LMFDB - Embedded newform 22.10.a.e.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [22,10,Mod(1,22)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(22, 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("22.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 22 = 2 \cdot 11 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	22.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:	$11.3307883956$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{463}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 463 $ x^2 - 463
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-21.5174$ of defining polynomial
Character	$\chi$	$=$	22.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-16.0000 q^{2} -155.139 q^{3} +256.000 q^{4} +982.395 q^{5} +2482.23 q^{6} +5991.53 q^{7} -4096.00 q^{8} +4385.26 q^{9} +O(q^{10})$	\(q-16.0000 q^{2} -155.139 q^{3} +256.000 q^{4} +982.395 q^{5} +2482.23 q^{6} +5991.53 q^{7} -4096.00 q^{8} +4385.26 q^{9} -15718.3 q^{10} -14641.0 q^{11} -39715.7 q^{12} -55973.8 q^{13} -95864.5 q^{14} -152408. q^{15} +65536.0 q^{16} -205366. q^{17} -70164.1 q^{18} -279746. q^{19} +251493. q^{20} -929523. q^{21} +234256. q^{22} -1.66070e6 q^{23} +635451. q^{24} -988025. q^{25} +895581. q^{26} +2.37328e6 q^{27} +1.53383e6 q^{28} -292603. q^{29} +2.43853e6 q^{30} +4.22388e6 q^{31} -1.04858e6 q^{32} +2.27140e6 q^{33} +3.28586e6 q^{34} +5.88605e6 q^{35} +1.12263e6 q^{36} -1.26399e7 q^{37} +4.47593e6 q^{38} +8.68375e6 q^{39} -4.02389e6 q^{40} -2.65729e7 q^{41} +1.48724e7 q^{42} -2.13800e7 q^{43} -3.74810e6 q^{44} +4.30805e6 q^{45} +2.65711e7 q^{46} +1.95666e7 q^{47} -1.01672e7 q^{48} -4.45512e6 q^{49} +1.58084e7 q^{50} +3.18604e7 q^{51} -1.43293e7 q^{52} -8.64352e7 q^{53} -3.79725e7 q^{54} -1.43832e7 q^{55} -2.45413e7 q^{56} +4.33996e7 q^{57} +4.68165e6 q^{58} -1.48166e8 q^{59} -3.90165e7 q^{60} +6.78553e7 q^{61} -6.75821e7 q^{62} +2.62744e7 q^{63} +1.67772e7 q^{64} -5.49884e7 q^{65} -3.63424e7 q^{66} +2.03091e8 q^{67} -5.25737e7 q^{68} +2.57639e8 q^{69} -9.41768e7 q^{70} +3.15187e8 q^{71} -1.79620e7 q^{72} +1.92010e8 q^{73} +2.02238e8 q^{74} +1.53282e8 q^{75} -7.16149e7 q^{76} -8.77221e7 q^{77} -1.38940e8 q^{78} +3.37959e8 q^{79} +6.43822e7 q^{80} -4.54505e8 q^{81} +4.25166e8 q^{82} -5.99250e8 q^{83} -2.37958e8 q^{84} -2.01751e8 q^{85} +3.42080e8 q^{86} +4.53943e7 q^{87} +5.99695e7 q^{88} +1.36415e7 q^{89} -6.89289e7 q^{90} -3.35369e8 q^{91} -4.25138e8 q^{92} -6.55291e8 q^{93} -3.13065e8 q^{94} -2.74821e8 q^{95} +1.62676e8 q^{96} -2.29779e8 q^{97} +7.12820e7 q^{98} -6.42046e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 32 q^{2} + 34 q^{3} + 512 q^{4} - 1478 q^{5} - 544 q^{6} + 8196 q^{7} - 8192 q^{8} + 20476 q^{9}+O(q^{10}) $ 2 * q - 32 * q^2 + 34 * q^3 + 512 * q^4 - 1478 * q^5 - 544 * q^6 + 8196 * q^7 - 8192 * q^8 + 20476 * q^9	\( 2 q - 32 q^{2} + 34 q^{3} + 512 q^{4} - 1478 q^{5} - 544 q^{6} + 8196 q^{7} - 8192 q^{8} + 20476 q^{9} + 23648 q^{10} - 29282 q^{11} + 8704 q^{12} - 196296 q^{13} - 131136 q^{14} - 617766 q^{15} + 131072 q^{16} - 548788 q^{17} - 327616 q^{18} - 90928 q^{19} - 378368 q^{20} - 512572 q^{21} + 468512 q^{22} - 3971046 q^{23} - 139264 q^{24} + 3112392 q^{25} + 3140736 q^{26} + 1693846 q^{27} + 2098176 q^{28} - 656128 q^{29} + 9884256 q^{30} - 872214 q^{31} - 2097152 q^{32} - 497794 q^{33} + 8780608 q^{34} + 462196 q^{35} + 5241856 q^{36} - 190722 q^{37} + 1454848 q^{38} - 17856712 q^{39} + 6053888 q^{40} + 3350080 q^{41} + 8201152 q^{42} + 3876012 q^{43} - 7496192 q^{44} - 35281524 q^{45} + 63536736 q^{46} + 38884544 q^{47} + 2228224 q^{48} - 39949062 q^{49} - 49798272 q^{50} - 33094260 q^{51} - 50251776 q^{52} - 134346316 q^{53} - 27101536 q^{54} + 21639398 q^{55} - 33570816 q^{56} + 79112528 q^{57} + 10498048 q^{58} - 125273754 q^{59} - 158148096 q^{60} + 114821880 q^{61} + 13955424 q^{62} + 61745912 q^{63} + 33554432 q^{64} + 290259544 q^{65} + 7964704 q^{66} - 91519714 q^{67} - 140489728 q^{68} - 179338950 q^{69} - 7395136 q^{70} + 411397438 q^{71} - 83869696 q^{72} + 506142392 q^{73} + 3051552 q^{74} + 928832584 q^{75} - 23277568 q^{76} - 119997636 q^{77} + 285707392 q^{78} + 810072516 q^{79} - 96862208 q^{80} - 899727614 q^{81} - 53601280 q^{82} - 718904884 q^{83} - 131218432 q^{84} + 643202972 q^{85} - 62016192 q^{86} - 23362560 q^{87} + 119939072 q^{88} - 810786322 q^{89} + 564504384 q^{90} - 644704528 q^{91} - 1016587776 q^{92} - 1619163382 q^{93} - 622152704 q^{94} - 739387248 q^{95} - 35651584 q^{96} - 230208654 q^{97} + 639184992 q^{98} - 299789116 q^{99}+O(q^{100}) \) 2 * q - 32 * q^2 + 34 * q^3 + 512 * q^4 - 1478 * q^5 - 544 * q^6 + 8196 * q^7 - 8192 * q^8 + 20476 * q^9 + 23648 * q^10 - 29282 * q^11 + 8704 * q^12 - 196296 * q^13 - 131136 * q^14 - 617766 * q^15 + 131072 * q^16 - 548788 * q^17 - 327616 * q^18 - 90928 * q^19 - 378368 * q^20 - 512572 * q^21 + 468512 * q^22 - 3971046 * q^23 - 139264 * q^24 + 3112392 * q^25 + 3140736 * q^26 + 1693846 * q^27 + 2098176 * q^28 - 656128 * q^29 + 9884256 * q^30 - 872214 * q^31 - 2097152 * q^32 - 497794 * q^33 + 8780608 * q^34 + 462196 * q^35 + 5241856 * q^36 - 190722 * q^37 + 1454848 * q^38 - 17856712 * q^39 + 6053888 * q^40 + 3350080 * q^41 + 8201152 * q^42 + 3876012 * q^43 - 7496192 * q^44 - 35281524 * q^45 + 63536736 * q^46 + 38884544 * q^47 + 2228224 * q^48 - 39949062 * q^49 - 49798272 * q^50 - 33094260 * q^51 - 50251776 * q^52 - 134346316 * q^53 - 27101536 * q^54 + 21639398 * q^55 - 33570816 * q^56 + 79112528 * q^57 + 10498048 * q^58 - 125273754 * q^59 - 158148096 * q^60 + 114821880 * q^61 + 13955424 * q^62 + 61745912 * q^63 + 33554432 * q^64 + 290259544 * q^65 + 7964704 * q^66 - 91519714 * q^67 - 140489728 * q^68 - 179338950 * q^69 - 7395136 * q^70 + 411397438 * q^71 - 83869696 * q^72 + 506142392 * q^73 + 3051552 * q^74 + 928832584 * q^75 - 23277568 * q^76 - 119997636 * q^77 + 285707392 * q^78 + 810072516 * q^79 - 96862208 * q^80 - 899727614 * q^81 - 53601280 * q^82 - 718904884 * q^83 - 131218432 * q^84 + 643202972 * q^85 - 62016192 * q^86 - 23362560 * q^87 + 119939072 * q^88 - 810786322 * q^89 + 564504384 * q^90 - 644704528 * q^91 - 1016587776 * q^92 - 1619163382 * q^93 - 622152704 * q^94 - 739387248 * q^95 - 35651584 * q^96 - 230208654 * q^97 + 639184992 * q^98 - 299789116 * 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 $

$2$	−16.0000	−0.707107
$2$	−16.0000	−0.707107
$3$	−155.139	−1.10580	−0.552900	−	0.833248i	$-0.686479\pi$
$3$	−155.139	−1.10580	−0.552900	+	0.833248i	$0.686479\pi$
$4$	256.000	0.500000
$5$	982.395	0.702944	0.351472	−	0.936198i	$-0.385681\pi$
$5$	982.395	0.702944	0.351472	+	0.936198i	$0.385681\pi$
$6$	2482.23	0.781919
$7$	5991.53	0.943185	0.471592	−	0.881817i	$-0.343679\pi$
$7$	5991.53	0.943185	0.471592	+	0.881817i	$0.343679\pi$
$8$	−4096.00	−0.353553
$9$	4385.26	0.222794
$10$	−15718.3	−0.497057
$11$	−14641.0	−0.301511
$11$	−14641.0	−0.301511
$12$	−39715.7	−0.552900
$13$	−55973.8	−0.543551	−0.271775	−	0.962361i	$-0.587611\pi$
