LMFDB - Embedded newform 15.10.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,10,Mod(1,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("15.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	15.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:	$7.72553754246$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{4729}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1182 $ x^2 - x - 1182
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$34.8839$ of defining polynomial
Character	$\chi$	$=$	15.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-24.8839 q^{2} +81.0000 q^{3} +107.207 q^{4} -625.000 q^{5} -2015.59 q^{6} -4010.50 q^{7} +10072.8 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-24.8839 q^{2} +81.0000 q^{3} +107.207 q^{4} -625.000 q^{5} -2015.59 q^{6} -4010.50 q^{7} +10072.8 q^{8} +6561.00 q^{9} +15552.4 q^{10} +84861.3 q^{11} +8683.74 q^{12} +119425. q^{13} +99796.8 q^{14} -50625.0 q^{15} -305541. q^{16} +116934. q^{17} -163263. q^{18} -234932. q^{19} -67004.1 q^{20} -324851. q^{21} -2.11168e6 q^{22} +2.34570e6 q^{23} +815899. q^{24} +390625. q^{25} -2.97176e6 q^{26} +531441. q^{27} -429953. q^{28} -464196. q^{29} +1.25975e6 q^{30} -5.11766e6 q^{31} +2.44574e6 q^{32} +6.87377e6 q^{33} -2.90976e6 q^{34} +2.50656e6 q^{35} +703383. q^{36} +8.69354e6 q^{37} +5.84601e6 q^{38} +9.67345e6 q^{39} -6.29551e6 q^{40} -9.05805e6 q^{41} +8.08354e6 q^{42} +8.63491e6 q^{43} +9.09769e6 q^{44} -4.10062e6 q^{45} -5.83701e7 q^{46} +3.31511e7 q^{47} -2.47488e7 q^{48} -2.42695e7 q^{49} -9.72026e6 q^{50} +9.47161e6 q^{51} +1.28032e7 q^{52} -6.41254e7 q^{53} -1.32243e7 q^{54} -5.30383e7 q^{55} -4.03971e7 q^{56} -1.90295e7 q^{57} +1.15510e7 q^{58} +1.49407e8 q^{59} -5.42733e6 q^{60} +1.54634e8 q^{61} +1.27347e8 q^{62} -2.63129e7 q^{63} +9.55772e7 q^{64} -7.46408e7 q^{65} -1.71046e8 q^{66} +2.72755e8 q^{67} +1.25360e7 q^{68} +1.90002e8 q^{69} -6.23730e7 q^{70} -3.56924e8 q^{71} +6.60878e7 q^{72} +2.06253e8 q^{73} -2.16329e8 q^{74} +3.16406e7 q^{75} -2.51862e7 q^{76} -3.40337e8 q^{77} -2.40713e8 q^{78} -4.04380e8 q^{79} +1.90963e8 q^{80} +4.30467e7 q^{81} +2.25399e8 q^{82} -5.17034e6 q^{83} -3.48262e7 q^{84} -7.30834e7 q^{85} -2.14870e8 q^{86} -3.75999e7 q^{87} +8.54793e8 q^{88} +4.32242e8 q^{89} +1.02039e8 q^{90} -4.78955e8 q^{91} +2.51475e8 q^{92} -4.14530e8 q^{93} -8.24928e8 q^{94} +1.46832e8 q^{95} +1.98105e8 q^{96} -1.32066e9 q^{97} +6.03918e8 q^{98} +5.56775e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 19 q^{2} + 162 q^{3} + 1521 q^{4} - 1250 q^{5} + 1539 q^{6} - 11872 q^{7} + 49647 q^{8} + 13122 q^{9}+O(q^{10}) $ 2 * q + 19 * q^2 + 162 * q^3 + 1521 * q^4 - 1250 * q^5 + 1539 * q^6 - 11872 * q^7 + 49647 * q^8 + 13122 * q^9	\( 2 q + 19 q^{2} + 162 q^{3} + 1521 q^{4} - 1250 q^{5} + 1539 q^{6} - 11872 q^{7} + 49647 q^{8} + 13122 q^{9} - 11875 q^{10} + 35488 q^{11} + 123201 q^{12} + 143676 q^{13} - 245196 q^{14} - 101250 q^{15} + 707265 q^{16} + 385156 q^{17} + 124659 q^{18} - 403296 q^{19} - 950625 q^{20} - 961632 q^{21} - 4278368 q^{22} + 223704 q^{23} + 4021407 q^{24} + 781250 q^{25} - 1907546 q^{26} + 1062882 q^{27} - 11544484 q^{28} - 74572 q^{29} - 961875 q^{30} - 5027128 q^{31} + 26629583 q^{32} + 2874528 q^{33} + 8860882 q^{34} + 7420000 q^{35} + 9979281 q^{36} + 5373628 q^{37} - 1542476 q^{38} + 11637756 q^{39} - 31029375 q^{40} + 14211332 q^{41} - 19860876 q^{42} + 27748920 q^{43} - 60705952 q^{44} - 8201250 q^{45} - 151491648 q^{46} + 95966440 q^{47} + 57288465 q^{48} - 2819950 q^{49} + 7421875 q^{50} + 31197636 q^{51} + 47088706 q^{52} - 64305596 q^{53} + 10097379 q^{54} - 22180000 q^{55} - 351509340 q^{56} - 32666976 q^{57} + 28649198 q^{58} + 187863136 q^{59} - 77000625 q^{60} + 154080060 q^{61} + 131320056 q^{62} - 77892192 q^{63} + 638301089 q^{64} - 89797500 q^{65} - 346547808 q^{66} + 33592376 q^{67} + 391747238 q^{68} + 18120024 q^{69} + 153247500 q^{70} - 228270976 q^{71} + 325733967 q^{72} - 33122316 q^{73} - 362019226 q^{74} + 63281250 q^{75} - 263218724 q^{76} + 47811456 q^{77} - 154511226 q^{78} - 932406760 q^{79} - 442040625 q^{80} + 86093442 q^{81} + 1246549646 q^{82} + 207040152 q^{83} - 935103204 q^{84} - 240722500 q^{85} + 623926708 q^{86} - 6040332 q^{87} - 1099114848 q^{88} + 224518164 q^{89} - 77911875 q^{90} - 669602528 q^{91} - 2748592992 q^{92} - 407197368 q^{93} + 1931650816 q^{94} + 252060000 q^{95} + 2156996223 q^{96} + 387134596 q^{97} + 1545205739 q^{98} + 232836768 q^{99}+O(q^{100}) \) 2 * q + 19 * q^2 + 162 * q^3 + 1521 * q^4 - 1250 * q^5 + 1539 * q^6 - 11872 * q^7 + 49647 * q^8 + 13122 * q^9 - 11875 * q^10 + 35488 * q^11 + 123201 * q^12 + 143676 * q^13 - 245196 * q^14 - 101250 * q^15 + 707265 * q^16 + 385156 * q^17 + 124659 * q^18 - 403296 * q^19 - 950625 * q^20 - 961632 * q^21 - 4278368 * q^22 + 223704 * q^23 + 4021407 * q^24 + 781250 * q^25 - 1907546 * q^26 + 1062882 * q^27 - 11544484 * q^28 - 74572 * q^29 - 961875 * q^30 - 5027128 * q^31 + 26629583 * q^32 + 2874528 * q^33 + 8860882 * q^34 + 7420000 * q^35 + 9979281 * q^36 + 5373628 * q^37 - 1542476 * q^38 + 11637756 * q^39 - 31029375 * q^40 + 14211332 * q^41 - 19860876 * q^42 + 27748920 * q^43 - 60705952 * q^44 - 8201250 * q^45 - 151491648 * q^46 + 95966440 * q^47 + 57288465 * q^48 - 2819950 * q^49 + 7421875 * q^50 + 31197636 * q^51 + 47088706 * q^52 - 64305596 * q^53 + 10097379 * q^54 - 22180000 * q^55 - 351509340 * q^56 - 32666976 * q^57 + 28649198 * q^58 + 187863136 * q^59 - 77000625 * q^60 + 154080060 * q^61 + 131320056 * q^62 - 77892192 * q^63 + 638301089 * q^64 - 89797500 * q^65 - 346547808 * q^66 + 33592376 * q^67 + 391747238 * q^68 + 18120024 * q^69 + 153247500 * q^70 - 228270976 * q^71 + 325733967 * q^72 - 33122316 * q^73 - 362019226 * q^74 + 63281250 * q^75 - 263218724 * q^76 + 47811456 * q^77 - 154511226 * q^78 - 932406760 * q^79 - 442040625 * q^80 + 86093442 * q^81 + 1246549646 * q^82 + 207040152 * q^83 - 935103204 * q^84 - 240722500 * q^85 + 623926708 * q^86 - 6040332 * q^87 - 1099114848 * q^88 + 224518164 * q^89 - 77911875 * q^90 - 669602528 * q^91 - 2748592992 * q^92 - 407197368 * q^93 + 1931650816 * q^94 + 252060000 * q^95 + 2156996223 * q^96 + 387134596 * q^97 + 1545205739 * q^98 + 232836768 * 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 $

$2$	−24.8839	−1.09972	−0.549861	−	0.835256i	$-0.685319\pi$
$2$	−24.8839	−1.09972	−0.549861	+	0.835256i	$0.685319\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	107.207	0.209388
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	−2015.59	−0.634925
$7$	−4010.50	−0.631332	−0.315666	−	0.948870i	$-0.602228\pi$
$7$	−4010.50	−0.631332	−0.315666	+	0.948870i	$0.602228\pi$
$8$	10072.8	0.869453
$9$	6561.00	0.333333
$10$	15552.4	0.491811
$11$	84861.3	1.74760	0.873801	−	0.486283i	$-0.161648\pi$
$11$	84861.3	1.74760	0.873801	+	0.486283i	$0.161648\pi$
$12$	8683.74	0.120890
$13$	119425.	1.15971	0.579857	−	0.814718i	$-0.303108\pi$
$13$	119425.	1.15971	0.579857	+	0.814718i	$0.303108\pi$
$14$	99796.8	0.694289
$15$	−50625.0	−0.258199
