$	−2.20269e10	−0.00213073
$781$	1.51778e13	1.45975
$782$	1.90796e13	1.82448
$783$	4.52654e11	0.0430366
$784$	5.20681e13	4.92209
$785$	1.25411e11	0.0117875
$786$	2.05818e10	0.00192345
$787$	−1.48219e12	−0.137726	−0.0688630	−	0.997626i	$-0.521937\pi$
$787$	−1.48219e12	−0.137726	−0.0688630	+	0.997626i	$0.521937\pi$
$788$	1.84034e12	0.170032
$789$	1.03926e12	0.0954722
$790$	3.16153e11	0.0288786
$791$	−1.61704e13	−1.46868
$792$	4.57845e13	4.13481
$793$	1.44095e13	1.29396
$794$	1.86881e13	1.66868
$795$	2.90198e9	0.000257657 0
$796$	1.90973e13	1.68602
$797$	1.43743e12	0.126190	0.0630950	−	0.998008i	$-0.479903\pi$
$797$	1.43743e12	0.126190	0.0630950	+	0.998008i	$0.479903\pi$
$798$	−6.98716e11	−0.0609940
$799$	−2.26408e11	−0.0196531
$800$	1.96621e13	1.69717
$801$	8.64684e12	0.742183
$802$	2.44116e13	2.08359
$803$	−3.64676e13	−3.09519
$804$	3.47465e12	0.293264
$805$	2.75972e11	0.0231624
$806$	3.72103e13	3.10567
$807$	1.37509e12	0.114130
$808$	−1.14927e11	−0.00948573
$809$	−1.65622e13	−1.35941	−0.679704	−	0.733486i	$-0.737892\pi$
$809$	−1.65622e13	−1.35941	−0.679704	+	0.733486i	$0.737892\pi$
$810$	−2.91258e11	−0.0237736
$811$	1.06569e13	0.865042	0.432521	−	0.901624i	$-0.357624\pi$
$811$	1.06569e13	0.865042	0.432521	+	0.901624i	$0.357624\pi$
$812$	−1.65325e13	−1.33455
$813$	8.78769e11	0.0705452
$814$	−3.32286e13	−2.65279
$815$	−1.11020e11	−0.00881439
$816$	−1.98086e12	−0.156404
$817$	3.79203e12	0.297764
$818$	−5.68333e12	−0.443827
$819$	2.26435e13	1.75860
$820$	2.44116e10	0.00188554
$821$	1.06055e13	0.814678	0.407339	−	0.913277i	$-0.366457\pi$
$821$	1.06055e13	0.814678	0.407339	+	0.913277i	$0.366457\pi$
$822$	5.52955e11	0.0422441
$823$	−7.80964e12	−0.593379	−0.296689	−	0.954974i	$-0.595883\pi$
$823$	−7.80964e12	−0.593379	−0.296689	+	0.954974i	$0.595883\pi$
$824$	−3.83650e13	−2.89910
$825$	−1.47841e12	−0.111110
$826$	6.67207e13	4.98713
$827$	−5.05136e12	−0.375521	−0.187760	−	0.982215i	$-0.560123\pi$
$827$	−5.05136e12	−0.375521	−0.187760	+	0.982215i	$0.560123\pi$
$828$	−3.20950e13	−2.37302
$829$	1.43161e13	1.05276	0.526381	−	0.850249i	$-0.323549\pi$
$829$	1.43161e13	1.05276	0.526381	+	0.850249i	$0.323549\pi$
$830$	−8.91799e10	−0.00652252
$831$	1.57071e12	0.114259
$832$	−1.12440e13	−0.813513
$833$	−2.93994e13	−2.11562
$834$	−2.09761e12	−0.150134
$835$	2.51613e10	0.00179120
$836$	1.50573e13	1.06615
$837$	−3.26893e12	−0.230219
$838$	1.04006e13	0.728552
$839$	1.19309e13	0.831274	0.415637	−	0.909531i	$-0.363559\pi$
$839$	1.19309e13	0.831274	0.415637	+	0.909531i	$0.363559\pi$