$13$	−55973.8	−0.543551	−0.271775	+	0.962361i	$0.587611\pi$
$14$	−95864.5	−0.666932
$15$	−152408.	−0.777316
$16$	65536.0	0.250000
$17$	−205366.	−0.596360	−0.298180	−	0.954510i	$-0.596380\pi$
$17$	−205366.	−0.596360	−0.298180	+	0.954510i	$0.596380\pi$
$18$	−70164.1	−0.157539
$19$	−279746.	−0.492462	−0.246231	−	0.969211i	$-0.579192\pi$
$19$	−279746.	−0.492462	−0.246231	+	0.969211i	$0.579192\pi$
$20$	251493.	0.351472
$21$	−929523.	−1.04297
$22$	234256.	0.213201
$23$	−1.66070e6	−1.23741	−0.618707	−	0.785622i	$-0.712343\pi$
$23$	−1.66070e6	−1.23741	−0.618707	+	0.785622i	$0.712343\pi$
$24$	635451.	0.390959
$25$	−988025.	−0.505869
$26$	895581.	0.384348
$27$	2.37328e6	0.859434
$28$	1.53383e6	0.471592
$29$	−292603.	−0.0768225	−0.0384112	−	0.999262i	$-0.512230\pi$
$29$	−292603.	−0.0768225	−0.0384112	+	0.999262i	$0.512230\pi$
$30$	2.43853e6	0.549646
$31$	4.22388e6	0.821455	0.410728	−	0.911758i	$-0.365275\pi$
$31$	4.22388e6	0.821455	0.410728	+	0.911758i	$0.365275\pi$
$32$	−1.04858e6	−0.176777
$33$	2.27140e6	0.333411
$34$	3.28586e6	0.421690
$35$	5.88605e6	0.663007
$36$	1.12263e6	0.111397
$37$	−1.26399e7	−1.10875	−0.554376	−	0.832266i	$-0.687043\pi$
$37$	−1.26399e7	−1.10875	−0.554376	+	0.832266i	$0.687043\pi$
$38$	4.47593e6	0.348223
$39$	8.68375e6	0.601058
$40$	−4.02389e6	−0.248528
$41$	−2.65729e7	−1.46863	−0.734313	−	0.678811i	$-0.762496\pi$
$41$	−2.65729e7	−1.46863	−0.734313	+	0.678811i	$0.762496\pi$
$42$	1.48724e7	0.737494
$43$	−2.13800e7	−0.953674	−0.476837	−	0.878992i	$-0.658217\pi$
$43$	−2.13800e7	−0.953674	−0.476837	+	0.878992i	$0.658217\pi$
$44$	−3.74810e6	−0.150756
$45$	4.30805e6	0.156612
$46$	2.65711e7	0.874983
$47$	1.95666e7	0.584890	0.292445	−	0.956282i	$-0.405531\pi$
$47$	1.95666e7	0.584890	0.292445	+	0.956282i	$0.405531\pi$
$48$	−1.01672e7	−0.276450
$49$	−4.45512e6	−0.110402
$50$	1.58084e7	0.357703
$51$	3.18604e7	0.659455
$52$	−1.43293e7	−0.271775
$53$	−8.64352e7	−1.50470	−0.752349	−	0.658765i	$-0.771079\pi$
$53$	−8.64352e7	−1.50470	−0.752349	+	0.658765i	$0.771079\pi$
$54$	−3.79725e7	−0.607712
$55$	−1.43832e7	−0.211946
$56$	−2.45413e7	−0.333466
$57$	4.33996e7	0.544564
$58$	4.68165e6	0.0543217
$59$	−1.48166e8	−1.59189	−0.795945	−	0.605368i	$-0.793026\pi$
$59$	−1.48166e8	−1.59189	−0.795945	+	0.605368i	$0.793026\pi$
$60$	−3.90165e7	−0.388658
$61$	6.78553e7	0.627480	0.313740	−	0.949509i	$-0.398418\pi$
$61$	6.78553e7	0.627480	0.313740	+	0.949509i	$0.398418\pi$
$62$	−6.75821e7	−0.580857
$63$	2.62744e7	0.210136
$64$	1.67772e7	0.125000
$65$	−5.49884e7	−0.382086
$66$	−3.63424e7	−0.235757
$67$	2.03091e8	1.23127	0.615636	−	0.788031i	$-0.288899\pi$
$67$	2.03091e8	1.23127	0.615636	+	0.788031i	$0.288899\pi$
$68$	−5.25737e7	−0.298180
$69$	2.57639e8	1.36833
$70$	−9.41768e7	−0.468817
$71$	3.15187e8	1.47199	0.735996	−	0.676986i	$-0.236714\pi$
$71$	3.15187e8	1.47199	0.735996	+	0.676986i	$0.236714\pi$
$72$	−1.79620e7	−0.0787696
$73$	1.92010e8	0.791355	0.395677	−	0.918390i	$-0.370510\pi$
$73$	1.92010e8	0.791355	0.395677	+	0.918390i	$0.370510\pi$
$74$	2.02238e8	0.784006
$75$	1.53282e8	0.559390
$76$	−7.16149e7	−0.246231
$77$	−8.77221e7	−0.284381
$78$	−1.38940e8	−0.425012
$79$	3.37959e8	0.976207	0.488104	−	0.872786i	$-0.337689\pi$
$79$	3.37959e8	0.976207	0.488104	+	0.872786i	$0.337689\pi$
$80$	6.43822e7	0.175736
$81$	−4.54505e8	−1.17316
$82$	4.25166e8	1.03848
$83$	−5.99250e8	−1.38598	−0.692989	−	0.720948i	$-0.743707\pi$
$83$	−5.99250e8	−1.38598	−0.692989	+	0.720948i	$0.743707\pi$
$84$	−2.37958e8	−0.521487
$85$	−2.01751e8	−0.419208
$86$	3.42080e8	0.674349
$87$	4.53943e7	0.0849503
$88$	5.99695e7	0.106600
$89$	1.36415e7	0.0230466	0.0115233	−	0.999934i	$-0.496332\pi$
$89$	1.36415e7	0.0230466	0.0115233	+	0.999934i	$0.496332\pi$
$90$	−6.89289e7	−0.110741
$91$	−3.35369e8	−0.512669
$92$	−4.25138e8	−0.618707
$93$	−6.55291e8	−0.908366
$94$	−3.13065e8	−0.413580
$95$	−2.74821e8	−0.346173
$96$	1.62676e8	0.195480
$97$	−2.29779e8	−0.263534	−0.131767	−	0.991281i	$-0.542065\pi$
$97$	−2.29779e8	−0.263534	−0.131767	+	0.991281i	$0.542065\pi$
$98$	7.12820e7	0.0780661
$99$	−6.42046e7	−0.0671750
$100$	−2.52935e8	−0.252935
$101$	6.33292e8	0.605561	0.302781	−	0.953060i	$-0.402085\pi$
$101$	6.33292e8	0.605561	0.302781	+	0.953060i	$0.402085\pi$
$102$	−5.09766e8	−0.466305
$103$	−5.61830e7	−0.0491856	−0.0245928	−	0.999698i	$-0.507829\pi$
$103$	−5.61830e7	−0.0491856	−0.0245928	+	0.999698i	$0.507829\pi$
$104$	2.29269e8	0.192174
$105$	−9.13159e8	−0.733153
$106$	1.38296e9	1.06398
$107$	−5.23811e8	−0.386321	−0.193160	−	0.981167i	$-0.561874\pi$
$107$	−5.23811e8	−0.386321	−0.193160	+	0.981167i	$0.561874\pi$
$108$	6.07561e8	0.429717
$109$	2.24828e9	1.52557	0.762783	−	0.646655i	$-0.223833\pi$
$109$	2.24828e9	1.52557	0.762783	+	0.646655i	$0.223833\pi$
$110$	2.30132e8	0.149868
$111$	1.96094e9	1.22606
$112$	3.92661e8	0.235796
$113$	−3.17664e9	−1.83280	−0.916399	−	0.400267i	$-0.868917\pi$
$113$	−3.17664e9	−1.83280	−0.916399	+	0.400267i	$0.868917\pi$
$114$	−6.94394e8	−0.385065
$115$	−1.63146e9	−0.869833
$116$	−7.49064e7	−0.0384112
$117$	−2.45460e8	−0.121100
$118$	2.37065e9	1.12564
$119$	−1.23046e9	−0.562478
$120$	6.24264e8	0.274823
$121$	2.14359e8	0.0909091
$122$	−1.08569e9	−0.443695
$123$	4.12250e9	1.62401
$124$	1.08131e9	0.410728
$125$	−2.88937e9	−1.05854
$126$	−4.20391e8	−0.148589
$127$	2.27534e9	0.776120	0.388060	−	0.921634i	$-0.373145\pi$
$127$	2.27534e9	0.776120	0.388060	+	0.921634i	$0.373145\pi$
$128$	−2.68435e8	−0.0883883
$129$	3.31688e9	1.05457
$130$	8.79814e8	0.270175
$131$	5.93103e9	1.75958	0.879790	−	0.475362i	$-0.157683\pi$
$131$	5.93103e9	1.75958	0.879790	+	0.475362i	$0.157683\pi$
$132$	5.81478e8	0.166706
$133$	−1.67611e9	−0.464482
$134$	−3.24946e9	−0.870641
$135$	2.33150e9	0.604135
$136$	8.41179e8	0.210845
$137$	−5.60834e9	−1.36017	−0.680083	−	0.733135i	$-0.738056\pi$
$137$	−5.60834e9	−1.36017	−0.680083	+	0.733135i	$0.738056\pi$
$138$	−4.12223e9	−0.967557
$139$	−1.75166e9	−0.398000	−0.199000	−	0.980000i	$-0.563769\pi$
$139$	−1.75166e9	−0.398000	−0.199000	+	0.980000i	$0.563769\pi$
$140$	1.50683e9	0.331503
$141$	−3.03555e9	−0.646771
$142$	−5.04299e9	−1.04086
$143$	8.19513e8	0.163887
$144$	2.87392e8	0.0556985
$145$	−2.87452e8	−0.0540019
$146$	−3.07216e9	−0.559572
$147$	6.91166e8	0.122083
$148$	−3.23580e9	−0.554376
$149$	−1.48510e9	−0.246841	−0.123420	−	0.992354i	$-0.539386\pi$
$149$	−1.48510e9	−0.246841	−0.123420	+	0.992354i	$0.539386\pi$
$150$	−2.45251e9	−0.395549
$151$	1.06512e10	1.66725	0.833625	−	0.552330i	$-0.186261\pi$
$151$	1.06512e10	1.66725	0.833625	+	0.552330i	$0.186261\pi$
$152$	1.14584e9	0.174111
$153$	−9.00583e8	−0.132866
$154$	1.40355e9	0.201088
$155$	4.14952e9	0.577438
$156$	2.22304e9	0.300529
$157$	−8.23902e9	−1.08225	−0.541124	−	0.840943i	$-0.682001\pi$
$157$	−8.23902e9	−1.08225	−0.541124	+	0.840943i	$0.682001\pi$
$158$	−5.40734e9	−0.690283
$159$	1.34095e10	1.66390
$160$	−1.03012e9	−0.124264
$161$	−9.95012e9	−1.16711
$162$	7.27208e9	0.829547
$163$	−1.56291e10	−1.73417	−0.867083	−	0.498164i	$-0.834008\pi$
$163$	−1.56291e10	−1.73417	−0.867083	+	0.498164i	$0.834008\pi$
