LMFDB - Embedded newform 5.22.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,22,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 22, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 22);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 22 $
Character orbit:	$[\chi]$	$=$	5.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:	$13.9738672144$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 1929606x^{2} - 743130000x + 239341586400 $ x^4 - x^3 - 1929606x^2 - 743130000x + 239341586400
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6}\cdot 3\cdot 5^{2}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1521.87$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2315.74 q^{2} +45067.6 q^{3} +3.26550e6 q^{4} +9.76562e6 q^{5} -1.04365e8 q^{6} -6.93632e8 q^{7} -2.70560e9 q^{8} -8.42927e9 q^{9} +O(q^{10})$	\(q-2315.74 q^{2} +45067.6 q^{3} +3.26550e6 q^{4} +9.76562e6 q^{5} -1.04365e8 q^{6} -6.93632e8 q^{7} -2.70560e9 q^{8} -8.42927e9 q^{9} -2.26147e10 q^{10} -1.34852e10 q^{11} +1.47168e11 q^{12} +7.82310e11 q^{13} +1.60627e12 q^{14} +4.40113e11 q^{15} -5.82789e11 q^{16} -3.22221e12 q^{17} +1.95200e13 q^{18} +9.87395e12 q^{19} +3.18897e13 q^{20} -3.12603e13 q^{21} +3.12281e13 q^{22} +2.96069e14 q^{23} -1.21935e14 q^{24} +9.53674e13 q^{25} -1.81163e15 q^{26} -8.51310e14 q^{27} -2.26506e15 q^{28} +2.05398e15 q^{29} -1.01919e15 q^{30} +5.62290e15 q^{31} +7.02364e15 q^{32} -6.07744e14 q^{33} +7.46180e15 q^{34} -6.77375e15 q^{35} -2.75258e16 q^{36} +5.49371e16 q^{37} -2.28655e16 q^{38} +3.52568e16 q^{39} -2.64219e16 q^{40} -1.44556e17 q^{41} +7.23908e16 q^{42} +2.52052e17 q^{43} -4.40359e16 q^{44} -8.23170e16 q^{45} -6.85618e17 q^{46} +7.91015e15 q^{47} -2.62649e16 q^{48} -7.74210e16 q^{49} -2.20846e17 q^{50} -1.45217e17 q^{51} +2.55464e18 q^{52} -2.16231e17 q^{53} +1.97141e18 q^{54} -1.31691e17 q^{55} +1.87669e18 q^{56} +4.44995e17 q^{57} -4.75648e18 q^{58} -2.98356e18 q^{59} +1.43719e18 q^{60} +2.24873e18 q^{61} -1.30212e19 q^{62} +5.84681e18 q^{63} -1.50427e19 q^{64} +7.63975e18 q^{65} +1.40738e18 q^{66} +5.10149e18 q^{67} -1.05221e19 q^{68} +1.33431e19 q^{69} +1.56862e19 q^{70} +2.66169e19 q^{71} +2.28062e19 q^{72} +2.85617e19 q^{73} -1.27220e20 q^{74} +4.29798e18 q^{75} +3.22434e19 q^{76} +9.35374e18 q^{77} -8.16457e19 q^{78} +8.75536e19 q^{79} -5.69130e18 q^{80} +4.98066e19 q^{81} +3.34754e20 q^{82} -1.76821e20 q^{83} -1.02081e20 q^{84} -3.14669e19 q^{85} -5.83687e20 q^{86} +9.25679e19 q^{87} +3.64855e19 q^{88} -3.17772e20 q^{89} +1.90625e20 q^{90} -5.42635e20 q^{91} +9.66813e20 q^{92} +2.53410e20 q^{93} -1.83179e19 q^{94} +9.64253e19 q^{95} +3.16539e20 q^{96} +4.33412e20 q^{97} +1.79287e20 q^{98} +1.13670e20 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2910 q^{2} + 83240 q^{3} + 9165268 q^{4} + 39062500 q^{5} - 158524712 q^{6} + 512613800 q^{7} + 5167363080 q^{8} + 21732888532 q^{9}+O(q^{10}) $ 4 * q + 2910 * q^2 + 83240 * q^3 + 9165268 * q^4 + 39062500 * q^5 - 158524712 * q^6 + 512613800 * q^7 + 5167363080 * q^8 + 21732888532 * q^9	$ 4 q + 2910 q^{2} + 83240 q^{3} + 9165268 q^{4} + 39062500 q^{5} - 158524712 q^{6} + 512613800 q^{7} + 5167363080 q^{8} + 21732888532 q^{9} + 28417968750 q^{10} + 33727076448 q^{11} - 142435377680 q^{12} + 863532165080 q^{13} + 2725405637616 q^{14} + 812890625000 q^{15} + 9168135122704 q^{16} + 17694691101480 q^{17} + 108219081471590 q^{18} + 65217596849840 q^{19} + 89504570312500 q^{20} - 248634744508992 q^{21} - 133302721028280 q^{22} + 306130984922520 q^{23} - 509427036802080 q^{24} + 381469726562500 q^{25} - 19\!\cdots\!12 q^{26}+ \cdots - 15\!\cdots\!16 q^{99}+O(q^{100}) $ 4 * q + 2910 * q^2 + 83240 * q^3 + 9165268 * q^4 + 39062500 * q^5 - 158524712 * q^6 + 512613800 * q^7 + 5167363080 * q^8 + 21732888532 * q^9 + 28417968750 * q^10 + 33727076448 * q^11 - 142435377680 * q^12 + 863532165080 * q^13 + 2725405637616 * q^14 + 812890625000 * q^15 + 9168135122704 * q^16 + 17694691101480 * q^17 + 108219081471590 * q^18 + 65217596849840 * q^19 + 89504570312500 * q^20 - 248634744508992 * q^21 - 133302721028280 * q^22 + 306130984922520 * q^23 - 509427036802080 * q^24 + 381469726562500 * q^25 - 1909802985226812 * q^26 - 3478503990916720 * q^27 - 2466701432057920 * q^28 - 1183867881941640 * q^29 - 1548092890625000 * q^30 + 8127647981305328 * q^31 + 6394106775900960 * q^32 - 27227776360130720 * q^33 + 32676043106528796 * q^34 + 5005994140625000 * q^35 + 132603401899613444 * q^36 + 50729262881561240 * q^37 + 35369554723756920 * q^38 - 90408012787467856 * q^39 + 50462530078125000 * q^40 - 151242912792059832 * q^41 - 584170109040328320 * q^42 + 195241056541629800 * q^43 - 614844690548787984 * q^44 + 212235239570312500 * q^45 - 156055372897688112 * q^46 - 461921266212226680 * q^47 - 268908035207420480 * q^48 + 348492786998301828 * q^49 + 277519226074218750 * q^50 + 3394366189837348048 * q^51 + 2124030127334250200 * q^52 + 1013253578565011640 * q^53 - 2325284713297481360 * q^54 + 329365980937500000 * q^55 + 3133890122325795840 * q^56 + 6889753607884864160 * q^57 - 15566576922395873820 * q^58 + 9994246603380823920 * q^59 - 1390970485156250000 * q^60 - 10817434481929098952 * q^61 + 3855611474231219520 * q^62 + 12245908869990535560 * q^63 - 45099981493147646912 * q^64 + 8432931299609375000 * q^65 - 81535658477725195744 * q^66 + 21966891437417653880 * q^67 - 2003292237110276760 * q^68 - 10872182089324606656 * q^69 + 26615289429843750000 * q^70 + 51295204524235287888 * q^71 + 203807399727091870440 * q^72 + 74737166154487034120 * q^73 - 95273704374004345644 * q^74 + 7938385009765625000 * q^75 + 33053497281514492880 * q^76 + 284152911785269322400 * q^77 - 411161554685929127600 * q^78 - 60935090437726582240 * q^79 + 89532569557656250000 * q^80 + 158163684388294667524 * q^81 + 209310572847889648620 * q^82 - 278730291142551479640 * q^83 - 1305319136534979185664 * q^84 + 172799717787890625000 * q^85 - 410177137146579139512 * q^86 + 180742525444629646640 * q^87 - 407444351717354555040 * q^88 - 323651892724949032920 * q^89 + 1056826967495996093750 * q^90 + 220855101702096981808 * q^91 + 2407334022772179833280 * q^92 + 193462123423446842880 * q^93 - 1285026294005215311264 * q^94 + 636890594236718750000 * q^95 - 20769436930632372352 * q^96 + 309141974076136362920 * q^97 + 746323122131488476270 * q^98 - 1516374777085318976416 * 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 $

$2$	−2315.74	−1.59910	−0.799549	−	0.600601i	$-0.794928\pi$
$2$	−2315.74	−1.59910	−0.799549	+	0.600601i	$0.794928\pi$
$3$	45067.6	0.440647	0.220324	−	0.975427i	$-0.429289\pi$
$3$	45067.6	0.440647	0.220324	+	0.975427i	$0.429289\pi$
$4$	3.26550e6	1.55711
$5$	9.76562e6	0.447214
$5$	9.76562e6	0.447214
$6$	−1.04365e8	−0.704638
$7$	−6.93632e8	−0.928110	−0.464055	−	0.885806i	$-0.653606\pi$
$7$	−6.93632e8	−0.928110	−0.464055	+	0.885806i	$0.653606\pi$
$8$	−2.70560e9	−0.890879
$9$	−8.42927e9	−0.805830
$10$	−2.26147e10	−0.715138
$11$	−1.34852e10	−0.156759	−0.0783796	−	0.996924i	$-0.524975\pi$
$11$	−1.34852e10	−0.156759	−0.0783796	+	0.996924i	$0.524975\pi$