$840$	−5.82662e10	−0.00403794
$841$	−1.30586e13	−0.900148
$842$	−9.71313e11	−0.0665970
$843$	−1.52186e12	−0.103789
$844$	−3.21717e13	−2.18239
$845$	−6.25501e8	−4.22059e−5 0
$846$	5.40444e11	0.0362730
$847$	4.37574e13	2.92130
$848$	1.00176e13	0.665249
$849$	−1.00188e12	−0.0661810
$850$	−2.77896e13	−1.82598
$851$	1.35329e13	0.884522
$852$	2.24636e12	0.146050
$853$	−1.48973e13	−0.963470	−0.481735	−	0.876317i	$-0.659993\pi$
$853$	−1.48973e13	−0.963470	−0.481735	+	0.876317i	$0.659993\pi$
$854$	6.56074e13	4.22078
$855$	−5.59132e10	−0.00357822
$856$	7.53916e13	4.79944
$857$	−1.09367e13	−0.692586	−0.346293	−	0.938126i	$-0.612560\pi$
$857$	−1.09367e13	−0.692586	−0.346293	+	0.938126i	$0.612560\pi$
$858$	3.24113e12	0.204175
$859$	6.04374e12	0.378736	0.189368	−	0.981906i	$-0.439356\pi$
$859$	6.04374e12	0.378736	0.189368	+	0.981906i	$0.439356\pi$
$860$	5.44287e11	0.0339301
$861$	1.17463e11	0.00728431
$862$	3.93988e12	0.243053
$863$	2.94916e13	1.80988	0.904940	−	0.425539i	$-0.139915\pi$
$863$	2.94916e13	1.80988	0.904940	+	0.425539i	$0.139915\pi$
$864$	3.78680e12	0.231185
$865$	−3.27235e11	−0.0198741
$866$	−2.70668e13	−1.63533
$867$	−1.71505e10	−0.00103084
$868$	1.19393e14	7.13902
$869$	−3.27832e13	−1.95012
$870$	8.78731e9	0.000520019 0
$871$	−3.05304e13	−1.79743
$872$	−4.97600e13	−2.91444
$873$	−3.07507e13	−1.79180
$874$	−8.70195e12	−0.504446
$875$	−8.03982e11	−0.0463671
$876$	−5.39732e12	−0.309678
$877$	−7.72822e12	−0.441145	−0.220573	−	0.975371i	$-0.570793\pi$
$877$	−7.72822e12	−0.441145	−0.220573	+	0.975371i	$0.570793\pi$
$878$	1.60278e12	0.0910225
$879$	1.13349e12	0.0640422
$880$	8.76167e11	0.0492510
$881$	1.71354e13	0.958302	0.479151	−	0.877732i	$-0.340945\pi$
$881$	1.71354e13	0.958302	0.479151	+	0.877732i	$0.340945\pi$
$882$	7.01775e13	3.90471
$883$	2.58779e13	1.43254	0.716268	−	0.697826i	$-0.245849\pi$
$883$	2.58779e13	1.43254	0.716268	+	0.697826i	$0.245849\pi$
$884$	4.29332e13	2.36460
$885$	−2.49913e10	−0.00136945
$886$	−3.41305e13	−1.86076
$887$	1.04919e13	0.569110	0.284555	−	0.958660i	$-0.408154\pi$
$887$	1.04919e13	0.569110	0.284555	+	0.958660i	$0.408154\pi$
$888$	−2.85722e12	−0.154200
$889$	3.74813e13	2.01260
$890$	3.36506e11	0.0179778
$891$	3.02016e13	1.60539
$892$	−6.01037e13	−3.17877
$893$	1.03262e11	0.00543386
$894$	9.74013e11	0.0509972
$895$	1.82645e11	0.00951491
$896$	6.75921e12	0.350356
$897$	−1.32000e12	−0.0680784
$898$	−1.89128e13	−0.970538
$899$	−1.04611e13	−0.534144
$900$	4.67468e13	2.37498
$901$	−5.65631e12	−0.285938
