LMFDB - Embedded newform 29.12.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,12,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 12, names="a")

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

chi := DirichletCharacter("29.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 12 $
Character orbit:	$[\chi]$	$=$	29.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:	$22.2819522362$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 23517 x^{12} - 42196 x^{11} + 214206700 x^{10} + 532863376 x^{9} - 951901011680 x^{8} + \cdots + 30\!\cdots\!04 $ x^14 - 23517x^12 - 42196x^11 + 214206700x^10 + 532863376x^9 - 951901011680x^8 - 1439668569088x^7 + 2125122050961664x^6 - 3617975849298944x^5 - 2179155305696991232x^4 + 15507015861824716800x^3 + 709645914927917694976x^2 - 9478460460037847384064x + 30797548279705794248704
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Root			$73.5071$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+73.5071 q^{2} +274.559 q^{3} +3355.30 q^{4} +7553.66 q^{5} +20182.1 q^{6} +46751.0 q^{7} +96095.7 q^{8} -101764. q^{9} +O(q^{10})$	\(q+73.5071 q^{2} +274.559 q^{3} +3355.30 q^{4} +7553.66 q^{5} +20182.1 q^{6} +46751.0 q^{7} +96095.7 q^{8} -101764. q^{9} +555248. q^{10} -91973.4 q^{11} +921228. q^{12} -1.62005e6 q^{13} +3.43653e6 q^{14} +2.07393e6 q^{15} +192069. q^{16} +5.89907e6 q^{17} -7.48039e6 q^{18} +3.33185e6 q^{19} +2.53448e7 q^{20} +1.28359e7 q^{21} -6.76070e6 q^{22} +2.81261e7 q^{23} +2.63840e7 q^{24} +8.22966e6 q^{25} -1.19085e8 q^{26} -7.65777e7 q^{27} +1.56863e8 q^{28} -2.05111e7 q^{29} +1.52448e8 q^{30} -1.31553e8 q^{31} -1.82686e8 q^{32} -2.52521e7 q^{33} +4.33623e8 q^{34} +3.53141e8 q^{35} -3.41449e8 q^{36} +8.54978e7 q^{37} +2.44915e8 q^{38} -4.44801e8 q^{39} +7.25874e8 q^{40} +1.41332e9 q^{41} +9.43532e8 q^{42} -2.61617e8 q^{43} -3.08598e8 q^{44} -7.68692e8 q^{45} +2.06747e9 q^{46} -1.99976e9 q^{47} +5.27344e7 q^{48} +2.08329e8 q^{49} +6.04939e8 q^{50} +1.61964e9 q^{51} -5.43576e9 q^{52} +1.74642e8 q^{53} -5.62900e9 q^{54} -6.94736e8 q^{55} +4.49257e9 q^{56} +9.14790e8 q^{57} -1.50772e9 q^{58} -6.44946e9 q^{59} +6.95865e9 q^{60} -7.14586e9 q^{61} -9.67010e9 q^{62} -4.75758e9 q^{63} -1.38220e10 q^{64} -1.22373e10 q^{65} -1.85621e9 q^{66} -3.96759e9 q^{67} +1.97931e10 q^{68} +7.72229e9 q^{69} +2.59584e10 q^{70} -8.71659e9 q^{71} -9.77910e9 q^{72} +1.16541e10 q^{73} +6.28470e9 q^{74} +2.25953e9 q^{75} +1.11793e10 q^{76} -4.29985e9 q^{77} -3.26960e10 q^{78} +3.00987e10 q^{79} +1.45082e9 q^{80} -2.99790e9 q^{81} +1.03889e11 q^{82} +4.75530e10 q^{83} +4.30683e10 q^{84} +4.45595e10 q^{85} -1.92307e10 q^{86} -5.63153e9 q^{87} -8.83824e9 q^{88} -6.59856e10 q^{89} -5.65043e10 q^{90} -7.57391e10 q^{91} +9.43715e10 q^{92} -3.61192e10 q^{93} -1.46997e11 q^{94} +2.51676e10 q^{95} -5.01580e10 q^{96} -1.15407e11 q^{97} +1.53136e10 q^{98} +9.35959e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9}+O(q^{10}) $ 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9} + 713576 q^{10} + 398020 q^{11} - 4026800 q^{12} + 2272440 q^{13} - 7199712 q^{14} - 4763864 q^{15} + 19015138 q^{16} + 5623508 q^{17} - 204156 q^{18} + 29803300 q^{19} + 65161006 q^{20} + 51227832 q^{21} + 167334266 q^{22} + 52654304 q^{23} + 221514842 q^{24} + 194970462 q^{25} + 373581536 q^{26} + 397348256 q^{27} + 319501772 q^{28} - 287156086 q^{29} + 423014226 q^{30} + 634041348 q^{31} + 1260290884 q^{32} + 1180833420 q^{33} + 1316105060 q^{34} + 1599853768 q^{35} + 3198076132 q^{36} + 488665204 q^{37} + 1892845072 q^{38} + 1972619104 q^{39} + 1826486880 q^{40} + 198215164 q^{41} + 1011384468 q^{42} + 2193188100 q^{43} + 26522720 q^{44} - 1129321956 q^{45} - 1567525268 q^{46} - 4175934476 q^{47} - 15582938120 q^{48} + 1105222462 q^{49} - 6630582612 q^{50} + 3297462720 q^{51} - 4557341374 q^{52} - 13223081840 q^{53} - 8946135054 q^{54} - 2726359424 q^{55} - 27538267872 q^{56} - 24477013312 q^{57} + 352219640 q^{59} - 36042747924 q^{60} - 7658546476 q^{61} - 10024135594 q^{62} - 23037581736 q^{63} + 14721327762 q^{64} + 1152802884 q^{65} - 99505241364 q^{66} + 21781534280 q^{67} - 104178000188 q^{68} - 14601399408 q^{69} - 67948872984 q^{70} - 5573287168 q^{71} - 24062143544 q^{72} + 39661511924 q^{73} + 28506052056 q^{74} + 81845109044 q^{75} + 166950090320 q^{76} + 38773567192 q^{77} + 54249159006 q^{78} + 105565209020 q^{79} + 146242150550 q^{80} + 170581084750 q^{81} + 47345182756 q^{82} + 127846064024 q^{83} + 215311861496 q^{84} + 83883234552 q^{85} - 103162039382 q^{86} - 9763306924 q^{87} + 418253082102 q^{88} + 187826099404 q^{89} + 96335639960 q^{90} + 58390389864 q^{91} - 259645875396 q^{92} + 394641636020 q^{93} + 117694719934 q^{94} + 69935059424 q^{95} + 12533631786 q^{96} + 137285937500 q^{97} - 484896369168 q^{98} + 235419947204 q^{99}+O(q^{100}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9 + 713576 * q^10 + 398020 * q^11 - 4026800 * q^12 + 2272440 * q^13 - 7199712 * q^14 - 4763864 * q^15 + 19015138 * q^16 + 5623508 * q^17 - 204156 * q^18 + 29803300 * q^19 + 65161006 * q^20 + 51227832 * q^21 + 167334266 * q^22 + 52654304 * q^23 + 221514842 * q^24 + 194970462 * q^25 + 373581536 * q^26 + 397348256 * q^27 + 319501772 * q^28 - 287156086 * q^29 + 423014226 * q^30 + 634041348 * q^31 + 1260290884 * q^32 + 1180833420 * q^33 + 1316105060 * q^34 + 1599853768 * q^35 + 3198076132 * q^36 + 488665204 * q^37 + 1892845072 * q^38 + 1972619104 * q^39 + 1826486880 * q^40 + 198215164 * q^41 + 1011384468 * q^42 + 2193188100 * q^43 + 26522720 * q^44 - 1129321956 * q^45 - 1567525268 * q^46 - 4175934476 * q^47 - 15582938120 * q^48 + 1105222462 * q^49 - 6630582612 * q^50 + 3297462720 * q^51 - 4557341374 * q^52 - 13223081840 * q^53 - 8946135054 * q^54 - 2726359424 * q^55 - 27538267872 * q^56 - 24477013312 * q^57 + 352219640 * q^59 - 36042747924 * q^60 - 7658546476 * q^61 - 10024135594 * q^62 - 23037581736 * q^63 + 14721327762 * q^64 + 1152802884 * q^65 - 99505241364 * q^66 + 21781534280 * q^67 - 104178000188 * q^68 - 14601399408 * q^69 - 67948872984 * q^70 - 5573287168 * q^71 - 24062143544 * q^72 + 39661511924 * q^73 + 28506052056 * q^74 + 81845109044 * q^75 + 166950090320 * q^76 + 38773567192 * q^77 + 54249159006 * q^78 + 105565209020 * q^79 + 146242150550 * q^80 + 170581084750 * q^81 + 47345182756 * q^82 + 127846064024 * q^83 + 215311861496 * q^84 + 83883234552 * q^85 - 103162039382 * q^86 - 9763306924 * q^87 + 418253082102 * q^88 + 187826099404 * q^89 + 96335639960 * q^90 + 58390389864 * q^91 - 259645875396 * q^92 + 394641636020 * q^93 + 117694719934 * q^94 + 69935059424 * q^95 + 12533631786 * q^96 + 137285937500 * q^97 - 484896369168 * q^98 + 235419947204 * 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 $

$2$	73.5071	1.62429	0.812147	−	0.583453i	$-0.198299\pi$
$2$	73.5071	1.62429	0.812147	+	0.583453i	$0.198299\pi$
$3$	274.559	0.652333	0.326166	−	0.945312i	$-0.394243\pi$
$3$	274.559	0.652333	0.326166	+	0.945312i	$0.394243\pi$