$12$	1.47168e11	0.686138
$13$	7.82310e11	1.57389	0.786944	−	0.617025i	$-0.211662\pi$
$13$	7.82310e11	1.57389	0.786944	+	0.617025i	$0.211662\pi$
$14$	1.60627e12	1.48414
$15$	4.40113e11	0.197063
$16$	−5.82789e11	−0.132511
$17$	−3.22221e12	−0.387650	−0.193825	−	0.981036i	$-0.562089\pi$
$17$	−3.22221e12	−0.387650	−0.193825	+	0.981036i	$0.562089\pi$
$18$	1.95200e13	1.28860
$19$	9.87395e12	0.369469	0.184734	−	0.982788i	$-0.440857\pi$
$19$	9.87395e12	0.369469	0.184734	+	0.982788i	$0.440857\pi$
$20$	3.18897e13	0.696362
$21$	−3.12603e13	−0.408969
$22$	3.12281e13	0.250673
$23$	2.96069e14	1.49022	0.745109	−	0.666942i	$-0.232397\pi$
$23$	2.96069e14	1.49022	0.745109	+	0.666942i	$0.232397\pi$
$24$	−1.21935e14	−0.392564
$25$	9.53674e13	0.200000
$26$	−1.81163e15	−2.51680
$27$	−8.51310e14	−0.795734
$28$	−2.26506e15	−1.44517
$29$	2.05398e15	0.906603	0.453301	−	0.891357i	$-0.350246\pi$
$29$	2.05398e15	0.906603	0.453301	+	0.891357i	$0.350246\pi$
$30$	−1.01919e15	−0.315124
$31$	5.62290e15	1.23215	0.616073	−	0.787689i	$-0.288723\pi$
$31$	5.62290e15	1.23215	0.616073	+	0.787689i	$0.288723\pi$
$32$	7.02364e15	1.10278
$33$	−6.07744e14	−0.0690755
$34$	7.46180e15	0.619890
$35$	−6.77375e15	−0.415063
$36$	−2.75258e16	−1.25477
$37$	5.49371e16	1.87823	0.939113	−	0.343607i	$-0.111649\pi$
$37$	5.49371e16	1.87823	0.939113	+	0.343607i	$0.111649\pi$
$38$	−2.28655e16	−0.590817
$39$	3.52568e16	0.693529
$40$	−2.64219e16	−0.398413
$41$	−1.44556e17	−1.68192	−0.840960	−	0.541098i	$-0.818009\pi$
$41$	−1.44556e17	−1.68192	−0.840960	+	0.541098i	$0.818009\pi$
$42$	7.23908e16	0.653982
$43$	2.52052e17	1.77857	0.889286	−	0.457352i	$-0.151202\pi$
$43$	2.52052e17	1.77857	0.889286	+	0.457352i	$0.151202\pi$
$44$	−4.40359e16	−0.244092
$45$	−8.23170e16	−0.360378
$46$	−6.85618e17	−2.38301
$47$	7.91015e15	0.0219360	0.0109680	−	0.999940i	$-0.496509\pi$
$47$	7.91015e15	0.0219360	0.0109680	+	0.999940i	$0.496509\pi$
$48$	−2.62649e16	−0.0583906
$49$	−7.74210e16	−0.138612
$50$	−2.20846e17	−0.319820
$51$	−1.45217e17	−0.170817
$52$	2.55464e18	2.45072
$53$	−2.16231e17	−0.169833	−0.0849163	−	0.996388i	$-0.527062\pi$
$53$	−2.16231e17	−0.169833	−0.0849163	+	0.996388i	$0.527062\pi$
$54$	1.97141e18	1.27246
$55$	−1.31691e17	−0.0701048
$56$	1.87669e18	0.826834
$57$	4.44995e17	0.162806
$58$	−4.75648e18	−1.44975
$59$	−2.98356e18	−0.759957	−0.379979	−	0.924995i	$-0.624069\pi$
$59$	−2.98356e18	−0.759957	−0.379979	+	0.924995i	$0.624069\pi$
$60$	1.43719e18	0.306850
$61$	2.24873e18	0.403621	0.201811	−	0.979425i	$-0.435317\pi$
$61$	2.24873e18	0.403621	0.201811	+	0.979425i	$0.435317\pi$
$62$	−1.30212e19	−1.97032
$63$	5.84681e18	0.747899
$64$	−1.50427e19	−1.63094
$65$	7.63975e18	0.703864
$66$	1.40738e18	0.110459
$67$	5.10149e18	0.341910	0.170955	−	0.985279i	$-0.445315\pi$
$67$	5.10149e18	0.341910	0.170955	+	0.985279i	$0.445315\pi$
$68$	−1.05221e19	−0.603615
$69$	1.33431e19	0.656661
$70$	1.56862e19	0.663727
$71$	2.66169e19	0.970388	0.485194	−	0.874407i	$-0.338749\pi$
$71$	2.66169e19	0.970388	0.485194	+	0.874407i	$0.338749\pi$
$72$	2.28062e19	0.717897
$73$	2.85617e19	0.777846	0.388923	−	0.921270i	$-0.372847\pi$
$73$	2.85617e19	0.777846	0.388923	+	0.921270i	$0.372847\pi$
$74$	−1.27220e20	−3.00347
$75$	4.29798e18	0.0881295
$76$	3.22434e19	0.575305
$77$	9.35374e18	0.145490
$78$	−8.16457e19	−1.10902
$79$	8.75536e19	1.04037	0.520187	−	0.854052i	$-0.325862\pi$
$79$	8.75536e19	1.04037	0.520187	+	0.854052i	$0.325862\pi$
$80$	−5.69130e18	−0.0592607
$81$	4.98066e19	0.455192
$82$	3.34754e20	2.68955
$83$	−1.76821e20	−1.25088	−0.625438	−	0.780274i	$-0.715080\pi$
$83$	−1.76821e20	−1.25088	−0.625438	+	0.780274i	$0.715080\pi$
$84$	−1.02081e20	−0.636812
$85$	−3.14669e19	−0.173362
$86$	−5.83687e20	−2.84411
$87$	9.25679e19	0.399492
$88$	3.64855e19	0.139653
$89$	−3.17772e20	−1.08024	−0.540121	−	0.841588i	$-0.681621\pi$
$89$	−3.17772e20	−1.08024	−0.540121	+	0.841588i	$0.681621\pi$
$90$	1.90625e20	0.576280
$91$	−5.42635e20	−1.46074
$92$	9.66813e20	2.32044
$93$	2.53410e20	0.542942
$94$	−1.83179e19	−0.0350778
$95$	9.64253e19	0.165232
$96$	3.16539e20	0.485936
$97$	4.33412e20	0.596757	0.298379	−	0.954448i	$-0.403554\pi$
$97$	4.33412e20	0.596757	0.298379	+	0.954448i	$0.403554\pi$
$98$	1.79287e20	0.221654
$99$	1.13670e20	0.126321
$100$	3.11423e20	0.311423
$101$	1.00905e21	0.908947	0.454474	−	0.890760i	$-0.349827\pi$
$101$	1.00905e21	0.908947	0.454474	+	0.890760i	$0.349827\pi$
$102$	3.36285e20	0.273153
$103$	−1.43623e21	−1.05301	−0.526506	−	0.850171i	$-0.676498\pi$
$103$	−1.43623e21	−1.05301	−0.526506	+	0.850171i	$0.676498\pi$
$104$	−2.11662e21	−1.40214
$105$	−3.05276e20	−0.182897
$106$	5.00735e20	0.271579
$107$	−1.79432e21	−0.881799	−0.440900	−	0.897556i	$-0.645341\pi$
$107$	−1.79432e21	−0.881799	−0.440900	+	0.897556i	$0.645341\pi$
$108$	−2.77995e21	−1.23905
$109$	−1.81656e21	−0.734973	−0.367486	−	0.930029i	$-0.619782\pi$
$109$	−1.81656e21	−0.734973	−0.367486	+	0.930029i	$0.619782\pi$
$110$	3.04962e20	0.112105
$111$	2.47588e21	0.827636
$112$	4.04241e20	0.122985
$113$	2.21102e21	0.612729	0.306364	−	0.951914i	$-0.400887\pi$
$113$	2.21102e21	0.612729	0.306364	+	0.951914i	$0.400887\pi$
$114$	−1.03049e21	−0.260342
$115$	2.89129e21	0.666446
$116$	6.70728e21	1.41168
$117$	−6.59430e21	−1.26829
$118$	6.90916e21	1.21525
$119$	2.23503e21	0.359782
$120$	−1.19077e21	−0.175560
$121$	−7.21840e21	−0.975427
$122$	−5.20748e21	−0.645430
$123$	−6.51478e21	−0.741133
$124$	1.83616e22	1.91859
$125$	9.31323e20	0.0894427
$126$	−1.35397e22	−1.19596
$127$	1.96517e21	0.159758	0.0798789	−	0.996805i	$-0.474547\pi$
$127$	1.96517e21	0.159758	0.0798789	+	0.996805i	$0.474547\pi$
$128$	2.01054e22	1.50525
$129$	1.13594e22	0.783723
$130$	−1.76917e22	−1.12555
$131$	−6.20397e21	−0.364184	−0.182092	−	0.983282i	$-0.558287\pi$
$131$	−6.20397e21	−0.364184	−0.182092	+	0.983282i	$0.558287\pi$
$132$	−1.98459e21	−0.107558
$133$	−6.84888e21	−0.342908
$134$	−1.18137e22	−0.546747
$135$	−8.31357e21	−0.355863
$136$	8.71801e21	0.345349
$137$	1.97065e22	0.722843	0.361421	−	0.932403i	$-0.382292\pi$
$137$	1.97065e22	0.722843	0.361421	+	0.932403i	$0.382292\pi$
$138$	−3.08992e22	−1.05006
$139$	3.96064e22	1.24770	0.623850	−	0.781544i	$-0.285568\pi$
$139$	3.96064e22	1.24770	0.623850	+	0.781544i	$0.285568\pi$
$140$	−2.21197e22	−0.646301
$141$	3.56492e20	0.00966604
$142$	−6.16379e22	−1.55174
$143$	−1.05496e22	−0.246721
$144$	4.91248e21	0.106781
$145$	2.00584e22	0.405445
$146$	−6.61414e22	−1.24385
$147$	−3.48918e21	−0.0610789
$148$	1.79397e23	2.92461
$149$	2.96141e22	0.449825	0.224912	−	0.974379i	$-0.427790\pi$
$149$	2.96141e22	0.449825	0.224912	+	0.974379i	$0.427790\pi$
$150$	−9.95301e21	−0.140928
$151$	1.17418e23	1.55051	0.775256	−	0.631648i	$-0.217621\pi$
$151$	1.17418e23	1.55051	0.775256	+	0.631648i	$0.217621\pi$
$152$	−2.67150e22	−0.329152
$153$	2.71608e22	0.312380
$154$	−2.16608e22	−0.232652
$155$	5.49111e22	0.551033
$156$	1.15131e23	1.07990
$157$	−6.65797e22	−0.583977	−0.291988	−	0.956422i	$-0.594317\pi$
$157$	−6.65797e22	−0.583977	−0.291988	+	0.956422i	$0.594317\pi$
$158$	−2.02751e23	−1.66366