$16$	−305541.	−1.16554
$17$	116934.	0.339562	0.169781	−	0.985482i	$-0.445694\pi$
$17$	116934.	0.339562	0.169781	+	0.985482i	$0.445694\pi$
$18$	−163263.	−0.366574
$19$	−234932.	−0.413571	−0.206786	−	0.978386i	$-0.566300\pi$
$19$	−234932.	−0.413571	−0.206786	+	0.978386i	$0.566300\pi$
$20$	−67004.1	−0.0936411
$21$	−324851.	−0.364500
$22$	−2.11168e6	−1.92188
$23$	2.34570e6	1.74782	0.873912	−	0.486084i	$-0.161575\pi$
$23$	2.34570e6	1.74782	0.873912	+	0.486084i	$0.161575\pi$
$24$	815899.	0.501979
$25$	390625.	0.200000
$26$	−2.97176e6	−1.27536
$27$	531441.	0.192450
$28$	−429953.	−0.132193
$29$	−464196.	−0.121874	−0.0609369	−	0.998142i	$-0.519409\pi$
$29$	−464196.	−0.121874	−0.0609369	+	0.998142i	$0.519409\pi$
$30$	1.25975e6	0.283947
$31$	−5.11766e6	−0.995277	−0.497638	−	0.867385i	$-0.665799\pi$
$31$	−5.11766e6	−0.995277	−0.497638	+	0.867385i	$0.665799\pi$
$32$	2.44574e6	0.412321
$33$	6.87377e6	1.00898
$34$	−2.90976e6	−0.373423
$35$	2.50656e6	0.282340
$36$	703383.	0.0697960
$37$	8.69354e6	0.762586	0.381293	−	0.924454i	$-0.375479\pi$
$37$	8.69354e6	0.762586	0.381293	+	0.924454i	$0.375479\pi$
$38$	5.84601e6	0.454813
$39$	9.67345e6	0.669562
$40$	−6.29551e6	−0.388831
$41$	−9.05805e6	−0.500619	−0.250310	−	0.968166i	$-0.580532\pi$
$41$	−9.05805e6	−0.500619	−0.250310	+	0.968166i	$0.580532\pi$
$42$	8.08354e6	0.400848
$43$	8.63491e6	0.385168	0.192584	−	0.981281i	$-0.438313\pi$
$43$	8.63491e6	0.385168	0.192584	+	0.981281i	$0.438313\pi$
$44$	9.09769e6	0.365927
$45$	−4.10062e6	−0.149071
$46$	−5.83701e7	−1.92212
$47$	3.31511e7	0.990964	0.495482	−	0.868618i	$-0.334991\pi$
$47$	3.31511e7	0.990964	0.495482	+	0.868618i	$0.334991\pi$
$48$	−2.47488e7	−0.672927
$49$	−2.42695e7	−0.601420
$50$	−9.72026e6	−0.219944
$51$	9.47161e6	0.196046
$52$	1.28032e7	0.242830
$53$	−6.41254e7	−1.11632	−0.558160	−	0.829733i	$-0.688492\pi$
$53$	−6.41254e7	−1.11632	−0.558160	+	0.829733i	$0.688492\pi$
$54$	−1.32243e7	−0.211642
$55$	−5.30383e7	−0.781551
$56$	−4.03971e7	−0.548914
$57$	−1.90295e7	−0.238775
$58$	1.15510e7	0.134027
$59$	1.49407e8	1.60523	0.802613	−	0.596500i	$-0.203442\pi$
$59$	1.49407e8	1.60523	0.802613	+	0.596500i	$0.203442\pi$
$60$	−5.42733e6	−0.0540637
$61$	1.54634e8	1.42995	0.714973	−	0.699152i	$-0.246439\pi$
$61$	1.54634e8	1.42995	0.714973	+	0.699152i	$0.246439\pi$
$62$	1.27347e8	1.09453
$63$	−2.63129e7	−0.210444
$64$	9.55772e7	0.712106
$65$	−7.46408e7	−0.518640
$66$	−1.71046e8	−1.10960
$67$	2.72755e8	1.65362	0.826811	−	0.562479i	$-0.190152\pi$
$67$	2.72755e8	1.65362	0.826811	+	0.562479i	$0.190152\pi$
$68$	1.25360e7	0.0711001
$69$	1.90002e8	1.00911
$70$	−6.23730e7	−0.310496
$71$	−3.56924e8	−1.66691	−0.833457	−	0.552584i	$-0.813642\pi$
$71$	−3.56924e8	−1.66691	−0.833457	+	0.552584i	$0.813642\pi$
$72$	6.60878e7	0.289818
$73$	2.06253e8	0.850057	0.425029	−	0.905180i	$-0.360264\pi$
$73$	2.06253e8	0.850057	0.425029	+	0.905180i	$0.360264\pi$
$74$	−2.16329e8	−0.838632
$75$	3.16406e7	0.115470
$76$	−2.51862e7	−0.0865968
$77$	−3.40337e8	−1.10332
$78$	−2.40713e8	−0.736331
$79$	−4.04380e8	−1.16807	−0.584033	−	0.811730i	$-0.698526\pi$
$79$	−4.04380e8	−1.16807	−0.584033	+	0.811730i	$0.698526\pi$
$80$	1.90963e8	0.521247
$81$	4.30467e7	0.111111
$82$	2.25399e8	0.550542
$83$	−5.17034e6	−0.0119582	−0.00597912	−	0.999982i	$-0.501903\pi$
$83$	−5.17034e6	−0.0119582	−0.00597912	+	0.999982i	$0.501903\pi$
$84$	−3.48262e7	−0.0763218
$85$	−7.30834e7	−0.151857
$86$	−2.14870e8	−0.423577
$87$	−3.75999e7	−0.0703639
$88$	8.54793e8	1.51946
$89$	4.32242e8	0.730250	0.365125	−	0.930958i	$-0.381026\pi$
$89$	4.32242e8	0.730250	0.365125	+	0.930958i	$0.381026\pi$
$90$	1.02039e8	0.163937
$91$	−4.78955e8	−0.732165
$92$	2.51475e8	0.365973
$93$	−4.14530e8	−0.574623
$94$	−8.24928e8	−1.08978
$95$	1.46832e8	0.184955
$96$	1.98105e8	0.238054
$97$	−1.32066e9	−1.51468	−0.757338	−	0.653023i	$-0.773501\pi$
$97$	−1.32066e9	−1.51468	−0.757338	+	0.653023i	$0.773501\pi$
$98$	6.03918e8	0.661395
$99$	5.56775e8	0.582534
$100$	4.18776e7	0.0418776
$101$	5.30458e8	0.507230	0.253615	−	0.967305i	$-0.418380\pi$
$101$	5.30458e8	0.507230	0.253615	+	0.967305i	$0.418380\pi$
$102$	−2.35690e8	−0.215596
$103$	−6.07207e7	−0.0531580	−0.0265790	−	0.999647i	$-0.508461\pi$
$103$	−6.07207e7	−0.0531580	−0.0265790	+	0.999647i	$0.508461\pi$
$104$	1.20295e9	1.00832
$105$	2.03032e8	0.163009
$106$	1.59569e9	1.22764
$107$	−1.00828e9	−0.743625	−0.371812	−	0.928308i	$-0.621264\pi$
$107$	−1.00828e9	−0.743625	−0.371812	+	0.928308i	$0.621264\pi$
$108$	5.69740e7	0.0402967
$109$	−1.77424e9	−1.20391	−0.601954	−	0.798531i	$-0.705611\pi$
$109$	−1.77424e9	−1.20391	−0.601954	+	0.798531i	$0.705611\pi$
$110$	1.31980e9	0.859489
$111$	7.04177e8	0.440279
$112$	1.22537e9	0.735846
$113$	9.45495e8	0.545514	0.272757	−	0.962083i	$-0.412064\pi$
$113$	9.45495e8	0.545514	0.272757	+	0.962083i	$0.412064\pi$
$114$	4.73526e8	0.262586
$115$	−1.46606e9	−0.781651
$116$	−4.97649e7	−0.0255189
$117$	7.83549e8	0.386572
$118$	−3.71782e9	−1.76530
$119$	−4.68962e8	−0.214376
$120$	−5.09937e8	−0.224492
$121$	4.84349e9	2.05411
$122$	−3.84788e9	−1.57254
$123$	−7.33702e8	−0.289033
$124$	−5.48647e8	−0.208399
$125$	−2.44141e8	−0.0894427
$126$	6.54767e8	0.231430
$127$	−5.19758e9	−1.77290	−0.886450	−	0.462825i	$-0.846836\pi$
$127$	−5.19758e9	−1.77290	−0.886450	+	0.462825i	$0.846836\pi$
$128$	−3.63055e9	−1.19544
$129$	6.99428e8	0.222377
$130$	1.85735e9	0.570360
$131$	5.28408e8	0.156765	0.0783824	−	0.996923i	$-0.475024\pi$
$131$	5.28408e8	0.156765	0.0783824	+	0.996923i	$0.475024\pi$
$132$	7.36913e8	0.211268
$133$	9.42194e8	0.261101
$134$	−6.78720e9	−1.81852
$135$	−3.32151e8	−0.0860663
$136$	1.17785e9	0.295233
$137$	5.01761e9	1.21690	0.608449	−	0.793593i	$-0.291792\pi$
$137$	5.01761e9	1.21690	0.608449	+	0.793593i	$0.291792\pi$
$138$	−4.72798e9	−1.10974
$139$	3.51872e9	0.799499	0.399750	−	0.916624i	$-0.369097\pi$
$139$	3.51872e9	0.799499	0.399750	+	0.916624i	$0.369097\pi$
$140$	2.68720e8	0.0591186
$141$	2.68524e9	0.572133
$142$	8.88165e9	1.83314
$143$	1.01346e10	2.02672
$144$	−2.00465e9	−0.388515
$145$	2.90123e8	0.0545036
$146$	−5.13238e9	−0.934827
$147$	−1.96583e9	−0.347230
$148$	9.32005e8	0.159676
$149$	4.32815e9	0.719390	0.359695	−	0.933070i	$-0.382881\pi$
$149$	4.32815e9	0.719390	0.359695	+	0.933070i	$0.382881\pi$
$150$	−7.87341e8	−0.126985
$151$	−5.61832e9	−0.879448	−0.439724	−	0.898133i	$-0.644924\pi$
$151$	−5.61832e9	−0.879448	−0.439724	+	0.898133i	$0.644924\pi$
$152$	−2.36642e9	−0.359581
$153$	7.67201e8	0.113187
$154$	8.46889e9	1.21334
$155$	3.19854e9	0.445101
$156$	1.03706e9	0.140198
$157$	1.55603e9	0.204394	0.102197	−	0.994764i	$-0.467413\pi$
$157$	1.55603e9	0.204394	0.102197	+	0.994764i	$0.467413\pi$
$158$	1.00625e10	1.28455
$159$	−5.19416e9	−0.644507
$160$	−1.52859e9	−0.184396
$161$	−9.40745e9	−1.10346
$162$	−1.07117e9	−0.122191
$163$	−1.15580e10	−1.28245	−0.641224	−	0.767354i	$-0.721573\pi$
$163$	−1.15580e10	−1.28245	−0.641224	+	0.767354i	$0.721573\pi$
$164$	−9.71083e8	−0.104824
$165$	−4.29610e9	−0.451229
$166$	1.28658e8	0.0131507
$167$	−1.50486e10	−1.49717	−0.748585	−	0.663039i	$-0.769266\pi$