$902$	−3.59202e12	−0.180680
$903$	2.61899e12	0.131081
$904$	4.25196e13	2.11754
$905$	3.03810e11	0.0150551
$906$	−3.67360e12	−0.181140
$907$	−2.64175e13	−1.29616	−0.648081	−	0.761571i	$-0.724428\pi$
$907$	−2.64175e13	−1.29616	−0.648081	+	0.761571i	$0.724428\pi$
$908$	4.94908e13	2.41623
$909$	−7.61695e10	−0.00370036
$910$	8.81209e11	0.0425984
$911$	−9.97528e12	−0.479835	−0.239918	−	0.970793i	$-0.577120\pi$
$911$	−9.97528e12	−0.479835	−0.239918	+	0.970793i	$0.577120\pi$
$912$	9.03444e11	0.0432439
$913$	9.24741e12	0.440455
$914$	1.04921e13	0.497284
$915$	−2.45743e10	−0.00115901
$916$	−1.42713e13	−0.669782
$917$	−5.80255e11	−0.0270992
$918$	−5.35210e12	−0.248732
$919$	−2.41824e13	−1.11835	−0.559177	−	0.829048i	$-0.688883\pi$
$919$	−2.41824e13	−1.11835	−0.559177	+	0.829048i	$0.688883\pi$
$920$	−7.25659e11	−0.0333955
$921$	−5.75733e10	−0.00263665
$922$	−2.70367e13	−1.23215
$923$	−1.97379e13	−0.895146
$924$	1.03994e13	0.469338
$925$	−1.97109e13	−0.885254
$926$	−7.26022e13	−3.24489
$927$	−2.54269e13	−1.13093
$928$	1.21183e13	0.536385
$929$	−1.86264e13	−0.820461	−0.410231	−	0.911982i	$-0.634552\pi$
$929$	−1.86264e13	−0.820461	−0.410231	+	0.911982i	$0.634552\pi$
$930$	−6.34593e10	−0.00278178
$931$	1.34087e13	0.584943
$932$	4.94749e12	0.214790
$933$	2.14802e11	0.00928048
$934$	3.95085e13	1.69875
$935$	−4.94714e11	−0.0211691
$936$	−5.95404e13	−2.53554
$937$	1.83167e13	0.776281	0.388140	−	0.921600i	$-0.373118\pi$
$937$	1.83167e13	0.776281	0.388140	+	0.921600i	$0.373118\pi$
$938$	−1.39007e14	−5.86304
$939$	9.57900e11	0.0402092
$940$	1.48216e10	0.000619186 0
$941$	4.53813e13	1.88679	0.943396	−	0.331668i	$-0.107611\pi$
$941$	4.53813e13	1.88679	0.943396	+	0.331668i	$0.107611\pi$
$942$	−2.73117e12	−0.113011
$943$	1.46291e12	0.0602443
$944$	−8.62703e13	−3.53580
$945$	−7.74143e10	−0.00315775
$946$	−8.00886e13	−3.25133
$947$	9.18185e11	0.0370984	0.0185492	−	0.999828i	$-0.494095\pi$
$947$	9.18185e11	0.0370984	0.0185492	+	0.999828i	$0.494095\pi$
$948$	−4.85201e12	−0.195112
$949$	4.74243e13	1.89803
$950$	1.26745e13	0.504864
$951$	4.07845e11	0.0161690
$952$	1.13568e14	4.48115
$953$	4.09918e13	1.60983	0.804913	−	0.593393i	$-0.202212\pi$
$953$	4.09918e13	1.60983	0.804913	+	0.593393i	$0.202212\pi$
$954$	1.35018e13	0.527745
$955$	−2.89704e11	−0.0112704
$956$	−6.00709e13	−2.32597
$957$	−9.11191e11	−0.0351160
$958$	−6.47985e13	−2.48554
$959$	−1.55893e13	−0.595171
$960$	1.91757e10	0.000728670 0
$961$	4.91072e13	1.85733
$962$	4.32121e13	1.62674
$963$	4.99669e13	1.87225
$964$	−1.88499e13	−0.703011