$4$	3355.30	1.63833
$5$	7553.66	1.08099	0.540496	−	0.841347i	$-0.318237\pi$
$5$	7553.66	1.08099	0.540496	+	0.841347i	$0.318237\pi$
$6$	20182.1	1.05958
$7$	46751.0	1.05136	0.525680	−	0.850682i	$-0.323811\pi$
$7$	46751.0	1.05136	0.525680	+	0.850682i	$0.323811\pi$
$8$	96095.7	1.03683
$9$	−101764.	−0.574462
$10$	555248.	1.75585
$11$	−91973.4	−0.172188	−0.0860939	−	0.996287i	$-0.527439\pi$
$11$	−91973.4	−0.172188	−0.0860939	+	0.996287i	$0.527439\pi$
$12$	921228.	1.06874
$13$	−1.62005e6	−1.21015	−0.605077	−	0.796167i	$-0.706858\pi$
$13$	−1.62005e6	−1.21015	−0.605077	+	0.796167i	$0.706858\pi$
$14$	3.43653e6	1.70772
$15$	2.07393e6	0.705167
$16$	192069.	0.0457928
$17$	5.89907e6	1.00766	0.503830	−	0.863803i	$-0.331924\pi$
$17$	5.89907e6	1.00766	0.503830	+	0.863803i	$0.331924\pi$
$18$	−7.48039e6	−0.933094
$19$	3.33185e6	0.308703	0.154351	−	0.988016i	$-0.450671\pi$
$19$	3.33185e6	0.308703	0.154351	+	0.988016i	$0.450671\pi$
$20$	2.53448e7	1.77102
$21$	1.28359e7	0.685837
$22$	−6.76070e6	−0.279683
$23$	2.81261e7	0.911185	0.455593	−	0.890188i	$-0.349427\pi$
$23$	2.81261e7	0.911185	0.455593	+	0.890188i	$0.349427\pi$
$24$	2.63840e7	0.676361
$25$	8.22966e6	0.168543
$26$	−1.19085e8	−1.96565
$27$	−7.65777e7	−1.02707
$28$	1.56863e8	1.72247
$29$	−2.05111e7	−0.185695
$29$	−2.05111e7	−0.185695
$30$	1.52448e8	1.14540
$31$	−1.31553e8	−0.825301	−0.412650	−	0.910890i	$-0.635397\pi$
$31$	−1.31553e8	−0.825301	−0.412650	+	0.910890i	$0.635397\pi$
$32$	−1.82686e8	−0.962453
$33$	−2.52521e7	−0.112324
$34$	4.33623e8	1.63674
$35$	3.53141e8	1.13651
$36$	−3.41449e8	−0.941157
$37$	8.54978e7	0.202696	0.101348	−	0.994851i	$-0.467684\pi$
$37$	8.54978e7	0.202696	0.101348	+	0.994851i	$0.467684\pi$
$38$	2.44915e8	0.501424
$39$	−4.44801e8	−0.789423
$40$	7.25874e8	1.12081
$41$	1.41332e9	1.90515	0.952574	−	0.304306i	$-0.0984245\pi$
$41$	1.41332e9	1.90515	0.952574	+	0.304306i	$0.0984245\pi$
$42$	9.43532e8	1.11400
$43$	−2.61617e8	−0.271387	−0.135694	−	0.990751i	$-0.543326\pi$
$43$	−2.61617e8	−0.271387	−0.135694	+	0.990751i	$0.543326\pi$
$44$	−3.08598e8	−0.282100
$45$	−7.68692e8	−0.620988
$46$	2.06747e9	1.48003
$47$	−1.99976e9	−1.27186	−0.635931	−	0.771746i	$-0.719384\pi$
$47$	−1.99976e9	−1.27186	−0.635931	+	0.771746i	$0.719384\pi$
$48$	5.27344e7	0.0298722
$49$	2.08329e8	0.105359
$50$	6.04939e8	0.273764
$51$	1.61964e9	0.657330
$52$	−5.43576e9	−1.98263
$53$	1.74642e8	0.0573628	0.0286814	−	0.999589i	$-0.490869\pi$
$53$	1.74642e8	0.0573628	0.0286814	+	0.999589i	$0.490869\pi$
$54$	−5.62900e9	−1.66827
$55$	−6.94736e8	−0.186134
$56$	4.49257e9	1.09009
$57$	9.14790e8	0.201377
$58$	−1.50772e9	−0.301624
$59$	−6.44946e9	−1.17446	−0.587229	−	0.809421i	$-0.699781\pi$
$59$	−6.44946e9	−1.17446	−0.587229	+	0.809421i	$0.699781\pi$
$60$	6.95865e9	1.15529
$61$	−7.14586e9	−1.08328	−0.541640	−	0.840611i	$-0.682196\pi$
$61$	−7.14586e9	−1.08328	−0.541640	+	0.840611i	$0.682196\pi$
$62$	−9.67010e9	−1.34053
$63$	−4.75758e9	−0.603966
$64$	−1.38220e10	−1.60910
$65$	−1.22373e10	−1.30817
$66$	−1.85621e9	−0.182447
$67$	−3.96759e9	−0.359017	−0.179509	−	0.983756i	$-0.557451\pi$
$67$	−3.96759e9	−0.359017	−0.179509	+	0.983756i	$0.557451\pi$
$68$	1.97931e10	1.65088
$69$	7.72229e9	0.594396
$70$	2.59584e10	1.84603
$71$	−8.71659e9	−0.573358	−0.286679	−	0.958027i	$-0.592551\pi$
$71$	−8.71659e9	−0.573358	−0.286679	+	0.958027i	$0.592551\pi$
$72$	−9.77910e9	−0.595621
$73$	1.16541e10	0.657964	0.328982	−	0.944336i	$-0.393294\pi$
$73$	1.16541e10	0.657964	0.328982	+	0.944336i	$0.393294\pi$
$74$	6.28470e9	0.329238
$75$	2.25953e9	0.109946
$76$	1.11793e10	0.505757
$77$	−4.29985e9	−0.181031
$78$	−3.26960e10	−1.28226
$79$	3.00987e10	1.10052	0.550261	−	0.834993i	$-0.314528\pi$
$79$	3.00987e10	1.10052	0.550261	+	0.834993i	$0.314528\pi$
$80$	1.45082e9	0.0495017
$81$	−2.99790e9	−0.0955320
$82$	1.03889e11	3.09452
$83$	4.75530e10	1.32510	0.662550	−	0.749018i	$-0.269474\pi$
$83$	4.75530e10	1.32510	0.662550	+	0.749018i	$0.269474\pi$
$84$	4.30683e10	1.12363
$85$	4.45595e10	1.08927
$86$	−1.92307e10	−0.440813
$87$	−5.63153e9	−0.121135
$88$	−8.83824e9	−0.178530
$89$	−6.59856e10	−1.25258	−0.626288	−	0.779591i	$-0.715427\pi$
$89$	−6.59856e10	−1.25258	−0.626288	+	0.779591i	$0.715427\pi$
$90$	−5.65043e10	−1.00867
$91$	−7.57391e10	−1.27231
$92$	9.43715e10	1.49282
$93$	−3.61192e10	−0.538371
$94$	−1.46997e11	−2.06588
$95$	2.51676e10	0.333705
$96$	−5.01580e10	−0.627839
$97$	−1.15407e11	−1.36455	−0.682273	−	0.731097i	$-0.739009\pi$
$97$	−1.15407e11	−1.36455	−0.682273	+	0.731097i	$0.739009\pi$
$98$	1.53136e10	0.171133
$99$	9.35959e9	0.0989153
$100$	2.76130e10	0.276130
$101$	1.28519e11	1.21675	0.608373	−	0.793651i	$-0.291822\pi$
$101$	1.28519e11	1.21675	0.608373	+	0.793651i	$0.291822\pi$
$102$	1.19055e11	1.06770
$103$	−5.33651e10	−0.453578	−0.226789	−	0.973944i	$-0.572823\pi$
$103$	−5.33651e10	−0.453578	−0.226789	+	0.973944i	$0.572823\pi$
$104$	−1.55680e11	−1.25473
$105$	9.69582e10	0.741384
$106$	1.28374e10	0.0931740
$107$	9.18340e10	0.632984	0.316492	−	0.948595i	$-0.397495\pi$
$107$	9.18340e10	0.632984	0.316492	+	0.948595i	$0.397495\pi$
$108$	−2.56941e11	−1.68268
$109$	1.76513e11	1.09883	0.549416	−	0.835549i	$-0.314850\pi$
$109$	1.76513e11	1.09883	0.549416	+	0.835549i	$0.314850\pi$
$110$	−5.10680e10	−0.302336
$111$	2.34742e10	0.132225
$112$	8.97942e9	0.0481448
$113$	2.90864e11	1.48511	0.742554	−	0.669787i	$-0.233614\pi$
$113$	2.90864e11	1.48511	0.742554	+	0.669787i	$0.233614\pi$
$114$	6.72436e10	0.327095
$115$	2.12455e11	0.984984
$116$	−6.88210e10	−0.304230
$117$	1.64863e11	0.695187
$118$	−4.74082e11	−1.90766
$119$	2.75787e11	1.05941
$120$	1.99296e11	0.731140
$121$	−2.76853e11	−0.970351
$122$	−5.25272e11	−1.75956
$123$	3.88040e11	1.24279
$124$	−4.41400e11	−1.35211
$125$	−3.06667e11	−0.898798
$126$	−3.49716e11	−0.981018
$127$	2.06208e11	0.553841	0.276920	−	0.960893i	$-0.410686\pi$
$127$	2.06208e11	0.553841	0.276920	+	0.960893i	$0.410686\pi$
$128$	−6.41879e11	−1.65119
$129$	−7.18294e10	−0.177035
$130$	−8.99531e11	−2.12485
$131$	8.32827e11	1.88609	0.943046	−	0.332664i	$-0.107947\pi$
$131$	8.32827e11	1.88609	0.943046	+	0.332664i	$0.107947\pi$
$132$	−8.47285e10	−0.184023
$133$	1.55767e11	0.324558
$134$	−2.91646e11	−0.583149
$135$	−5.78442e11	−1.11026
$136$	5.66875e11	1.04478
$137$	4.75804e11	0.842297	0.421148	−	0.906992i	$-0.361627\pi$
$137$	4.75804e11	0.842297	0.421148	+	0.906992i	$0.361627\pi$
$138$	5.67643e11	0.965474
$139$	2.09477e11	0.342416	0.171208	−	0.985235i	$-0.445233\pi$
$139$	2.09477e11	0.342416	0.171208	+	0.985235i	$0.445233\pi$
$140$	1.18489e12	1.86198
$141$	−5.49053e11	−0.829677
$142$	−6.40732e11	−0.931301
$143$	1.49002e11	0.208374
$144$	−1.95457e10	−0.0263062
$145$	−1.54934e11	−0.200735
$146$	8.56658e11	1.06873
$147$	5.71985e10	0.0687289
$148$	2.86871e11	0.332083
$149$	1.40871e12	1.57144	0.785720	−	0.618582i	$-0.212293\pi$
$149$	1.40871e12	1.57144	0.785720	+	0.618582i	$0.212293\pi$
$150$	1.66092e11	0.178585
$151$	−3.43968e11	−0.356570	−0.178285	−	0.983979i	$-0.557055\pi$