$167$	−1.50486e10	−1.49717	−0.748585	+	0.663039i	$0.769266\pi$
$168$	−3.27216e9	−0.316915
$169$	3.65789e9	0.344938
$170$	1.81860e9	0.167000
$171$	−1.54139e9	−0.137857
$172$	9.25719e8	0.0806494
$173$	2.23157e10	1.89410	0.947052	−	0.321081i	$-0.104046\pi$
$173$	2.23157e10	1.89410	0.947052	+	0.321081i	$0.104046\pi$
$174$	9.35630e8	0.0773807
$175$	−1.56660e9	−0.126266
$176$	−2.59286e10	−2.03691
$177$	1.21019e10	0.926778
$178$	−1.07558e10	−0.803072
$179$	−1.73543e10	−1.26348	−0.631742	−	0.775179i	$-0.717660\pi$
$179$	−1.73543e10	−1.26348	−0.631742	+	0.775179i	$0.717660\pi$
$180$	−4.39614e8	−0.0312137
$181$	−1.34040e10	−0.928282	−0.464141	−	0.885761i	$-0.653637\pi$
$181$	−1.34040e10	−0.928282	−0.464141	+	0.885761i	$0.653637\pi$
$182$	1.19183e10	0.805178
$183$	1.25253e10	0.825580
$184$	2.36278e10	1.51965
$185$	−5.43346e9	−0.341039
$186$	1.03151e10	0.631926
$187$	9.92313e9	0.593419
$188$	3.55402e9	0.207496
$189$	−2.13135e9	−0.121500
$190$	−3.65375e9	−0.203399
$191$	−6.01312e9	−0.326926	−0.163463	−	0.986549i	$-0.552266\pi$
$191$	−6.01312e9	−0.326926	−0.163463	+	0.986549i	$0.552266\pi$
$192$	7.74175e9	0.411134
$193$	−6.91844e9	−0.358922	−0.179461	−	0.983765i	$-0.557435\pi$
$193$	−6.91844e9	−0.358922	−0.179461	+	0.983765i	$0.557435\pi$
$194$	3.28632e10	1.66572
$195$	−6.04590e9	−0.299437
$196$	−2.60185e9	−0.125930
$197$	1.66139e10	0.785909	0.392955	−	0.919558i	$-0.371453\pi$
$197$	1.66139e10	0.785909	0.392955	+	0.919558i	$0.371453\pi$
$198$	−1.38547e10	−0.640625
$199$	−3.06711e10	−1.38641	−0.693204	−	0.720742i	$-0.743801\pi$
$199$	−3.06711e10	−1.38641	−0.693204	+	0.720742i	$0.743801\pi$
$200$	3.93470e9	0.173891
$201$	2.20932e10	0.954719
$202$	−1.31998e10	−0.557812
$203$	1.86166e9	0.0769428
$204$	1.01542e9	0.0410497
$205$	5.66128e9	0.223884
$206$	1.51096e9	0.0584591
$207$	1.53902e10	0.582608
$208$	−3.64893e10	−1.35170
$209$	−1.99366e10	−0.722758
$210$	−5.05221e9	−0.179265
$211$	3.85598e10	1.33926	0.669628	−	0.742697i	$-0.266454\pi$
$211$	3.85598e10	1.33926	0.669628	+	0.742697i	$0.266454\pi$
$212$	−6.87467e9	−0.233744
$213$	−2.89108e10	−0.962393
$214$	2.50899e10	0.817780
$215$	−5.39682e9	−0.172252
$216$	5.35311e9	0.167326
$217$	2.05244e10	0.628350
$218$	4.41500e10	1.32396
$219$	1.67065e10	0.490781
$220$	−5.68606e9	−0.163647
$221$	1.39648e10	0.393795
$222$	−1.75226e10	−0.484185
$223$	−3.11357e10	−0.843115	−0.421558	−	0.906802i	$-0.638516\pi$
$223$	−3.11357e10	−0.843115	−0.421558	+	0.906802i	$0.638516\pi$
$224$	−9.80866e9	−0.260312
$225$	2.56289e9	0.0666667
$226$	−2.35276e10	−0.599914
$227$	−1.14589e10	−0.286436	−0.143218	−	0.989691i	$-0.545745\pi$
$227$	−1.14589e10	−0.286436	−0.143218	+	0.989691i	$0.545745\pi$
$228$	−2.04008e9	−0.0499967
$229$	−3.04556e10	−0.731825	−0.365913	−	0.930649i	$-0.619243\pi$
$229$	−3.04556e10	−0.731825	−0.365913	+	0.930649i	$0.619243\pi$
$230$	3.64813e10	0.859598
$231$	−2.75673e10	−0.637000
$232$	−4.67576e9	−0.105964
$233$	2.83630e9	0.0630451	0.0315225	−	0.999503i	$-0.489964\pi$
$233$	2.83630e9	0.0630451	0.0315225	+	0.999503i	$0.489964\pi$
$234$	−1.94977e10	−0.425121
$235$	−2.07195e10	−0.443173
$236$	1.60174e10	0.336115
$237$	−3.27548e10	−0.674384
$238$	1.16696e10	0.235754
$239$	−6.25862e10	−1.24076	−0.620381	−	0.784301i	$-0.713022\pi$
$239$	−6.25862e10	−1.24076	−0.620381	+	0.784301i	$0.713022\pi$
$240$	1.54680e10	0.300942
$241$	7.24015e10	1.38252	0.691259	−	0.722607i	$-0.257056\pi$
$241$	7.24015e10	1.38252	0.691259	+	0.722607i	$0.257056\pi$
$242$	−1.20525e11	−2.25895
$243$	3.48678e9	0.0641500
$244$	1.65778e10	0.299414
$245$	1.51684e10	0.268963
$246$	1.82573e10	0.317855
$247$	−2.80568e10	−0.479624
$248$	−5.15493e10	−0.865347
$249$	−4.18797e8	−0.00690410
$250$	6.07516e9	0.0983621
$251$	−5.65927e10	−0.899971	−0.449986	−	0.893036i	$-0.648571\pi$
$251$	−5.65927e10	−0.899971	−0.449986	+	0.893036i	$0.648571\pi$
$252$	−2.82092e9	−0.0440644
$253$	1.99059e11	3.05450
$254$	1.29336e11	1.94970
$255$	−5.91976e9	−0.0876745
$256$	4.14066e10	0.602545
$257$	4.95688e10	0.708777	0.354388	−	0.935098i	$-0.384689\pi$
$257$	4.95688e10	0.708777	0.354388	+	0.935098i	$0.384689\pi$
$258$	−1.74045e10	−0.244552
$259$	−3.48655e10	−0.481445
$260$	−8.00199e9	−0.108597
$261$	−3.04559e9	−0.0406246
$262$	−1.31488e10	−0.172398
$263$	3.59498e10	0.463336	0.231668	−	0.972795i	$-0.425582\pi$
$263$	3.59498e10	0.463336	0.231668	+	0.972795i	$0.425582\pi$
$264$	6.92382e10	0.877260
$265$	4.00784e10	0.499233
$266$	−2.34454e10	−0.287138
$267$	3.50116e10	0.421610
$268$	2.92412e10	0.346249
$269$	−7.09650e10	−0.826340	−0.413170	−	0.910654i	$-0.635579\pi$
$269$	−7.09650e10	−0.826340	−0.413170	+	0.910654i	$0.635579\pi$
$270$	8.26519e9	0.0946490
$271$	1.47201e11	1.65786	0.828930	−	0.559352i	$-0.188950\pi$
$271$	1.47201e11	1.65786	0.828930	+	0.559352i	$0.188950\pi$
$272$	−3.57279e10	−0.395774
$273$	−3.87954e10	−0.422716
$274$	−1.24857e11	−1.33825
$275$	3.31489e10	0.349520
$276$	2.03695e10	0.211295
$277$	−2.87336e10	−0.293245	−0.146622	−	0.989193i	$-0.546840\pi$
$277$	−2.87336e10	−0.293245	−0.146622	+	0.989193i	$0.546840\pi$
$278$	−8.75593e10	−0.879227
$279$	−3.35770e10	−0.331759
$280$	2.52482e10	0.245482
$281$	5.17071e10	0.494734	0.247367	−	0.968922i	$-0.420435\pi$
$281$	5.17071e10	0.494734	0.247367	+	0.968922i	$0.420435\pi$
$282$	−6.68192e10	−0.629187
$283$	−3.22434e9	−0.0298814	−0.0149407	−	0.999888i	$-0.504756\pi$
$283$	−3.22434e9	−0.0298814	−0.0149407	+	0.999888i	$0.504756\pi$
$284$	−3.82646e10	−0.349032
$285$	1.18934e10	0.106784
$286$	−2.52188e11	−2.22883
$287$	3.63273e10	0.316057
$288$	1.60465e10	0.137440
$289$	−1.04914e11	−0.884698
$290$	−7.21937e9	−0.0599388
$291$	−1.06974e11	−0.874499
$292$	2.21117e10	0.177992
$293$	−1.13591e11	−0.900409	−0.450204	−	0.892926i	$-0.648649\pi$
$293$	−1.13591e11	−0.900409	−0.450204	+	0.892926i	$0.648649\pi$
$294$	4.89174e10	0.381856
$295$	−9.33792e10	−0.717879
$296$	8.75685e10	0.663033
$297$	4.50988e10	0.336326
$298$	−1.07701e11	−0.791129
$299$	2.80136e11	2.02698
$300$	3.39208e9	0.0241780
$301$	−3.46303e10	−0.243169
$302$	1.39805e11	0.967148
$303$	4.29671e10	0.292849
$304$	7.17811e10	0.482036
$305$	−9.66460e10	−0.639492
$306$	−1.90909e10	−0.124474
$307$	−2.30543e10	−0.148125	−0.0740627	−	0.997254i	$-0.523597\pi$
$307$	−2.30543e10	−0.148125	−0.0740627	+	0.997254i	$0.523597\pi$
$308$	−3.64863e10	−0.231021
$309$	−4.91837e9	−0.0306908
$310$	−7.95920e10	−0.489488
$311$	7.71709e10	0.467769	0.233885	−	0.972264i	$-0.424856\pi$
$311$	7.71709e10	0.467769	0.233885	+	0.972264i	$0.424856\pi$
$312$	9.74389e10	0.582152
$313$	−4.68832e10	−0.276101	−0.138050	−	0.990425i	$-0.544084\pi$
$313$	−4.68832e10	−0.276101	−0.138050	+	0.990425i	$0.544084\pi$
$314$	−3.87200e10	−0.224777
$315$	1.64456e10	0.0941134
$316$	−4.33522e10	−0.244579
$317$	2.19420e11	1.22042	0.610210	−	0.792240i	$-0.291085\pi$
$317$	2.19420e11	1.22042	0.610210	+	0.792240i	$0.291085\pi$
$318$	1.29251e11	0.708779
$319$	−3.93923e10	−0.212987
$320$	−5.97358e10	−0.318463
$321$	−8.16706e10	−0.429332
$322$	2.34094e11	1.21350
$323$	−2.74714e10	−0.140433