$965$	−2.87858e11	−0.0106858
$966$	−6.01005e12	−0.222066
$967$	−2.76762e13	−1.01786	−0.508929	−	0.860808i	$-0.669959\pi$
$967$	−2.76762e13	−1.01786	−0.508929	+	0.860808i	$0.669959\pi$
$968$	−1.15059e14	−4.21192
$969$	−5.10116e11	−0.0185871
$970$	−1.19671e12	−0.0434027
$971$	−6.07375e12	−0.219266	−0.109633	−	0.993972i	$-0.534967\pi$
$971$	−6.07375e12	−0.219266	−0.109633	+	0.993972i	$0.534967\pi$
$972$	1.35152e13	0.485652
$973$	5.91373e13	2.11521
$974$	−8.27771e13	−2.94710
$975$	1.92260e12	0.0681347
$976$	−8.48308e13	−2.99247
$977$	−3.01355e13	−1.05816	−0.529082	−	0.848570i	$-0.677464\pi$
$977$	−3.01355e13	−1.05816	−0.529082	+	0.848570i	$0.677464\pi$
$978$	2.41777e12	0.0845064
$979$	−3.48936e13	−1.21401
$980$	1.92461e12	0.0666540
$981$	−3.29791e13	−1.13692
$982$	8.38360e12	0.287693
$983$	−1.52100e13	−0.519562	−0.259781	−	0.965668i	$-0.583650\pi$
$983$	−1.52100e13	−0.519562	−0.259781	+	0.965668i	$0.583650\pi$
$984$	−3.08866e11	−0.0105025
$985$	2.75773e10	0.000933446 0
$986$	−1.71276e13	−0.577098
$987$	7.13184e10	0.00239207
$988$	−1.95813e13	−0.653785
$989$	3.26174e13	1.08409
$990$	1.18090e12	0.0390710
$991$	−2.11126e13	−0.695360	−0.347680	−	0.937613i	$-0.613030\pi$
$991$	−2.11126e13	−0.695360	−0.347680	+	0.937613i	$0.613030\pi$
$992$	−8.75150e13	−2.86933
$993$	−7.74111e11	−0.0252657
$994$	−8.98679e13	−2.91989
$995$	2.86171e11	0.00925598
$996$	1.36865e12	0.0440681
$997$	4.02750e13	1.29094	0.645472	−	0.763784i	$-0.276661\pi$
$997$	4.02750e13	1.29094	0.645472	+	0.763784i	$0.276661\pi$
$998$	9.90304e12	0.315996
$999$	−3.79619e12	−0.120588

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.10.a.b.1.3	✓	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.10.a.b.1.3	✓	76	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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	197.a (trivial)

\(f(q)\)	\(=\)	\(q-41.6400 q^{2} +9.57611 q^{3} +1221.89 q^{4} +18.3099 q^{5} -398.750 q^{6} +11241.8 q^{7} -29560.0 q^{8} -19591.3 q^{9} +O(q^{10})\)	\(q-41.6400 q^{2} +9.57611 q^{3} +1221.89 q^{4} +18.3099 q^{5} -398.750 q^{6} +11241.8 q^{7} -29560.0 q^{8} -19591.3 q^{9} -762.427 q^{10} +79059.0 q^{11} +11701.0 q^{12} -102812. q^{13} -468110. q^{14} +175.338 q^{15} +605269. q^{16} -341756. q^{17} +815782. q^{18} +155870. q^{19} +22372.8 q^{20} +107653. q^{21} -3.29202e6 q^{22} +1.34073e6 q^{23} -283070. q^{24} -1.95279e6 q^{25} +4.28110e6 q^{26} -376095. q^{27} +1.37363e7 q^{28} -1.20356e6 q^{29} -7301.09 q^{30} +8.69177e6 q^{31} -1.00687e7 q^{32} +757078. q^{33} +1.42307e7 