$151$	−3.43968e11	−0.356570	−0.178285	+	0.983979i	$0.557055\pi$
$152$	3.20176e11	0.320073
$153$	−6.00314e11	−0.578862
$154$	−3.16069e11	−0.294048
$155$	−9.93708e11	−0.892143
$156$	−1.49244e12	−1.29334
$157$	−1.45594e12	−1.21814	−0.609069	−	0.793117i	$-0.708457\pi$
$157$	−1.45594e12	−1.21814	−0.609069	+	0.793117i	$0.708457\pi$
$158$	2.21247e12	1.78757
$159$	4.79495e10	0.0374196
$160$	−1.37994e12	−1.04040
$161$	1.31492e12	0.957984
$162$	−2.20367e11	−0.155172
$163$	−6.58596e11	−0.448319	−0.224160	−	0.974552i	$-0.571964\pi$
$163$	−6.58596e11	−0.448319	−0.224160	+	0.974552i	$0.571964\pi$
$164$	4.74211e12	3.12126
$165$	−1.90746e11	−0.121421
$166$	3.49548e12	2.15235
$167$	−2.55207e12	−1.52038	−0.760189	−	0.649702i	$-0.774894\pi$
$167$	−2.55207e12	−1.52038	−0.760189	+	0.649702i	$0.774894\pi$
$168$	1.23348e12	0.711099
$169$	8.32409e11	0.464473
$170$	3.27544e12	1.76930
$171$	−3.39063e11	−0.177338
$172$	−8.77803e11	−0.444622
$173$	3.31364e12	1.62574	0.812871	−	0.582444i	$-0.197903\pi$
$173$	3.31364e12	1.62574	0.812871	+	0.582444i	$0.197903\pi$
$174$	−4.13957e11	−0.196759
$175$	3.84745e11	0.177200
$176$	−1.76652e10	−0.00788497
$177$	−1.77076e12	−0.766138
$178$	−4.85042e12	−2.03455
$179$	−1.02904e12	−0.418542	−0.209271	−	0.977858i	$-0.567109\pi$
$179$	−1.02904e12	−0.418542	−0.209271	+	0.977858i	$0.567109\pi$
$180$	−2.57919e12	−1.01738
$181$	2.67452e12	1.02332	0.511662	−	0.859187i	$-0.329030\pi$
$181$	2.67452e12	1.02332	0.511662	+	0.859187i	$0.329030\pi$
$182$	−5.56736e12	−2.06660
$183$	−1.96196e12	−0.706659
$184$	2.70280e12	0.944748
$185$	6.45822e11	0.219113
$186$	−2.65502e12	−0.874472
$187$	−5.42557e11	−0.173507
$188$	−6.70979e12	−2.08373
$189$	−3.58008e12	−1.07982
$190$	1.85000e12	0.542035
$191$	2.02166e11	0.0575474	0.0287737	−	0.999586i	$-0.490840\pi$
$191$	2.02166e11	0.0575474	0.0287737	+	0.999586i	$0.490840\pi$
$192$	−3.79497e12	−1.04967
$193$	3.67392e12	0.987563	0.493781	−	0.869586i	$-0.335614\pi$
$193$	3.67392e12	0.987563	0.493781	+	0.869586i	$0.335614\pi$
$194$	−8.48325e12	−2.21642
$195$	−3.35987e12	−0.853360
$196$	6.99004e11	0.172612
$197$	3.20488e11	0.0769569	0.0384785	−	0.999259i	$-0.487749\pi$
$197$	3.20488e11	0.0769569	0.0384785	+	0.999259i	$0.487749\pi$
$198$	6.87997e11	0.160667
$199$	−1.45137e12	−0.329675	−0.164838	−	0.986321i	$-0.552710\pi$
$199$	−1.45137e12	−0.329675	−0.164838	+	0.986321i	$0.552710\pi$
$200$	7.90835e11	0.174751
$201$	−1.08934e12	−0.234199
$202$	9.44707e12	1.97635
$203$	−9.58917e11	−0.195233
$204$	5.43439e12	1.07692
$205$	1.06757e13	2.05945
$206$	−3.92271e12	−0.736744
$207$	−2.86223e12	−0.523441
$208$	−3.11162e11	−0.0554164
$209$	−3.06441e11	−0.0531548
$210$	7.12712e12	1.20423
$211$	−3.02678e12	−0.498226	−0.249113	−	0.968474i	$-0.580139\pi$
$211$	−3.02678e12	−0.498226	−0.249113	+	0.968474i	$0.580139\pi$
$212$	5.85974e11	0.0939791
$213$	−2.39322e12	−0.374020
$214$	6.75045e12	1.02815
$215$	−1.97617e12	−0.293367
$216$	−7.35878e12	−1.06490
$217$	−6.15024e12	−0.867688
$218$	1.29750e13	1.78482
$219$	3.19974e12	0.429212
$220$	−2.33104e12	−0.304948
$221$	−9.55680e12	−1.21942
$222$	1.72552e12	0.214773
$223$	1.55372e13	1.88668	0.943338	−	0.331834i	$-0.107667\pi$
$223$	1.55372e13	1.88668	0.943338	+	0.331834i	$0.107667\pi$
$224$	−8.54073e12	−1.01188
$225$	−8.37485e11	−0.0968218
$226$	2.13805e13	2.41225
$227$	5.95253e11	0.0655480	0.0327740	−	0.999463i	$-0.489566\pi$
$227$	5.95253e11	0.0655480	0.0327740	+	0.999463i	$0.489566\pi$
$228$	3.06939e12	0.329922
$229$	1.33959e13	1.40564	0.702822	−	0.711366i	$-0.251923\pi$
$229$	1.33959e13	1.40564	0.702822	+	0.711366i	$0.251923\pi$
$230$	1.56170e13	1.59990
$231$	−1.18056e12	−0.118093
$232$	−1.97103e12	−0.192535
$233$	−1.13309e13	−1.08095	−0.540475	−	0.841360i	$-0.681755\pi$
$233$	−1.13309e13	−1.08095	−0.540475	+	0.841360i	$0.681755\pi$
$234$	1.21186e13	1.12919
$235$	−1.51055e13	−1.37487
$236$	−2.16399e13	−1.92415
$237$	8.26388e12	0.717907
$238$	2.02723e13	1.72080
$239$	7.40886e12	0.614558	0.307279	−	0.951620i	$-0.400582\pi$
$239$	7.40886e12	0.614558	0.307279	+	0.951620i	$0.400582\pi$
$240$	3.98337e11	0.0322916
$241$	−2.50187e13	−1.98231	−0.991153	−	0.132722i	$-0.957628\pi$
$241$	−2.50187e13	−1.98231	−0.991153	+	0.132722i	$0.957628\pi$
$242$	−2.03506e13	−1.57614
$243$	1.27424e13	0.964755
$244$	−2.39765e13	−1.77477
$245$	1.57364e12	0.113892
$246$	2.85237e13	2.01866
$247$	−5.39777e12	−0.373578
$248$	−1.26417e13	−0.855699
$249$	1.30561e13	0.864406
$250$	−2.25422e13	−1.45991
$251$	−9.41608e12	−0.596574	−0.298287	−	0.954476i	$-0.596415\pi$
$251$	−9.41608e12	−0.596574	−0.298287	+	0.954476i	$0.596415\pi$
$252$	−1.59631e13	−0.989495
$253$	−2.58685e12	−0.156895
$254$	1.51577e13	0.899599
$255$	1.22342e13	0.710568
$256$	−1.88751e13	−1.07293
$257$	1.52536e13	0.848673	0.424336	−	0.905505i	$-0.360507\pi$
$257$	1.52536e13	0.848673	0.424336	+	0.905505i	$0.360507\pi$
$258$	−5.27997e12	−0.287557
$259$	3.99711e12	0.213107
$260$	−4.10599e13	−2.14321
$261$	2.08730e12	0.106675
$262$	6.12187e13	3.06357
$263$	2.89044e13	1.41647	0.708235	−	0.705976i	$-0.249492\pi$
$263$	2.89044e13	1.41647	0.708235	+	0.705976i	$0.249492\pi$
$264$	−2.42662e12	−0.116461
$265$	1.31918e12	0.0620087
$266$	1.14500e13	0.527177
$267$	−1.81170e13	−0.817097
$268$	−1.33124e13	−0.588188
$269$	−3.87972e13	−1.67943	−0.839716	−	0.543026i	$-0.817278\pi$
$269$	−3.87972e13	−1.67943	−0.839716	+	0.543026i	$0.817278\pi$
$270$	−4.25196e13	−1.80338
$271$	−1.21906e13	−0.506635	−0.253318	−	0.967383i	$-0.581522\pi$
$271$	−1.21906e13	−0.506635	−0.253318	+	0.967383i	$0.581522\pi$
$272$	1.13303e12	0.0461436
$273$	−2.07949e13	−0.829968
$274$	3.49750e13	1.36814
$275$	−7.56910e11	−0.0290211
$276$	2.59106e13	0.973817
$277$	−9.85698e12	−0.363166	−0.181583	−	0.983376i	$-0.558122\pi$
$277$	−9.85698e12	−0.363166	−0.181583	+	0.983376i	$0.558122\pi$
$278$	1.53980e13	0.556185
$279$	1.33874e13	0.474104
$280$	3.39353e13	1.17837
$281$	−2.97037e13	−1.01141	−0.505703	−	0.862707i	$-0.668767\pi$
$281$	−2.97037e13	−1.01141	−0.505703	+	0.862707i	$0.668767\pi$
$282$	−4.03593e13	−1.34764
$283$	1.32270e13	0.433147	0.216574	−	0.976266i	$-0.430512\pi$
$283$	1.32270e13	0.433147	0.216574	+	0.976266i	$0.430512\pi$
$284$	−2.92468e13	−0.939349
$285$	6.91001e12	0.217687
$286$	1.09527e13	0.338460
$287$	6.60741e13	2.00300
$288$	1.85908e13	0.552892
$289$	5.27084e11	0.0153795
$290$	−1.13888e13	−0.326053
$291$	−3.16861e13	−0.890139
$292$	3.91029e13	1.07796
$293$	−2.67482e13	−0.723640	−0.361820	−	0.932248i	$-0.617845\pi$
$293$	−2.67482e13	−0.723640	−0.361820	+	0.932248i	$0.617845\pi$
$294$	4.20450e12	0.111636
$295$	−4.87171e13	−1.26958
$296$	8.21597e12	0.210162
$297$	7.04311e12	0.176849
$298$	1.03550e14	2.55248
$299$	−4.55658e13	−1.10267
$300$	7.58140e12	0.180128
$301$	−1.22309e13	−0.285326
$302$	−2.52841e13	−0.579174
$303$	3.52861e13	0.793723
$304$	6.39945e11	0.0141364
$305$	−5.39774e13	−1.17102
$306$	−4.41273e13	−0.940242
$307$	−1.69328e13	−0.354378	−0.177189	−	0.984177i	$-0.556700\pi$