$164$	−6.80266e9	−0.734313
$165$	2.23141e9	0.234370
$166$	9.58800e9	0.980035
$167$	3.53455e9	0.351650	0.175825	−	0.984421i	$-0.443741\pi$
$167$	3.53455e9	0.351650	0.175825	+	0.984421i	$0.443741\pi$
$168$	3.80733e9	0.368747
$169$	−7.47143e9	−0.704553
$170$	3.22801e9	0.296425
$171$	−1.22676e9	−0.109718
$172$	−5.47328e9	−0.476837
$173$	−2.93930e9	−0.249480	−0.124740	−	0.992189i	$-0.539810\pi$
$173$	−2.93930e9	−0.249480	−0.124740	+	0.992189i	$0.539810\pi$
$174$	−7.26309e8	−0.0600689
$175$	−5.91979e9	−0.477128
$176$	−9.59513e8	−0.0753778
$177$	2.29863e10	1.76031
$178$	−2.18264e8	−0.0162964
$179$	−3.84357e9	−0.279831	−0.139916	−	0.990163i	$-0.544683\pi$
$179$	−3.84357e9	−0.279831	−0.139916	+	0.990163i	$0.544683\pi$
$180$	1.10286e9	0.0783060
$181$	1.68864e10	1.16945	0.584726	−	0.811231i	$-0.301202\pi$
$181$	1.68864e10	1.16945	0.584726	+	0.811231i	$0.301202\pi$
$182$	5.36591e9	0.362512
$183$	−1.05270e10	−0.693867
$184$	6.80221e9	0.437492
$185$	−1.24173e10	−0.779391
$186$	1.04847e10	0.642312
$187$	3.00676e9	0.179809
$188$	5.00904e9	0.292445
$189$	1.42196e10	0.810606
$190$	4.39713e9	0.244781
$191$	−1.24372e10	−0.676193	−0.338097	−	0.941111i	$-0.609783\pi$
$191$	−1.24372e10	−0.676193	−0.338097	+	0.941111i	$0.609783\pi$
$192$	−2.60281e9	−0.138225
$193$	2.92654e10	1.51826	0.759131	−	0.650938i	$-0.225624\pi$
$193$	2.92654e10	1.51826	0.759131	+	0.650938i	$0.225624\pi$
$194$	3.67646e9	0.186347
$195$	8.53087e9	0.422511
$196$	−1.14051e9	−0.0552011
$197$	−7.81637e9	−0.369749	−0.184875	−	0.982762i	$-0.559188\pi$
$197$	−7.81637e9	−0.369749	−0.184875	+	0.982762i	$0.559188\pi$
$198$	1.02727e9	0.0474999
$199$	3.53801e10	1.59926	0.799632	−	0.600490i	$-0.205028\pi$
$199$	3.53801e10	1.59926	0.799632	+	0.600490i	$0.205028\pi$
$200$	4.04695e9	0.178852
$201$	−3.15074e10	−1.36154
$202$	−1.01327e10	−0.428196
$203$	−1.75314e9	−0.0724578
$204$	8.15626e9	0.329728
$205$	−2.61051e10	−1.03236
$206$	8.98929e8	0.0347795
$207$	−7.28258e9	−0.275689
$208$	−3.66830e9	−0.135888
$209$	4.09576e9	0.148483
$210$	1.46105e10	0.518417
$211$	−3.96997e10	−1.37885	−0.689424	−	0.724358i	$-0.742136\pi$
$211$	−3.96997e10	−1.37885	−0.689424	+	0.724358i	$0.742136\pi$
$212$	−2.21274e10	−0.752349
$213$	−4.88979e10	−1.62773
$214$	8.38098e9	0.273170
$215$	−2.10036e10	−0.670380
$216$	−9.72097e9	−0.303856
$217$	2.53075e10	0.774784
$218$	−3.59725e10	−1.07874
$219$	−2.97883e10	−0.875080
$220$	−3.68211e9	−0.105973
$221$	1.14951e10	0.324152
$222$	−3.13750e10	−0.866954
$223$	−5.16898e9	−0.139969	−0.0699847	−	0.997548i	$-0.522295\pi$
$223$	−5.16898e9	−0.139969	−0.0699847	+	0.997548i	$0.522295\pi$
$224$	−6.28258e9	−0.166733
$225$	−4.33275e9	−0.112705
$226$	5.08262e10	1.29598
$227$	−4.08121e10	−1.02017	−0.510085	−	0.860124i	$-0.670386\pi$
$227$	−4.08121e10	−1.02017	−0.510085	+	0.860124i	$0.670386\pi$
$228$	1.11103e10	0.272282
$229$	4.76063e10	1.14394	0.571972	−	0.820273i	$-0.306179\pi$
$229$	4.76063e10	1.14394	0.571972	+	0.820273i	$0.306179\pi$
$230$	2.61033e10	0.615065
$231$	1.36092e10	0.314469
$232$	1.19850e9	0.0271608
$233$	7.19215e10	1.59866	0.799332	−	0.600890i	$-0.205187\pi$
$233$	7.19215e10	1.59866	0.799332	+	0.600890i	$0.205187\pi$
$234$	3.92735e9	0.0856306
$235$	1.92221e10	0.411145
$236$	−3.79304e10	−0.795945
$237$	−5.24308e10	−1.07949
$238$	1.96873e10	0.397732
$239$	9.22418e10	1.82868	0.914339	−	0.404950i	$-0.132711\pi$
$239$	9.22418e10	1.82868	0.914339	+	0.404950i	$0.132711\pi$
$240$	−9.98822e9	−0.194329
$241$	−1.51226e10	−0.288768	−0.144384	−	0.989522i	$-0.546120\pi$
$241$	−1.51226e10	−0.288768	−0.144384	+	0.989522i	$0.546120\pi$
$242$	−3.42974e9	−0.0642824
$243$	2.37983e10	0.437843
$244$	1.73710e10	0.313740
$245$	−4.37669e9	−0.0776066
$246$	−6.59600e10	−1.14835
$247$	1.56584e10	0.267678
$248$	−1.73010e10	−0.290428
$249$	9.29673e10	1.53262
$250$	4.62299e10	0.748502
$251$	3.62358e9	0.0576244	0.0288122	−	0.999585i	$-0.490828\pi$
$251$	3.62358e9	0.0576244	0.0288122	+	0.999585i	$0.490828\pi$
$252$	6.72625e9	0.105068
$253$	2.43142e10	0.373094
$254$	−3.64054e10	−0.548800
$255$	3.12995e10	0.463560
$256$	4.29497e9	0.0625000
$257$	4.26391e10	0.609690	0.304845	−	0.952402i	$-0.401395\pi$
$257$	4.26391e10	0.609690	0.304845	+	0.952402i	$0.401395\pi$
$258$	−5.30701e10	−0.745695
$259$	−7.57321e10	−1.04576
$260$	−1.40770e10	−0.191043
$261$	−1.28314e9	−0.0171156
$262$	−9.48965e10	−1.24421
$263$	1.05950e11	1.36552	0.682762	−	0.730641i	$-0.260779\pi$
$263$	1.05950e11	1.36552	0.682762	+	0.730641i	$0.260779\pi$
$264$	−9.30364e9	−0.117879
$265$	−8.49135e10	−1.05772
$266$	2.68177e10	0.328439
$267$	−2.11633e9	−0.0254849
$268$	5.19913e10	0.615636
$269$	2.67969e10	0.312032	0.156016	−	0.987755i	$-0.450135\pi$
$269$	2.67969e10	0.312032	0.156016	+	0.987755i	$0.450135\pi$
$270$	−3.73040e10	−0.427188
$271$	−1.34536e11	−1.51523	−0.757613	−	0.652705i	$-0.773634\pi$
$271$	−1.34536e11	−1.51523	−0.757613	+	0.652705i	$0.773634\pi$
$272$	−1.34589e10	−0.149090
$273$	5.20290e10	0.566909
$274$	8.97335e10	0.961783
$275$	1.44657e10	0.152525
$276$	6.59557e10	0.684166
$277$	3.20043e10	0.326625	0.163312	−	0.986574i	$-0.447782\pi$
$277$	3.20043e10	0.326625	0.163312	+	0.986574i	$0.447782\pi$
$278$	2.80265e10	0.281428
$279$	1.85228e10	0.183015
$280$	−2.41093e10	−0.234408
$281$	−7.65012e10	−0.731964	−0.365982	−	0.930622i	$-0.619267\pi$
$281$	−7.65012e10	−0.731964	−0.365982	+	0.930622i	$0.619267\pi$
$282$	4.85687e10	0.457336
$283$	−1.59687e11	−1.47990	−0.739948	−	0.672665i	$-0.765150\pi$
$283$	−1.59687e11	−1.47990	−0.739948	+	0.672665i	$0.765150\pi$
$284$	8.06878e10	0.735996
$285$	4.26356e10	0.382798
$286$	−1.31122e10	−0.115885
$287$	−1.59212e11	−1.38519
$288$	−4.59828e9	−0.0393848
$289$	−7.64127e10	−0.644355
$290$	4.59923e9	0.0381851
$291$	3.56478e10	0.291416
$292$	4.91546e10	0.395677
$293$	5.81683e10	0.461086	0.230543	−	0.973062i	$-0.425950\pi$
$293$	5.81683e10	0.461086	0.230543	+	0.973062i	$0.425950\pi$
$294$	−1.10587e10	−0.0863255
$295$	−1.45557e11	−1.11901
$296$	5.17728e10	0.392003
$297$	−3.47472e10	−0.259129
$298$	2.37615e10	0.174543
$299$	9.29555e10	0.672597
$300$	3.92401e10	0.279695
$301$	−1.28099e11	−0.899491
$302$	−1.70419e11	−1.17892
$303$	−9.82486e10	−0.669630
$304$	−1.83334e10	−0.123115
$305$	6.66607e10	0.441083
$306$	1.44093e10	0.0939501
$307$	−8.83500e10	−0.567654	−0.283827	−	0.958875i	$-0.591604\pi$
$307$	−8.83500e10	−0.567654	−0.283827	+	0.958875i	$0.591604\pi$
$308$	−2.24568e10	−0.142190
$309$	8.71621e9	0.0543894
$310$	−6.63923e10	−0.408310
$311$	−3.56793e10	−0.216269	−0.108135	−	0.994136i	$-0.534488\pi$
$311$	−3.56793e10	−0.216269	−0.108135	+	0.994136i	$0.534488\pi$
$312$	−3.55686e10	−0.212506
$313$	1.18432e11	0.697458	0.348729	−	0.937224i	$-0.386613\pi$
$313$	1.18432e11	0.697458	0.348729	+	0.937224i	$0.386613\pi$
$314$	1.31824e11	0.765265
$315$	2.58119e10	0.147714
$316$	8.65175e10	0.488104
$317$	1.60630e11	0.893429	0.446714	−	0.894677i	$-0.352594\pi$
$317$	1.60630e11	0.893429	0.446714	+	0.894677i	$0.352594\pi$
$318$	−2.14552e11	−1.17655
$319$	4.28400e9	0.0231628