q^{34} +205837. q^{35} -2.39385e7 q^{36} +1.00937e7 q^{37} -6.49045e6 q^{38} -984541. q^{39} -541241. q^{40} +1.09113e6 q^{41} -4.48267e6 q^{42} +2.43281e7 q^{43} +9.66016e7 q^{44} -358716. q^{45} -5.58281e7 q^{46} +662485. q^{47} +5.79612e6 q^{48} +8.60248e7 q^{49} +8.13142e7 q^{50} -3.27269e6 q^{51} -1.25625e8 q^{52} +1.65507e7 q^{53} +1.56606e7 q^{54} +1.44757e6 q^{55} -3.32308e8 q^{56} +1.49263e6 q^{57} +5.01164e7 q^{58} -1.42532e8 q^{59} +214244. q^{60} -1.40154e8 q^{61} -3.61926e8 q^{62} -2.20242e8 q^{63} +1.09364e8 q^{64} -1.88249e6 q^{65} -3.15248e7 q^{66} +2.96953e8 q^{67} -4.17589e8 q^{68} +1.28390e7 q^{69} -8.57106e6 q^{70} +1.91980e8 q^{71} +5.79118e8 q^{72} -4.61271e8 q^{73} -4.20302e8 q^{74} -1.87001e7 q^{75} +1.90457e8 q^{76} +8.88767e8 q^{77} +4.09963e7 q^{78} -4.14667e8 q^{79} +1.10824e7 q^{80} +3.82014e8 q^{81} -4.54347e7 q^{82} +1.16968e8 q^{83} +1.31540e8 q^{84} -6.25753e6 q^{85} -1.01302e9 q^{86} -1.15255e7 q^{87} -2.33698e9 q^{88} -4.41361e8 q^{89} +1.49369e7 q^{90} -1.15579e9 q^{91} +1.63823e9 q^{92} +8.32333e7 q^{93} -2.75859e7 q^{94} +2.85398e6 q^{95} -9.64192e7 q^{96} +1.56961e9 q^{97} -3.58207e9 q^{98} -1.54887e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9}+O(q^{10}) \) 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9	\( 76 q + 48 q^{2} + 890 q^{3} + 20736 q^{4} + 5171 q^{5} + 2688 q^{6} + 38986 q^{7} + 36507 q^{8} + 518318 q^{9} + 121093 q^{10} + 120464 q^{11} + 415744 q^{12} + 480131 q^{13} + 330849 q^{14} + 544874 q^{15} + 5963776 q^{16} + 942582 q^{17} + 1483945 q^{18} + 3097319 q^{19} + 3237739 q^{20} + 889076 q^{21} + 3791921 q^{22} + 5139200 q^{23} + 1999533 q^{24} + 34080519 q^{25} + 2791454 q^{26} + 24386486 q^{27} + 20891166 q^{28} + 6886818 q^{29} + 14171083 q^{30} + 28002851 q^{31} + 16857332 q^{32} + 30921422 q^{33} + 33506194 q^{34} + 16271736 q^{35} + 151430458 q^{36} + 55950976 q^{37} + 62370882 q^{38} - 11569592 q^{39} + 129854766 q^{40} + 14990859 q^{41} + 82216531 q^{42} + 169867467 q^{43} + 41872434 q^{44} + 205007649 q^{45} + 144032301 q^{46} + 78743342 q^{47} + 156250562 q^{48} + 533861890 q^{49} + 626841163 q^{50} + 477099244 q^{51} + 560784114 q^{52} + 188670216 q^{53} + 525901687 q^{54} + 298497914 q^{55} + 56575048 q^{56} + 213972590 q^{57} + 338315251 q^{58} + 208222151 q^{59} - 615921507 q^{60} - 233556134 q^{61} - 399368105 q^{62} + 329825056 q^{63} + 876517017 q^{64} - 840557006 q^{65} - 2482481592 q^{66} + 1210808414 q^{67} - 1266757099 q^{68} + 327801786 q^{69} - 