$307$	−1.69328e13	−0.354378	−0.177189	+	0.984177i	$0.556700\pi$
$308$	−1.44273e13	−0.296589
$309$	−1.46519e13	−0.295884
$310$	−7.30446e13	−1.44910
$311$	9.43063e13	1.83806	0.919028	−	0.394193i	$-0.128976\pi$
$311$	9.43063e13	1.83806	0.919028	+	0.394193i	$0.128976\pi$
$312$	−4.27434e13	−0.818501
$313$	6.79891e13	1.27922	0.639610	−	0.768699i	$-0.279096\pi$
$313$	6.79891e13	1.27922	0.639610	+	0.768699i	$0.279096\pi$
$314$	−1.07022e14	−1.97861
$315$	−3.59371e13	−0.652883
$316$	1.00990e14	1.80302
$317$	−2.24047e13	−0.393109	−0.196554	−	0.980493i	$-0.562975\pi$
$317$	−2.24047e13	−0.393109	−0.196554	+	0.980493i	$0.562975\pi$
$318$	3.52463e12	0.0607805
$319$	1.88648e12	0.0319745
$320$	−1.04407e14	−1.73942
$321$	2.52139e13	0.412916
$322$	9.66563e13	1.55605
$323$	1.96548e13	0.311067
$324$	−1.00588e13	−0.156513
$325$	−1.33325e13	−0.203964
$326$	−4.84115e13	−0.728202
$327$	4.84633e13	0.716804
$328$	1.35814e14	1.97532
$329$	−9.34908e13	−1.33718
$330$	−1.40212e13	−0.197223
$331$	1.29341e14	1.78929	0.894645	−	0.446778i	$-0.147428\pi$
$331$	1.29341e14	1.78929	0.894645	+	0.446778i	$0.147428\pi$
$332$	1.59554e14	2.17095
$333$	−8.70062e12	−0.116441
$334$	−1.87595e14	−2.46954
$335$	−2.99698e13	−0.388095
$336$	2.46538e12	0.0314064
$337$	−7.33684e13	−0.919485	−0.459743	−	0.888052i	$-0.652058\pi$
$337$	−7.33684e13	−0.919485	−0.459743	+	0.888052i	$0.652058\pi$
$338$	6.11880e13	0.754440
$339$	7.98593e13	0.968784
$340$	1.49511e14	1.78459
$341$	1.20994e13	0.142107
$342$	−2.49235e13	−0.288049
$343$	−8.27024e13	−0.940590
$344$	−2.51403e13	−0.281383
$345$	5.83316e13	0.642538
$346$	2.43576e14	2.64068
$347$	1.51765e14	1.61942	0.809708	−	0.586833i	$-0.199626\pi$
$347$	1.51765e14	1.61942	0.809708	+	0.586833i	$0.199626\pi$
$348$	−1.88955e13	−0.198459
$349$	1.02995e14	1.06482	0.532411	−	0.846486i	$-0.321286\pi$
$349$	1.02995e14	1.06482	0.532411	+	0.846486i	$0.321286\pi$
$350$	2.82815e13	0.287825
$351$	1.24060e14	1.24292
$352$	1.68022e13	0.165723
$353$	6.23019e13	0.604979	0.302490	−	0.953153i	$-0.402182\pi$
$353$	6.23019e13	0.604979	0.302490	+	0.953153i	$0.402182\pi$
$354$	−1.30164e14	−1.24443
$355$	−6.58422e13	−0.619795
$356$	−2.21401e14	−2.05213
$357$	7.57199e13	0.691091
$358$	−7.56415e13	−0.679835
$359$	−6.92528e13	−0.612940	−0.306470	−	0.951880i	$-0.599148\pi$
$359$	−6.92528e13	−0.612940	−0.306470	+	0.951880i	$0.599148\pi$
$360$	−7.38680e13	−0.643862
$361$	−1.05389e14	−0.904703
$362$	1.96596e14	1.66218
$363$	−7.60125e13	−0.632992
$364$	−2.54127e14	−2.08446
$365$	8.80309e13	0.711254
$366$	−1.44218e14	−1.14782
$367$	9.77885e13	0.766698	0.383349	−	0.923603i	$-0.374771\pi$
$367$	9.77885e13	0.766698	0.383349	+	0.923603i	$0.374771\pi$
$368$	5.40216e12	0.0417258
$369$	−1.43825e14	−1.09444
$370$	4.74725e13	0.355904
$371$	8.16467e12	0.0603090
$372$	−1.21191e14	−0.882028
$373$	1.86701e14	1.33890	0.669449	−	0.742858i	$-0.266530\pi$
$373$	1.86701e14	1.33890	0.669449	+	0.742858i	$0.266530\pi$
$374$	−3.98818e13	−0.281826
$375$	−8.41983e13	−0.586315
$376$	−1.92168e14	−1.31871
$377$	3.32291e13	0.224720
$378$	−2.63162e14	−1.75395
$379$	−1.90903e14	−1.25400	−0.626999	−	0.779020i	$-0.715717\pi$
$379$	−1.90903e14	−1.25400	−0.626999	+	0.779020i	$0.715717\pi$
$380$	8.44450e13	0.546719
$381$	5.66163e13	0.361288
$382$	1.48607e13	0.0934738
$383$	−2.70805e14	−1.67905	−0.839525	−	0.543321i	$-0.817167\pi$
$383$	−2.70805e14	−1.67905	−0.839525	+	0.543321i	$0.817167\pi$
$384$	−1.76234e14	−1.07713
$385$	−3.24796e13	−0.195693
$386$	2.70059e14	1.60409
$387$	2.66232e13	0.155902
$388$	−3.87226e14	−2.23558
$389$	−8.69151e13	−0.494735	−0.247367	−	0.968922i	$-0.579565\pi$
$389$	−8.69151e13	−0.494735	−0.247367	+	0.968922i	$0.579565\pi$
$390$	−2.46975e14	−1.38611
$391$	1.65918e14	0.918166
$392$	2.00195e13	0.109239
$393$	2.28660e14	1.23036
$394$	2.35582e13	0.125001
$395$	2.27355e14	1.18966
$396$	3.14042e13	0.162056
$397$	9.81411e13	0.499463	0.249731	−	0.968315i	$-0.419658\pi$
$397$	9.81411e13	0.499463	0.249731	+	0.968315i	$0.419658\pi$
$398$	−1.06686e14	−0.535489
$399$	4.27673e13	0.211720
$400$	1.58066e12	0.00771808
$401$	−3.36807e14	−1.62213	−0.811067	−	0.584954i	$-0.801113\pi$
$401$	−3.36807e14	−1.62213	−0.811067	+	0.584954i	$0.801113\pi$
$402$	−8.00741e13	−0.380407
$403$	2.13123e14	0.998741
$404$	4.31220e14	1.99343
$405$	−2.26451e13	−0.103269
$406$	−7.04872e13	−0.317115
$407$	−7.86352e12	−0.0349018
$408$	1.55641e14	0.681542
$409$	2.11237e14	0.912622	0.456311	−	0.889820i	$-0.349170\pi$
$409$	2.11237e14	0.912622	0.456311	+	0.889820i	$0.349170\pi$
$410$	7.84742e14	3.34515
$411$	1.30636e14	0.549458
$412$	−1.79056e14	−0.743110
$413$	−3.01519e14	−1.23478
$414$	−2.10394e14	−0.850222
$415$	3.59199e14	1.43242
$416$	2.95960e14	1.16472
$417$	5.75138e13	0.223370
$418$	−2.25256e13	−0.0863390
$419$	−4.31473e14	−1.63221	−0.816105	−	0.577903i	$-0.803871\pi$
$419$	−4.31473e14	−1.63221	−0.816105	+	0.577903i	$0.803871\pi$
$420$	3.25324e14	1.21463
$421$	−3.46609e14	−1.27728	−0.638642	−	0.769504i	$-0.720504\pi$
$421$	−3.46609e14	−1.27728	−0.638642	+	0.769504i	$0.720504\pi$
$422$	−2.22490e14	−0.809266
$423$	2.03504e14	0.730636
$424$	1.67823e13	0.0594757
$425$	4.85473e13	0.169835
$426$	−1.75919e14	−0.607519
$427$	−3.34076e14	−1.13892
$428$	3.08130e14	1.03704
$429$	4.09098e13	0.135929
$430$	−1.45262e14	−0.476515
$431$	5.47179e14	1.77217	0.886083	−	0.463527i	$-0.153416\pi$
$431$	5.47179e14	1.77217	0.886083	+	0.463527i	$0.153416\pi$
$432$	−1.47082e13	−0.0470326
$433$	1.61608e14	0.510244	0.255122	−	0.966909i	$-0.417884\pi$
$433$	1.61608e14	0.510244	0.255122	+	0.966909i	$0.417884\pi$
$434$	−4.52087e14	−1.40938
$435$	−4.25386e13	−0.130946
$436$	5.92254e14	1.80025
$437$	9.37120e13	0.281285
$438$	2.35203e14	0.697166
$439$	1.70871e14	0.500165	0.250083	−	0.968225i	$-0.419542\pi$
$439$	1.70871e14	0.500165	0.250083	+	0.968225i	$0.419542\pi$
$440$	−6.67611e13	−0.192990
$441$	−2.12004e13	−0.0605245
$442$	−7.02493e14	−1.98070
$443$	1.66717e14	0.464258	0.232129	−	0.972685i	$-0.425431\pi$
$443$	1.66717e14	0.464258	0.232129	+	0.972685i	$0.425431\pi$
$444$	7.87630e13	0.216629
$445$	−4.98433e14	−1.35403
$446$	1.14210e15	3.06452
$447$	3.86775e14	1.02510
$448$	−6.46194e14	−1.69174
$449$	−5.86510e14	−1.51677	−0.758386	−	0.651805i	$-0.774012\pi$
$449$	−5.86510e14	−1.51677	−0.758386	+	0.651805i	$0.774012\pi$
$450$	−6.15611e13	−0.157267
$451$	−1.29988e14	−0.328043
$452$	9.75934e14	2.43309
$453$	−9.44396e13	−0.232602
$454$	4.37553e13	0.106469
$455$	−5.72107e14	−1.37535
$456$	8.79074e13	0.208794
$457$	1.26515e13	0.0296894	0.0148447	−	0.999890i	$-0.495275\pi$
$457$	1.26515e13	0.0296894	0.0148447	+	0.999890i	$0.495275\pi$
$458$	9.84691e14	2.28318
$459$	−4.51737e14	−1.03494
$460$	7.12850e14	1.61373
$461$	−3.58075e14	−0.800976	−0.400488	−	0.916302i	$-0.631159\pi$
$461$	−3.58075e14	−0.800976	−0.400488	+	0.916302i	$0.631159\pi$
$462$	−8.67798e13	−0.191817
$463$	−5.55392e14	−1.21312	−0.606561	−	0.795037i	$-0.707451\pi$
$463$	−5.55392e14	−1.21312	−0.606561	+	0.795037i	$0.707451\pi$