$159$	−9.74500e21	−0.0748363
$160$	6.85903e22	0.493177
$161$	−2.05363e23	−1.38309
$162$	−1.15339e23	−0.727896
$163$	−2.12835e23	−1.25914	−0.629570	−	0.776944i	$-0.716769\pi$
$163$	−2.12835e23	−1.25914	−0.629570	+	0.776944i	$0.716769\pi$
$164$	−4.72048e23	−2.61894
$165$	−5.93500e21	−0.0308915
$166$	4.09472e23	2.00027
$167$	1.14667e22	0.0525913	0.0262956	−	0.999654i	$-0.491629\pi$
$167$	1.14667e22	0.0525913	0.0262956	+	0.999654i	$0.491629\pi$
$168$	8.45779e22	0.364342
$169$	3.64944e23	1.47712
$170$	7.28691e22	0.277223
$171$	−8.32301e22	−0.297729
$172$	8.23077e23	2.76944
$173$	−4.61501e23	−1.46113	−0.730565	−	0.682843i	$-0.760743\pi$
$173$	−4.61501e23	−1.46113	−0.730565	+	0.682843i	$0.760743\pi$
$174$	−2.14363e23	−0.638827
$175$	−6.61499e22	−0.185622
$176$	7.85900e21	0.0207723
$177$	−1.34462e23	−0.334873
$178$	7.35878e23	1.72741
$179$	4.71545e22	0.104368	0.0521839	−	0.998637i	$-0.483382\pi$
$179$	4.71545e22	0.104368	0.0521839	+	0.998637i	$0.483382\pi$
$180$	−2.68807e23	−0.561150
$181$	−9.46222e23	−1.86366	−0.931832	−	0.362889i	$-0.881790\pi$
$181$	−9.46222e23	−1.86366	−0.931832	+	0.362889i	$0.881790\pi$
$182$	1.25660e24	2.33587
$183$	1.01345e23	0.177855
$184$	−8.01043e23	−1.32760
$185$	5.36496e23	0.839969
$186$	−5.86833e23	−0.868218
$187$	4.34520e22	0.0607677
$188$	2.58306e22	0.0341568
$189$	5.90495e23	0.738529
$190$	−2.23296e23	−0.264221
$191$	−2.53410e23	−0.283774	−0.141887	−	0.989883i	$-0.545317\pi$
$191$	−2.53410e23	−0.283774	−0.141887	+	0.989883i	$0.545317\pi$
$192$	−6.77940e23	−0.718668
$193$	−3.20672e23	−0.321891	−0.160945	−	0.986963i	$-0.551454\pi$
$193$	−3.20672e23	−0.321891	−0.160945	+	0.986963i	$0.551454\pi$
$194$	−1.00367e24	−0.954273
$195$	3.44305e23	0.310156
$196$	−2.52819e23	−0.215834
$197$	2.01644e24	1.63189	0.815944	−	0.578131i	$-0.196218\pi$
$197$	2.01644e24	1.63189	0.815944	+	0.578131i	$0.196218\pi$
$198$	−2.63230e23	−0.202000
$199$	1.53942e24	1.12047	0.560235	−	0.828334i	$-0.310711\pi$
$199$	1.53942e24	1.12047	0.560235	+	0.828334i	$0.310711\pi$
$200$	−2.58026e23	−0.178176
$201$	2.29912e23	0.150662
$202$	−2.33670e24	−1.45350
$203$	−1.42470e24	−0.841427
$204$	−4.74207e23	−0.265981
$205$	−1.41168e24	−0.752177
$206$	3.32594e24	1.68387
$207$	−2.49564e24	−1.20086
$208$	−4.55922e23	−0.208557
$209$	−1.33152e23	−0.0579177
$210$	7.06941e23	0.292470
$211$	3.35451e24	1.32027	0.660136	−	0.751146i	$-0.270499\pi$
$211$	3.35451e24	1.32027	0.660136	+	0.751146i	$0.270499\pi$
$212$	−7.06103e23	−0.264449
$213$	1.19956e24	0.427599
$214$	4.15517e24	1.41008
$215$	2.46144e24	0.795401
$216$	2.30330e24	0.708903
$217$	−3.90022e24	−1.14357
$218$	4.20668e24	1.17529
$219$	1.28721e24	0.342756
$220$	−4.30038e23	−0.109161
$221$	−2.52077e24	−0.610118
$222$	−5.73351e24	−1.32347
$223$	2.44427e24	0.538205	0.269103	−	0.963112i	$-0.413273\pi$
$223$	2.44427e24	0.538205	0.269103	+	0.963112i	$0.413273\pi$
$224$	−4.87182e24	−1.02350
$225$	−8.03877e23	−0.161166
$226$	−5.12014e24	−0.979813
$227$	1.91414e24	0.349705	0.174852	−	0.984595i	$-0.444055\pi$
$227$	1.91414e24	0.349705	0.174852	+	0.984595i	$0.444055\pi$
$228$	1.45313e24	0.253507
$229$	−5.63376e24	−0.938699	−0.469349	−	0.883013i	$-0.655511\pi$
$229$	−5.63376e24	−0.938699	−0.469349	+	0.883013i	$0.655511\pi$
$230$	−6.69549e24	−1.06571
$231$	4.21550e23	0.0641097
$232$	−5.55725e24	−0.807673
$233$	−1.94290e24	−0.269906	−0.134953	−	0.990852i	$-0.543088\pi$
$233$	−1.94290e24	−0.269906	−0.134953	+	0.990852i	$0.543088\pi$
$234$	1.52707e25	2.02811
$235$	7.72476e22	0.00981008
$236$	−9.74284e24	−1.18334
$237$	3.94583e24	0.458438
$238$	−5.17574e24	−0.575326
$239$	8.04031e24	0.855253	0.427627	−	0.903955i	$-0.359350\pi$
$239$	8.04031e24	0.855253	0.427627	+	0.903955i	$0.359350\pi$
$240$	−2.56493e23	−0.0261131
$241$	−2.92862e24	−0.285420	−0.142710	−	0.989765i	$-0.545582\pi$
$241$	−2.92862e24	−0.285420	−0.142710	+	0.989765i	$0.545582\pi$
$242$	1.67159e25	1.55980
$243$	1.11497e25	0.996313
$244$	7.34324e24	0.628484
$245$	−7.56065e23	−0.0619891
$246$	1.50866e25	1.18514
$247$	7.72449e24	0.581503
$248$	−1.52133e25	−1.09769
$249$	−7.96891e24	−0.551196
$250$	−2.15670e24	−0.143028
$251$	−3.17722e24	−0.202057	−0.101028	−	0.994884i	$-0.532213\pi$
$251$	−3.17722e24	−0.202057	−0.101028	+	0.994884i	$0.532213\pi$
$252$	1.90928e25	1.16456
$253$	−3.99253e24	−0.233605
$254$	−4.55083e24	−0.255468
$255$	−1.41814e24	−0.0763917
$256$	−1.50121e25	−0.776106
$257$	−2.22110e25	−1.10223	−0.551113	−	0.834430i	$-0.685797\pi$
$257$	−2.22110e25	−1.10223	−0.551113	+	0.834430i	$0.685797\pi$
$258$	−2.63054e25	−1.25325
$259$	−3.81061e25	−1.74320
$260$	2.49476e25	1.09600
$261$	−1.73135e25	−0.730568
$262$	1.43668e25	0.582366
$263$	4.88860e25	1.90392	0.951961	−	0.306218i	$-0.0990636\pi$
$263$	4.88860e25	1.90392	0.951961	+	0.306218i	$0.0990636\pi$
$264$	1.64431e24	0.0615379
$265$	−2.11163e24	−0.0759514
$266$	1.58602e25	0.548343
$267$	−1.43212e25	−0.476005
$268$	1.66589e25	0.532393
$269$	−1.45572e25	−0.447382	−0.223691	−	0.974660i	$-0.571811\pi$
$269$	−1.45572e25	−0.447382	−0.223691	+	0.974660i	$0.571811\pi$
$270$	1.92521e25	0.569060
$271$	2.47185e25	0.702821	0.351410	−	0.936221i	$-0.385702\pi$
$271$	2.47185e25	0.702821	0.351410	+	0.936221i	$0.385702\pi$
$272$	1.87787e24	0.0513678
$273$	−2.44553e25	−0.643672
$274$	−4.56352e25	−1.15590
$275$	−1.28605e24	−0.0313518
$276$	4.35719e25	1.02250
$277$	−2.23962e25	−0.505984	−0.252992	−	0.967468i	$-0.581415\pi$
$277$	−2.23962e25	−0.505984	−0.252992	+	0.967468i	$0.581415\pi$
$278$	−9.17182e25	−1.99519
$279$	−4.73969e25	−0.992901
$280$	1.83270e25	0.369771
$281$	3.50831e25	0.681839	0.340919	−	0.940093i	$-0.389262\pi$
$281$	3.50831e25	0.681839	0.340919	+	0.940093i	$0.389262\pi$
$282$	−8.25542e23	−0.0154569
$283$	5.89425e25	1.06334	0.531669	−	0.846952i	$-0.321565\pi$
$283$	5.89425e25	1.06334	0.531669	+	0.846952i	$0.321565\pi$
$284$	8.69177e25	1.51100
$285$	4.34565e24	0.0728088
$286$	2.44301e25	0.394532
$287$	1.00269e26	1.56101
$288$	−5.92042e25	−0.888651
$289$	−5.87093e25	−0.849727
$290$	−4.64500e25	−0.648346
$291$	1.95328e25	0.262960
$292$	9.32682e25	1.21119
$293$	8.58635e25	1.07572	0.537859	−	0.843035i	$-0.319233\pi$
$293$	8.58635e25	1.07572	0.537859	+	0.843035i	$0.319233\pi$
$294$	8.08003e24	0.0976711
$295$	−2.91364e25	−0.339863
$296$	−1.48638e26	−1.67327
$297$	1.14800e25	0.124739
$298$	−6.85787e25	−0.719313
$299$	2.31617e26	2.34544
$300$	1.40351e25	0.137228
$301$	−1.74831e26	−1.65071
$302$	−2.71909e26	−2.47942
$303$	4.54755e25	0.400525
$304$	−5.75443e24	−0.0489587
$305$	2.19603e25	0.180505
$306$	−6.28975e25	−0.499526
$307$	5.72667e25	0.439490	0.219745	−	0.975557i	$-0.429477\pi$
$307$	5.72667e25	0.439490	0.219745	+	0.975557i	$0.429477\pi$
$308$	3.05447e25	0.226544
$309$	−6.47275e25	−0.464007
$310$	−1.27160e26	−0.881155
$311$	−1.59743e26	−1.07014	−0.535068	−	0.844809i	$-0.679714\pi$
$311$	−1.59743e26	−1.07014	−0.535068	+	0.844809i	$0.679714\pi$
$312$	−9.53909e25	−0.617851
$313$	1.88639e26	1.18145	0.590726	−	0.806872i	$-0.298841\pi$
$313$	1.88639e26	1.18145	0.590726	+	0.806872i	$0.298841\pi$
$314$	1.54181e26	0.933836