546384313 q^{70} + 345300221 q^{71} - 1549481681 q^{72} + 1192286460 q^{73} - 1471133595 q^{74} + 761630676 q^{75} - 398699826 q^{76} - 101106252 q^{77} - 2609825943 q^{78} + 955627631 q^{79} + 1059617770 q^{80} + 3387041436 q^{81} + 1062705523 q^{82} + 1538917201 q^{83} + 1394513218 q^{84} + 225481100 q^{85} + 701644810 q^{86} + 1758812842 q^{87} + 3151474875 q^{88} + 855413630 q^{89} + 6070671455 q^{90} + 4652436248 q^{91} + 8082863606 q^{92} + 3462095982 q^{93} + 2660342117 q^{94} + 1036805508 q^{95} + 12370989029 q^{96} + 6393874545 q^{97} + 7510976010 q^{98} + 8731109606 q^{99}+O(q^{100}) \) 76 * q + 48 * q^2 + 890 * q^3 + 20736 * q^4 + 5171 * q^5 + 2688 * q^6 + 38986 * q^7 + 36507 * q^8 + 518318 * q^9 + 121093 * q^10 + 120464 * q^11 + 415744 * q^12 + 480131 * q^13 + 330849 * q^14 + 544874 * q^15 + 5963776 * q^16 + 942582 * q^17 + 1483945 * q^18 + 3097319 * q^19 + 3237739 * q^20 + 889076 * q^21 + 3791921 * q^22 + 5139200 * q^23 + 1999533 * q^24 + 34080519 * q^25 + 2791454 * q^26 + 24386486 * q^27 + 20891166 * q^28 + 6886818 * q^29 + 14171083 * q^30 + 28002851 * q^31 + 16857332 * q^32 + 30921422 * q^33 + 33506194 * q^34 + 16271736 * q^35 + 151430458 * q^36 + 55950976 * q^37 + 62370882 * q^38 - 11569592 * q^39 + 129854766 * q^40 + 14990859 * q^41 + 82216531 * q^42 + 169867467 * q^43 + 41872434 * q^44 + 205007649 * q^45 + 144032301 * q^46 + 78743342 * q^47 + 156250562 * q^48 + 533861890 * q^49 + 626841163 * q^50 + 477099244 * q^51 + 560784114 * q^52 + 188670216 * q^53 + 525901687 * q^54 + 298497914 * q^55 + 56575048 * q^56 + 213972590 * q^57 + 338315251 * q^58 + 208222151 * q^59 - 615921507 * q^60 - 233556134 * q^61 - 399368105 * q^62 + 329825056 * q^63 + 876517017 * q^64 - 840557006 * q^65 - 2482481592 * q^66 + 1210808414 * q^67 - 1266757099 * q^68 + 327801786 * q^69 - 546384313 * q^70 + 345300221 * q^71 - 1549481681 * q^72 + 1192286460 * q^73 - 1471133595 * q^74 + 761630676 * q^75 - 398699826 * q^76 - 101106252 * q^77 - 2609825943 * q^78 + 955627631 * q^79 + 1059617770 * q^80 + 3387041436 * q^81 + 1062705523 * q^82 + 1538917201 * q^83 + 1394513218 * q^84 + 225481100 * q^85 + 701644810 * q^86 + 1758812842 * q^87 + 3151474875 * q^88 + 855413630 * q^89 + 6070671455 * q^90 + 4652436248 * q^91 + 8082863606 * q^92 + 3462095982 * q^93 + 2660342117 * q^94 + 1036805508 * q^95 + 12370989029 * q^96 + 6393874545 * q^97 + 7510976010 * q^98 + 8731109606 * q^99

Introduction

L-functions

Modular forms

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