$464$	−3.93956e12	−0.00850352
$465$	−2.72832e14	−0.581974
$466$	−8.32899e14	−1.75578
$467$	9.12640e14	1.90133	0.950663	−	0.310225i	$-0.100404\pi$
$467$	9.12640e14	1.90133	0.950663	+	0.310225i	$0.100404\pi$
$468$	5.53165e14	1.13895
$469$	−1.85489e14	−0.377456
$470$	−1.11036e15	−2.23319
$471$	−3.99743e14	−0.794632
$472$	−6.19766e14	−1.21772
$473$	2.40618e13	0.0467296
$474$	6.07454e14	1.16609
$475$	2.74200e13	0.0520298
$476$	9.25348e14	1.73567
$477$	−1.77723e13	−0.0329527
$478$	5.44604e14	0.998222
$479$	−7.29338e14	−1.32155	−0.660775	−	0.750584i	$-0.729772\pi$
$479$	−7.29338e14	−1.32155	−0.660775	+	0.750584i	$0.729772\pi$
$480$	−3.78877e14	−0.678689
$481$	−1.38511e14	−0.245294
$482$	−1.83905e15	−3.21985
$483$	3.61025e14	0.624925
$484$	−9.28923e14	−1.58975
$485$	−8.71747e14	−1.47506
$486$	9.36657e14	1.56704
$487$	1.02122e15	1.68932	0.844659	−	0.535305i	$-0.179803\pi$
$487$	1.02122e15	1.68932	0.844659	+	0.535305i	$0.179803\pi$
$488$	−6.86686e14	−1.12318
$489$	−1.80824e14	−0.292454
$490$	1.15674e14	0.184994
$491$	−4.30114e14	−0.680198	−0.340099	−	0.940390i	$-0.610461\pi$
$491$	−4.30114e14	−0.680198	−0.340099	+	0.940390i	$0.610461\pi$
$492$	1.30199e15	2.03610
$493$	−1.20997e14	−0.187118
$494$	−3.96774e14	−0.606800
$495$	7.06992e13	0.106927
$496$	−2.52673e13	−0.0377928
$497$	−4.07509e14	−0.602806
$498$	9.59718e14	1.40405
$499$	−6.77918e14	−0.980898	−0.490449	−	0.871470i	$-0.663167\pi$
$499$	−6.77918e14	−0.980898	−0.490449	+	0.871470i	$0.663167\pi$
$500$	−1.02896e15	−1.47253
$501$	−7.00694e14	−0.991792
$502$	−6.92149e14	−0.969012
$503$	7.41120e14	1.02628	0.513139	−	0.858306i	$-0.328483\pi$
$503$	7.41120e14	1.02628	0.513139	+	0.858306i	$0.328483\pi$
$504$	−4.57183e14	−0.626213
$505$	9.70789e14	1.31529
$506$	−1.90152e14	−0.254843
$507$	2.28546e14	0.302991
$508$	6.91889e14	0.907373
$509$	−1.84330e14	−0.239138	−0.119569	−	0.992826i	$-0.538151\pi$
$509$	−1.84330e14	−0.239138	−0.119569	+	0.992826i	$0.538151\pi$
$510$	8.99304e14	1.15417
$511$	5.44840e14	0.691757
$512$	−7.28882e13	−0.0915530
$513$	−2.55145e14	−0.317060
$514$	1.12125e15	1.37849
$515$	−4.03101e14	−0.490314
$516$	−2.41009e14	−0.290041
$517$	1.83925e14	0.218999
$518$	2.93816e14	0.346148
$519$	9.09790e14	1.06052
$520$	−1.17595e15	−1.35635
$521$	3.62967e14	0.414247	0.207124	−	0.978315i	$-0.433590\pi$
$521$	3.62967e14	0.414247	0.207124	+	0.978315i	$0.433590\pi$
$522$	1.53431e14	0.173271
$523$	1.14089e15	1.27492	0.637460	−	0.770484i	$-0.279985\pi$
$523$	1.14089e15	1.27492	0.637460	+	0.770484i	$0.279985\pi$
$524$	2.79438e15	3.09004
$525$	1.05635e14	0.115593
$526$	2.12468e15	2.30076
$527$	−7.76041e14	−0.831623
$528$	−4.85016e12	−0.00514362
$529$	−1.61731e14	−0.169741
$530$	9.69693e13	0.100720
$531$	6.56324e14	0.674681
$532$	5.22645e14	0.531732
$533$	−2.28965e15	−2.30552
$534$	−1.33173e15	−1.32721
$535$	6.93683e14	0.684251
$536$	−3.81268e14	−0.372241
$537$	−2.82531e14	−0.273029
$538$	−2.85187e15	−2.72789
$539$	−1.91607e13	−0.0181415
$540$	−1.94084e15	−1.81897
$541$	−7.30458e14	−0.677658	−0.338829	−	0.940848i	$-0.610031\pi$
$541$	−7.30458e14	−0.677658	−0.338829	+	0.940848i	$0.610031\pi$
$542$	−8.96099e14	−0.822924
$543$	7.34313e14	0.667548
$544$	−1.07767e15	−0.969825
$545$	1.33332e15	1.18783
$546$	−1.52857e15	−1.34811
$547$	−1.21723e15	−1.06278	−0.531389	−	0.847128i	$-0.678330\pi$
$547$	−1.21723e15	−1.06278	−0.531389	+	0.847128i	$0.678330\pi$
$548$	1.59646e15	1.37996
$549$	7.27192e14	0.622302
$550$	−5.56382e13	−0.0471388
$551$	−6.83400e13	−0.0573246
$552$	7.42079e14	0.616290
$553$	1.40714e15	1.15705
$554$	−7.24558e14	−0.589888
$555$	1.77316e14	0.142935
$556$	7.02857e14	0.560991
$557$	−1.41546e15	−1.11865	−0.559325	−	0.828948i	$-0.688940\pi$
$557$	−1.41546e15	−1.11865	−0.559325	+	0.828948i	$0.688940\pi$
$558$	9.84070e14	0.770083
$559$	4.23833e14	0.328420
$560$	6.78275e13	0.0520441
$561$	−1.48964e14	−0.113184
$562$	−2.18343e15	−1.64282
$563$	−2.27649e14	−0.169617	−0.0848084	−	0.996397i	$-0.527028\pi$
$563$	−2.27649e14	−0.169617	−0.0848084	+	0.996397i	$0.527028\pi$
$564$	−1.84224e15	−1.35928
$565$	2.19708e15	1.60539
$566$	9.72278e14	0.703558
$567$	−1.40155e14	−0.100439
$568$	−8.37627e14	−0.594477
$569$	−2.19090e14	−0.153994	−0.0769971	−	0.997031i	$-0.524533\pi$
$569$	−2.19090e14	−0.153994	−0.0769971	+	0.997031i	$0.524533\pi$
$570$	5.07935e14	0.353587
$571$	1.60829e14	0.110883	0.0554417	−	0.998462i	$-0.482343\pi$
$571$	1.60829e14	0.110883	0.0554417	+	0.998462i	$0.482343\pi$
$572$	4.99945e14	0.341385
$573$	5.55067e13	0.0375400
$574$	4.85691e15	3.25346
$575$	2.31468e14	0.153574
$576$	1.40659e15	0.924365
$577$	1.17248e15	0.763199	0.381599	−	0.924328i	$-0.375373\pi$
$577$	1.17248e15	0.763199	0.381599	+	0.924328i	$0.375373\pi$
$578$	3.87444e13	0.0249808
$579$	1.00871e15	0.644220
$580$	−5.19851e14	−0.328870
$581$	2.22315e15	1.39316
$582$	−2.32916e15	−1.44585
$583$	−1.60624e13	−0.00987717
$584$	1.11991e15	0.682199
$585$	1.24532e15	0.751492
$586$	−1.96618e15	−1.17540
$587$	−7.28635e14	−0.431520	−0.215760	−	0.976446i	$-0.569223\pi$
$587$	−7.28635e14	−0.431520	−0.215760	+	0.976446i	$0.569223\pi$
$588$	1.91918e14	0.112601
$589$	−4.38315e14	−0.254772
$590$	−3.58105e15	−2.06217
$591$	8.79930e13	0.0502015
$592$	1.64215e13	0.00928203
$593$	9.61737e14	0.538587	0.269293	−	0.963058i	$-0.413210\pi$
$593$	9.61737e14	0.538587	0.269293	+	0.963058i	$0.413210\pi$
$594$	5.17718e14	0.287255
$595$	2.08320e15	1.14522
$596$	4.72665e15	2.57454
$597$	−3.98487e14	−0.215058
$598$	−3.34941e15	−1.79107
$599$	3.24472e15	1.71921	0.859606	−	0.510957i	$-0.170709\pi$
$599$	3.24472e15	1.71921	0.859606	+	0.510957i	$0.170709\pi$
$600$	2.17131e14	0.113996
$601$	−1.32780e15	−0.690753	−0.345377	−	0.938464i	$-0.612249\pi$
$601$	−1.32780e15	−0.690753	−0.345377	+	0.938464i	$0.612249\pi$
$602$	−8.99055e14	−0.463453
$603$	4.03758e14	0.206242
$604$	−1.15411e15	−0.584179
$605$	−2.09125e15	−1.04894
$606$	2.59378e15	1.28924
$607$	−1.47255e15	−0.725327	−0.362663	−	0.931920i	$-0.618132\pi$
$607$	−1.47255e15	−0.725327	−0.362663	+	0.931920i	$0.618132\pi$
$608$	−6.08680e14	−0.297112
$609$	−2.63279e14	−0.127357
$610$	−3.96772e15	−1.90207
$611$	3.23972e15	1.53915
$612$	−2.01423e15	−0.948367
$613$	−1.53895e15	−0.718110	−0.359055	−	0.933316i	$-0.616901\pi$
$613$	−1.53895e15	−0.718110	−0.359055	+	0.933316i	$0.616901\pi$
$614$	−1.24468e15	−0.575615
$615$	2.93112e15	1.34345
$616$	−4.13197e14	−0.187699
$617$	−2.60026e14	−0.117071	−0.0585355	−	0.998285i	$-0.518643\pi$
$617$	−2.60026e14	−0.117071	−0.0585355	+	0.998285i	$0.518643\pi$
$618$	−1.07702e15	−0.480602
$619$	−2.24232e15	−0.991745	−0.495872	−	0.868395i	$-0.665152\pi$
$619$	−2.24232e15	−0.991745	−0.495872	+	0.868395i	$0.665152\pi$
$620$	−3.33419e15	−1.46162
$621$	−2.15383e15	−0.935854
$622$	6.93219e15	2.98554
$623$	−3.08489e15	−1.31691
$624$	−8.54324e13	−0.0361499
$625$	−2.71830e15	−1.14014
$626$	4.99768e15	2.07783
$627$	−8.41363e13	−0.0346746
$628$	−4.88513e15	−1.99571
$629$	5.04357e14	0.204249
$630$	−2.64163e15	−1.06047