$324$	4.61489e9	0.0232653
$325$	4.66505e10	0.231943
$326$	2.87609e11	1.41034
$327$	−1.43714e11	−0.695077
$328$	−9.12401e10	−0.435265
$329$	−1.32953e11	−0.625627
$330$	1.06904e11	0.496226
$331$	3.89075e9	0.0178159	0.00890794	−	0.999960i	$-0.497164\pi$
$331$	3.89075e9	0.0178159	0.00890794	+	0.999960i	$0.497164\pi$
$332$	−5.54295e8	−0.00250391
$333$	5.70383e10	0.254195
$334$	3.74466e11	1.64647
$335$	−1.70472e11	−0.739522
$336$	9.92551e10	0.424841
$337$	−1.48259e11	−0.626163	−0.313082	−	0.949726i	$-0.601361\pi$
$337$	−1.48259e11	−0.626163	−0.313082	+	0.949726i	$0.601361\pi$
$338$	−9.10225e10	−0.379336
$339$	7.65851e10	0.314953
$340$	−7.83503e9	−0.0317969
$341$	−4.34291e11	−1.73935
$342$	3.83556e10	0.151604
$343$	2.59171e11	1.01103
$344$	8.69779e10	0.334885
$345$	−1.18751e11	−0.451286
$346$	−5.55302e11	−2.08299
$347$	−1.63695e11	−0.606114	−0.303057	−	0.952972i	$-0.598007\pi$
$347$	−1.63695e11	−0.606114	−0.303057	+	0.952972i	$0.598007\pi$
$348$	−4.03096e9	−0.0147333
$349$	7.02057e10	0.253313	0.126657	−	0.991947i	$-0.459575\pi$
$349$	7.02057e10	0.253313	0.126657	+	0.991947i	$0.459575\pi$
$350$	3.89831e10	0.138858
$351$	6.34675e10	0.223187
$352$	2.07549e11	0.720574
$353$	−1.55727e10	−0.0533798	−0.0266899	−	0.999644i	$-0.508497\pi$
$353$	−1.55727e10	−0.0533798	−0.0266899	+	0.999644i	$0.508497\pi$
$354$	−3.01143e11	−1.01920
$355$	2.23078e11	0.745467
$356$	4.63392e10	0.152906
$357$	−3.79859e10	−0.123770
$358$	4.31843e11	1.38948
$359$	3.28525e10	0.104386	0.0521931	−	0.998637i	$-0.483379\pi$
$359$	3.28525e10	0.104386	0.0521931	+	0.998637i	$0.483379\pi$
$360$	−4.13049e10	−0.129610
$361$	−2.67495e11	−0.828959
$362$	3.33543e11	1.02085
$363$	3.92323e11	1.18594
$364$	−5.13472e10	−0.153306
$365$	−1.28908e11	−0.380157
$366$	−3.11679e11	−0.907908
$367$	−4.76030e11	−1.36974	−0.684868	−	0.728667i	$-0.740140\pi$
$367$	−4.76030e11	−1.36974	−0.684868	+	0.728667i	$0.740140\pi$
$368$	−7.16707e11	−2.03717
$369$	−5.94299e10	−0.166873
$370$	1.35205e11	0.375048
$371$	2.57175e11	0.704768
$372$	−4.44404e10	−0.120319
$373$	−9.72745e10	−0.260201	−0.130101	−	0.991501i	$-0.541530\pi$
$373$	−9.72745e10	−0.260201	−0.130101	+	0.991501i	$0.541530\pi$
$374$	−2.46926e11	−0.652596
$375$	−1.97754e10	−0.0516398
$376$	3.33925e11	0.861597
$377$	−5.54367e10	−0.141339
$378$	5.30361e10	0.133616
$379$	4.45171e11	1.10828	0.554141	−	0.832423i	$-0.313047\pi$
$379$	4.45171e11	1.10828	0.554141	+	0.832423i	$0.313047\pi$
$380$	1.57414e10	0.0387273
$381$	−4.21004e11	−1.02358
$382$	1.49630e11	0.359528
$383$	2.19414e11	0.521039	0.260519	−	0.965469i	$-0.416106\pi$
$383$	2.19414e11	0.521039	0.260519	+	0.965469i	$0.416106\pi$
$384$	−2.94075e11	−0.690187
$385$	2.12710e11	0.493418
$386$	1.72157e11	0.394714
$387$	5.66536e10	0.128389
$388$	−1.41584e11	−0.317155
$389$	−3.71956e11	−0.823603	−0.411801	−	0.911274i	$-0.635100\pi$
$389$	−3.71956e11	−0.823603	−0.411801	+	0.911274i	$0.635100\pi$
$390$	1.50445e11	0.329297
$391$	2.74291e11	0.593494
$392$	−2.44462e11	−0.522907
$393$	4.28011e10	0.0905082
$394$	−4.13417e11	−0.864281
$395$	2.52737e11	0.522375
$396$	5.96900e10	0.121976
$397$	−1.38786e11	−0.280406	−0.140203	−	0.990123i	$-0.544776\pi$
$397$	−1.38786e11	−0.280406	−0.140203	+	0.990123i	$0.544776\pi$
$398$	7.63216e11	1.52466
$399$	7.63177e10	0.150747
$400$	−1.19352e11	−0.233109
$401$	6.95127e11	1.34250	0.671251	−	0.741231i	$-0.265757\pi$
$401$	6.95127e11	1.34250	0.671251	+	0.741231i	$0.265757\pi$
$402$	−5.49763e11	−1.04993
$403$	−6.11178e11	−1.15424
$404$	5.68686e10	0.106208
$405$	−2.69042e10	−0.0496904
$406$	−4.63253e10	−0.0846157
$407$	7.37745e11	1.33270
$408$	9.54059e10	0.170453
$409$	9.10800e11	1.60942	0.804708	−	0.593671i	$-0.202322\pi$
$409$	9.10800e11	1.60942	0.804708	+	0.593671i	$0.202322\pi$
$410$	−1.40875e11	−0.246210
$411$	4.06426e11	0.702577
$412$	−6.50966e9	−0.0111307
$413$	−5.99196e11	−1.01343
$414$	−3.82967e11	−0.640707
$415$	3.23146e9	0.00534789
$416$	2.92084e11	0.478175
$417$	2.85016e11	0.461591
$418$	4.96100e11	0.794832
$419$	3.11152e11	0.493184	0.246592	−	0.969119i	$-0.420689\pi$
$419$	3.11152e11	0.493184	0.246592	+	0.969119i	$0.420689\pi$
$420$	2.17663e10	0.0341322
$421$	7.63941e11	1.18520	0.592598	−	0.805498i	$-0.298102\pi$
$421$	7.63941e11	1.18520	0.592598	+	0.805498i	$0.298102\pi$
$422$	−9.59516e11	−1.47281
$423$	2.17505e11	0.330321
$424$	−6.45924e11	−0.970588
$425$	4.56771e10	0.0679124
$426$	7.19414e11	1.05836
$427$	−6.20159e11	−0.902771
$428$	−1.08094e11	−0.155706
$429$	8.20901e11	1.17013
$430$	1.34294e11	0.189429
$431$	6.54629e10	0.0913792	0.0456896	−	0.998956i	$-0.485451\pi$
$431$	6.54629e10	0.0913792	0.0456896	+	0.998956i	$0.485451\pi$
$432$	−1.62377e11	−0.224309
$433$	−7.87434e11	−1.07651	−0.538256	−	0.842781i	$-0.680917\pi$
$433$	−7.87434e11	−1.07651	−0.538256	+	0.842781i	$0.680917\pi$
$434$	−5.10726e11	−0.691010
$435$	2.34999e10	0.0314677
$436$	−1.90210e11	−0.252084
$437$	−5.51080e11	−0.722850
$438$	−4.15723e11	−0.539722
$439$	−8.39211e11	−1.07840	−0.539201	−	0.842177i	$-0.681274\pi$
$439$	−8.39211e11	−1.07840	−0.539201	+	0.842177i	$0.681274\pi$
$440$	−5.34246e11	−0.679523
$441$	−1.59232e11	−0.200473
$442$	−3.47499e11	−0.433065
$443$	−1.28252e12	−1.58215	−0.791074	−	0.611720i	$-0.790478\pi$
$443$	−1.28252e12	−1.58215	−0.791074	+	0.611720i	$0.790478\pi$
$444$	7.54924e10	0.0921891
$445$	−2.70151e11	−0.326578
$446$	7.74777e11	0.927192
$447$	3.50581e11	0.415340
$448$	−3.83313e11	−0.449575
$449$	8.02030e10	0.0931284	0.0465642	−	0.998915i	$-0.485173\pi$
$449$	8.02030e10	0.0931284	0.0465642	+	0.998915i	$0.485173\pi$
$450$	−6.37746e10	−0.0733148
$451$	−7.68678e11	−0.874883
$452$	1.01363e11	0.114224
$453$	−4.55084e11	−0.507749
$454$	2.85143e11	0.315000
$455$	2.99347e11	0.327434
$456$	−1.91680e11	−0.207604
$457$	1.27085e11	0.136292	0.0681461	−	0.997675i	$-0.478292\pi$
$457$	1.27085e11	0.136292	0.0681461	+	0.997675i	$0.478292\pi$
$458$	7.57853e11	0.804804
$459$	6.21433e10	0.0653487
$460$	−1.57172e11	−0.163668
$461$	−7.39880e11	−0.762970	−0.381485	−	0.924375i	$-0.624587\pi$
$461$	−7.39880e11	−0.762970	−0.381485	+	0.924375i	$0.624587\pi$
$462$	6.85980e11	0.700523
$463$	5.71025e11	0.577485	0.288742	−	0.957407i	$-0.406763\pi$
$463$	5.71025e11	0.577485	0.288742	+	0.957407i	$0.406763\pi$
$464$	1.41831e11	0.142049
$465$	2.59082e11	0.256979
$466$	−7.05782e10	−0.0693320
$467$	1.19075e12	1.15850	0.579249	−	0.815150i	$-0.303346\pi$
$467$	1.19075e12	1.15850	0.579249	+	0.815150i	$0.303346\pi$
$468$	8.40017e10	0.0809434
$469$	−1.09389e12	−1.04398
$470$	5.15580e11	0.487367
$471$	1.26038e11	0.118007
$472$	1.50495e12	1.39567
$473$	7.32770e11	0.673120
$474$	8.15065e11	0.741634
$475$	−9.17701e10	−0.0827142
$476$	−5.02759e10	−0.0448878
$477$	−4.20727e11	−0.372107
$478$	1.55739e12	1.36449
$479$	1.46074e12	1.26784	0.633919	−	0.773400i	$-0.281445\pi$
$479$	1.46074e12	1.26784	0.633919	+	0.773400i	$0.281445\pi$
$480$	−1.23816e11	−0.106461
$481$	1.03823e12	0.884382
$482$	−1.80163e12	−1.52038
$483$	−7.62003e11	−0.637081
$484$	5.19254e11	0.430107
$485$	8.25416e11	0.677384
$486$	−8.67647e10	−0.0705472