$320$	1.64818e10	0.0878681
$321$	8.12638e10	0.427193
$322$	1.59202e11	0.825271
$323$	5.74503e10	0.293684
$324$	−1.16353e11	−0.586578
$325$	5.53036e10	0.274965
$326$	2.50066e11	1.22624
$327$	−3.48797e11	−1.68697
$328$	1.08843e11	0.519238
$329$	1.17234e11	0.551659
$330$	−3.57025e10	−0.165724
$331$	−1.60954e11	−0.737015	−0.368507	−	0.929625i	$-0.620131\pi$
$331$	−1.60954e11	−0.737015	−0.368507	+	0.929625i	$0.620131\pi$
$332$	−1.53408e11	−0.692989
$333$	−5.54290e10	−0.247023
$334$	−5.65528e10	−0.248654
$335$	1.99516e11	0.865516
$336$	−6.09173e10	−0.260744
$337$	2.38076e11	1.00550	0.502748	−	0.864433i	$-0.332322\pi$
$337$	2.38076e11	1.00550	0.502748	+	0.864433i	$0.332322\pi$
$338$	1.19543e11	0.498194
$339$	4.92822e11	2.02671
$340$	−5.16481e10	−0.209604
$341$	−6.18418e10	−0.247678
$342$	1.96281e10	0.0775820
$343$	−2.68473e11	−1.04731
$344$	8.75725e10	0.337175
$345$	2.53104e11	0.961861
$346$	4.70287e10	0.176409
$347$	3.88663e11	1.43910	0.719550	−	0.694441i	$-0.244348\pi$
$347$	3.88663e11	1.43910	0.719550	+	0.694441i	$0.244348\pi$
$348$	1.16209e10	0.0424751
$349$	−4.35657e11	−1.57192	−0.785959	−	0.618278i	$-0.787830\pi$
$349$	−4.35657e11	−1.57192	−0.785959	+	0.618278i	$0.787830\pi$
$350$	9.47166e10	0.337381
$351$	−1.32842e11	−0.467146
$352$	1.53522e10	0.0533002
$353$	−2.50105e9	−0.00857307	−0.00428653	−	0.999991i	$-0.501364\pi$
$353$	−2.50105e9	−0.00857307	−0.00428653	+	0.999991i	$0.501364\pi$
$354$	−3.67781e11	−1.24473
$355$	3.09638e11	1.03473
$356$	3.49222e9	0.0115233
$357$	1.90893e11	0.621988
$358$	6.14972e10	0.197871
$359$	−1.46303e11	−0.464866	−0.232433	−	0.972612i	$-0.574669\pi$
$359$	−1.46303e11	−0.464866	−0.232433	+	0.972612i	$0.574669\pi$
$360$	−1.76458e10	−0.0553707
$361$	−2.44430e11	−0.757482
$362$	−2.70182e11	−0.826927
$363$	−3.32555e10	−0.100527
$364$	−8.58545e10	−0.256334
$365$	1.88630e11	0.556278
$366$	1.68433e11	0.490638
$367$	2.15538e11	0.620192	0.310096	−	0.950705i	$-0.399639\pi$
$367$	2.15538e11	0.620192	0.310096	+	0.950705i	$0.399639\pi$
$368$	−1.08835e11	−0.309353
$369$	−1.16529e11	−0.327201
$370$	1.98677e11	0.551113
$371$	−5.17880e11	−1.41921
$372$	−1.67754e11	−0.454183
$373$	−4.94826e11	−1.32362	−0.661810	−	0.749672i	$-0.730211\pi$
$373$	−4.94826e11	−1.32362	−0.661810	+	0.749672i	$0.730211\pi$
$374$	−4.81082e10	−0.127144
$375$	4.48255e11	1.17054
$376$	−8.01446e10	−0.206790
$377$	1.63781e10	0.0417569
$378$	−2.27514e11	−0.573185
$379$	3.86719e11	0.962763	0.481382	−	0.876511i	$-0.340135\pi$
$379$	3.86719e11	0.962763	0.481382	+	0.876511i	$0.340135\pi$
$380$	−7.03541e10	−0.173087
$381$	−3.52995e11	−0.858234
$382$	1.98994e11	0.478141
$383$	−2.29225e11	−0.544337	−0.272169	−	0.962250i	$-0.587741\pi$
$383$	−2.29225e11	−0.544337	−0.272169	+	0.962250i	$0.587741\pi$
$384$	4.16449e10	0.0977399
$385$	−8.61777e10	−0.199904
$386$	−4.68247e11	−1.07357
$387$	−9.37568e10	−0.212473
$388$	−5.88234e10	−0.131767
$389$	8.75249e11	1.93802	0.969010	−	0.247020i	$-0.0794515\pi$
$389$	8.75249e11	1.93802	0.969010	+	0.247020i	$0.0794515\pi$
$390$	−1.36494e11	−0.298760
$391$	3.41051e11	0.737944
$392$	1.82482e10	0.0390330
$393$	−9.20137e11	−1.94574
$394$	1.25062e11	0.261452
$395$	3.32009e11	0.686220
$396$	−1.64364e10	−0.0335875
$397$	−7.65484e11	−1.54660	−0.773301	−	0.634039i	$-0.781396\pi$
$397$	−7.65484e11	−1.54660	−0.773301	+	0.634039i	$0.781396\pi$
$398$	−5.66082e11	−1.13085
$399$	2.60030e11	0.513625
$400$	−6.47512e10	−0.126467
$401$	−1.30845e11	−0.252701	−0.126351	−	0.991986i	$-0.540326\pi$
$401$	−1.30845e11	−0.252701	−0.126351	+	0.991986i	$0.540326\pi$
$402$	5.04119e11	0.962755
$403$	−2.36427e11	−0.446503
$404$	1.62123e11	0.302781
$405$	−4.46503e11	−0.824664
$406$	2.80503e10	0.0512354
$407$	1.85060e11	0.334301
$408$	−1.30500e11	−0.233153
$409$	1.01842e12	1.79959	0.899794	−	0.436315i	$-0.143717\pi$
$409$	1.01842e12	1.79959	0.899794	+	0.436315i	$0.143717\pi$
$410$	4.17681e11	0.729991
$411$	8.70075e11	1.50407
$412$	−1.43829e10	−0.0245928
$413$	−8.87739e11	−1.50145
$414$	1.16521e11	0.194941
$415$	−5.88700e11	−0.974266
$416$	5.86928e10	0.0960871
$417$	2.71751e11	0.440108
$418$	−6.55321e10	−0.104993
$419$	−5.99288e10	−0.0949888	−0.0474944	−	0.998872i	$-0.515124\pi$
$419$	−5.99288e10	−0.0949888	−0.0474944	+	0.998872i	$0.515124\pi$
$420$	−2.33769e11	−0.366576
$421$	−4.05978e11	−0.629845	−0.314922	−	0.949117i	$-0.601978\pi$
$421$	−4.05978e11	−0.629845	−0.314922	+	0.949117i	$0.601978\pi$
$422$	6.35195e11	0.974993
$423$	8.58044e10	0.130310
$424$	3.54039e11	0.531991
$425$	2.02907e11	0.301680
$426$	7.82367e11	1.15098
$427$	4.06558e11	0.591829
$428$	−1.34096e11	−0.193160
$429$	−1.27139e11	−0.181226
$430$	3.36058e11	0.474030
$431$	−7.06170e10	−0.0985738	−0.0492869	−	0.998785i	$-0.515695\pi$
$431$	−7.06170e10	−0.0985738	−0.0492869	+	0.998785i	$0.515695\pi$
$432$	1.55536e11	0.214859
$433$	7.08580e11	0.968709	0.484355	−	0.874872i	$-0.339054\pi$
$433$	7.08580e11	0.968709	0.484355	+	0.874872i	$0.339054\pi$
$434$	−4.04920e11	−0.547855
$435$	4.45951e10	0.0597153
$436$	5.75559e11	0.762783
$437$	4.64573e11	0.609379
$438$	4.76613e11	0.618775
$439$	6.80870e11	0.874932	0.437466	−	0.899235i	$-0.355876\pi$
$439$	6.80870e11	0.874932	0.437466	+	0.899235i	$0.355876\pi$
$440$	5.89138e10	0.0749341
$441$	−1.95369e10	−0.0245970
$442$	−1.83922e11	−0.229210
$443$	−3.84421e11	−0.474231	−0.237116	−	0.971481i	$-0.576202\pi$
$443$	−3.84421e11	−0.474231	−0.237116	+	0.971481i	$0.576202\pi$
$444$	5.02001e11	0.613029
$445$	1.34013e10	0.0162005
$446$	8.27036e10	0.0989732
$447$	2.30397e11	0.272956
$448$	1.00521e11	0.117898
$449$	−3.82392e11	−0.444018	−0.222009	−	0.975045i	$-0.571261\pi$
$449$	−3.82392e11	−0.444018	−0.222009	+	0.975045i	$0.571261\pi$
$450$	6.93239e10	0.0796942
$451$	3.89053e11	0.442807
$452$	−8.13219e11	−0.916399
$453$	−1.65242e12	−1.84365
$454$	6.52994e11	0.721370
$455$	−3.29465e11	−0.360378
$456$	−1.77765e11	−0.192533
$457$	−1.31034e11	−0.140528	−0.0702638	−	0.997528i	$-0.522384\pi$
$457$	−1.31034e11	−0.140528	−0.0702638	+	0.997528i	$0.522384\pi$
$458$	−7.61700e11	−0.808890
$459$	−4.87392e11	−0.512532
$460$	−4.17653e11	−0.434916
$461$	−1.59538e12	−1.64516	−0.822581	−	0.568648i	$-0.807467\pi$
$461$	−1.59538e12	−1.64516	−0.822581	+	0.568648i	$0.807467\pi$
$462$	−2.17746e11	−0.222363
$463$	−8.36499e11	−0.845962	−0.422981	−	0.906139i	$-0.639016\pi$
$463$	−8.36499e11	−0.845962	−0.422981	+	0.906139i	$0.639016\pi$
$464$	−1.91760e10	−0.0192056
$465$	−6.43754e11	−0.638531
$466$	−1.15074e12	−1.13043
$467$	−1.59301e12	−1.54986	−0.774928	−	0.632049i	$-0.782214\pi$
$467$	−1.59301e12	−1.54986	−0.774928	+	0.632049i	$0.782214\pi$
$468$	−6.28377e10	−0.0605499
$469$	1.21683e12	1.16132
$470$	−3.07553e11	−0.290723
$471$	1.27820e12	1.19675
$472$	6.06886e11	0.562818
$473$	3.13025e11	0.287543
$474$	8.38893e11	0.763315
$475$	2.76396e11	0.249121
$476$	−3.14997e11	−0.281239
$477$	−3.79041e11	−0.335238
$478$	−1.47587e12	−1.29307
$479$	−3.14204e11	−0.272710	−0.136355	−	0.990660i	$-0.543539\pi$
$479$	−3.14204e11	−0.272710	−0.136355	+	0.990660i	$0.543539\pi$