$631$	−5.26286e14	−0.209440	−0.104720	−	0.994502i	$-0.533395\pi$
$631$	−5.26286e14	−0.209440	−0.104720	+	0.994502i	$0.533395\pi$
$632$	2.89236e15	1.14106
$633$	−8.31029e14	−0.325009
$634$	−1.64690e15	−0.638524
$635$	1.55762e15	0.598697
$636$	1.60885e14	0.0613057
$637$	−3.37503e14	−0.127500
$638$	1.38670e14	0.0519359
$639$	8.87037e14	0.329372
$640$	−4.84854e15	−1.78493
$641$	−2.30807e15	−0.842423	−0.421211	−	0.906962i	$-0.638395\pi$
$641$	−2.30807e15	−0.842423	−0.421211	+	0.906962i	$0.638395\pi$
$642$	1.85340e15	0.670697
$643$	7.47445e14	0.268175	0.134088	−	0.990969i	$-0.457190\pi$
$643$	7.47445e14	0.268175	0.134088	+	0.990969i	$0.457190\pi$
$644$	4.41196e15	1.56949
$645$	−5.42575e14	−0.191373
$646$	1.44477e15	0.505265
$647$	4.78295e14	0.165852	0.0829262	−	0.996556i	$-0.473573\pi$
$647$	4.78295e14	0.165852	0.0829262	+	0.996556i	$0.473573\pi$
$648$	−2.88085e14	−0.0990508
$649$	5.93179e14	0.202227
$650$	−9.80032e14	−0.331297
$651$	−1.68861e15	−0.566022
$652$	−2.20979e15	−0.734495
$653$	−4.85296e15	−1.59950	−0.799751	−	0.600332i	$-0.795035\pi$
$653$	−4.85296e15	−1.59950	−0.799751	+	0.600332i	$0.795035\pi$
$654$	3.56240e15	1.16430
$655$	6.29089e15	2.03885
$656$	2.71455e14	0.0872422
$657$	−1.18597e15	−0.377975
$658$	−6.87224e15	−2.17198
$659$	−2.61459e15	−0.819470	−0.409735	−	0.912205i	$-0.634379\pi$
$659$	−2.61459e15	−0.819470	−0.409735	+	0.912205i	$0.634379\pi$
$660$	−6.40010e14	−0.198928
$661$	−3.37559e15	−1.04050	−0.520249	−	0.854014i	$-0.674161\pi$
$661$	−3.37559e15	−1.04050	−0.520249	+	0.854014i	$0.674161\pi$
$662$	9.50745e15	2.90633
$663$	−2.62391e15	−0.795471
$664$	4.56964e15	1.37391
$665$	1.17661e15	0.350844
$666$	−6.39557e14	−0.189135
$667$	−5.76899e14	−0.169203
$668$	−8.56294e15	−2.49088
$669$	4.26590e15	1.23074
$670$	−2.20300e15	−0.630380
$671$	6.57229e14	0.186527
$672$	−2.34494e15	−0.660086
$673$	−1.36509e15	−0.381135	−0.190568	−	0.981674i	$-0.561033\pi$
$673$	−1.36509e15	−0.381135	−0.190568	+	0.981674i	$0.561033\pi$
$674$	−5.39310e15	−1.49351
$675$	−6.30208e14	−0.173106
$676$	2.79298e15	0.760959
$677$	−2.32018e15	−0.627025	−0.313512	−	0.949584i	$-0.601506\pi$
$677$	−2.32018e15	−0.627025	−0.313512	+	0.949584i	$0.601506\pi$
$678$	5.87023e15	1.57359
$679$	−5.39540e15	−1.43463
$680$	4.28198e15	1.12939
$681$	1.63432e14	0.0427591
$682$	8.89391e14	0.230823
$683$	5.38906e15	1.38739	0.693696	−	0.720268i	$-0.255981\pi$
$683$	5.38906e15	1.38739	0.693696	+	0.720268i	$0.255981\pi$
$684$	−1.13766e15	−0.290538
$685$	3.59406e15	0.910516
$686$	−6.07922e15	−1.52779
$687$	3.67796e15	0.916948
$688$	−5.02485e13	−0.0124276
$689$	−2.82928e14	−0.0694178
$690$	4.28778e15	1.04367
$691$	5.51138e15	1.33086	0.665428	−	0.746462i	$-0.268249\pi$
$691$	5.51138e15	1.33086	0.665428	+	0.746462i	$0.268249\pi$
$692$	1.11182e16	2.66350
$693$	4.37570e14	0.103996
$694$	1.11558e16	2.63041
$695$	1.58232e15	0.370149
$696$	−5.41166e14	−0.125597
$697$	8.33726e15	1.91974
$698$	7.57088e15	1.72958
$699$	−3.11099e15	−0.705139
$700$	1.29093e15	0.290312
$701$	1.68249e15	0.375407	0.187704	−	0.982226i	$-0.439896\pi$
$701$	1.68249e15	0.375407	0.187704	+	0.982226i	$0.439896\pi$
$702$	9.11928e15	2.01886
$703$	2.84866e14	0.0625729
$704$	1.27126e15	0.277067
$705$	−4.14736e15	−0.896874
$706$	4.57963e15	0.982663
$707$	6.00839e15	1.27924
$708$	−5.94143e15	−1.25519
$709$	−4.52773e15	−0.949131	−0.474565	−	0.880220i	$-0.657395\pi$
$709$	−4.52773e15	−0.949131	−0.474565	+	0.880220i	$0.657395\pi$
$710$	−4.83987e15	−1.00673
$711$	−3.06297e15	−0.632208
$712$	−6.34094e15	−1.29871
$713$	−3.70008e15	−0.752002
$714$	5.56596e15	1.12253
$715$	1.12551e15	0.225250
$716$	−3.45272e15	−0.685709
$717$	2.03417e15	0.400896
$718$	−5.09058e15	−0.995595
$719$	−7.61223e15	−1.47742	−0.738708	−	0.674025i	$-0.764564\pi$
$719$	−7.61223e15	−1.47742	−0.738708	+	0.674025i	$0.764564\pi$
$720$	−1.47642e14	−0.0284368
$721$	−2.49487e15	−0.476874
$722$	−7.74685e15	−1.46950
$723$	−6.86911e15	−1.29312
$724$	8.97380e15	1.67654
$725$	−1.68800e14	−0.0312977
$726$	−5.58746e15	−1.02816
$727$	1.14242e15	0.208635	0.104317	−	0.994544i	$-0.466734\pi$
$727$	1.14242e15	0.208635	0.104317	+	0.994544i	$0.466734\pi$
$728$	−7.27820e15	−1.31917
$729$	4.02961e15	0.724873
$730$	6.47090e15	1.15528
$731$	−1.54330e15	−0.273466
$732$	−6.58297e15	−1.15774
$733$	−6.31569e14	−0.110242	−0.0551212	−	0.998480i	$-0.517555\pi$
$733$	−6.31569e14	−0.110242	−0.0551212	+	0.998480i	$0.517555\pi$
$734$	7.18815e15	1.24534
$735$	4.32058e14	0.0742954
$736$	−5.13824e15	−0.876973
$737$	3.64912e14	0.0618184
$738$	−1.05722e16	−1.77768
$739$	3.82946e15	0.639136	0.319568	−	0.947563i	$-0.396462\pi$
$739$	3.82946e15	0.639136	0.319568	+	0.947563i	$0.396462\pi$
$740$	2.16692e15	0.358979
$741$	−1.48201e15	−0.243697
$742$	6.00161e14	0.0979595
$743$	−8.73266e15	−1.41484	−0.707421	−	0.706792i	$-0.750142\pi$
$743$	−8.73266e15	−1.41484	−0.707421	+	0.706792i	$0.750142\pi$
$744$	−3.47090e15	−0.558201
$745$	1.06409e16	1.69871
$746$	1.37238e16	2.17476
$747$	−4.83919e15	−0.761219
$748$	−1.82044e15	−0.284261
$749$	4.29333e15	0.665494
$750$	−6.18917e15	−0.952348
$751$	−5.86622e15	−0.896063	−0.448032	−	0.894018i	$-0.647875\pi$
$751$	−5.86622e15	−0.896063	−0.448032	+	0.894018i	$0.647875\pi$
$752$	−3.84092e14	−0.0582421
$753$	−2.58527e15	−0.389165
$754$	2.44258e15	0.365011
$755$	−2.59822e15	−0.385449
$756$	−1.20122e16	−1.76911
$757$	−3.70211e14	−0.0541280	−0.0270640	−	0.999634i	$-0.508616\pi$
$757$	−3.70211e14	−0.0541280	−0.0270640	+	0.999634i	$0.508616\pi$
$758$	−1.40327e16	−2.03686
$759$	−7.10245e14	−0.102348
$760$	2.41850e15	0.345997
$761$	−6.87224e15	−0.976074	−0.488037	−	0.872823i	$-0.662287\pi$
$761$	−6.87224e15	−0.976074	−0.488037	+	0.872823i	$0.662287\pi$
$762$	4.16170e15	0.586838
$763$	8.25216e15	1.15527
$764$	6.78328e14	0.0942815
$765$	−4.53456e15	−0.625745
$766$	−1.99061e16	−2.72727
$767$	1.04485e16	1.42128
$768$	−5.18234e15	−0.699905
$769$	1.12747e16	1.51185	0.755927	−	0.654655i	$-0.227186\pi$
$769$	1.12747e16	1.51185	0.755927	+	0.654655i	$0.227186\pi$
$770$	−2.38748e15	−0.317864
$771$	4.18802e15	0.553617
$772$	1.23271e16	1.61795
$773$	−6.66882e15	−0.869085	−0.434542	−	0.900651i	$-0.643090\pi$
$773$	−6.66882e15	−0.869085	−0.434542	+	0.900651i	$0.643090\pi$
$774$	1.95700e15	0.253230
$775$	−1.08264e15	−0.139099
$776$	−1.10901e16	−1.41481
$777$	1.09744e15	0.139017
$778$	−6.38888e15	−0.803594
$779$	4.70896e15	0.588124
$780$	−1.12734e16	−1.39808
$781$	8.01694e14	0.0987252
$782$	1.21961e16	1.49137
$783$	1.57070e15	0.190723
$784$	4.00135e13	0.00482467
$785$	−1.09977e16	−1.31680
$786$	1.68082e16	1.99846
$787$	−6.19590e15	−0.731549	−0.365775	−	0.930703i	$-0.619196\pi$
$787$	−6.19590e15	−0.731549	−0.365775	+	0.930703i	$0.619196\pi$
$788$	1.07533e15	0.126081
$789$	7.93598e15	0.924010
$790$	1.67122e16	1.93235
$791$	1.35982e16	1.56138
$792$	8.99417e14	0.102559
$793$	1.15767e16	1.31093
$794$	7.21407e15	0.811274
$795$	3.62194e14	0.0404503
$796$	−4.86978e15	−0.540116
$797$	−6.22882e15	−0.686097	−0.343048	−	0.939318i	$-0.611459\pi$