$315$	5.70977e25	0.334471
$316$	2.85907e26	1.61998
$317$	−2.17104e26	−1.19000	−0.594999	−	0.803726i	$-0.702848\pi$
$317$	−2.17104e26	−1.19000	−0.594999	+	0.803726i	$0.702848\pi$
$318$	2.25669e25	0.119671
$319$	−2.76982e25	−0.142118
$320$	−1.46902e26	−0.729377
$321$	−8.08656e25	−0.388562
$322$	4.75566e26	2.21169
$323$	−3.18159e25	−0.143225
$324$	1.62644e26	0.708785
$325$	7.46069e25	0.314778
$326$	4.92872e26	2.01349
$327$	−8.18679e25	−0.323864
$328$	3.91110e26	1.49839
$329$	−5.48673e24	−0.0203590
$330$	1.37439e25	0.0493986
$331$	1.21879e26	0.424361	0.212180	−	0.977231i	$-0.431944\pi$
$331$	1.21879e26	0.424361	0.212180	+	0.977231i	$0.431944\pi$
$332$	−5.77411e26	−1.94776
$333$	−4.63080e26	−1.51353
$334$	−2.65538e25	−0.0840986
$335$	4.98193e25	0.152907
$336$	1.82182e25	0.0541929
$337$	−5.13241e26	−1.47982	−0.739908	−	0.672708i	$-0.765131\pi$
$337$	−5.13241e26	−1.47982	−0.739908	+	0.672708i	$0.765131\pi$
$338$	−8.45117e26	−2.36206
$339$	9.96452e25	0.269997
$340$	−1.02755e26	−0.269945
$341$	−7.58257e25	−0.193150
$342$	1.92739e26	0.476098
$343$	4.41127e26	1.05676
$344$	−6.81952e26	−1.58449
$345$	1.30304e26	0.293668
$346$	1.06872e27	2.33649
$347$	−8.77941e25	−0.186211	−0.0931056	−	0.995656i	$-0.529679\pi$
$347$	−8.77941e25	−0.186211	−0.0931056	+	0.995656i	$0.529679\pi$
$348$	3.02281e26	0.622055
$349$	−2.22184e26	−0.443656	−0.221828	−	0.975086i	$-0.571202\pi$
$349$	−2.22184e26	−0.443656	−0.221828	+	0.975086i	$0.571202\pi$
$350$	1.53186e26	0.296828
$351$	−6.65988e26	−1.25240
$352$	−9.47150e25	−0.172870
$353$	4.65443e26	0.824579	0.412290	−	0.911053i	$-0.364729\pi$
$353$	4.65443e26	0.824579	0.412290	+	0.911053i	$0.364729\pi$
$354$	3.11379e26	0.535495
$355$	2.59931e26	0.433971
$356$	−1.03769e27	−1.68206
$357$	1.00727e26	0.158537
$358$	−1.09198e26	−0.166894
$359$	6.90600e26	1.02503	0.512513	−	0.858680i	$-0.328715\pi$
$359$	6.90600e26	1.02503	0.512513	+	0.858680i	$0.328715\pi$
$360$	2.22717e26	0.321053
$361$	−6.16715e26	−0.863493
$362$	2.19120e27	2.98018
$363$	−3.25316e26	−0.429819
$364$	−1.77198e27	−2.27454
$365$	2.78923e26	0.347863
$366$	−2.34688e26	−0.284407
$367$	2.75839e26	0.324834	0.162417	−	0.986722i	$-0.448071\pi$
$367$	2.75839e26	0.324834	0.162417	+	0.986722i	$0.448071\pi$
$368$	−1.72545e26	−0.197470
$369$	1.21850e27	1.35534
$370$	−1.24238e27	−1.34319
$371$	1.49985e26	0.157623
$372$	8.27513e26	0.845423
$373$	−1.12740e26	−0.111979	−0.0559896	−	0.998431i	$-0.517831\pi$
$373$	−1.12740e26	−0.111979	−0.0559896	+	0.998431i	$0.517831\pi$
$374$	−1.00624e26	−0.0971735
$375$	4.19725e25	0.0394127
$376$	−2.14017e25	−0.0195423
$377$	1.60685e27	1.42689
$378$	−1.36743e27	−1.18098
$379$	−1.64376e27	−1.38078	−0.690392	−	0.723435i	$-0.742562\pi$
$379$	−1.64376e27	−1.38078	−0.690392	+	0.723435i	$0.742562\pi$
$380$	3.14877e26	0.257284
$381$	8.85656e25	0.0703968
$382$	5.86832e26	0.453783
$383$	1.91710e26	0.144230	0.0721152	−	0.997396i	$-0.477025\pi$
$383$	1.91710e26	0.144230	0.0721152	+	0.997396i	$0.477025\pi$
$384$	9.06104e26	0.663285
$385$	9.13451e25	0.0650650
$386$	7.42592e26	0.514735
$387$	−2.12461e27	−1.43323
$388$	1.41531e27	0.929219
$389$	1.35529e27	0.866085	0.433043	−	0.901373i	$-0.357440\pi$
$389$	1.35529e27	0.866085	0.433043	+	0.901373i	$0.357440\pi$
$390$	−7.97321e26	−0.495969
$391$	−9.53994e26	−0.577683
$392$	2.09470e26	0.123486
$393$	−2.79598e26	−0.160477
$394$	−4.66956e27	−2.60955
$395$	8.55015e26	0.465269
$396$	3.71190e26	0.196697
$397$	−1.44638e27	−0.746416	−0.373208	−	0.927748i	$-0.621742\pi$
$397$	−1.44638e27	−0.746416	−0.373208	+	0.927748i	$0.621742\pi$
$398$	−3.56490e27	−1.79174
$399$	−3.08663e26	−0.151101
$400$	−5.55791e25	−0.0265022
$401$	−2.52848e27	−1.17448	−0.587238	−	0.809414i	$-0.699785\pi$
$401$	−2.52848e27	−1.17448	−0.587238	+	0.809414i	$0.699785\pi$
$402$	−5.32416e26	−0.240923
$403$	4.39885e27	1.93926
$404$	3.29506e27	1.41533
$405$	4.86393e26	0.203568
$406$	3.29925e27	1.34552
$407$	−7.40836e26	−0.294429
$408$	3.92900e26	0.152177
$409$	1.75503e27	0.662506	0.331253	−	0.943542i	$-0.392529\pi$
$409$	1.75503e27	0.662506	0.331253	+	0.943542i	$0.392529\pi$
$410$	3.26908e27	1.20281
$411$	8.88125e26	0.318519
$412$	−4.69002e27	−1.63966
$413$	2.06949e27	0.705324
$414$	5.77926e27	1.92030
$415$	−1.72677e27	−0.559409
$416$	5.49467e27	1.73565
$417$	1.78497e27	0.549796
$418$	3.08345e26	0.0926160
$419$	−5.97842e27	−1.75121	−0.875607	−	0.483025i	$-0.839538\pi$
$419$	−5.97842e27	−1.75121	−0.875607	+	0.483025i	$0.839538\pi$
$420$	−9.96881e26	−0.284791
$421$	3.75133e27	1.04526	0.522628	−	0.852561i	$-0.324952\pi$
$421$	3.75133e27	1.04526	0.522628	+	0.852561i	$0.324952\pi$
$422$	−7.76818e27	−2.11124
$423$	−6.66768e25	−0.0176767
$424$	5.85034e26	0.151300
$425$	−3.07294e26	−0.0775300
$426$	−2.77787e27	−0.683772
$427$	−1.55979e27	−0.374605
$428$	−5.85935e27	−1.37306
$429$	−4.75444e26	−0.108717
$430$	−5.70007e27	−1.27192
$431$	−3.07888e27	−0.670472	−0.335236	−	0.942134i	$-0.608816\pi$
$431$	−3.07888e27	−0.670472	−0.335236	+	0.942134i	$0.608816\pi$
$432$	4.96134e26	0.105443
$433$	3.70544e27	0.768629	0.384315	−	0.923202i	$-0.374438\pi$
$433$	3.70544e27	0.768629	0.384315	+	0.923202i	$0.374438\pi$
$434$	9.03190e27	1.82868
$435$	9.03983e26	0.178658
$436$	−5.93198e27	−1.14444
$437$	2.92336e27	0.550590
$438$	−2.98083e27	−0.548100
$439$	−5.53945e27	−0.994465	−0.497232	−	0.867617i	$-0.665650\pi$
$439$	−5.53945e27	−0.994465	−0.497232	+	0.867617i	$0.665650\pi$
$440$	3.56303e26	0.0624549
$441$	6.52602e26	0.111697
$442$	5.83744e27	0.975638
$443$	−6.01696e27	−0.982059	−0.491030	−	0.871143i	$-0.663379\pi$
$443$	−6.01696e27	−0.982059	−0.491030	+	0.871143i	$0.663379\pi$
$444$	8.08501e27	1.28872
$445$	−3.10324e27	−0.483099
$446$	−5.66029e27	−0.860643
$447$	1.33464e27	0.198214
$448$	1.04341e28	1.51369
$449$	−2.70237e27	−0.382964	−0.191482	−	0.981496i	$-0.561329\pi$
$449$	−2.70237e27	−0.382964	−0.191482	+	0.981496i	$0.561329\pi$
$450$	1.86157e27	0.257720
$451$	1.94936e27	0.263656
$452$	7.22008e27	0.954088
$453$	5.29172e27	0.683229
$454$	−4.43265e27	−0.559212
$455$	−5.29917e27	−0.653263
$456$	−1.20398e27	−0.145040
$457$	1.80723e27	0.212762	0.106381	−	0.994325i	$-0.466074\pi$
$457$	1.80723e27	0.212762	0.106381	+	0.994325i	$0.466074\pi$
$458$	1.30463e28	1.50107
$459$	2.74310e27	0.308466
$460$	9.44153e27	1.03773
$461$	−1.42694e28	−1.53301	−0.766507	−	0.642236i	$-0.778007\pi$
$461$	−1.42694e28	−1.53301	−0.766507	+	0.642236i	$0.778007\pi$
$462$	−9.76201e26	−0.102518
$463$	4.80416e27	0.493193	0.246596	−	0.969118i	$-0.420688\pi$
$463$	4.80416e27	0.493193	0.246596	+	0.969118i	$0.420688\pi$
$464$	−1.19704e27	−0.120135
$465$	2.47471e27	0.242811
$466$	4.49925e27	0.431607
$467$	−9.90981e27	−0.929476	−0.464738	−	0.885448i	$-0.653851\pi$
$467$	−9.90981e27	−0.929476	−0.464738	+	0.885448i	$0.653851\pi$
$468$	−2.15337e28	−1.97486
$469$	−3.53856e27	−0.317330
$470$	−1.78885e26	−0.0156873
$471$	−3.00059e27	−0.257328
$472$	8.07233e27	0.677030
$473$	−3.39896e27	−0.278807
$474$	−9.13752e27	−0.733087
$475$	9.41653e26	0.0738938
$476$	7.29848e27	0.560221
$477$	1.82267e27	0.136856
$478$	−1.86193e28	−1.36763