$480$	1.59812e11	0.137411
$481$	7.07501e11	0.602663
$482$	2.41961e11	0.204189
$483$	1.54366e12	1.29059
$484$	5.48759e10	0.0454545
$485$	−2.25734e11	−0.185250
$486$	−3.80773e11	−0.309602
$487$	1.12565e12	0.906824	0.453412	−	0.891301i	$-0.350207\pi$
$487$	1.12565e12	0.906824	0.453412	+	0.891301i	$0.350207\pi$
$488$	−2.77935e11	−0.221848
$489$	2.42470e12	1.91764
$490$	7.00271e10	0.0548761
$491$	−1.17493e12	−0.912313	−0.456157	−	0.889899i	$-0.650774\pi$
$491$	−1.17493e12	−0.912313	−0.456157	+	0.889899i	$0.650774\pi$
$492$	1.05536e12	0.812003
$493$	6.00908e10	0.0458138
$494$	−2.50535e11	−0.189277
$495$	−6.30742e10	−0.0472203
$496$	2.76816e11	0.205364
$497$	1.88845e12	1.38836
$498$	−1.48748e12	−1.08372
$499$	−1.94228e12	−1.40236	−0.701180	−	0.712985i	$-0.747343\pi$
$499$	−1.94228e12	−1.40236	−0.701180	+	0.712985i	$0.747343\pi$
$500$	−7.39679e11	−0.529271
$501$	−5.48348e11	−0.388854
$502$	−5.79773e10	−0.0407466
$503$	9.17834e10	0.0639305	0.0319653	−	0.999489i	$-0.489823\pi$
$503$	9.17834e10	0.0639305	0.0319653	+	0.999489i	$0.489823\pi$
$504$	−1.07620e11	−0.0742943
$505$	6.22143e11	0.425676
$506$	−3.89028e11	−0.263817
$507$	1.15911e12	0.779095
$508$	5.82486e11	0.388060
$509$	−2.47867e12	−1.63677	−0.818385	−	0.574670i	$-0.805131\pi$
$509$	−2.47867e12	−1.63677	−0.818385	+	0.574670i	$0.805131\pi$
$510$	−5.00792e11	−0.327787
$511$	1.15043e12	0.746394
$512$	−6.87195e10	−0.0441942
$513$	−6.63916e11	−0.423238
$514$	−6.82226e11	−0.431116
$515$	−5.51939e10	−0.0345747
$516$	8.49122e11	0.527286
$517$	−2.86474e11	−0.176351
$518$	1.21171e12	0.739462
$519$	4.56001e11	0.275875
$520$	2.25232e11	0.135088
$521$	5.28475e11	0.314235	0.157118	−	0.987580i	$-0.449780\pi$
$521$	5.28475e11	0.314235	0.157118	+	0.987580i	$0.449780\pi$
$522$	2.05303e10	0.0121026
$523$	−1.39583e12	−0.815782	−0.407891	−	0.913031i	$-0.633736\pi$
$523$	−1.39583e12	−0.815782	−0.407891	+	0.913031i	$0.633736\pi$
$524$	1.51834e12	0.879790
$525$	9.18393e11	0.527608
$526$	−1.69520e12	−0.965571
$527$	−8.67442e11	−0.489883
$528$	1.48858e11	0.0833528
$529$	9.56758e11	0.531192
$530$	1.35862e12	0.747920
$531$	−6.49744e11	−0.354664
$532$	−4.29083e11	−0.232241
$533$	1.48739e12	0.798272
$534$	3.38614e10	0.0180206
$535$	−5.14589e11	−0.271562
$536$	−8.31861e11	−0.435320
$537$	5.96290e11	0.309438
$538$	−4.28750e11	−0.220640
$539$	6.52275e10	0.0332875
$540$	5.96864e11	0.302067
$541$	1.21374e12	0.609170	0.304585	−	0.952485i	$-0.401482\pi$
$541$	1.21374e12	0.609170	0.304585	+	0.952485i	$0.401482\pi$
$542$	2.15258e12	1.07143
$543$	−2.61974e12	−1.29318
$544$	2.15342e11	0.105423
$545$	2.20870e12	1.07239
$546$	−8.32464e11	−0.400865
$547$	1.05919e12	0.505861	0.252930	−	0.967485i	$-0.418606\pi$
$547$	1.05919e12	0.505861	0.252930	+	0.967485i	$0.418606\pi$
$548$	−1.43574e12	−0.680083
$549$	2.97563e11	0.139799
$550$	−2.31451e11	−0.107852
$551$	8.18545e10	0.0378321
$552$	−1.05529e12	−0.483778
$553$	2.02489e12	0.920744
$554$	−5.12069e11	−0.230959
$555$	1.92642e12	0.861851
$556$	−4.48425e11	−0.199000
$557$	−7.62432e11	−0.335624	−0.167812	−	0.985819i	$-0.553670\pi$
$557$	−7.62432e11	−0.335624	−0.167812	+	0.985819i	$0.553670\pi$
$558$	−2.96365e11	−0.129411
$559$	1.19672e12	0.518370
$560$	3.85748e11	0.165752
$561$	−4.66468e11	−0.198833
$562$	1.22402e12	0.517577
$563$	2.51555e12	1.05522	0.527612	−	0.849485i	$-0.323087\pi$
$563$	2.51555e12	1.05522	0.527612	+	0.849485i	$0.323087\pi$
$564$	−7.77100e11	−0.323386
$565$	−3.12071e12	−1.28835
$566$	2.55499e12	1.04644
$567$	−2.72318e12	−1.10650
$568$	−1.29101e12	−0.520428
$569$	3.85447e12	1.54156	0.770778	−	0.637104i	$-0.219868\pi$
$569$	3.85447e12	1.54156	0.770778	+	0.637104i	$0.219868\pi$
$570$	−6.82169e11	−0.270679
$571$	−2.42148e12	−0.953276	−0.476638	−	0.879100i	$-0.658145\pi$
$571$	−2.42148e12	−0.953276	−0.476638	+	0.879100i	$0.658145\pi$
$572$	2.09795e11	0.0819433
$573$	1.92949e12	0.747735
$574$	2.54740e12	0.979474
$575$	1.64081e12	0.625969
$576$	7.35724e10	0.0278493
$577$	−2.63094e12	−0.988143	−0.494071	−	0.869421i	$-0.664492\pi$
$577$	−2.63094e12	−0.988143	−0.494071	+	0.869421i	$0.664492\pi$
$578$	1.22260e12	0.455628
$579$	−4.54022e12	−1.67890
$580$	−7.35877e10	−0.0270010
$581$	−3.59043e12	−1.30723
$582$	−5.70364e11	−0.206062
$583$	1.26550e12	0.453684
$584$	−7.86473e11	−0.279786
$585$	−2.41138e11	−0.0851265
$586$	−9.30692e11	−0.326037
$587$	−4.85843e12	−1.68898	−0.844489	−	0.535573i	$-0.820096\pi$
$587$	−4.85843e12	−1.68898	−0.844489	+	0.535573i	$0.820096\pi$
$588$	1.76938e11	0.0610414
$589$	−1.18161e12	−0.404535
$590$	2.32891e12	0.791260
$591$	1.21263e12	0.408869
$592$	−8.28365e11	−0.277188
$593$	−4.71935e12	−1.56724	−0.783621	−	0.621239i	$-0.786630\pi$
$593$	−4.71935e12	−1.56724	−0.783621	+	0.621239i	$0.786630\pi$
$594$	5.55956e11	0.183232
$595$	−1.20880e12	−0.395391
$596$	−3.80185e11	−0.123420
$597$	−5.48885e12	−1.76847
$598$	−1.48729e12	−0.475598
$599$	−6.42727e11	−0.203988	−0.101994	−	0.994785i	$-0.532522\pi$
$599$	−6.42727e11	−0.203988	−0.101994	+	0.994785i	$0.532522\pi$
$600$	−6.27842e11	−0.197774
$601$	1.18276e12	0.369797	0.184898	−	0.982758i	$-0.440804\pi$
$601$	1.18276e12	0.369797	0.184898	+	0.982758i	$0.440804\pi$
$602$	2.04958e12	0.636036
$603$	8.90606e11	0.274320
$604$	2.72670e12	0.833625
$605$	2.10585e11	0.0639040
$606$	1.57198e12	0.473500
$607$	−4.30358e12	−1.28671	−0.643356	−	0.765568i	$-0.722458\pi$
$607$	−4.30358e12	−1.28671	−0.643356	+	0.765568i	$0.722458\pi$
$608$	2.93335e11	0.0870557
$609$	2.71982e11	0.0801238
$610$	−1.06657e12	−0.311893
$611$	−1.09522e12	−0.317917
$612$	−2.30549e11	−0.0664328
$613$	3.10379e12	0.887811	0.443905	−	0.896074i	$-0.353593\pi$
$613$	3.10379e12	0.887811	0.443905	+	0.896074i	$0.353593\pi$
$614$	1.41360e12	0.401392
$615$	4.04992e12	1.14159
$616$	3.59310e11	0.100544
$617$	2.99353e12	0.831572	0.415786	−	0.909462i	$-0.363507\pi$
$617$	2.99353e12	0.831572	0.415786	+	0.909462i	$0.363507\pi$
$618$	−1.39459e11	−0.0384591
$619$	2.89342e12	0.792143	0.396071	−	0.918220i	$-0.370373\pi$
$619$	2.89342e12	0.792143	0.396071	+	0.918220i	$0.370373\pi$
$620$	1.06228e12	0.288719
$621$	−3.94130e12	−1.06348
$622$	5.70869e11	0.152925
$623$	8.17335e10	0.0217372
$624$	5.69098e11	0.150265
$625$	−9.08766e11	−0.238227
$626$	−1.89491e12	−0.493177
$627$	−6.35414e11	−0.164192
$628$	−2.10919e12	−0.541124
$629$	2.59580e12	0.661215
$630$	−4.12990e11	−0.104450
$631$	3.08692e12	0.775165	0.387582	−	0.921835i	$-0.373310\pi$
$631$	3.08692e12	0.775165	0.387582	+	0.921835i	$0.373310\pi$
$632$	−1.38428e12	−0.345141
$633$	6.15899e12	1.52473
$634$	−2.57008e12	−0.631750
$635$	2.23528e12	0.545570
$636$	3.43284e12	0.831948
$637$	2.49370e11	0.0600091
$638$	−6.85441e10	−0.0163786
$639$	1.38218e12	0.327951
$640$	−2.63710e11	−0.0621321
$641$	−2.25517e11	−0.0527617	−0.0263809	−	0.999652i	$-0.508398\pi$
$641$	−2.25517e11	−0.0527617	−0.0263809	+	0.999652i	$0.508398\pi$
$642$	−1.30022e12	−0.302071
$643$	−1.05226e12	−0.242759	−0.121379	−	0.992606i	$-0.538732\pi$
$643$	−1.05226e12	−0.242759	−0.121379	+	0.992606i	$0.538732\pi$