$487$	−1.46931e12	−1.18368	−0.591839	−	0.806056i	$-0.701598\pi$
$487$	−1.46931e12	−1.18368	−0.591839	+	0.806056i	$0.701598\pi$
$488$	1.55760e12	1.24327
$489$	−9.36201e11	−0.740422
$490$	−3.77449e11	−0.295785
$491$	−1.76138e12	−1.36769	−0.683843	−	0.729629i	$-0.739693\pi$
$491$	−1.76138e12	−1.36769	−0.683843	+	0.729629i	$0.739693\pi$
$492$	−7.86577e10	−0.0605199
$493$	−5.42801e10	−0.0413837
$494$	6.98161e11	0.527453
$495$	−3.47984e11	−0.260517
$496$	1.56365e12	1.16004
$497$	1.43145e12	1.05238
$498$	1.04213e10	0.00759259
$499$	−1.63016e12	−1.17700	−0.588502	−	0.808496i	$-0.700282\pi$
$499$	−1.63016e12	−1.17700	−0.588502	+	0.808496i	$0.700282\pi$
$500$	−2.61735e10	−0.0187282
$501$	−1.21893e12	−0.864391
$502$	1.40825e12	0.989718
$503$	9.47625e11	0.660056	0.330028	−	0.943971i	$-0.392942\pi$
$503$	9.47625e11	0.660056	0.330028	+	0.943971i	$0.392942\pi$
$504$	−2.65045e11	−0.182971
$505$	−3.31536e11	−0.226840
$506$	−4.95337e12	−3.35910
$507$	2.96289e11	0.199150
$508$	−5.57214e11	−0.371224
$509$	−2.90709e11	−0.191968	−0.0959838	−	0.995383i	$-0.530600\pi$
$509$	−2.90709e11	−0.191968	−0.0959838	+	0.995383i	$0.530600\pi$
$510$	1.47306e11	0.0964175
$511$	−8.27180e11	−0.536668
$512$	8.28486e11	0.532808
$513$	−1.24852e11	−0.0795918
$514$	−1.23346e12	−0.779457
$515$	3.79504e10	0.0237730
$516$	7.49833e10	0.0465630
$517$	2.81325e12	1.73181
$518$	8.67587e11	0.529455
$519$	1.80757e12	1.09356
$520$	−7.51843e11	−0.450933
$521$	−2.04811e12	−1.21782	−0.608910	−	0.793240i	$-0.708393\pi$
$521$	−2.04811e12	−1.21782	−0.608910	+	0.793240i	$0.708393\pi$
$522$	7.57860e10	0.0446758
$523$	8.49299e10	0.0496367	0.0248184	−	0.999692i	$-0.492099\pi$
$523$	8.49299e10	0.0496367	0.0248184	+	0.999692i	$0.492099\pi$
$524$	5.66488e10	0.0328247
$525$	−1.26895e11	−0.0728999
$526$	−8.94570e11	−0.509540
$527$	−5.98426e11	−0.337958
$528$	−2.10021e12	−1.17601
$529$	3.70117e12	2.05489
$530$	−9.97305e11	−0.549018
$531$	9.80258e11	0.535075
$532$	1.01009e11	0.0546713
$533$	−1.08176e12	−0.580575
$534$	−8.71224e11	−0.463654
$535$	6.30175e11	0.332559
$536$	2.74741e12	1.43775
$537$	−1.40570e12	−0.729472
$538$	1.76588e12	0.908745
$539$	−2.05954e12	−1.05104
$540$	−3.56087e10	−0.0180212
$541$	−1.29101e12	−0.647949	−0.323974	−	0.946066i	$-0.605019\pi$
$541$	−1.29101e12	−0.647949	−0.323974	+	0.946066i	$0.605019\pi$
$542$	−3.66292e12	−1.82318
$543$	−1.08572e12	−0.535944
$544$	2.85989e11	0.140009
$545$	1.10890e12	0.538404
$546$	9.65379e11	0.464870
$547$	−5.30222e11	−0.253230	−0.126615	−	0.991952i	$-0.540411\pi$
$547$	−5.30222e11	−0.253230	−0.126615	+	0.991952i	$0.540411\pi$
$548$	5.37921e11	0.254804
$549$	1.01455e12	0.476649
$550$	−8.24874e11	−0.384375
$551$	1.09054e11	0.0504035
$552$	1.91386e12	0.877371
$553$	1.62177e12	0.737438
$554$	7.15002e11	0.322488
$555$	−4.40110e11	−0.196899
$556$	3.77230e11	0.167405
$557$	8.17386e11	0.359815	0.179907	−	0.983684i	$-0.442420\pi$
$557$	8.17386e11	0.359815	0.179907	+	0.983684i	$0.442420\pi$
$558$	8.35525e11	0.364842
$559$	1.03123e12	0.446684
$560$	−7.65857e11	−0.329080
$561$	8.03773e11	0.342611
$562$	−1.28667e12	−0.544069
$563$	−1.42197e12	−0.596488	−0.298244	−	0.954490i	$-0.596401\pi$
$563$	−1.42197e12	−0.596488	−0.298244	+	0.954490i	$0.596401\pi$
$564$	2.87876e11	0.119798
$565$	−5.90934e11	−0.243961
$566$	8.02339e10	0.0328613
$567$	−1.72639e11	−0.0701480
$568$	−3.59523e12	−1.44930
$569$	−1.04614e12	−0.418394	−0.209197	−	0.977874i	$-0.567085\pi$
$569$	−1.04614e12	−0.418394	−0.209197	+	0.977874i	$0.567085\pi$
$570$	−2.95954e11	−0.117432
$571$	2.09508e12	0.824780	0.412390	−	0.911007i	$-0.364694\pi$
$571$	2.09508e12	0.824780	0.412390	+	0.911007i	$0.364694\pi$
$572$	1.08649e12	0.424371
$573$	−4.87063e11	−0.188751
$574$	−9.03965e11	−0.347575
$575$	9.16290e11	0.349565
$576$	6.27082e11	0.237369
$577$	2.68760e12	1.00942	0.504711	−	0.863288i	$-0.331599\pi$
$577$	2.68760e12	1.00942	0.504711	+	0.863288i	$0.331599\pi$
$578$	2.61068e12	0.972921
$579$	−5.60394e11	−0.207224
$580$	3.11031e10	0.0114124
$581$	2.07357e10	0.00754962
$582$	2.66192e12	0.961705
$583$	−5.44176e12	−1.95088
$584$	2.07755e12	0.739085
$585$	−4.89718e11	−0.172880
$586$	2.82658e12	0.990199
$587$	1.61925e12	0.562913	0.281457	−	0.959574i	$-0.409182\pi$
$587$	1.61925e12	0.562913	0.281457	+	0.959574i	$0.409182\pi$
$588$	−2.10750e11	−0.0727058
$589$	1.20230e12	0.411618
$590$	2.32364e12	0.789467
$591$	1.34572e12	0.453745
$592$	−2.65623e12	−0.888828
$593$	5.82677e12	1.93500	0.967502	−	0.252863i	$-0.0813722\pi$
$593$	5.82677e12	1.93500	0.967502	+	0.252863i	$0.0813722\pi$
$594$	−1.12223e12	−0.369865
$595$	2.93101e11	0.0958719
$596$	4.64007e11	0.150632
$597$	−2.48436e12	−0.800442
$598$	−6.97087e12	−2.22911
$599$	−3.89086e12	−1.23488	−0.617441	−	0.786617i	$-0.711831\pi$
$599$	−3.89086e12	−1.23488	−0.617441	+	0.786617i	$0.711831\pi$
$600$	3.18710e11	0.100396
$601$	2.13051e12	0.666115	0.333058	−	0.942907i	$-0.391920\pi$
$601$	2.13051e12	0.666115	0.333058	+	0.942907i	$0.391920\pi$
$602$	8.61737e11	0.267418
$603$	1.78955e12	0.551207
$604$	−6.02321e11	−0.184146
$605$	−3.02718e12	−0.918628
$606$	−1.06919e12	−0.322053
$607$	−2.52733e12	−0.755637	−0.377818	−	0.925880i	$-0.623326\pi$
$607$	−2.52733e12	−0.755637	−0.377818	+	0.925880i	$0.623326\pi$
$608$	−5.74582e11	−0.170524
$609$	1.50794e11	0.0444230
$610$	2.40493e12	0.703263
$611$	3.95908e12	1.14924
$612$	8.22490e10	0.0237000
$613$	1.89788e12	0.542870	0.271435	−	0.962457i	$-0.412502\pi$
$613$	1.89788e12	0.542870	0.271435	+	0.962457i	$0.412502\pi$
$614$	5.73681e11	0.162897
$615$	4.58564e11	0.129259
$616$	−3.42815e12	−0.959283
$617$	−1.40480e12	−0.390240	−0.195120	−	0.980779i	$-0.562510\pi$
$617$	−1.40480e12	−0.390240	−0.195120	+	0.980779i	$0.562510\pi$
$618$	1.22388e11	0.0337514
$619$	−2.81250e12	−0.769989	−0.384995	−	0.922919i	$-0.625797\pi$
$619$	−2.81250e12	−0.769989	−0.384995	+	0.922919i	$0.625797\pi$
$620$	3.42904e11	0.0931988
$621$	1.24660e12	0.336369
$622$	−1.92031e12	−0.514416
$623$	−1.73351e12	−0.461030
$624$	−2.95563e12	−0.780404
$625$	1.52588e11	0.0400000
$626$	1.16664e12	0.303634
$627$	−1.61486e12	−0.417284
$628$	1.66817e11	0.0427977
$629$	1.01657e12	0.258945
$630$	−4.09229e11	−0.103499
$631$	−1.92653e12	−0.483775	−0.241888	−	0.970304i	$-0.577767\pi$
$631$	−1.92653e12	−0.483775	−0.241888	+	0.970304i	$0.577767\pi$
$632$	−4.07325e12	−1.01558
$633$	3.12334e12	0.773219
$634$	−5.46001e12	−1.34212
$635$	3.24848e12	0.792865
$636$	−5.56848e11	−0.134952
$637$	−2.89839e12	−0.697476
$638$	9.80232e11	0.234226
$639$	−2.34178e12	−0.555638
$640$	2.26909e12	0.534617
$641$	−7.10318e12	−1.66185	−0.830924	−	0.556385i	$-0.812188\pi$
$641$	−7.10318e12	−1.66185	−0.830924	+	0.556385i	$0.812188\pi$
$642$	2.03228e12	0.472146
$643$	3.40733e12	0.786077	0.393038	−	0.919522i	$-0.371424\pi$
$643$	3.40733e12	0.786077	0.393038	+	0.919522i	$0.371424\pi$
$644$	−1.00854e12	−0.231051
$645$	−4.37142e11	−0.0994498
$646$	6.83594e11	0.154437
$647$	−4.31347e12	−0.967737	−0.483868	−	0.875141i	$-0.660769\pi$
$647$	−4.31347e12	−0.967737	−0.483868	+	0.875141i	$0.660769\pi$