$479$	1.34988e28	0.970003	0.485001	−	0.874513i	$-0.338819\pi$
$479$	1.34988e28	0.970003	0.485001	+	0.874513i	$0.338819\pi$
$480$	3.09120e27	0.217317
$481$	4.29779e28	2.95612
$482$	6.78192e27	0.456414
$483$	−9.25519e27	−0.609454
$484$	−2.35717e28	−1.51885
$485$	4.23254e27	0.266878
$486$	−2.58197e28	−1.59320
$487$	2.26943e28	1.37045	0.685223	−	0.728333i	$-0.259705\pi$
$487$	2.26943e28	1.37045	0.685223	+	0.728333i	$0.259705\pi$
$488$	−6.08416e27	−0.359578
$489$	−9.59198e27	−0.554837
$490$	1.75085e27	0.0991266
$491$	2.30166e28	1.27552	0.637758	−	0.770237i	$-0.279862\pi$
$491$	2.30166e28	1.27552	0.637758	+	0.770237i	$0.279862\pi$
$492$	−2.12741e28	−1.15403
$493$	−6.61835e27	−0.351445
$494$	−1.78879e28	−0.929880
$495$	1.11006e27	0.0564926
$496$	−3.27696e27	−0.163273
$497$	−1.84623e28	−0.900627
$498$	1.84539e28	0.881416
$499$	−2.18105e28	−1.02002	−0.510011	−	0.860168i	$-0.670359\pi$
$499$	−2.18105e28	−1.02002	−0.510011	+	0.860168i	$0.670359\pi$
$500$	3.04124e27	0.139272
$501$	5.16774e26	0.0231742
$502$	7.35761e27	0.323108
$503$	6.24118e27	0.268412	0.134206	−	0.990953i	$-0.457152\pi$
$503$	6.24118e27	0.268412	0.134206	+	0.990953i	$0.457152\pi$
$504$	−1.58191e28	−0.666287
$505$	9.85401e27	0.406494
$506$	9.24567e27	0.373558
$507$	1.64472e28	0.650890
$508$	6.41728e27	0.248761
$509$	5.04618e28	1.91614	0.958068	−	0.286541i	$-0.0925054\pi$
$509$	5.04618e28	1.91614	0.958068	+	0.286541i	$0.0925054\pi$
$510$	3.28404e27	0.122158
$511$	−1.98113e28	−0.721926
$512$	−7.40008e27	−0.264181
$513$	−8.40579e27	−0.293999
$514$	5.14350e28	1.76257
$515$	−1.40257e28	−0.470921
$516$	3.70941e28	1.22035
$517$	−1.06670e26	−0.00343867
$518$	8.82440e28	2.78755
$519$	−2.07988e28	−0.643843
$520$	−2.06701e28	−0.627058
$521$	−5.72660e28	−1.70255	−0.851277	−	0.524717i	$-0.824171\pi$
$521$	−5.72660e28	−1.70255	−0.851277	+	0.524717i	$0.824171\pi$
$522$	4.00937e28	1.16825
$523$	−8.19755e27	−0.234108	−0.117054	−	0.993126i	$-0.537345\pi$
$523$	−8.19755e27	−0.234108	−0.117054	+	0.993126i	$0.537345\pi$
$524$	−2.02591e28	−0.567076
$525$	−2.98122e27	−0.0817938
$526$	−1.13207e29	−3.04456
$527$	−1.81181e28	−0.477642
$528$	3.54186e26	0.00915326
$529$	4.81850e28	1.22075
$530$	4.88999e27	0.121454
$531$	2.51493e28	0.612396
$532$	−2.23650e28	−0.533946
$533$	−1.13088e29	−2.64715
$534$	3.31642e28	0.761179
$535$	−1.75226e28	−0.394353
$536$	−1.38026e28	−0.304600
$537$	2.12514e27	0.0459894
$538$	3.37107e28	0.715408
$539$	1.04404e27	0.0217287
$540$	−2.71480e28	−0.554119
$541$	2.36289e28	0.473013	0.236506	−	0.971630i	$-0.423998\pi$
$541$	2.36289e28	0.473013	0.236506	+	0.971630i	$0.423998\pi$
$542$	−5.72417e28	−1.12388
$543$	−4.26439e28	−0.821219
$544$	−2.26316e28	−0.427492
$545$	−1.77398e28	−0.328690
$546$	5.66320e28	1.02929
$547$	3.85003e28	0.686431	0.343216	−	0.939257i	$-0.388484\pi$
$547$	3.85003e28	0.686431	0.343216	+	0.939257i	$0.388484\pi$
$548$	6.43517e28	1.12555
$549$	−1.89551e28	−0.325250
$550$	2.97815e27	0.0501347
$551$	2.02809e28	0.334962
$552$	−3.61011e28	−0.585005
$553$	−6.07299e28	−0.965581
$554$	5.18638e28	0.809118
$555$	2.41786e28	0.370130
$556$	1.29335e29	1.94281
$557$	−5.83152e27	−0.0859611	−0.0429805	−	0.999076i	$-0.513685\pi$
$557$	−5.83152e27	−0.0859611	−0.0429805	+	0.999076i	$0.513685\pi$
$558$	1.09759e29	1.58775
$559$	1.97183e29	2.79927
$560$	3.94766e27	0.0550004
$561$	1.95828e27	0.0267771
$562$	−8.12434e28	−1.09033
$563$	5.74420e28	0.756644	0.378322	−	0.925674i	$-0.376501\pi$
$563$	5.74420e28	0.756644	0.378322	+	0.925674i	$0.376501\pi$
$564$	1.16412e27	0.0150511
$565$	2.15920e28	0.274021
$566$	−1.36496e29	−1.70038
$567$	−3.45474e28	−0.422468
$568$	−7.20148e28	−0.864498
$569$	−1.19857e29	−1.41249	−0.706245	−	0.707968i	$-0.749612\pi$
$569$	−1.19857e29	−1.41249	−0.706245	+	0.707968i	$0.749612\pi$
$570$	−1.00634e28	−0.116428
$571$	−1.23798e28	−0.140616	−0.0703078	−	0.997525i	$-0.522398\pi$
$571$	−1.23798e28	−0.140616	−0.0703078	+	0.997525i	$0.522398\pi$
$572$	−3.44497e28	−0.384173
$573$	−1.14206e28	−0.125044
$574$	−2.32196e29	−2.49620
$575$	2.82353e28	0.298044
$576$	1.26799e29	1.31426
$577$	−7.16986e28	−0.729734	−0.364867	−	0.931060i	$-0.618886\pi$
$577$	−7.16986e28	−0.729734	−0.364867	+	0.931060i	$0.618886\pi$
$578$	1.35956e29	1.35880
$579$	−1.44519e28	−0.141840
$580$	6.55007e28	0.631324
$581$	1.22649e29	1.16095
$582$	−4.52330e28	−0.420498
$583$	2.91591e27	0.0266228
$584$	−7.72764e28	−0.692967
$585$	−6.43975e28	−0.567195
$586$	−1.98838e29	−1.72018
$587$	1.81827e29	1.54511	0.772554	−	0.634950i	$-0.218979\pi$
$587$	1.81827e29	1.54511	0.772554	+	0.634950i	$0.218979\pi$
$588$	−1.13939e28	−0.0951068
$589$	5.55202e28	0.455240
$590$	6.74723e28	0.543475
$591$	9.08762e28	0.719087
$592$	−3.20168e28	−0.248885
$593$	2.35655e28	0.179971	0.0899855	−	0.995943i	$-0.471318\pi$
$593$	2.35655e28	0.179971	0.0899855	+	0.995943i	$0.471318\pi$
$594$	−2.65848e28	−0.199469
$595$	2.18264e28	0.160899
$596$	9.67051e28	0.700428
$597$	6.93780e28	0.493732
$598$	−5.36366e29	−3.75058
$599$	−1.49208e29	−1.02521	−0.512603	−	0.858626i	$-0.671319\pi$
$599$	−1.49208e29	−1.02521	−0.512603	+	0.858626i	$0.671319\pi$
$600$	−1.16286e28	−0.0785127
$601$	−1.44916e29	−0.961470	−0.480735	−	0.876866i	$-0.659630\pi$
$601$	−1.44916e29	−0.961470	−0.480735	+	0.876866i	$0.659630\pi$
$602$	4.04864e29	2.63965
$603$	−4.30018e28	−0.275521
$604$	3.83427e29	2.41432
$605$	−7.04922e28	−0.436224
$606$	−1.05309e29	−0.640479
$607$	−1.00050e29	−0.598049	−0.299024	−	0.954245i	$-0.596661\pi$
$607$	−1.00050e29	−0.598049	−0.299024	+	0.954245i	$0.596661\pi$
$608$	6.93511e28	0.407442
$609$	−6.42080e28	−0.370773
$610$	−5.08543e28	−0.288645
$611$	6.18819e27	0.0345248
$612$	8.86938e28	0.486411
$613$	8.64941e28	0.466285	0.233143	−	0.972443i	$-0.425099\pi$
$613$	8.64941e28	0.466285	0.233143	+	0.972443i	$0.425099\pi$
$614$	−1.32615e29	−0.702788
$615$	−6.36209e28	−0.331445
$616$	−2.53075e28	−0.129614
$617$	2.25371e29	1.13476	0.567380	−	0.823456i	$-0.307957\pi$
$617$	2.25371e29	1.13476	0.567380	+	0.823456i	$0.307957\pi$
$618$	1.49892e29	0.741993
$619$	2.59767e28	0.126425	0.0632124	−	0.998000i	$-0.479865\pi$
$619$	2.59767e28	0.126425	0.0632124	+	0.998000i	$0.479865\pi$
$620$	1.79312e29	0.858021
$621$	−2.52046e29	−1.18582
$622$	3.69924e29	1.71125
$623$	2.20417e29	1.00258
$624$	−2.05473e28	−0.0919002
$625$	9.09495e27	0.0400000
$626$	−4.36839e29	−1.88926
$627$	−6.00083e27	−0.0255213
$628$	−2.17416e29	−0.909318
$629$	−1.77019e29	−0.728095
$630$	−1.32223e29	−0.534851
$631$	3.64093e29	1.44845	0.724226	−	0.689562i	$-0.242197\pi$
$631$	3.64093e29	1.44845	0.724226	+	0.689562i	$0.242197\pi$
$632$	−2.36885e29	−0.926847
$633$	1.51180e29	0.581774
$634$	5.02757e29	1.90292
$635$	1.91911e28	0.0714458
$636$	−3.18223e28	−0.116529
$637$	−6.05672e28	−0.218159
$638$	6.41420e28	0.227261
$639$	−2.24361e29	−0.781967
$640$	1.96342e29	0.673169
$641$	1.59229e29	0.537049	0.268525	−	0.963273i	$-0.413464\pi$
$641$	1.59229e29	0.537049	0.268525	+	0.963273i	$0.413464\pi$
$642$	1.87264e29	0.621349
$643$	−1.71642e29	−0.560283	−0.280141	−	0.959959i	$-0.590381\pi$
$643$	−1.71642e29	−0.560283	−0.280141	+	0.959959i	$0.590381\pi$