$644$	−2.54723e12	−0.583555
$645$	3.25849e12	0.741306
$646$	−9.19205e11	−0.207666
$647$	−4.89509e12	−1.09822	−0.549112	−	0.835749i	$-0.685034\pi$
$647$	−4.89509e12	−1.09822	−0.549112	+	0.835749i	$0.685034\pi$
$648$	1.86165e12	0.414774
$649$	2.16929e12	0.479973
$650$	−8.84857e11	−0.194430
$651$	−3.92620e12	−0.856757
$652$	−4.00106e12	−0.867083
$653$	6.92165e12	1.48971	0.744853	−	0.667229i	$-0.232520\pi$
$653$	6.92165e12	1.48971	0.744853	+	0.667229i	$0.232520\pi$
$654$	5.58075e12	1.19287
$655$	5.82661e12	1.23689
$656$	−1.74148e12	−0.367156
$657$	8.42014e11	0.176309
$658$	−1.87574e12	−0.390082
$659$	3.61099e12	0.745834	0.372917	−	0.927865i	$-0.378358\pi$
$659$	3.61099e12	0.745834	0.372917	+	0.927865i	$0.378358\pi$
$660$	5.71241e11	0.117185
$661$	1.42978e12	0.291316	0.145658	−	0.989335i	$-0.453470\pi$
$661$	1.42978e12	0.291316	0.145658	+	0.989335i	$0.453470\pi$
$662$	2.57527e12	0.521148
$663$	−1.78335e12	−0.358447
$664$	2.45453e12	0.490018
$665$	−1.64660e12	−0.326505
$666$	8.86864e11	0.174672
$667$	4.85925e11	0.0950611
$668$	9.04845e11	0.175825
$669$	8.01913e11	0.154778
$670$	−3.19225e12	−0.612012
$671$	−9.93470e11	−0.189192
$672$	9.74676e11	0.184374
$673$	7.92324e11	0.148879	0.0744397	−	0.997226i	$-0.476283\pi$
$673$	7.92324e11	0.148879	0.0744397	+	0.997226i	$0.476283\pi$
$674$	−3.80921e12	−0.710993
$675$	−2.34486e12	−0.434761
$676$	−1.91269e12	−0.352276
$677$	3.33816e12	0.610742	0.305371	−	0.952233i	$-0.401220\pi$
$677$	3.33816e12	0.610742	0.305371	+	0.952233i	$0.401220\pi$
$678$	−7.88515e12	−1.43310
$679$	−1.37673e12	−0.248562
$680$	8.26370e11	0.148212
$681$	6.33157e12	1.12811
$682$	9.89469e11	0.175135
$683$	4.35975e12	0.766599	0.383300	−	0.923624i	$-0.374788\pi$
$683$	4.35975e12	0.766599	0.383300	+	0.923624i	$0.374788\pi$
$684$	−3.14050e11	−0.0548588
$685$	−5.50961e12	−0.956121
$686$	4.29557e12	0.740563
$687$	−7.38561e12	−1.26497
$688$	−1.40116e12	−0.238418
$689$	4.83811e12	0.817879
$690$	−4.04966e12	−0.680139
$691$	−2.24525e12	−0.374639	−0.187320	−	0.982299i	$-0.559980\pi$
$691$	−2.24525e12	−0.374639	−0.187320	+	0.982299i	$0.559980\pi$
$692$	−7.52460e11	−0.124740
$693$	−3.84684e11	−0.0633584
$694$	−6.21861e12	−1.01760
$695$	−1.72082e12	−0.279772
$696$	−1.85935e11	−0.0300345
$697$	5.45717e12	0.875830
$698$	6.97051e12	1.11151
$699$	−1.11579e13	−1.76780
$700$	−1.51547e12	−0.238564
$701$	−7.86229e12	−1.22975	−0.614877	−	0.788623i	$-0.710794\pi$
$701$	−7.86229e12	−1.22975	−0.614877	+	0.788623i	$0.710794\pi$
$702$	2.12547e12	0.330322
$703$	3.53595e12	0.546018
$704$	−2.45635e11	−0.0376889
$705$	−2.98210e12	−0.454644
$706$	4.00168e10	0.00606207
$707$	3.79439e12	0.571156
$708$	5.88450e12	0.880157
$709$	−1.95116e12	−0.289991	−0.144995	−	0.989432i	$-0.546317\pi$
$709$	−1.95116e12	−0.289991	−0.144995	+	0.989432i	$0.546317\pi$
$710$	−4.95421e12	−0.731664
$711$	1.48204e12	0.217493
$712$	−5.58756e10	−0.00814821
$713$	−7.01458e12	−1.01648
$714$	−3.05428e12	−0.439812
$715$	8.05085e11	0.115203
$716$	−9.83955e11	−0.139916
$717$	−1.43103e13	−2.02215
$718$	2.34085e12	0.328710
$719$	−2.80420e12	−0.391317	−0.195658	−	0.980672i	$-0.562684\pi$
$719$	−2.80420e12	−0.391317	−0.195658	+	0.980672i	$0.562684\pi$
$720$	2.82333e11	0.0391530
$721$	−3.36623e11	−0.0463911
$722$	3.91088e12	0.535620
$723$	2.34610e12	0.319319
$724$	4.32291e12	0.584726
$725$	2.89099e11	0.0388621
$726$	5.32088e11	0.0710835
$727$	−3.12483e11	−0.0414880	−0.0207440	−	0.999785i	$-0.506603\pi$
$727$	−3.12483e11	−0.0414880	−0.0207440	+	0.999785i	$0.506603\pi$
$728$	1.37367e12	0.181256
$729$	5.25396e12	0.688990
$730$	−3.01807e12	−0.393348
$731$	4.39073e12	0.568733
$732$	−2.69492e12	−0.346934
$733$	−1.04146e13	−1.33253	−0.666263	−	0.745717i	$-0.732107\pi$
$733$	−1.04146e13	−1.33253	−0.666263	+	0.745717i	$0.732107\pi$
$734$	−3.44861e12	−0.438542
$735$	6.78998e11	0.0858174
$736$	1.74137e12	0.218746
$737$	−2.97346e12	−0.371243
$738$	1.86446e12	0.231366
$739$	1.30922e12	0.161478	0.0807388	−	0.996735i	$-0.474272\pi$
$739$	1.30922e12	0.161478	0.0807388	+	0.996735i	$0.474272\pi$
$740$	−3.17884e12	−0.389695
$741$	−2.42924e12	−0.295998
$742$	8.28607e12	1.00353
$743$	8.36552e12	1.00703	0.503516	−	0.863986i	$-0.332040\pi$
$743$	8.36552e12	1.00703	0.503516	+	0.863986i	$0.332040\pi$
$744$	2.68407e12	0.321156
$745$	−1.45895e12	−0.173515
$746$	7.91722e12	0.935940
$747$	−2.62787e12	−0.308788
$748$	7.69732e11	0.0899047
$749$	−3.13843e12	−0.364372
$750$	−7.17209e12	−0.827694
$751$	1.24635e13	1.42975	0.714876	−	0.699252i	$-0.246483\pi$
$751$	1.24635e13	1.42975	0.714876	+	0.699252i	$0.246483\pi$
$752$	1.28231e12	0.146222
$753$	−5.62161e11	−0.0637211
$754$	−2.62050e11	−0.0295266
$755$	1.04636e13	1.17198
$756$	3.64022e12	0.405303
$757$	4.63500e12	0.513001	0.256500	−	0.966544i	$-0.417430\pi$
$757$	4.63500e12	0.513001	0.256500	+	0.966544i	$0.417430\pi$
$758$	−6.18751e12	−0.680776
$759$	−3.77210e12	−0.412568
$760$	1.12567e12	0.122391
$761$	2.08645e12	0.225515	0.112758	−	0.993623i	$-0.464032\pi$
$761$	2.08645e12	0.225515	0.112758	+	0.993623i	$0.464032\pi$
$762$	5.64791e12	0.606863
$763$	1.34706e13	1.43889
$764$	−3.18391e12	−0.338097
$765$	−8.84728e11	−0.0933971
$766$	3.66760e12	0.384905
$767$	8.29339e12	0.865273
$768$	−6.66319e11	−0.0691125
$769$	−1.61310e13	−1.66338	−0.831692	−	0.555237i	$-0.812628\pi$
$769$	−1.61310e13	−1.66338	−0.831692	+	0.555237i	$0.812628\pi$
$770$	1.37884e12	0.141353
$771$	−6.61501e12	−0.674196
$772$	7.49195e12	0.759131
$773$	4.62705e12	0.466118	0.233059	−	0.972463i	$-0.425126\pi$
$773$	4.62705e12	0.466118	0.233059	+	0.972463i	$0.425126\pi$
$774$	1.50011e12	0.150241
$775$	−4.17330e12	−0.415549
$776$	9.41174e11	0.0931735
$777$	1.17490e13	1.15640
$778$	−1.40040e13	−1.37039
$779$	7.43365e12	0.723242
$780$	2.18390e12	0.211255
$781$	−4.61465e12	−0.443822
$782$	−5.45681e12	−0.521805
$783$	−6.94431e11	−0.0660239
$784$	−2.91971e11	−0.0276005
$785$	−8.09397e12	−0.760761
$786$	1.47222e13	1.37585
$787$	2.07424e13	1.92741	0.963703	−	0.266978i	$-0.0860252\pi$
$787$	2.07424e13	1.92741	0.963703	+	0.266978i	$0.0860252\pi$
$788$	−2.00099e12	−0.184875
$789$	−1.64370e13	−1.51000
$790$	−5.31215e12	−0.485231
$791$	−1.90329e13	−1.72867
$792$	2.62982e11	0.0237499
$793$	−3.79812e12	−0.341067
$794$	1.22477e13	1.09361
$795$	1.31734e13	1.16963
$796$	9.05731e12	0.799632
$797$	−8.24751e12	−0.724036	−0.362018	−	0.932171i	$-0.617912\pi$
$797$	−8.24751e12	−0.724036	−0.362018	+	0.932171i	$0.617912\pi$
$798$	−4.16049e12	−0.363188
$799$	−4.01831e12	−0.348805
$800$	1.03602e12	0.0894259
$801$	5.98215e10	0.00513465
$802$	2.09352e12	0.178687
$803$	−2.81122e12	−0.238602
$804$	−8.06590e12	−0.680771
$805$	−9.77494e12	−0.820413
$806$	3.78283e12	0.315725
$807$	−4.15725e12	−0.345045
$808$	−2.59397e12	−0.214098
$809$	2.40624e12	0.197501	0.0987507	−	0.995112i	$-0.468515\pi$
$809$	2.40624e12	0.197501	0.0987507	+	0.995112i	$0.468515\pi$
$810$	7.14405e12	0.583126
$811$	−6.19213e12	−0.502628	−0.251314	−	0.967906i	$-0.580863\pi$
$811$	−6.19213e12	−0.502628	−0.251314	+	0.967906i	$0.580863\pi$
$812$	−4.48804e11	−0.0362289