$797$	−6.22882e15	−0.686097	−0.343048	+	0.939318i	$0.611459\pi$
$798$	3.14370e15	0.343895
$799$	−1.17967e16	−1.28160
$800$	−1.50344e15	−0.162215
$801$	6.71497e15	0.719558
$802$	−2.47577e16	−2.63482
$803$	−1.07186e15	−0.113293
$804$	−3.65505e15	−0.383695
$805$	9.93249e15	1.03557
$806$	1.56661e16	1.62225
$807$	−1.06521e16	−1.09555
$808$	1.23501e16	1.26156
$809$	−1.62665e16	−1.65035	−0.825175	−	0.564878i	$-0.808923\pi$
$809$	−1.62665e16	−1.65035	−0.825175	+	0.564878i	$0.808923\pi$
$810$	−1.66458e15	−0.167740
$811$	1.36049e16	1.36170	0.680851	−	0.732422i	$-0.261610\pi$
$811$	1.36049e16	1.36170	0.680851	+	0.732422i	$0.261610\pi$
$812$	−3.21745e15	−0.319855
$813$	−3.34705e15	−0.330495
$814$	−5.78025e14	−0.0566908
$815$	−4.97481e15	−0.484630
$816$	3.11083e14	0.0301010
$817$	−8.71668e14	−0.0837780
$818$	1.55274e16	1.48237
$819$	7.70752e15	0.730892
$820$	3.58203e16	3.37406
$821$	−1.09717e15	−0.102656	−0.0513281	−	0.998682i	$-0.516345\pi$
$821$	−1.09717e15	−0.102656	−0.0513281	+	0.998682i	$0.516345\pi$
$822$	9.60271e15	0.892481
$823$	−1.91138e16	−1.76461	−0.882305	−	0.470678i	$-0.844009\pi$
$823$	−1.91138e16	−1.76461	−0.882305	+	0.470678i	$0.844009\pi$
$824$	−5.12815e15	−0.470285
$825$	−2.07817e14	−0.0189314
$826$	−2.21638e16	−2.00564
$827$	−1.66420e14	−0.0149598	−0.00747991	−	0.999972i	$-0.502381\pi$
$827$	−1.66420e14	−0.0149598	−0.00747991	+	0.999972i	$0.502381\pi$
$828$	−9.60364e15	−0.857569
$829$	−3.31553e15	−0.294105	−0.147053	−	0.989129i	$-0.546979\pi$
$829$	−3.31553e15	−0.294105	−0.147053	+	0.989129i	$0.546979\pi$
$830$	2.64037e16	2.32667
$831$	−2.70633e15	−0.236905
$832$	2.23924e16	1.94726
$833$	1.22894e15	0.106166
$834$	4.22768e15	0.362818
$835$	−1.92774e16	−1.64352
$836$	−1.02820e15	−0.0870851
$837$	1.00740e16	0.847644
$838$	−3.17163e16	−2.65119
$839$	−1.57566e16	−1.30850	−0.654248	−	0.756280i	$-0.727015\pi$
$839$	−1.57566e16	−1.30850	−0.654248	+	0.756280i	$0.727015\pi$
$840$	9.31727e15	0.768692
$841$	4.20707e14	0.0344828
$842$	−2.54782e16	−2.07469
$843$	−8.15543e15	−0.659774
$844$	−1.01557e16	−0.816259
$845$	6.28774e15	0.502091
$846$	1.49590e16	1.18677
$847$	−1.29431e16	−1.02019
$848$	3.35432e13	0.00262680
$849$	3.63159e15	0.282556
$850$	3.56857e15	0.275861
$851$	2.40472e15	0.184694
$852$	−8.02997e15	−0.612768
$853$	7.74799e15	0.587448	0.293724	−	0.955890i	$-0.405105\pi$
$853$	7.74799e15	0.587448	0.293724	+	0.955890i	$0.405105\pi$
$854$	−2.45570e16	−1.84993
$855$	−2.56116e15	−0.191701
$856$	8.82485e15	0.656299
$857$	−2.22228e16	−1.64212	−0.821059	−	0.570844i	$-0.806616\pi$
$857$	−2.22228e16	−1.64212	−0.821059	+	0.570844i	$0.806616\pi$
$858$	3.00716e15	0.220789
$859$	2.11120e16	1.54017	0.770084	−	0.637943i	$-0.220214\pi$
$859$	2.11120e16	1.54017	0.770084	+	0.637943i	$0.220214\pi$
$860$	−6.63063e15	−0.480632
$861$	1.81412e16	1.30662
$862$	4.02215e16	2.87852
$863$	2.33924e14	0.0166347	0.00831735	−	0.999965i	$-0.497352\pi$
$863$	2.33924e14	0.0166347	0.00831735	+	0.999965i	$0.497352\pi$
$864$	1.39896e16	0.988509
$865$	2.50301e16	1.75741
$866$	1.18793e16	0.828786
$867$	1.44716e14	0.0100325
$868$	−2.06359e16	−1.42156
$869$	−2.76828e15	−0.189496
$870$	−3.12689e15	−0.212695
$871$	6.42770e15	0.434466
$872$	1.69621e16	1.13931
$873$	1.17443e16	0.783880
$874$	6.88850e15	0.456890
$875$	−1.43370e16	−0.944960
$876$	1.07361e16	0.703190
$877$	−1.52073e16	−0.989813	−0.494907	−	0.868946i	$-0.664798\pi$
$877$	−1.52073e16	−0.989813	−0.494907	+	0.868946i	$0.664798\pi$
$878$	1.25602e16	0.812415
$879$	−7.34397e15	−0.472054
$880$	−1.33437e14	−0.00852358
$881$	1.42893e16	0.907073	0.453537	−	0.891238i	$-0.350162\pi$
$881$	1.42893e16	0.907073	0.453537	+	0.891238i	$0.350162\pi$
$882$	−1.55838e15	−0.0983096
$883$	−7.12053e15	−0.446404	−0.223202	−	0.974772i	$-0.571651\pi$
$883$	−7.12053e15	−0.446404	−0.223202	+	0.974772i	$0.571651\pi$
$884$	−3.20659e16	−1.99782
$885$	−1.33757e16	−0.828189
$886$	1.22549e16	0.754092
$887$	−1.43090e16	−0.875041	−0.437521	−	0.899208i	$-0.644143\pi$
$887$	−1.43090e16	−0.875041	−0.437521	+	0.899208i	$0.644143\pi$
$888$	2.25577e15	0.137096
$889$	9.64042e15	0.582286
$890$	−3.66384e16	−2.19933
$891$	2.75727e14	0.0164494
$892$	5.21321e16	3.09100
$893$	−6.66290e15	−0.392627
$894$	2.84307e16	1.66507
$895$	−7.77299e15	−0.452440
$896$	−3.00085e16	−1.73600
$897$	−1.25105e16	−0.719311
$898$	−4.31127e16	−2.46368
$899$	2.69831e15	0.153254
$900$	−2.81001e15	−0.158626
$901$	1.03022e15	0.0578022
$902$	−9.55502e15	−0.532839
$903$	−3.35810e15	−0.186127
$904$	2.79507e16	1.53981
$905$	2.02024e16	1.10620
$906$	−6.94198e15	−0.377814
$907$	1.15271e16	0.623562	0.311781	−	0.950154i	$-0.399074\pi$
$907$	1.15271e16	0.623562	0.311781	+	0.950154i	$0.399074\pi$
$908$	1.99725e15	0.107389
$909$	−1.30786e16	−0.698974
$910$	−4.20540e16	−2.23398
$911$	1.51373e16	0.799275	0.399637	−	0.916673i	$-0.369136\pi$
$911$	1.51373e16	0.799275	0.399637	+	0.916673i	$0.369136\pi$
$912$	1.75703e14	0.00922162
$913$	−4.37361e15	−0.228166
$914$	9.29973e14	0.0482244
$915$	−1.48200e16	−0.763892
$916$	4.49471e16	2.30291
$917$	3.89355e16	1.98296
$918$	−3.32059e16	−1.68105
$919$	−1.80745e16	−0.909560	−0.454780	−	0.890604i	$-0.650282\pi$
$919$	−1.80745e16	−0.909560	−0.454780	+	0.890604i	$0.650282\pi$
$920$	2.04160e16	1.02126
$921$	−4.64905e15	−0.231173
$922$	−2.63211e16	−1.30102
$923$	1.41213e16	0.693851
$924$	−3.96114e15	−0.193475
$925$	7.03618e14	0.0341631
$926$	−4.08253e16	−1.97047
$927$	5.43065e15	0.260563
$928$	3.74709e15	0.178723
$929$	−7.68004e15	−0.364147	−0.182074	−	0.983285i	$-0.558281\pi$
$929$	−7.68004e15	−0.364147	−0.182074	+	0.983285i	$0.558281\pi$
$930$	−2.00551e16	−0.945297
$931$	6.94119e14	0.0325245
$932$	−3.80184e16	−1.77095
$933$	2.58927e16	1.19902
$934$	6.70855e16	3.08831
$935$	−4.09829e15	−0.187559
$936$	1.58427e16	0.720793
$937$	2.24132e16	1.01376	0.506882	−	0.862015i	$-0.330798\pi$
$937$	2.24132e16	1.01376	0.506882	+	0.862015i	$0.330798\pi$
$938$	−1.36347e16	−0.613100
$939$	1.86670e16	0.834478
$940$	−5.06835e16	−2.25249
$941$	2.02660e16	0.895415	0.447708	−	0.894180i	$-0.352241\pi$
$941$	2.02660e16	0.895415	0.447708	+	0.894180i	$0.352241\pi$
$942$	−2.93840e16	−1.29072
$943$	3.97512e16	1.73594
$944$	−1.23874e15	−0.0537818
$945$	−2.70427e16	−1.16728
$946$	1.76871e15	0.0759025
$947$	−2.51760e16	−1.07414	−0.537070	−	0.843538i	$-0.680469\pi$
$947$	−2.51760e16	−1.07414	−0.537070	+	0.843538i	$0.680469\pi$
$948$	2.77278e16	1.17617
$949$	−1.88802e16	−0.796238
$950$	2.01556e15	0.0845117
$951$	−6.15141e15	−0.256438
$952$	2.65020e16	1.09844
$953$	3.13908e16	1.29358	0.646788	−	0.762670i	$-0.276112\pi$
$953$	3.13908e16	1.29358	0.646788	+	0.762670i	$0.276112\pi$
$954$	−1.30639e15	−0.0535249
$955$	1.52710e15	0.0622082
$956$	2.48589e16	1.00685
$957$	5.17951e14	0.0208580
$958$	−5.36116e16	−2.14659
$959$	2.22443e16	0.885558
$960$	−2.86659e16	−1.13468
$961$	−8.10223e15	−0.318879
$962$	−1.01815e16	−0.398429
$963$	−9.34541e15	−0.363625
$964$	−8.39452e16	−3.24767
$965$	2.77516e16	1.06755