$644$	−6.70612e29	−2.15362
$645$	1.10931e29	0.350491
$646$	7.36774e28	0.229030
$647$	−5.42976e29	−1.66068	−0.830340	−	0.557257i	$-0.811854\pi$
$647$	−5.42976e29	−1.66068	−0.830340	+	0.557257i	$0.811854\pi$
$648$	−1.34757e29	−0.405521
$649$	4.02339e28	0.119130
$650$	−1.72770e29	−0.503360
$651$	−1.75774e29	−0.503910
$652$	−6.95015e29	−1.96062
$653$	2.61666e29	0.726373	0.363186	−	0.931716i	$-0.381689\pi$
$653$	2.61666e29	0.726373	0.363186	+	0.931716i	$0.381689\pi$
$654$	1.89585e29	0.517890
$655$	−6.05856e28	−0.162868
$656$	8.42456e28	0.222873
$657$	−2.40754e29	−0.626811
$658$	1.27059e28	0.0325561
$659$	−8.05602e28	−0.203153	−0.101577	−	0.994828i	$-0.532389\pi$
$659$	−8.05602e28	−0.203153	−0.101577	+	0.994828i	$0.532389\pi$
$660$	−1.93808e28	−0.0481016
$661$	1.99479e29	0.487284	0.243642	−	0.969865i	$-0.421658\pi$
$661$	1.99479e29	0.487284	0.243642	+	0.969865i	$0.421658\pi$
$662$	−2.82240e29	−0.678594
$663$	−1.13605e29	−0.268847
$664$	4.78408e29	1.11438
$665$	−6.68836e28	−0.153353
$666$	1.07237e30	2.42028
$667$	6.08119e29	1.35104
$668$	3.74444e28	0.0818906
$669$	1.10157e29	0.237159
$670$	−1.15368e29	−0.244513
$671$	−3.03245e28	−0.0632714
$672$	−2.19561e29	−0.451002
$673$	1.82510e29	0.369087	0.184544	−	0.982824i	$-0.440919\pi$
$673$	1.82510e29	0.369087	0.184544	+	0.982824i	$0.440919\pi$
$674$	1.18853e30	2.36637
$675$	−8.11872e28	−0.159147
$676$	1.19173e30	2.30005
$677$	−3.71489e29	−0.705936	−0.352968	−	0.935635i	$-0.614828\pi$
$677$	−3.71489e29	−0.705936	−0.352968	+	0.935635i	$0.614828\pi$
$678$	−2.30752e29	−0.431752
$679$	−3.00628e29	−0.553857
$680$	8.51368e28	0.154445
$681$	8.62656e28	0.154097
$682$	1.75593e29	0.308866
$683$	7.08347e28	0.122696	0.0613478	−	0.998116i	$-0.480460\pi$
$683$	7.08347e28	0.122696	0.0613478	+	0.998116i	$0.480460\pi$
$684$	−2.71788e29	−0.463598
$685$	1.92446e29	0.323265
$686$	−1.02154e30	−1.68986
$687$	−2.53900e29	−0.413635
$688$	−1.46893e29	−0.235680
$689$	−1.69160e29	−0.267297
$690$	−3.01750e29	−0.469603
$691$	−1.05962e30	−1.62417	−0.812087	−	0.583536i	$-0.801669\pi$
$691$	−1.05962e30	−1.62417	−0.812087	+	0.583536i	$0.801669\pi$
$692$	−1.50703e30	−2.27515
$693$	−7.88451e28	−0.117240
$694$	2.03308e29	0.297770
$695$	3.86781e29	0.557988
$696$	−2.50452e29	−0.355899
$697$	4.65789e29	0.651996
$698$	5.14522e29	0.709450
$699$	−8.75618e28	−0.118934
$700$	−2.16013e29	−0.289035
$701$	−7.40102e29	−0.975557	−0.487778	−	0.872968i	$-0.662193\pi$
$701$	−7.40102e29	−0.975557	−0.487778	+	0.872968i	$0.662193\pi$
$702$	1.54226e30	2.00270
$703$	5.42446e29	0.693946
$704$	2.02854e29	0.255664
$705$	3.48136e27	0.00432278
$706$	−1.07785e30	−1.31858
$707$	−6.99910e29	−0.843603
$708$	−4.39086e29	−0.521436
$709$	6.32985e29	0.740641	0.370321	−	0.928904i	$-0.379248\pi$
$709$	6.32985e29	0.740641	0.370321	+	0.928904i	$0.379248\pi$
$710$	−6.01933e29	−0.693961
$711$	−7.38012e29	−0.838364
$712$	8.59764e29	0.962364
$713$	1.66476e30	1.83617
$714$	−2.33258e29	−0.253516
$715$	−1.03023e29	−0.110337
$716$	1.53983e29	0.162513
$717$	3.62357e29	0.376865
$718$	−1.59925e30	−1.63912
$719$	1.45847e30	1.47314	0.736569	−	0.676362i	$-0.236445\pi$
$719$	1.45847e30	1.47314	0.736569	+	0.676362i	$0.236445\pi$
$720$	4.79735e28	0.0477540
$721$	9.96215e29	0.977311
$722$	1.42815e30	1.38081
$723$	−1.31986e29	−0.125769
$724$	−3.08989e30	−2.90194
$725$	1.95883e29	0.181321
$726$	7.53347e29	0.687323
$727$	3.68387e29	0.331278	0.165639	−	0.986186i	$-0.447031\pi$
$727$	3.68387e29	0.331278	0.165639	+	0.986186i	$0.447031\pi$
$728$	1.46815e30	1.30134
$729$	−1.85064e28	−0.0161690
$730$	−6.45912e29	−0.556267
$731$	−8.12164e29	−0.689463
$732$	3.30942e29	0.276940
$733$	−3.10836e29	−0.256412	−0.128206	−	0.991748i	$-0.540922\pi$
$733$	−3.10836e29	−0.256412	−0.128206	+	0.991748i	$0.540922\pi$
$734$	−6.38771e29	−0.519442
$735$	−3.40740e28	−0.0273153
$736$	2.07948e30	1.64338
$737$	−6.87944e28	−0.0535975
$738$	−2.82173e30	−2.16732
$739$	9.09413e29	0.688644	0.344322	−	0.938852i	$-0.388109\pi$
$739$	9.09413e29	0.688644	0.344322	+	0.938852i	$0.388109\pi$
$740$	1.75193e30	1.30793
$741$	3.48124e29	0.256238
$742$	−3.47325e29	−0.252055
$743$	−2.27536e30	−1.62805	−0.814023	−	0.580832i	$-0.802727\pi$
$743$	−2.27536e30	−1.62805	−0.814023	+	0.580832i	$0.802727\pi$
$744$	−6.85627e29	−0.483696
$745$	2.89200e29	0.201168
$746$	2.61078e29	0.179066
$747$	1.49047e30	1.00799
$748$	1.41893e29	0.0946222
$749$	1.24460e30	0.818407
$750$	−9.71974e28	−0.0630248
$751$	−5.99587e29	−0.383383	−0.191691	−	0.981455i	$-0.561397\pi$
$751$	−5.99587e29	−0.383383	−0.191691	+	0.981455i	$0.561397\pi$
$752$	−4.60995e27	−0.00290676
$753$	−1.43190e29	−0.0890357
$754$	−3.72104e30	−2.28174
$755$	1.14666e30	0.693410
$756$	1.92826e30	1.14997
$757$	−7.12708e29	−0.419184	−0.209592	−	0.977789i	$-0.567214\pi$
$757$	−7.12708e29	−0.419184	−0.209592	+	0.977789i	$0.567214\pi$
$758$	3.80651e30	2.20801
$759$	−1.79934e29	−0.102938
$760$	−2.60888e29	−0.147201
$761$	−2.19781e29	−0.122307	−0.0611534	−	0.998128i	$-0.519478\pi$
$761$	−2.19781e29	−0.122307	−0.0611534	+	0.998128i	$0.519478\pi$
$762$	−2.05095e29	−0.112571
$763$	1.26002e30	0.682135
$764$	−8.27511e29	−0.441869
$765$	2.65243e29	0.139701
$766$	−4.43950e29	−0.230639
$767$	−2.33407e30	−1.19609
$768$	−6.76558e29	−0.341989
$769$	−2.98360e30	−1.48770	−0.743848	−	0.668349i	$-0.767001\pi$
$769$	−2.98360e30	−1.48770	−0.743848	+	0.668349i	$0.767001\pi$
$770$	−2.11532e29	−0.104045
$771$	−1.00100e30	−0.485693
$772$	−1.04715e30	−0.501221
$773$	−1.85756e30	−0.877119	−0.438560	−	0.898702i	$-0.644511\pi$
$773$	−1.85756e30	−0.877119	−0.438560	+	0.898702i	$0.644511\pi$
$774$	4.92005e30	2.29187
$775$	5.36241e29	0.246429
$776$	−1.17264e30	−0.531639
$777$	−1.71735e30	−0.768137
$778$	−3.13849e30	−1.38495
$779$	−1.42734e30	−0.621417
$780$	1.12433e30	0.482948
$781$	−3.58934e29	−0.152117
$782$	2.20920e30	0.923772
$783$	−1.74857e30	−0.721415
$784$	4.51201e28	0.0183676
$785$	−6.50192e29	−0.261162
$786$	6.47476e29	0.256618
$787$	−8.13402e29	−0.318105	−0.159053	−	0.987270i	$-0.550844\pi$
$787$	−8.13402e29	−0.318105	−0.159053	+	0.987270i	$0.550844\pi$
$788$	6.58470e30	2.54104
$789$	2.20318e30	0.838959
$790$	−1.97999e30	−0.744011
$791$	−1.53363e30	−0.568680
$792$	−3.07546e29	−0.112537
$793$	1.75920e30	0.635255
$794$	3.34943e30	1.19359
$795$	−9.51661e28	−0.0334678
$796$	5.02698e30	1.74470
$797$	2.24419e30	0.768683	0.384341	−	0.923191i	$-0.374429\pi$
$797$	2.24419e30	0.768683	0.384341	+	0.923191i	$0.374429\pi$
$798$	7.14783e29	0.241626
$799$	−2.54882e28	−0.00850349
$800$	6.69827e29	0.220555
$801$	2.67859e30	0.870491
$802$	5.85531e30	1.87810
$803$	−3.85159e29	−0.121934
$804$	7.50778e29	0.234597
$805$	−2.00549e30	−0.618535
$806$	−1.01866e31	−3.10107
$807$	−6.56057e29	−0.197138
$808$	−2.73009e30	−0.809762
$809$	−2.58920e30	−0.758063	−0.379032	−	0.925384i	$-0.623743\pi$
$809$	−2.58920e30	−0.758063	−0.379032	+	0.925384i	$0.623743\pi$
$810$	−1.12636e30	−0.325525
$811$	5.80298e30	1.65551	0.827755	−	0.561090i	$-0.189618\pi$
$811$	5.80298e30	1.65551	0.827755	+	0.561090i	$0.189618\pi$
$812$	−4.65238e30	−1.31020