$813$	2.08719e13	1.67554
$814$	−2.96096e12	−0.236387
$815$	−1.53540e13	−1.21902
$816$	2.08800e12	0.164864
$817$	5.98097e12	0.469648
$818$	−1.62948e13	−1.27250
$819$	−1.47068e12	−0.114220
$820$	−6.68289e12	−0.516181
$821$	5.69887e12	0.437769	0.218884	−	0.975751i	$-0.429758\pi$
$821$	5.69887e12	0.437769	0.218884	+	0.975751i	$0.429758\pi$
$822$	−1.39212e13	−1.06354
$823$	2.23147e13	1.69547	0.847737	−	0.530416i	$-0.177964\pi$
$823$	2.23147e13	1.69547	0.847737	+	0.530416i	$0.177964\pi$
$824$	2.30126e11	0.0173897
$825$	−2.24420e12	−0.168662
$826$	1.42038e13	1.06168
$827$	−4.00351e12	−0.297623	−0.148811	−	0.988866i	$-0.547545\pi$
$827$	−4.00351e12	−0.297623	−0.148811	+	0.988866i	$0.547545\pi$
$828$	−1.86434e12	−0.137844
$829$	−1.97674e13	−1.45363	−0.726815	−	0.686833i	$-0.759000\pi$
$829$	−1.97674e13	−1.45363	−0.726815	+	0.686833i	$0.759000\pi$
$830$	9.41920e12	0.688910
$831$	−4.96513e12	−0.361182
$832$	−9.39085e11	−0.0679438
$833$	9.14931e11	0.0658394
$834$	−4.34802e12	−0.311204
$835$	3.47232e12	0.247190
$836$	1.04851e12	0.0742414
$837$	1.00245e13	0.705987
$838$	9.58860e11	0.0671672
$839$	−1.76893e13	−1.23249	−0.616243	−	0.787556i	$-0.711346\pi$
$839$	−1.76893e13	−1.23249	−0.616243	+	0.787556i	$0.711346\pi$
$840$	3.74030e12	0.259209
$841$	−1.44215e13	−0.994098
$842$	6.49565e12	0.445367
$843$	1.18684e13	0.809406
$844$	−1.01631e13	−0.689424
$845$	−7.33989e12	−0.495262
$846$	−1.37287e12	−0.0921431
$847$	1.28434e12	0.0857441
$848$	−5.66462e12	−0.376174
$849$	2.47738e13	1.63647
$850$	−3.24651e12	−0.213320
$851$	2.09910e13	1.37198
$852$	−1.25179e13	−0.813865
$853$	7.30918e12	0.472713	0.236357	−	0.971666i	$-0.424047\pi$
$853$	7.30918e12	0.472713	0.236357	+	0.971666i	$0.424047\pi$
$854$	−6.50492e12	−0.418487
$855$	−1.20516e12	−0.0771254
$856$	2.14553e12	0.136585
$857$	−2.21345e11	−0.0140171	−0.00700853	−	0.999975i	$-0.502231\pi$
$857$	−2.21345e11	−0.0140171	−0.00700853	+	0.999975i	$0.502231\pi$
$858$	2.03422e12	0.128146
$859$	−1.64953e13	−1.03369	−0.516845	−	0.856079i	$-0.672893\pi$
$859$	−1.64953e13	−1.03369	−0.516845	+	0.856079i	$0.672893\pi$
$860$	−5.37692e12	−0.335190
$861$	2.47001e13	1.53174
$862$	1.12987e12	0.0697022
$863$	7.33700e12	0.450267	0.225133	−	0.974328i	$-0.427718\pi$
$863$	7.33700e12	0.450267	0.225133	+	0.974328i	$0.427718\pi$
$864$	−2.48857e12	−0.151928
$865$	−2.88755e12	−0.175371
$866$	−1.13373e13	−0.684981
$867$	1.18546e13	0.712528
$868$	6.47873e12	0.387392
$869$	−4.94806e12	−0.294338
$870$	−7.13522e11	−0.0422251
$871$	−1.13678e13	−0.669259
$872$	−9.20895e12	−0.539369
$873$	−1.00764e12	−0.0587139
$874$	−7.43316e12	−0.430896
$875$	−1.73118e13	−0.998401
$876$	−7.62581e12	−0.437540
$877$	−3.69862e12	−0.211126	−0.105563	−	0.994413i	$-0.533664\pi$
$877$	−3.69862e12	−0.211126	−0.105563	+	0.994413i	$0.533664\pi$
$878$	−1.08939e13	−0.618670
$879$	−9.02420e12	−0.509869
$880$	−9.42620e11	−0.0529864
$881$	−2.56917e13	−1.43681	−0.718407	−	0.695623i	$-0.755128\pi$
$881$	−2.56917e13	−1.43681	−0.718407	+	0.695623i	$0.755128\pi$
$882$	3.12590e11	0.0173927
$883$	−1.85885e13	−1.02901	−0.514506	−	0.857487i	$-0.672025\pi$
$883$	−1.85885e13	−1.02901	−0.514506	+	0.857487i	$0.672025\pi$
$884$	2.94275e12	0.162076
$885$	2.25817e13	1.23740
$886$	6.15074e12	0.335332
$887$	1.89678e13	1.02887	0.514435	−	0.857530i	$-0.328002\pi$
$887$	1.89678e13	1.02887	0.514435	+	0.857530i	$0.328002\pi$
$888$	−8.03201e12	−0.433477
$889$	1.36328e13	0.732025
$890$	−2.14421e11	−0.0114555
$891$	6.65441e12	0.353720
$892$	−1.32326e12	−0.0699847
$893$	−5.47366e12	−0.288036
$894$	−3.68635e12	−0.193009
$895$	−3.77591e12	−0.196706
$896$	−1.60834e12	−0.0833666
$897$	−1.44211e13	−0.743758
$898$	6.11827e12	0.313968
$899$	−1.23592e12	−0.0631062
$900$	−1.10918e12	−0.0563523
$901$	1.77509e13	0.897342
$902$	−6.22486e12	−0.313112
$903$	1.98732e13	0.994657
$904$	1.30115e13	0.647992
$905$	1.65891e13	0.822060
$906$	2.64387e13	1.30365
$907$	2.22825e12	0.109328	0.0546640	−	0.998505i	$-0.482591\pi$
$907$	2.22825e12	0.109328	0.0546640	+	0.998505i	$0.482591\pi$
$908$	−1.04479e13	−0.510085
$909$	2.77715e12	0.134916
$910$	5.27144e12	0.254825
$911$	−5.00799e12	−0.240897	−0.120448	−	0.992720i	$-0.538433\pi$
$911$	−5.00799e12	−0.240897	−0.120448	+	0.992720i	$0.538433\pi$
$912$	2.84424e12	0.136141
$913$	8.77362e12	0.417888
$914$	2.09655e12	0.0993681
$915$	−1.03417e13	−0.487750
$916$	1.21872e13	0.571972
$917$	3.55360e13	1.65961
$918$	7.79827e12	0.362415
$919$	−7.07960e12	−0.327408	−0.163704	−	0.986510i	$-0.552344\pi$
$919$	−7.07960e12	−0.327408	−0.163704	+	0.986510i	$0.552344\pi$
$920$	6.68246e12	0.307532
$921$	1.37066e13	0.627712
$922$	2.55260e13	1.16331
$923$	−1.76422e13	−0.800102
$924$	3.48394e12	0.157234
$925$	1.24885e13	0.560883
$926$	1.33840e13	0.598186
$927$	−2.46377e11	−0.0109583
$928$	3.06817e11	0.0135804
$929$	−1.04030e13	−0.458234	−0.229117	−	0.973399i	$-0.573584\pi$
$929$	−1.04030e13	−0.458234	−0.229117	+	0.973399i	$0.573584\pi$
$930$	1.03001e13	0.451509
$931$	1.24630e12	0.0543688
$932$	1.84119e13	0.799332
$933$	5.53527e12	0.239151
$934$	2.54881e13	1.09591
$935$	2.95383e12	0.126396
$936$	1.00540e12	0.0428153
$937$	−2.46961e13	−1.04665	−0.523324	−	0.852134i	$-0.675308\pi$
$937$	−2.46961e13	−1.04665	−0.523324	+	0.852134i	$0.675308\pi$
$938$	−1.94692e13	−0.821175
$939$	−1.83734e13	−0.771249
$940$	4.92085e12	0.205573
$941$	−1.59645e13	−0.663745	−0.331872	−	0.943324i	$-0.607680\pi$
$941$	−1.59645e13	−0.663745	−0.331872	+	0.943324i	$0.607680\pi$
$942$	−2.04512e13	−0.846231
$943$	4.41295e13	1.81730
$944$	−9.71018e12	−0.397973
$945$	1.39693e13	0.569811
$946$	−5.00840e12	−0.203324
$947$	−7.31572e12	−0.295585	−0.147793	−	0.989018i	$-0.547217\pi$
$947$	−7.31572e12	−0.295585	−0.147793	+	0.989018i	$0.547217\pi$
$948$	−1.34223e13	−0.539745
$949$	−1.07475e13	−0.430141
$950$	−4.42234e12	−0.176155
$951$	−2.49201e13	−0.987954
$952$	5.03996e12	0.198866
$953$	−1.96699e13	−0.772476	−0.386238	−	0.922399i	$-0.626226\pi$
$953$	−1.96699e13	−0.772476	−0.386238	+	0.922399i	$0.626226\pi$
$954$	6.06465e12	0.237049
$955$	−1.22182e13	−0.475326
$956$	2.36139e13	0.914339
$957$	−6.64618e11	−0.0256135
$958$	5.02726e12	0.192835
$959$	−3.36026e13	−1.28289
$960$	−2.55699e12	−0.0971645
$961$	−8.59845e12	−0.325211
$962$	−1.13200e13	−0.426147
$963$	−2.29705e12	−0.0860700
$964$	−3.87137e12	−0.144384
$965$	2.87502e13	1.06725
$966$	−2.46985e13	−0.912585
$967$	−1.63671e13	−0.601941	−0.300970	−	0.953634i	$-0.597311\pi$
$967$	−1.63671e13	−0.601941	−0.300970	+	0.953634i	$0.597311\pi$
$968$	−8.78014e11	−0.0321412
$969$	−8.91281e12	−0.324756
$970$	3.61174e12	0.130992
$971$	−5.41329e13	−1.95423	−0.977114	−	0.212718i	$-0.931768\pi$
$971$	−5.41329e13	−1.95423	−0.977114	+	0.212718i	$0.931768\pi$
$972$	6.09237e12	0.218921
$973$	−1.04951e13	−0.375387
$974$	−1.80104e13	−0.641222
$975$	−8.57977e12	−0.304057
$976$	4.44697e12	0.156870
$977$	−2.41304e13	−0.847305	−0.423652	−	0.905825i	$-0.639252\pi$
$977$	−2.41304e13	−0.847305	−0.423652	+	0.905825i	$0.639252\pi$
$978$	−3.87951e13	−1.35598
$979$	−1.99725e11	−0.00694881