$648$	4.33602e11	0.0966059
$649$	1.26789e13	2.80530
$650$	−1.16084e12	−0.255073
$651$	1.66248e12	0.362778
$652$	−1.23910e12	−0.268529
$653$	−2.53169e12	−0.544880	−0.272440	−	0.962173i	$-0.587831\pi$
$653$	−2.53169e12	−0.544880	−0.272440	+	0.962173i	$0.587831\pi$
$654$	3.57615e12	0.764391
$655$	−3.30255e11	−0.0701074
$656$	2.76760e12	0.583494
$657$	1.35323e12	0.283352
$658$	3.30838e12	0.688016
$659$	−4.43263e12	−0.915540	−0.457770	−	0.889071i	$-0.651352\pi$
$659$	−4.43263e12	−0.915540	−0.457770	+	0.889071i	$0.651352\pi$
$660$	−4.60571e11	−0.0944819
$661$	9.79827e11	0.199638	0.0998189	−	0.995006i	$-0.468174\pi$
$661$	9.79827e11	0.199638	0.0998189	+	0.995006i	$0.468174\pi$
$662$	−9.68168e10	−0.0195925
$663$	1.13115e12	0.227358
$664$	−5.20799e10	−0.0103971
$665$	−5.88871e11	−0.116768
$666$	−1.41933e12	−0.279544
$667$	−1.08887e12	−0.213014
$668$	−1.61331e12	−0.313489
$669$	−2.52199e12	−0.486773
$670$	4.24200e12	0.813269
$671$	1.31224e13	2.49898
$672$	−7.94502e11	−0.150291
$673$	7.69434e12	1.44578	0.722892	−	0.690961i	$-0.242812\pi$
$673$	7.69434e12	1.44578	0.722892	+	0.690961i	$0.242812\pi$
$674$	3.68927e12	0.688605
$675$	2.07594e11	0.0384900
$676$	3.92151e11	0.0722258
$677$	2.45111e12	0.448451	0.224225	−	0.974537i	$-0.428015\pi$
$677$	2.45111e12	0.448451	0.224225	+	0.974537i	$0.428015\pi$
$678$	−1.90573e12	−0.346360
$679$	5.29653e12	0.956264
$680$	−7.36157e11	−0.132032
$681$	−9.28174e11	−0.165374
$682$	1.08068e13	1.91280
$683$	3.13070e12	0.550488	0.275244	−	0.961374i	$-0.411241\pi$
$683$	3.13070e12	0.550488	0.275244	+	0.961374i	$0.411241\pi$
$684$	−1.65247e11	−0.0288656
$685$	−3.13601e12	−0.544213
$686$	−6.44918e12	−1.11185
$687$	−2.46690e12	−0.422519
$688$	−2.63831e12	−0.448930
$689$	−7.65819e12	−1.29461
$690$	2.95499e12	0.496289
$691$	−8.92815e12	−1.48974	−0.744870	−	0.667210i	$-0.767488\pi$
$691$	−8.92815e12	−1.48974	−0.744870	+	0.667210i	$0.767488\pi$
$692$	2.39239e12	0.396602
$693$	−2.23295e12	−0.367772
$694$	4.07338e12	0.666556
$695$	−2.19920e12	−0.357547
$696$	−3.78737e11	−0.0611781
$697$	−1.05919e12	−0.169991
$698$	−1.74699e12	−0.278574
$699$	2.29741e11	0.0363991
$700$	−1.67950e11	−0.0264387
$701$	−1.44295e12	−0.225695	−0.112847	−	0.993612i	$-0.535997\pi$
$701$	−1.44295e12	−0.225695	−0.112847	+	0.993612i	$0.535997\pi$
$702$	−1.57932e12	−0.245444
$703$	−2.04239e12	−0.315383
$704$	8.11081e12	1.24448
$705$	−1.67828e12	−0.255866
$706$	3.87509e11	0.0587030
$707$	−2.12740e12	−0.320230
$708$	1.29741e12	0.194056
$709$	−7.40550e12	−1.10064	−0.550321	−	0.834953i	$-0.685495\pi$
$709$	−7.40550e12	−1.10064	−0.550321	+	0.834953i	$0.685495\pi$
$710$	−5.55103e12	−0.819806
$711$	−2.65314e12	−0.389355
$712$	4.35390e12	0.634919
$713$	−1.20045e13	−1.73957
$714$	9.45237e11	0.136113
$715$	−6.33411e12	−0.906377
$716$	−1.86050e12	−0.264558
$717$	−5.06949e12	−0.716354
$718$	−8.17496e11	−0.114796
$719$	−3.90289e12	−0.544636	−0.272318	−	0.962207i	$-0.587790\pi$
$719$	−3.90289e12	−0.544636	−0.272318	+	0.962207i	$0.587790\pi$
$720$	1.25291e12	0.173749
$721$	2.43520e11	0.0335604
$722$	6.65631e12	0.911624
$723$	5.86452e12	0.798197
$724$	−1.43699e12	−0.194371
$725$	−1.81327e11	−0.0243748
$726$	−9.76251e12	−1.30421
$727$	1.33674e12	0.177477	0.0887384	−	0.996055i	$-0.471716\pi$
$727$	1.33674e12	0.177477	0.0887384	+	0.996055i	$0.471716\pi$
$728$	−4.82443e12	−0.636583
$729$	2.82430e11	0.0370370
$730$	3.20774e12	0.418067
$731$	1.00971e12	0.130788
$732$	1.34280e12	0.172866
$733$	−5.98863e11	−0.0766231	−0.0383116	−	0.999266i	$-0.512198\pi$
$733$	−5.98863e11	−0.0766231	−0.0383116	+	0.999266i	$0.512198\pi$
$734$	1.18455e13	1.50633
$735$	1.22864e12	0.155286
$736$	5.73699e12	0.720665
$737$	2.31464e13	2.88987
$738$	1.47884e12	0.183514
$739$	−1.40697e13	−1.73534	−0.867671	−	0.497138i	$-0.834384\pi$
$739$	−1.40697e13	−1.73534	−0.867671	+	0.497138i	$0.834384\pi$
$740$	−5.82503e11	−0.0714094
$741$	−2.27260e12	−0.276911
$742$	−6.39951e12	−0.775049
$743$	−2.52604e12	−0.304082	−0.152041	−	0.988374i	$-0.548585\pi$
$743$	−2.52604e12	−0.304082	−0.152041	+	0.988374i	$0.548585\pi$
$744$	−4.17549e12	−0.499608
$745$	−2.70510e12	−0.321721
$746$	2.42056e12	0.286149
$747$	−3.39226e10	−0.00398608
$748$	1.06383e12	0.124255
$749$	4.04371e12	0.469474
$750$	4.92088e11	0.0567894
$751$	3.78704e12	0.434430	0.217215	−	0.976124i	$-0.430303\pi$
$751$	3.78704e12	0.434430	0.217215	+	0.976124i	$0.430303\pi$
$752$	−1.01290e13	−1.15501
$753$	−4.58401e12	−0.519599
$754$	1.37948e12	0.155433
$755$	3.51145e12	0.393301
$756$	−2.28494e11	−0.0254406
$757$	3.55646e12	0.393629	0.196814	−	0.980441i	$-0.436940\pi$
$757$	3.55646e12	0.393629	0.196814	+	0.980441i	$0.436940\pi$
$758$	−1.10776e13	−1.21880
$759$	1.61238e13	1.76352
$760$	1.47902e12	0.160809
$761$	1.67100e13	1.80612	0.903058	−	0.429519i	$-0.141317\pi$
$761$	1.67100e13	1.80612	0.903058	+	0.429519i	$0.141317\pi$
$762$	1.04762e13	1.12566
$763$	7.11560e12	0.760066
$764$	−6.44647e11	−0.0684544
$765$	−4.79500e11	−0.0506189
$766$	−5.45987e12	−0.572997
$767$	1.78429e13	1.86160
$768$	3.35393e12	0.347880
$769$	−7.51512e12	−0.774939	−0.387469	−	0.921883i	$-0.626651\pi$
$769$	−7.51512e12	−0.774939	−0.387469	+	0.921883i	$0.626651\pi$
$770$	−5.29306e12	−0.542623
$771$	4.01507e12	0.409213
$772$	−7.41702e11	−0.0751540
$773$	−8.52580e12	−0.858870	−0.429435	−	0.903098i	$-0.641287\pi$
$773$	−8.52580e12	−0.858870	−0.429435	+	0.903098i	$0.641287\pi$
$774$	−1.40976e12	−0.141192
$775$	−1.99909e12	−0.199055
$776$	−1.33028e13	−1.31694
$777$	−2.82410e12	−0.277962
$778$	9.25569e12	0.905734
$779$	2.12802e12	0.207042
$780$	−6.48161e11	−0.0626985
$781$	−3.02890e13	−2.91310
$782$	−6.82543e12	−0.652679
$783$	−2.46693e11	−0.0234546
$784$	7.41531e12	0.700982
$785$	−9.72518e11	−0.0914080
$786$	−1.06506e12	−0.0995338
$787$	3.20742e12	0.298037	0.149018	−	0.988834i	$-0.452389\pi$
$787$	3.20742e12	0.298037	0.149018	+	0.988834i	$0.452389\pi$
$788$	1.78112e12	0.164560
$789$	2.91194e12	0.267507
$790$	−6.28908e12	−0.574467
$791$	−3.79191e12	−0.344401
$792$	5.60830e12	0.506486
$793$	1.84672e13	1.65833
$794$	3.45353e12	0.308369
$795$	3.24635e12	0.288233
$796$	−3.28815e12	−0.290297
$797$	−1.83036e13	−1.60684	−0.803421	−	0.595412i	$-0.796989\pi$
$797$	−1.83036e13	−1.60684	−0.803421	+	0.595412i	$0.796989\pi$
$798$	−1.89908e12	−0.165779
$799$	3.87648e12	0.336494
$800$	9.55368e11	0.0824643
$801$	2.83594e12	0.243417
$802$	−1.72975e13	−1.47638
$803$	1.75029e13	1.48556
$804$	2.36853e12	0.199907
$805$	5.87966e12	0.493481
$806$	1.52085e13	1.26934
$807$	−5.74817e12	−0.477088
$808$	5.34321e12	0.441013
$809$	9.38919e12	0.770655	0.385327	−	0.922780i	$-0.374089\pi$
$809$	9.38919e12	0.770655	0.385327	+	0.922780i	$0.374089\pi$
$810$	6.69480e11	0.0546456
$811$	2.03949e13	1.65549	0.827746	−	0.561103i	$-0.189623\pi$
$811$	2.03949e13	1.65549	0.827746	+	0.561103i	$0.189623\pi$
$812$	1.99582e11	0.0161109
$813$	1.19232e13	0.957166
$814$	−1.83579e13	−1.46560
$815$	7.22377e12	0.573528
$816$	−2.89396e12	−0.228500
$817$	−2.02861e12	−0.159294
$818$	−2.26642e13	−1.76991
$819$	−3.14243e12	−0.244055