$813$	1.11400e30	0.309696
$814$	1.71559e30	0.470821
$815$	−2.07847e30	−0.563105
$816$	8.46309e28	0.0226351
$817$	2.48875e30	0.657127
$818$	−4.06420e30	−1.05941
$819$	4.57401e30	1.17711
$820$	−4.60984e30	−1.17123
$821$	−5.43394e30	−1.36305	−0.681525	−	0.731795i	$-0.738683\pi$
$821$	−5.43394e30	−1.36305	−0.681525	+	0.731795i	$0.738683\pi$
$822$	−2.05667e30	−0.509343
$823$	6.93165e30	1.69488	0.847439	−	0.530893i	$-0.178144\pi$
$823$	6.93165e30	1.69488	0.847439	+	0.530893i	$0.178144\pi$
$824$	3.88587e30	0.938107
$825$	−5.79590e28	−0.0138151
$826$	−4.79241e30	−1.12788
$827$	3.90494e30	0.907417	0.453708	−	0.891150i	$-0.350101\pi$
$827$	3.90494e30	0.907417	0.453708	+	0.891150i	$0.350101\pi$
$828$	−8.14952e30	−1.86988
$829$	8.90933e28	0.0201847	0.0100924	−	0.999949i	$-0.496787\pi$
$829$	8.90933e28	0.0201847	0.0100924	+	0.999949i	$0.496787\pi$
$830$	3.99875e30	0.894550
$831$	−1.00934e30	−0.222961
$832$	−1.17681e31	−2.56691
$833$	2.49467e29	0.0537329
$834$	−4.13352e30	−0.879177
$835$	1.11979e29	0.0235195
$836$	−4.34808e29	−0.0901844
$837$	−4.78683e30	−0.980461
$838$	1.38445e31	2.80036
$839$	−7.03003e30	−1.40429	−0.702145	−	0.712034i	$-0.747774\pi$
$839$	−7.03003e30	−1.40429	−0.702145	+	0.712034i	$0.747774\pi$
$840$	8.25956e29	0.162939
$841$	−9.14014e29	−0.178072
$842$	−8.68710e30	−1.67147
$843$	1.58111e30	0.300450
$844$	1.09542e31	2.05581
$845$	3.56391e30	0.660589
$846$	1.54406e29	0.0282667
$847$	5.00691e30	0.905303
$848$	1.26017e29	0.0225047
$849$	2.65640e30	0.468557
$850$	7.11613e29	0.123978
$851$	1.62652e31	2.79897
$852$	3.91717e30	0.665820
$853$	−5.57196e30	−0.935499	−0.467749	−	0.883861i	$-0.654935\pi$
$853$	−5.57196e30	−0.935499	−0.467749	+	0.883861i	$0.654935\pi$
$854$	3.61207e30	0.599030
$855$	−8.12794e29	−0.133149
$856$	4.85471e30	0.785576
$857$	−1.72389e30	−0.275557	−0.137779	−	0.990463i	$-0.543996\pi$
$857$	−1.72389e30	−0.275557	−0.137779	+	0.990463i	$0.543996\pi$
$858$	1.10101e30	0.173849
$859$	−9.93204e30	−1.54921	−0.774605	−	0.632445i	$-0.782051\pi$
$859$	−9.93204e30	−1.54921	−0.774605	+	0.632445i	$0.782051\pi$
$860$	8.03786e30	1.23853
$861$	4.51886e30	0.687853
$862$	7.12988e30	1.07215
$863$	−1.40958e30	−0.209400	−0.104700	−	0.994504i	$-0.533388\pi$
$863$	−1.40958e30	−0.209400	−0.104700	+	0.994504i	$0.533388\pi$
$864$	−5.97929e30	−0.877517
$865$	−4.50685e30	−0.653437
$866$	−8.58084e30	−1.22911
$867$	−2.64589e30	−0.374430
$868$	−1.27362e31	−1.78066
$869$	−1.18067e30	−0.163088
$870$	−2.09339e30	−0.285692
$871$	3.99095e30	0.538128
$872$	4.91488e30	0.654772
$873$	−3.65335e30	−0.480885
$874$	−6.76976e30	−0.880446
$875$	−6.45995e29	−0.0830127
$876$	4.20337e30	0.533710
$877$	−5.80927e30	−0.728829	−0.364414	−	0.931237i	$-0.618731\pi$
$877$	−5.80927e30	−0.728829	−0.364414	+	0.931237i	$0.618731\pi$
$878$	1.28279e31	1.59025
$879$	3.86966e30	0.474012
$880$	7.67481e28	0.00928965
$881$	−6.39976e30	−0.765450	−0.382725	−	0.923862i	$-0.625014\pi$
$881$	−6.39976e30	−0.765450	−0.382725	+	0.923862i	$0.625014\pi$
$882$	−1.51126e30	−0.178615
$883$	−8.20502e30	−0.958280	−0.479140	−	0.877739i	$-0.659051\pi$
$883$	−8.20502e30	−0.958280	−0.479140	+	0.877739i	$0.659051\pi$
$884$	−8.23157e30	−0.950022
$885$	−1.31311e30	−0.149760
$886$	1.39337e31	1.57041
$887$	1.01230e31	1.12749	0.563744	−	0.825950i	$-0.309361\pi$
$887$	1.01230e31	1.12749	0.563744	+	0.825950i	$0.309361\pi$
$888$	−6.69875e30	−0.737323
$889$	−1.36311e30	−0.148273
$890$	7.18631e30	0.772522
$891$	−6.71650e29	−0.0713555
$892$	7.98177e30	0.838047
$893$	7.81044e28	0.00810467
$894$	−3.09067e30	−0.316964
$895$	4.60493e29	0.0466747
$896$	−1.39458e31	−1.39704
$897$	1.04384e31	1.03351
$898$	6.25799e30	0.612397
$899$	1.15493e31	1.11707
$900$	−2.62506e30	−0.250954
$901$	6.96741e29	0.0658356
$902$	−4.51421e30	−0.421612
$903$	−7.87922e30	−0.727381
$904$	−5.98213e30	−0.545867
$905$	−9.24044e30	−0.833456
$906$	−1.22543e31	−1.09255
$907$	−2.61002e29	−0.0230021	−0.0115010	−	0.999934i	$-0.503661\pi$
$907$	−2.61002e29	−0.0230021	−0.0115010	+	0.999934i	$0.503661\pi$
$908$	6.25062e30	0.544530
$909$	−8.50556e30	−0.732457
$910$	1.22715e31	1.04463
$911$	−1.15850e31	−0.974880	−0.487440	−	0.873156i	$-0.662069\pi$
$911$	−1.15850e31	−0.974880	−0.487440	+	0.873156i	$0.662069\pi$
$912$	−2.59338e29	−0.0215735
$913$	2.38446e30	0.196086
$914$	−4.18509e30	−0.340227
$915$	9.89696e29	0.0795390
$916$	−1.83971e31	−1.46166
$917$	4.30327e30	0.338003
$918$	−6.35230e30	−0.493268
$919$	−2.64591e30	−0.203124	−0.101562	−	0.994829i	$-0.532384\pi$
$919$	−2.64591e30	−0.203124	−0.101562	+	0.994829i	$0.532384\pi$
$920$	−7.82269e30	−0.593723
$921$	2.58087e30	0.193660
$922$	3.30443e31	2.45144
$923$	2.08227e31	1.52728
$924$	1.37657e30	0.0998261
$925$	5.23921e30	0.375645
$926$	−1.11252e31	−0.788663
$927$	1.21064e31	0.848549
$928$	1.44264e31	0.999780
$929$	3.27326e30	0.224293	0.112147	−	0.993692i	$-0.464227\pi$
$929$	3.27326e30	0.224293	0.112147	+	0.993692i	$0.464227\pi$
$930$	−5.73079e30	−0.388279
$931$	−7.64451e29	−0.0512127
$932$	−6.34455e30	−0.420275
$933$	−7.19925e30	−0.471552
$934$	2.29485e31	1.48632
$935$	4.24336e29	0.0271761
$936$	1.78415e31	1.12989
$937$	−2.13717e31	−1.33836	−0.669181	−	0.743100i	$-0.733355\pi$
$937$	−2.13717e31	−1.33836	−0.669181	+	0.743100i	$0.733355\pi$
$938$	8.19438e30	0.507442
$939$	8.50151e30	0.520604
$940$	2.52252e29	0.0152754
$941$	5.44605e30	0.326130	0.163065	−	0.986615i	$-0.447862\pi$
$941$	5.44605e30	0.326130	0.163065	+	0.986615i	$0.447862\pi$
$942$	6.94858e30	0.411492
$943$	−4.27984e31	−2.50643
$944$	1.73879e30	0.100703
$945$	5.76656e30	0.330280
$946$	7.87111e30	0.445840
$947$	−6.51801e30	−0.365124	−0.182562	−	0.983194i	$-0.558439\pi$
$947$	−6.51801e30	−0.365124	−0.182562	+	0.983194i	$0.558439\pi$
$948$	1.28851e31	0.713840
$949$	2.23441e31	1.22424
$950$	−2.18062e30	−0.118163
$951$	−9.78437e30	−0.524369
$952$	−6.04708e30	−0.320522
$953$	−3.14795e30	−0.165026	−0.0825130	−	0.996590i	$-0.526295\pi$
$953$	−3.14795e30	−0.165026	−0.0825130	+	0.996590i	$0.526295\pi$
$954$	−4.22083e30	−0.218846
$955$	−2.47471e30	−0.126908
$956$	2.62557e31	1.33173
$957$	−1.24829e30	−0.0626241
$958$	−3.12598e31	−1.55113
$959$	−1.36691e31	−0.670878
$960$	−6.62051e30	−0.321398
$961$	1.07915e31	0.518185
$962$	−9.95256e31	−4.72712
$963$	1.51248e31	0.710580
$964$	−9.56341e30	−0.444431
$965$	−3.13156e30	−0.143954
$966$	2.14326e31	0.974576
$967$	−1.41219e31	−0.635208	−0.317604	−	0.948223i	$-0.602878\pi$
$967$	−1.41219e31	−0.635208	−0.317604	+	0.948223i	$0.602878\pi$
$968$	1.95301e31	0.868987
$969$	−1.43387e30	−0.0631116
$970$	−9.80147e30	−0.426764
$971$	1.28654e31	0.554141	0.277071	−	0.960850i	$-0.410636\pi$
$971$	1.28654e31	0.554141	0.277071	+	0.960850i	$0.410636\pi$
$972$	3.64093e31	1.55137
$973$	−2.74723e31	−1.15800
$974$	−5.25541e31	−2.19148
$975$	3.36235e30	0.138706
$976$	−1.31054e30	−0.0534842
$977$	2.31062e30	0.0932902	0.0466451	−	0.998912i	$-0.485147\pi$
$977$	2.31062e30	0.0932902	0.0466451	+	0.998912i	$0.485147\pi$
$978$	2.22125e31	0.887238
$979$	4.28521e30	0.169338
$980$	−2.46893e30	−0.0965240
$981$	1.53123e31	0.592263
$982$	−5.33005e31	−2.03968