$980$	−1.12043e12	−0.0388033
$981$	9.85928e12	0.339887
$982$	1.87988e13	0.645103
$983$	3.05809e13	1.04462	0.522311	−	0.852755i	$-0.325070\pi$
$983$	3.05809e13	1.04462	0.522311	+	0.852755i	$0.325070\pi$
$984$	−1.68858e13	−0.574173
$985$	−7.67876e12	−0.259913
$986$	−9.61453e11	−0.0323953
$987$	−1.81876e13	−0.610025
$988$	4.00856e12	0.133839
$989$	3.55057e13	1.18009
$990$	1.00919e12	0.0333898
$991$	1.25356e13	0.412871	0.206436	−	0.978460i	$-0.433814\pi$
$991$	1.25356e13	0.412871	0.206436	+	0.978460i	$0.433814\pi$
$992$	−4.42906e12	−0.145214
$993$	2.49703e13	0.814991
$994$	−3.02152e13	−0.981719
$995$	3.47572e13	1.12419
$996$	2.37996e13	0.766308
$997$	−2.58505e13	−0.828593	−0.414297	−	0.910142i	$-0.635972\pi$
$997$	−2.58505e13	−0.828593	−0.414297	+	0.910142i	$0.635972\pi$
$998$	3.10765e13	0.991618
$999$	−2.99980e13	−0.952899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	22.10.a.e.1.1	✓	2
3.2	odd	2		198.10.a.o.1.1		2
4.3	odd	2		176.10.a.d.1.2		2
11.10	odd	2		242.10.a.f.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.10.a.e.1.1	✓	2	1.1	even	1	trivial
176.10.a.d.1.2		2	4.3	odd	2
198.10.a.o.1.1		2	3.2	odd	2
242.10.a.f.1.1		2	11.10	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:	\( N \)	\(=\)	\( 22 = 2 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	22.a (trivial)

\(f(q)\)	\(=\)	\(q-16.0000 q^{2} -155.139 q^{3} +256.000 q^{4} +982.395 q^{5} +2482.23 q^{6} +5991.53 q^{7} -4096.00 q^{8} +4385.26 q^{9} +O(q^{10})\)	\(q-16.0000 q^{2} -155.139 q^{3} +256.000 q^{4} +982.395 q^{5} +2482.23 q^{6} +5991.53 q^{7} -4096.00 q^{8} +4385.26 q^{9} -15718.3 q^{10} -14641.0 q^{11} -39715.7 q^{12} -55973.8 q^{13} -95864.5 q^{14} -152408. q^{15} +65536.0 q^{16} -205366. q^{17} -70164.1 q^{18} -279746. q^{19} +251493. q^{20} -929523. q^{21} +234256. q^{22} -1.66070e6 q^{23} +635451. q^{24} -988025. q^{25} +895581. q^{26} +2.37328e6 q^{27} +1.53383e6 q^{28} -292603. q^{29} +2.43853e6 q^{30} +4.22388e6 q^{31} -1.04858e6 q^{32} +2.27140e6 q^{33} +3.28586e6 q^{34} +5.88605e6 q^{35} +1.12263e6 q^{36} -1.26399e7 q^{37} +4.47593e6 q^{38} +8.68375e6 q^{39} -4.02389e6 q^{40} -2.65729e7 q^{41} +1.48724e7 q^{42} -2.13800e7 q^{43} -3.74810e6 q^{44} +4.30805e6 q^{45} +2.65711e7 q^{46} +1.95666e7 q^{47} -1.01672e7 q^{48} -4.45512e6 q^{49} +1.58084e7 q^{50} +3.18604e7 q^{51} -1.43293e7 q^{52} -8.64352e7 q^{53} -3.79725e7 q^{54} -1.43832e7 q^{55} -2.45413e7 q^{56} +4.33996e7 q^{57} +4.68165e6 q^{58} -1.48166e8 q^{59} -3.90165e7 q^{60} +6.78553e7 q^{61} -6.75821e7 q^{62} +2.62744e7 q^{63} +1.67772e7 q^{64} -5.49884e7 q^{65} -3.63424e7 q^{66} +2.03091e8 q^{67} -5.25737e7 q^{68} +2.57639e8 q^{69} -9.41768e7 q^{70} +3.15187e8 q^{71} -1.79620e7 q^{72} +1.92010e8 q^{73} +2.02238e8 q^{74} +1.53282e8 q^{75} -7.16149e7 q^{76} -8.77221e7 q^{77} -1.38940e8 q^{78} +3.37959e8 q^{79} +6.43822e7 q^{80} -4.54505e8 q^{81} +4.25166e8 q^{82} -5.99250e8 q^{83} -2.37958e8 q^{84} -2.01751e8 q^{85} +3.42080e8 q^{86} +4.53943e7 q^{87} +5.99695e7 q^{88} +1.36415e7 q^{89} -6.89289e7 q^{90} -3.35369e8 q^{91} -4.25138e8 q^{92} -6.55291e8 q^{93} -3.13065e8 q^{94} -2.74821e8 q^{95} +1.62676e8 q^{96} -2.29779e8 q^{97} +7.12820e7 q^{98} -6.42046e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 32 q^{2} + 34 q^{3} + 512 q^{4} - 1478 q^{5} - 544 q^{6} + 8196 q^{7} - 8192 q^{8} + 20476 q^{9}+O(q^{10}) \) 2 * q - 32 * q^2 + 34 * q^3 + 512 * q^4 - 1478 * q^5 - 544 * q^6 + 8196 * q^7 - 8192 * q^8 + 20476 * q^9	\( 2 q - 32 q^{2} + 34 q^{3} + 512 q^{4} - 1478 q^{5} - 544 q^{6} + 8196 q^{7} - 8192 q^{8} + 20476 q^{9} + 23648 q^{10} - 29282 q^{11} + 8704 q^{12} - 196296 q^{13} - 131136 q^{14} - 617766 q^{15} + 131072 q^{16} - 548788 q^{17} - 327616 q^{18} - 90928 q^{19} - 378368 q^{20} - 512572 q^{21} + 468512 q^{22} - 3971046 q^{23} - 139264 q^{24} + 3112392 q^{25} + 3140736 q^{26} + 1693846 q^{27} + 2098176 q^{28} - 656128 q^{29} + 9884256 q^{30} - 872214 q^{31} - 2097152 q^{32} - 497794 q^{33} + 8780608 q^{34} + 462196 q^{35} + 5241856 q^{36} - 190722 q^{37} + 1454848 q^{38} - 17856712 q^{39} + 6053888 q^{40} + 3350080 q^{41} + 8201152 q^{42} + 3876012 q^{43} - 7496192 q^{44} - 35281524 q^{45} + 63536736 q^{46} + 38884544 q^{47} + 2228224 q^{48} - 39949062 q^{49} - 49798272 q^{50} - 33094260 q^{51} - 50251776 q^{52} - 134346316 q^{53} - 27101536 q^{54} + 21639398 q^{55} - 33570816 q^{56} + 79112528 q^{57} + 10498048 q^{58} - 125273754 q^{59} - 158148096 q^{60} + 114821880 q^{61} + 13955424 q^{62} + 61745912 q^{63} + 33554432 q^{64} + 290259544 q^{65} + 7964704 q^{66} - 91519714 q^{67} - 140489728 q^{68} - 179338950 q^{69} - 7395136 q^{70} + 411397438 q^{71} - 83869696 q^{72} + 506142392 q^{73} + 3051552 q^{74} + 928832584 q^{75} - 23277568 q^{76} - 119997636 q^{77} + 285707392 q^{78} + 810072516 q^{79} - 96862208 q^{80} - 899727614 q^{81} - 53601280 q^{82} - 718904884 q^{83} - 131218432 q^{84} + 643202972 q^{85} - 62016192 q^{86} - 23362560 q^{87} + 119939072 q^{88} - 810786322 q^{89} + 564504384 q^{90} - 644704528 q^{91} - 1016587776 q^{92} - 1619163382 q^{93} - 622152704 q^{94} - 739387248 q^{95} - 35651584 q^{96} - 230208654 q^{97} + 639184992 q^{98} - 299789116 q^{99}+O(q^{100}) \) 2 * q - 32 * q^2 + 34 * q^3 + 512 * q^4 - 1478 * q^5 - 544 * q^6 + 8196 * q^7 - 8192 * q^8 + 20476 * q^9 + 23648 * q^10 - 29282 * q^11 + 8704 * q^12 - 196296 * q^13 - 131136 * q^14 - 617766 * q^15 + 131072 * q^16 - 548788 * q^17 - 327616 * q^18 - 90928 * q^19 - 378368 * q^20 - 512572 * q^21 + 468512 * q^22 - 3971046 * q^23 - 139264 * q^24 + 3112392 * q^25 + 3140736 * q^26 + 1693846 * q^27 + 2098176 * q^28 - 656128 * q^29 + 9884256 * q^30 - 872214 * q^31 - 2097152 * q^32 - 497794 * q^33 + 8780608 * q^34 + 462196 * q^35 + 5241856 * q^36 - 190722 * q^37 + 1454848 * q^38 - 17856712 * q^39 + 6053888 * q^40 + 3350080 * q^41 + 8201152 * q^42 + 3876012 * q^43 - 7496192 * q^44 - 35281524 * q^45 + 63536736 * q^46 + 38884544 * q^47 + 2228224 * q^48 - 39949062 * q^49 - 49798272 * q^50 - 33094260 * q^51 - 50251776 * q^52 - 134346316 * q^53 - 27101536 * q^54 + 21639398 * q^55 - 33570816 * q^56 + 79112528 * q^57 + 10498048 * q^58 - 125273754 * q^59 - 158148096 * q^60 + 114821880 * q^61 + 13955424 * q^62 + 61745912 * q^63 + 33554432 * q^64 + 290259544 * q^65 + 7964704 * q^66 - 91519714 * q^67 - 140489728 * q^68 - 179338950 * q^69 - 7395136 * q^70 + 411397438 * q^71 - 83869696 * q^72 + 506142392 * q^73 + 3051552 * q^74 + 928832584 * q^75 - 23277568 * q^76 - 119997636 * q^77 + 285707392 * q^78 + 810072516 * q^79 - 96862208 * q^80 - 899727614 * q^81 - 53601280 * q^82 - 718904884 * q^83 - 131218432 * q^84 + 643202972 * q^85 - 62016192 * q^86 - 23362560 * q^87 + 119939072 * q^88 - 810786322 * q^89 + 564504384 * q^90 - 644704528 * q^91 - 1016587776 * q^92 - 1619163382 * q^93 - 622152704 * q^94 - 739387248 * q^95 - 35651584 * q^96 - 230208654 * q^97 + 639184992 * q^98 - 299789116 * q^99

Introduction

L-functions

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