$820$	6.06927e11	0.0468785
$821$	−1.52259e13	−1.16961	−0.584803	−	0.811176i	$-0.698828\pi$
$821$	−1.52259e13	−1.16961	−0.584803	+	0.811176i	$0.698828\pi$
$822$	−1.01135e13	−0.772639
$823$	−2.70705e12	−0.205682	−0.102841	−	0.994698i	$-0.532793\pi$
$823$	−2.70705e12	−0.205682	−0.102841	+	0.994698i	$0.532793\pi$
$824$	−6.11629e11	−0.0462184
$825$	2.68506e12	0.201796
$826$	1.49103e13	1.11449
$827$	5.67203e10	0.00421661	0.00210831	−	0.999998i	$-0.499329\pi$
$827$	5.67203e10	0.00421661	0.00210831	+	0.999998i	$0.499329\pi$
$828$	1.64993e12	0.121991
$829$	−1.43206e13	−1.05309	−0.526547	−	0.850146i	$-0.676513\pi$
$829$	−1.43206e13	−1.05309	−0.526547	+	0.850146i	$0.676513\pi$
$830$	−8.04113e10	−0.00588119
$831$	−2.32742e12	−0.169305
$832$	1.14143e13	0.825839
$833$	−2.83791e12	−0.204219
$834$	−7.09231e12	−0.507622
$835$	9.40535e12	0.669555
$836$	−2.13734e12	−0.151337
$837$	−2.71973e12	−0.191541
$838$	−7.74265e12	−0.542365
$839$	−2.13693e13	−1.48889	−0.744443	−	0.667686i	$-0.767285\pi$
$839$	−2.13693e13	−1.48889	−0.744443	+	0.667686i	$0.767285\pi$
$840$	2.04510e12	0.141729
$841$	−1.42917e13	−0.985147
$842$	−1.90098e13	−1.30339
$843$	4.18827e12	0.285635
$844$	4.13386e12	0.280424
$845$	−2.28618e12	−0.154261
$846$	−5.41235e12	−0.363262
$847$	−1.94248e13	−1.29683
$848$	1.95929e13	1.30112
$849$	−2.61171e11	−0.0172521
$850$	−1.13662e12	−0.0746847
$851$	2.03925e13	1.33287
$852$	−3.09943e12	−0.201514
$853$	−1.18123e13	−0.763948	−0.381974	−	0.924173i	$-0.624756\pi$
$853$	−1.18123e13	−0.763948	−0.381974	+	0.924173i	$0.624756\pi$
$854$	1.54319e13	0.992797
$855$	9.63366e11	0.0616515
$856$	−1.01562e13	−0.646547
$857$	2.69459e13	1.70640	0.853198	−	0.521587i	$-0.174660\pi$
$857$	2.69459e13	1.70640	0.853198	+	0.521587i	$0.174660\pi$
$858$	−2.04272e13	−1.28681
$859$	9.66669e12	0.605771	0.302885	−	0.953027i	$-0.402050\pi$
$859$	9.66669e12	0.605771	0.302885	+	0.953027i	$0.402050\pi$
$860$	−5.78575e11	−0.0360675
$861$	2.94251e12	0.182475
$862$	−1.62897e12	−0.100492
$863$	2.80982e12	0.172437	0.0862185	−	0.996276i	$-0.472522\pi$
$863$	2.80982e12	0.172437	0.0862185	+	0.996276i	$0.472522\pi$
$864$	1.29977e12	0.0793513
$865$	−1.39473e13	−0.847069
$866$	1.95944e13	1.18386
$867$	−8.49807e12	−0.510781
$868$	2.20035e12	0.131569
$869$	−3.43162e13	−2.04132
$870$	−5.84769e11	−0.0346057
$871$	3.25739e13	1.91773
$872$	−1.78716e13	−1.04674
$873$	−8.66488e12	−0.504892
$874$	1.37130e13	0.794933
$875$	9.79127e11	0.0564680
$876$	1.79105e12	0.102764
$877$	3.37045e13	1.92393	0.961966	−	0.273169i	$-0.0880718\pi$
$877$	3.37045e13	1.92393	0.961966	+	0.273169i	$0.0880718\pi$
$878$	2.08828e13	1.18594
$879$	−9.20087e12	−0.519851
$880$	1.62054e13	0.910933
$881$	−1.20571e13	−0.674297	−0.337148	−	0.941452i	$-0.609462\pi$
$881$	−1.20571e13	−0.674297	−0.337148	+	0.941452i	$0.609462\pi$
$882$	3.96231e12	0.220465
$883$	−1.91595e13	−1.06062	−0.530311	−	0.847803i	$-0.677925\pi$
$883$	−1.91595e13	−1.06062	−0.530311	+	0.847803i	$0.677925\pi$
$884$	1.49712e12	0.0824559
$885$	−7.56372e12	−0.414468
$886$	3.19140e13	1.73992
$887$	−2.24991e13	−1.22042	−0.610209	−	0.792241i	$-0.708914\pi$
$887$	−2.24991e13	−1.22042	−0.610209	+	0.792241i	$0.708914\pi$
$888$	7.09305e12	0.382802
$889$	2.08449e13	1.11929
$890$	6.72241e12	0.359145
$891$	3.65300e12	0.194178
$892$	−3.33795e12	−0.176538
$893$	−7.78825e12	−0.409834
$894$	−8.72380e12	−0.456759
$895$	1.08465e13	0.565047
$896$	1.45603e13	0.754719
$897$	2.26910e13	1.17028
$898$	−1.99576e12	−0.102415
$899$	2.37560e12	0.121298
$900$	2.74759e11	0.0139592
$901$	−7.49841e12	−0.379060
$902$	1.91277e13	0.962128
$903$	−2.80506e12	−0.140393
$904$	9.52380e12	0.474299
$905$	8.37748e12	0.415140
$906$	1.13242e13	0.558383
$907$	−2.39724e13	−1.17619	−0.588096	−	0.808791i	$-0.700122\pi$
$907$	−2.39724e13	−1.17619	−0.588096	+	0.808791i	$0.700122\pi$
$908$	−1.22847e12	−0.0599763
$909$	3.48033e12	0.169077
$910$	−7.44891e12	−0.360086
$911$	−6.54470e12	−0.314816	−0.157408	−	0.987534i	$-0.550314\pi$
$911$	−6.54470e12	−0.314816	−0.157408	+	0.987534i	$0.550314\pi$
$912$	5.81427e12	0.278303
$913$	−4.38762e11	−0.0208983
$914$	−3.16236e12	−0.149884
$915$	−7.82833e12	−0.369211
$916$	−3.26504e12	−0.153235
$917$	−2.11918e12	−0.0989706
$918$	−1.54636e12	−0.0718654
$919$	2.63348e12	0.121789	0.0608947	−	0.998144i	$-0.480605\pi$
$919$	2.63348e12	0.121789	0.0608947	+	0.998144i	$0.480605\pi$
$920$	−1.47674e13	−0.679609
$921$	−1.86740e12	−0.0855203
$922$	1.84111e13	0.839055
$923$	−4.26258e13	−1.93314
$924$	−2.95539e12	−0.133380
$925$	3.39591e12	0.152517
$926$	−1.42093e13	−0.635073
$927$	−3.98388e11	−0.0177193
$928$	−1.13530e12	−0.0502512
$929$	2.94271e13	1.29621	0.648106	−	0.761550i	$-0.275561\pi$
$929$	2.94271e13	1.29621	0.648106	+	0.761550i	$0.275561\pi$
$930$	−6.44695e12	−0.282606
$931$	5.70166e12	0.248730
$932$	3.04070e11	0.0132009
$933$	6.25084e12	0.270067
$934$	−2.96305e13	−1.27403
$935$	−6.20196e12	−0.265385
$936$	7.89255e12	0.336106
$937$	−1.71769e13	−0.727974	−0.363987	−	0.931404i	$-0.618585\pi$
$937$	−1.71769e13	−0.727974	−0.363987	+	0.931404i	$0.618585\pi$
$938$	2.72201e13	1.14809
$939$	−3.79754e12	−0.159407
$940$	−2.22126e12	−0.0927950
$941$	−2.46944e13	−1.02670	−0.513352	−	0.858178i	$-0.671596\pi$
$941$	−2.46944e13	−1.02670	−0.513352	+	0.858178i	$0.671596\pi$
$942$	−3.13632e12	−0.129775
$943$	−2.12475e13	−0.874994
$944$	−4.56498e13	−1.87096
$945$	1.33209e12	0.0543364
$946$	−1.82341e13	−0.740244
$947$	−1.19428e12	−0.0482537	−0.0241268	−	0.999709i	$-0.507681\pi$
$947$	−1.19428e12	−0.0482537	−0.0241268	+	0.999709i	$0.507681\pi$
$948$	−3.51153e12	−0.141208
$949$	2.46319e13	0.985824
$950$	2.28360e12	0.0909626
$951$	1.77730e13	0.704610
$952$	−4.72377e12	−0.186390
$953$	1.47694e13	0.580023	0.290011	−	0.957023i	$-0.406341\pi$
$953$	1.47694e13	0.580023	0.290011	+	0.957023i	$0.406341\pi$
$954$	1.04693e13	0.409214
$955$	3.75820e12	0.146206
$956$	−6.70966e12	−0.259800
$957$	−3.19077e12	−0.122968
$958$	−3.63489e13	−1.39427
$959$	−2.01231e13	−0.768267
$960$	−4.83860e12	−0.183865
$961$	−2.49176e11	−0.00942435
$962$	−2.58351e13	−0.972574
$963$	−6.61532e12	−0.247875
$964$	7.76192e12	0.289483
$965$	4.32402e12	0.160515
$966$	1.89616e13	0.700612
$967$	−8.95584e12	−0.329372	−0.164686	−	0.986346i	$-0.552661\pi$
$967$	−8.95584e12	−0.329372	−0.164686	+	0.986346i	$0.552661\pi$
$968$	4.87876e13	1.78596
$969$	−2.22518e12	−0.0810790
$970$	−2.05395e13	−0.744934
$971$	−2.20587e13	−0.796330	−0.398165	−	0.917314i	$-0.630353\pi$
$971$	−2.20587e13	−0.796330	−0.398165	+	0.917314i	$0.630353\pi$
$972$	3.73806e11	0.0134322
$973$	−1.41118e13	−0.504749
$974$	3.65621e13	1.30172
$975$	3.77869e12	0.133912
$976$	−4.72469e13	−1.66667
$977$	3.56972e13	1.25345	0.626727	−	0.779239i	$-0.284394\pi$
$977$	3.56972e13	1.25345	0.626727	+	0.779239i	$0.284394\pi$
$978$	2.32963e13	0.814258
$979$	3.66806e13	1.27619
$980$	1.62615e12	0.0563176
$981$	−1.16408e13	−0.401303
$982$	4.38300e13	1.50408
$983$	3.19525e13	1.09147	0.545737	−	0.837956i	$-0.316250\pi$
$983$	3.19525e13	1.09147	0.545737	+	0.837956i	$0.316250\pi$
$984$	−7.39045e12	−0.251300