$983$	1.18550e31	0.448840	0.224420	−	0.974493i	$-0.427951\pi$
$983$	1.18550e31	0.448840	0.224420	+	0.974493i	$0.427951\pi$
$984$	1.76264e31	0.660260
$985$	1.96918e31	0.729803
$986$	1.53264e31	0.561994
$987$	−2.47274e29	−0.00897115
$988$	2.52243e31	0.905466
$989$	7.46246e31	2.65046
$990$	−2.57061e30	−0.0903372
$991$	−3.83008e31	−1.33179	−0.665893	−	0.746047i	$-0.731949\pi$
$991$	−3.83008e31	−1.33179	−0.665893	+	0.746047i	$0.731949\pi$
$992$	3.94932e31	1.35878
$993$	5.49280e30	0.186993
$994$	4.27540e31	1.44019
$995$	1.50334e31	0.501089
$996$	−2.60225e31	−0.858274
$997$	4.80076e30	0.156679	0.0783396	−	0.996927i	$-0.475038\pi$
$997$	4.80076e30	0.156679	0.0783396	+	0.996927i	$0.475038\pi$
$998$	5.05074e31	1.63112
$999$	−4.67685e31	−1.49457

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.22.a.b.1.1	✓	4
3.2	odd	2		45.22.a.f.1.4		4
4.3	odd	2		80.22.a.g.1.3		4
5.2	odd	4		25.22.b.c.24.3		8
5.3	odd	4		25.22.b.c.24.6		8
5.4	even	2		25.22.a.c.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.22.a.b.1.1	✓	4	1.1	even	1	trivial
25.22.a.c.1.4		4	5.4	even	2
25.22.b.c.24.3		8	5.2	odd	4
25.22.b.c.24.6		8	5.3	odd	4
45.22.a.f.1.4		4	3.2	odd	2
80.22.a.g.1.3		4	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 22 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q-2315.74 q^{2} +45067.6 q^{3} +3.26550e6 q^{4} +9.76562e6 q^{5} -1.04365e8 q^{6} -6.93632e8 q^{7} -2.70560e9 q^{8} -8.42927e9 q^{9} +O(q^{10})\)	\(q-2315.74 q^{2} +45067.6 q^{3} +3.26550e6 q^{4} +9.76562e6 q^{5} -1.04365e8 q^{6} -6.93632e8 q^{7} -2.70560e9 q^{8} -8.42927e9 q^{9} -2.26147e10 q^{10} -1.34852e10 q^{11} +1.47168e11 q^{12} +7.82310e11 q^{13} +1.60627e12 q^{14} +4.40113e11 q^{15} -5.82789e11 q^{16} -3.22221e12 q^{17} +1.95200e13 q^{18} +9.87395e12 q^{19} +3.18897e13 q^{20} -3.12603e13 q^{21} +3.12281e13 q^{22} +2.96069e14 q^{23} -1.21935e14 q^{24} +9.53674e13 q^{25} -1.81163e15 q^{26} -8.51310e14 q^{27} -2.26506e15 q^{28} +2.05398e15 q^{29} -1.01919e15 q^{30} +5.62290e15 q^{31} +7.02364e15 q^{32} -6.07744e14 q^{33} +7.46180e15 q^{34} -6.77375e15 q^{35} -2.75258e16 q^{36} +5.49371e16 q^{37} -2.28655e16 q^{38} +3.52568e16 q^{39} -2.64219e16 q^{40} -1.44556e17 q^{41} +7.23908e16 q^{42} +2.52052e17 q^{43} -4.40359e16 q^{44} -8.23170e16 q^{45} -6.85618e17 q^{46} +7.91015e15 q^{47} -2.62649e16 q^{48} -7.74210e16 q^{49} -2.20846e17 q^{50} -1.45217e17 q^{51} +2.55464e18 q^{52} -2.16231e17 q^{53} +1.97141e18 q^{54} -1.31691e17 q^{55} +1.87669e18 q^{56} +4.44995e17 q^{57} -4.75648e18 q^{58} -2.98356e18 q^{59} +1.43719e18 q^{60} +2.24873e18 q^{61} -1.30212e19 q^{62} +5.84681e18 q^{63} -1.50427e19 q^{64} +7.63975e18 q^{65} +1.40738e18 q^{66} +5.10149e18 q^{67} -1.05221e19 q^{68} +1.33431e19 q^{69} +1.56862e19 q^{70} +2.66169e19 q^{71} +2.28062e19 q^{72} +2.85617e19 q^{73} -1.27220e20 q^{74} +4.29798e18 q^{75} +3.22434e19 q^{76} +9.35374e18 q^{77} -8.16457e19 q^{78} +8.75536e19 q^{79} -5.69130e18 q^{80} +4.98066e19 q^{81} +3.34754e20 q^{82} -1.76821e20 q^{83} -1.02081e20 q^{84} -3.14669e19 q^{85} -5.83687e20 q^{86} +9.25679e19 q^{87} +3.64855e19 q^{88} -3.17772e20 q^{89} +1.90625e20 q^{90} -5.42635e20 q^{91} +9.66813e20 q^{92} +2.53410e20 q^{93} -1.83179e19 q^{94} +9.64253e19 q^{95} +3.16539e20 q^{96} +4.33412e20 q^{97} +1.79287e20 q^{98} +1.13670e20 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2910 q^{2} + 83240 q^{3} + 9165268 q^{4} + 39062500 q^{5} - 158524712 q^{6} + 512613800 q^{7} + 5167363080 q^{8} + 21732888532 q^{9}+O(q^{10}) \) 4 * q + 2910 * q^2 + 83240 * q^3 + 9165268 * q^4 + 39062500 * q^5 - 158524712 * q^6 + 512613800 * q^7 + 5167363080 * q^8 + 21732888532 * q^9	\( 4 q + 2910 q^{2} + 83240 q^{3} + 9165268 q^{4} + 39062500 q^{5} - 158524712 q^{6} + 512613800 q^{7} + 5167363080 q^{8} + 21732888532 q^{9} + 28417968750 q^{10} + 33727076448 q^{11} - 142435377680 q^{12} + 863532165080 q^{13} + 2725405637616 q^{14} + 812890625000 q^{15} + 9168135122704 q^{16} + 17694691101480 q^{17} + 108219081471590 q^{18} + 65217596849840 q^{19} + 89504570312500 q^{20} - 248634744508992 q^{21} - 133302721028280 q^{22} + 306130984922520 q^{23} - 509427036802080 q^{24} + 381469726562500 q^{25} - 19\!\cdots\!12 q^{26}+ \cdots - 15\!\cdots\!16 q^{99}+O(q^{100}) \) 4 * q + 2910 * q^2 + 83240 * q^3 + 9165268 * q^4 + 39062500 * q^5 - 158524712 * q^6 + 512613800 * q^7 + 5167363080 * q^8 + 21732888532 * q^9 + 28417968750 * q^10 + 33727076448 * q^11 - 142435377680 * q^12 + 863532165080 * q^13 + 2725405637616 * q^14 + 812890625000 * q^15 + 9168135122704 * q^16 + 17694691101480 * q^17 + 108219081471590 * q^18 + 65217596849840 * q^19 + 89504570312500 * q^20 - 248634744508992 * q^21 - 133302721028280 * q^22 + 306130984922520 * q^23 - 509427036802080 * q^24 + 381469726562500 * q^25 - 1909802985226812 * q^26 - 3478503990916720 * q^27 - 2466701432057920 * q^28 - 1183867881941640 * q^29 - 1548092890625000 * q^30 + 8127647981305328 * q^31 + 6394106775900960 * q^32 - 27227776360130720 * q^33 + 32676043106528796 * q^34 + 5005994140625000 * q^35 + 132603401899613444 * q^36 + 50729262881561240 * q^37 + 35369554723756920 * q^38 - 90408012787467856 * q^39 + 50462530078125000 * q^40 - 151242912792059832 * q^41 - 584170109040328320 * q^42 + 195241056541629800 * q^43 - 614844690548787984 * q^44 + 212235239570312500 * q^45 - 156055372897688112 * q^46 - 461921266212226680 * q^47 - 268908035207420480 * q^48 + 348492786998301828 * q^49 + 277519226074218750 * q^50 + 3394366189837348048 * q^51 + 2124030127334250200 * q^52 + 1013253578565011640 * q^53 - 2325284713297481360 * q^54 + 329365980937500000 * q^55 + 3133890122325795840 * q^56 + 6889753607884864160 * q^57 - 15566576922395873820 * q^58 + 9994246603380823920 * q^59 - 1390970485156250000 * q^60 - 10817434481929098952 * q^61 + 3855611474231219520 * q^62 + 12245908869990535560 * q^63 - 45099981493147646912 * q^64 + 8432931299609375000 * q^65 - 81535658477725195744 * q^66 + 21966891437417653880 * q^67 - 2003292237110276760 * q^68 - 10872182089324606656 * q^69 + 26615289429843750000 * q^70 + 51295204524235287888 * q^71 + 203807399727091870440 * q^72 + 74737166154487034120 * q^73 - 95273704374004345644 * q^74 + 7938385009765625000 * q^75 + 33053497281514492880 * q^76 + 284152911785269322400 * q^77 - 411161554685929127600 * q^78 - 60935090437726582240 * q^79 + 89532569557656250000 * q^80 + 158163684388294667524 * q^81 + 209310572847889648620 * q^82 - 278730291142551479640 * q^83 - 1305319136534979185664 * q^84 + 172799717787890625000 * q^85 - 410177137146579139512 * q^86 + 180742525444629646640 * q^87 - 407444351717354555040 * q^88 - 323651892724949032920 * q^89 + 1056826967495996093750 * q^90 + 220855101702096981808 * q^91 + 2407334022772179833280 * q^92 + 193462123423446842880 * q^93 - 1285026294005215311264 * q^94 + 636890594236718750000 * q^95 - 20769436930632372352 * q^96 + 309141974076136362920 * q^97 + 746323122131488476270 * q^98 - 1516374777085318976416 * q^99

Introduction

L-functions

Modular forms

Varieties

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