$985$	−1.03837e13	−0.351469
$986$	1.35070e12	0.0455105
$987$	−1.07692e13	−0.361206
$988$	−3.00787e12	−0.100428
$989$	2.02549e13	0.673205
$990$	8.65920e12	0.286496
$991$	1.56883e13	0.516706	0.258353	−	0.966051i	$-0.416820\pi$
$991$	1.56883e13	0.516706	0.258353	+	0.966051i	$0.416820\pi$
$992$	−1.25165e13	−0.410374
$993$	3.15151e11	0.0102860
$994$	−3.56199e13	−1.15732
$995$	1.91694e13	0.620020
$996$	−4.48979e10	−0.00144563
$997$	6.52145e12	0.209033	0.104517	−	0.994523i	$-0.466670\pi$
$997$	6.52145e12	0.209033	0.104517	+	0.994523i	$0.466670\pi$
$998$	4.05647e13	1.29438
$999$	4.62010e12	0.146760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.10.a.c.1.1	✓	2
3.2	odd	2		45.10.a.e.1.2		2
4.3	odd	2		240.10.a.m.1.1		2
5.2	odd	4		75.10.b.e.49.2		4
5.3	odd	4		75.10.b.e.49.3		4
5.4	even	2		75.10.a.g.1.2		2
15.2	even	4		225.10.b.g.199.3		4
15.8	even	4		225.10.b.g.199.2		4
15.14	odd	2		225.10.a.j.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.10.a.c.1.1	✓	2	1.1	even	1	trivial
45.10.a.e.1.2		2	3.2	odd	2
75.10.a.g.1.2		2	5.4	even	2
75.10.b.e.49.2		4	5.2	odd	4
75.10.b.e.49.3		4	5.3	odd	4
225.10.a.j.1.1		2	15.14	odd	2
225.10.b.g.199.2		4	15.8	even	4
225.10.b.g.199.3		4	15.2	even	4
240.10.a.m.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	15.a (trivial)

\(f(q)\)	\(=\)	\(q-24.8839 q^{2} +81.0000 q^{3} +107.207 q^{4} -625.000 q^{5} -2015.59 q^{6} -4010.50 q^{7} +10072.8 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-24.8839 q^{2} +81.0000 q^{3} +107.207 q^{4} -625.000 q^{5} -2015.59 q^{6} -4010.50 q^{7} +10072.8 q^{8} +6561.00 q^{9} +15552.4 q^{10} +84861.3 q^{11} +8683.74 q^{12} +119425. q^{13} +99796.8 q^{14} -50625.0 q^{15} -305541. q^{16} +116934. q^{17} -163263. q^{18} -234932. q^{19} -67004.1 q^{20} -324851. q^{21} -2.11168e6 q^{22} +2.34570e6 q^{23} +815899. q^{24} +390625. q^{25} -2.97176e6 q^{26} +531441. q^{27} -429953. q^{28} -464196. q^{29} +1.25975e6 q^{30} -5.11766e6 q^{31} +2.44574e6 q^{32} +6.87377e6 q^{33} -2.90976e6 q^{34} +2.50656e6 q^{35} +703383. q^{36} +8.69354e6 q^{37} +5.84601e6 q^{38} +9.67345e6 q^{39} -6.29551e6 q^{40} -9.05805e6 q^{41} +8.08354e6 q^{42} +8.63491e6 q^{43} +9.09769e6 q^{44} -4.10062e6 q^{45} -5.83701e7 q^{46} +3.31511e7 q^{47} -2.47488e7 q^{48} -2.42695e7 q^{49} -9.72026e6 q^{50} +9.47161e6 q^{51} +1.28032e7 q^{52} -6.41254e7 q^{53} -1.32243e7 q^{54} -5.30383e7 q^{55} -4.03971e7 q^{56} -1.90295e7 q^{57} +1.15510e7 q^{58} +1.49407e8 q^{59} -5.42733e6 q^{60} +1.54634e8 q^{61} +1.27347e8 q^{62} -2.63129e7 q^{63} +9.55772e7 q^{64} -7.46408e7 q^{65} -1.71046e8 q^{66} +2.72755e8 q^{67} +1.25360e7 q^{68} +1.90002e8 q^{69} -6.23730e7 q^{70} -3.56924e8 q^{71} +6.60878e7 q^{72} +2.06253e8 q^{73} -2.16329e8 q^{74} +3.16406e7 q^{75} -2.51862e7 q^{76} -3.40337e8 q^{77} -2.40713e8 q^{78} -4.04380e8 q^{79} +1.90963e8 q^{80} +4.30467e7 q^{81} +2.25399e8 q^{82} -5.17034e6 q^{83} -3.48262e7 q^{84} -7.30834e7 q^{85} -2.14870e8 q^{86} -3.75999e7 q^{87} +8.54793e8 q^{88} +4.32242e8 q^{89} +1.02039e8 q^{90} -4.78955e8 q^{91} +2.51475e8 q^{92} -4.14530e8 q^{93} -8.24928e8 q^{94} +1.46832e8 q^{95} +1.98105e8 q^{96} -1.32066e9 q^{97} +6.03918e8 q^{98} +5.56775e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 19 q^{2} + 162 q^{3} + 1521 q^{4} - 1250 q^{5} + 1539 q^{6} - 11872 q^{7} + 49647 q^{8} + 13122 q^{9}+O(q^{10}) \) 2 * q + 19 * q^2 + 162 * q^3 + 1521 * q^4 - 1250 * q^5 + 1539 * q^6 - 11872 * q^7 + 49647 * q^8 + 13122 * q^9	\( 2 q + 19 q^{2} + 162 q^{3} + 1521 q^{4} - 1250 q^{5} + 1539 q^{6} - 11872 q^{7} + 49647 q^{8} + 13122 q^{9} - 11875 q^{10} + 35488 q^{11} + 123201 q^{12} + 143676 q^{13} - 245196 q^{14} - 101250 q^{15} + 707265 q^{16} + 385156 q^{17} + 124659 q^{18} - 403296 q^{19} - 950625 q^{20} - 961632 q^{21} - 4278368 q^{22} + 223704 q^{23} + 4021407 q^{24} + 781250 q^{25} - 1907546 q^{26} + 1062882 q^{27} - 11544484 q^{28} - 74572 q^{29} - 961875 q^{30} - 5027128 q^{31} + 26629583 q^{32} + 2874528 q^{33} + 8860882 q^{34} + 7420000 q^{35} + 9979281 q^{36} + 5373628 q^{37} - 1542476 q^{38} + 11637756 q^{39} - 31029375 q^{40} + 14211332 q^{41} - 19860876 q^{42} + 27748920 q^{43} - 60705952 q^{44} - 8201250 q^{45} - 151491648 q^{46} + 95966440 q^{47} + 57288465 q^{48} - 2819950 q^{49} + 7421875 q^{50} + 31197636 q^{51} + 47088706 q^{52} - 64305596 q^{53} + 10097379 q^{54} - 22180000 q^{55} - 351509340 q^{56} - 32666976 q^{57} + 28649198 q^{58} + 187863136 q^{59} - 77000625 q^{60} + 154080060 q^{61} + 131320056 q^{62} - 77892192 q^{63} + 638301089 q^{64} - 89797500 q^{65} - 346547808 q^{66} + 33592376 q^{67} + 391747238 q^{68} + 18120024 q^{69} + 153247500 q^{70} - 228270976 q^{71} + 325733967 q^{72} - 33122316 q^{73} - 362019226 q^{74} + 63281250 q^{75} - 263218724 q^{76} + 47811456 q^{77} - 154511226 q^{78} - 932406760 q^{79} - 442040625 q^{80} + 86093442 q^{81} + 1246549646 q^{82} + 207040152 q^{83} - 935103204 q^{84} - 240722500 q^{85} + 623926708 q^{86} - 6040332 q^{87} - 1099114848 q^{88} + 224518164 q^{89} - 77911875 q^{90} - 669602528 q^{91} - 2748592992 q^{92} - 407197368 q^{93} + 1931650816 q^{94} + 252060000 q^{95} + 2156996223 q^{96} + 387134596 q^{97} + 1545205739 q^{98} + 232836768 q^{99}+O(q^{100}) \) 2 * q + 19 * q^2 + 162 * q^3 + 1521 * q^4 - 1250 * q^5 + 1539 * q^6 - 11872 * q^7 + 49647 * q^8 + 13122 * q^9 - 11875 * q^10 + 35488 * q^11 + 123201 * q^12 + 143676 * q^13 - 245196 * q^14 - 101250 * q^15 + 707265 * q^16 + 385156 * q^17 + 124659 * q^18 - 403296 * q^19 - 950625 * q^20 - 961632 * q^21 - 4278368 * q^22 + 223704 * q^23 + 4021407 * q^24 + 781250 * q^25 - 1907546 * q^26 + 1062882 * q^27 - 11544484 * q^28 - 74572 * q^29 - 961875 * q^30 - 5027128 * q^31 + 26629583 * q^32 + 2874528 * q^33 + 8860882 * q^34 + 7420000 * q^35 + 9979281 * q^36 + 5373628 * q^37 - 1542476 * q^38 + 11637756 * q^39 - 31029375 * q^40 + 14211332 * q^41 - 19860876 * q^42 + 27748920 * q^43 - 60705952 * q^44 - 8201250 * q^45 - 151491648 * q^46 + 95966440 * q^47 + 57288465 * q^48 - 2819950 * q^49 + 7421875 * q^50 + 31197636 * q^51 + 47088706 * q^52 - 64305596 * q^53 + 10097379 * q^54 - 22180000 * q^55 - 351509340 * q^56 - 32666976 * q^57 + 28649198 * q^58 + 187863136 * q^59 - 77000625 * q^60 + 154080060 * q^61 + 131320056 * q^62 - 77892192 * q^63 + 638301089 * q^64 - 89797500 * q^65 - 346547808 * q^66 + 33592376 * q^67 + 391747238 * q^68 + 18120024 * q^69 + 153247500 * q^70 - 228270976 * q^71 + 325733967 * q^72 - 33122316 * q^73 - 362019226 * q^74 + 63281250 * q^75 - 263218724 * q^76 + 47811456 * q^77 - 154511226 * q^78 - 932406760 * q^79 - 442040625 * q^80 + 86093442 * q^81 + 1246549646 * q^82 + 207040152 * q^83 - 935103204 * q^84 - 240722500 * q^85 + 623926708 * q^86 - 6040332 * q^87 - 1099114848 * q^88 + 224518164 * q^89 - 77911875 * q^90 - 669602528 * q^91 - 2748592992 * q^92 - 407197368 * q^93 + 1931650816 * q^94 + 252060000 * q^95 + 2156996223 * q^96 + 387134596 * q^97 + 1545205739 * q^98 + 232836768 * q^99

Introduction

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