$966$	2.65379e16	1.01506
$967$	−3.64552e15	−0.138648	−0.0693240	−	0.997594i	$-0.522084\pi$
$967$	−3.64552e15	−0.138648	−0.0693240	+	0.997594i	$0.522084\pi$
$968$	−2.66043e16	−1.00609
$969$	5.39641e15	0.202920
$970$	−6.40796e16	−2.39594
$971$	−1.58276e16	−0.588451	−0.294226	−	0.955736i	$-0.595062\pi$
$971$	−1.58276e16	−0.588451	−0.294226	+	0.955736i	$0.595062\pi$
$972$	4.27546e16	1.58059
$973$	9.79325e15	0.360003
$974$	7.50672e16	2.74395
$975$	−3.66056e15	−0.133052
$976$	−1.37250e15	−0.0496064
$977$	−2.50430e16	−0.900050	−0.450025	−	0.893016i	$-0.648585\pi$
$977$	−2.50430e16	−0.900050	−0.450025	+	0.893016i	$0.648585\pi$
$978$	−1.32918e16	−0.475030
$979$	6.06892e15	0.215678
$980$	5.28004e15	0.186592
$981$	−1.79627e16	−0.631237
$982$	−3.16164e16	−1.10484
$983$	2.38756e16	0.829679	0.414840	−	0.909895i	$-0.363838\pi$
$983$	2.38756e16	0.829679	0.414840	+	0.909895i	$0.363838\pi$
$984$	3.72890e16	1.28857
$985$	2.42086e15	0.0831898
$986$	−8.89411e15	−0.303934
$987$	−2.56688e16	−0.872290
$988$	−1.81111e16	−0.612043
$989$	−7.35827e15	−0.247284
$990$	5.19689e15	0.173680
$991$	4.25523e16	1.41422	0.707112	−	0.707101i	$-0.249998\pi$
$991$	4.25523e16	1.41422	0.707112	+	0.707101i	$0.249998\pi$
$992$	2.40329e16	0.794313
$993$	3.55117e16	1.16721
$994$	−2.99548e16	−0.979133
$995$	−1.09632e16	−0.356376
$996$	4.38072e16	1.41618
$997$	2.89148e16	0.929601	0.464800	−	0.885415i	$-0.346126\pi$
$997$	2.89148e16	0.929601	0.464800	+	0.885415i	$0.346126\pi$
$998$	−4.98318e16	−1.59327
$999$	−6.54722e15	−0.208184

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.12.a.b.1.12	✓	14
3.2	odd	2		261.12.a.e.1.3		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.12.a.b.1.12	✓	14	1.1	even	1	trivial
261.12.a.e.1.3		14	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q+73.5071 q^{2} +274.559 q^{3} +3355.30 q^{4} +7553.66 q^{5} +20182.1 q^{6} +46751.0 q^{7} +96095.7 q^{8} -101764. q^{9} +O(q^{10})\)	\(q+73.5071 q^{2} +274.559 q^{3} +3355.30 q^{4} +7553.66 q^{5} +20182.1 q^{6} +46751.0 q^{7} +96095.7 q^{8} -101764. q^{9} +555248. q^{10} -91973.4 q^{11} +921228. q^{12} -1.62005e6 q^{13} +3.43653e6 q^{14} +2.07393e6 q^{15} +192069. q^{16} +5.89907e6 q^{17} -7.48039e6 q^{18} +3.33185e6 q^{19} +2.53448e7 q^{20} +1.28359e7 q^{21} -6.76070e6 q^{22} +2.81261e7 q^{23} +2.63840e7 q^{24} +8.22966e6 q^{25} -1.19085e8 q^{26} -7.65777e7 q^{27} +1.56863e8 q^{28} -2.05111e7 q^{29} +1.52448e8 q^{30} -1.31553e8 q^{31} -1.82686e8 q^{32} -2.52521e7 q^{33} +4.33623e8 q^{34} +3.53141e8 q^{35} -3.41449e8 q^{36} +8.54978e7 q^{37} +2.44915e8 q^{38} -4.44801e8 q^{39} +7.25874e8 q^{40} +1.41332e9 q^{41} +9.43532e8 q^{42} -2.61617e8 q^{43} -3.08598e8 q^{44} -7.68692e8 q^{45} +2.06747e9 q^{46} -1.99976e9 q^{47} +5.27344e7 q^{48} +2.08329e8 q^{49} +6.04939e8 q^{50} +1.61964e9 q^{51} -5.43576e9 q^{52} +1.74642e8 q^{53} -5.62900e9 q^{54} -6.94736e8 q^{55} +4.49257e9 q^{56} +9.14790e8 q^{57} -1.50772e9 q^{58} -6.44946e9 q^{59} +6.95865e9 q^{60} -7.14586e9 q^{61} -9.67010e9 q^{62} -4.75758e9 q^{63} -1.38220e10 q^{64} -1.22373e10 q^{65} -1.85621e9 q^{66} -3.96759e9 q^{67} +1.97931e10 q^{68} +7.72229e9 q^{69} +2.59584e10 q^{70} -8.71659e9 q^{71} -9.77910e9 q^{72} +1.16541e10 q^{73} +6.28470e9 q^{74} +2.25953e9 q^{75} +1.11793e10 q^{76} -4.29985e9 q^{77} -3.26960e10 q^{78} +3.00987e10 q^{79} +1.45082e9 q^{80} -2.99790e9 q^{81} +1.03889e11 q^{82} +4.75530e10 q^{83} +4.30683e10 q^{84} +4.45595e10 q^{85} -1.92307e10 q^{86} -5.63153e9 q^{87} -8.83824e9 q^{88} -6.59856e10 q^{89} -5.65043e10 q^{90} -7.57391e10 q^{91} +9.43715e10 q^{92} -3.61192e10 q^{93} -1.46997e11 q^{94} +2.51676e10 q^{95} -5.01580e10 q^{96} -1.15407e11 q^{97} +1.53136e10 q^{98} +9.35959e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9}+O(q^{10}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9	\( 14 q + 476 q^{3} + 18362 q^{4} + 9760 q^{5} + 18454 q^{6} + 85024 q^{7} + 126588 q^{8} + 1372146 q^{9} + 713576 q^{10} + 398020 q^{11} - 4026800 q^{12} + 2272440 q^{13} - 7199712 q^{14} - 4763864 q^{15} + 19015138 q^{16} + 5623508 q^{17} - 204156 q^{18} + 29803300 q^{19} + 65161006 q^{20} + 51227832 q^{21} + 167334266 q^{22} + 52654304 q^{23} + 221514842 q^{24} + 194970462 q^{25} + 373581536 q^{26} + 397348256 q^{27} + 319501772 q^{28} - 287156086 q^{29} + 423014226 q^{30} + 634041348 q^{31} + 1260290884 q^{32} + 1180833420 q^{33} + 1316105060 q^{34} + 1599853768 q^{35} + 3198076132 q^{36} + 488665204 q^{37} + 1892845072 q^{38} + 1972619104 q^{39} + 1826486880 q^{40} + 198215164 q^{41} + 1011384468 q^{42} + 2193188100 q^{43} + 26522720 q^{44} - 1129321956 q^{45} - 1567525268 q^{46} - 4175934476 q^{47} - 15582938120 q^{48} + 1105222462 q^{49} - 6630582612 q^{50} + 3297462720 q^{51} - 4557341374 q^{52} - 13223081840 q^{53} - 8946135054 q^{54} - 2726359424 q^{55} - 27538267872 q^{56} - 24477013312 q^{57} + 352219640 q^{59} - 36042747924 q^{60} - 7658546476 q^{61} - 10024135594 q^{62} - 23037581736 q^{63} + 14721327762 q^{64} + 1152802884 q^{65} - 99505241364 q^{66} + 21781534280 q^{67} - 104178000188 q^{68} - 14601399408 q^{69} - 67948872984 q^{70} - 5573287168 q^{71} - 24062143544 q^{72} + 39661511924 q^{73} + 28506052056 q^{74} + 81845109044 q^{75} + 166950090320 q^{76} + 38773567192 q^{77} + 54249159006 q^{78} + 105565209020 q^{79} + 146242150550 q^{80} + 170581084750 q^{81} + 47345182756 q^{82} + 127846064024 q^{83} + 215311861496 q^{84} + 83883234552 q^{85} - 103162039382 q^{86} - 9763306924 q^{87} + 418253082102 q^{88} + 187826099404 q^{89} + 96335639960 q^{90} + 58390389864 q^{91} - 259645875396 q^{92} + 394641636020 q^{93} + 117694719934 q^{94} + 69935059424 q^{95} + 12533631786 q^{96} + 137285937500 q^{97} - 484896369168 q^{98} + 235419947204 q^{99}+O(q^{100}) \) 14 * q + 476 * q^3 + 18362 * q^4 + 9760 * q^5 + 18454 * q^6 + 85024 * q^7 + 126588 * q^8 + 1372146 * q^9 + 713576 * q^10 + 398020 * q^11 - 4026800 * q^12 + 2272440 * q^13 - 7199712 * q^14 - 4763864 * q^15 + 19015138 * q^16 + 5623508 * q^17 - 204156 * q^18 + 29803300 * q^19 + 65161006 * q^20 + 51227832 * q^21 + 167334266 * q^22 + 52654304 * q^23 + 221514842 * q^24 + 194970462 * q^25 + 373581536 * q^26 + 397348256 * q^27 + 319501772 * q^28 - 287156086 * q^29 + 423014226 * q^30 + 634041348 * q^31 + 1260290884 * q^32 + 1180833420 * q^33 + 1316105060 * q^34 + 1599853768 * q^35 + 3198076132 * q^36 + 488665204 * q^37 + 1892845072 * q^38 + 1972619104 * q^39 + 1826486880 * q^40 + 198215164 * q^41 + 1011384468 * q^42 + 2193188100 * q^43 + 26522720 * q^44 - 1129321956 * q^45 - 1567525268 * q^46 - 4175934476 * q^47 - 15582938120 * q^48 + 1105222462 * q^49 - 6630582612 * q^50 + 3297462720 * q^51 - 4557341374 * q^52 - 13223081840 * q^53 - 8946135054 * q^54 - 2726359424 * q^55 - 27538267872 * q^56 - 24477013312 * q^57 + 352219640 * q^59 - 36042747924 * q^60 - 7658546476 * q^61 - 10024135594 * q^62 - 23037581736 * q^63 + 14721327762 * q^64 + 1152802884 * q^65 - 99505241364 * q^66 + 21781534280 * q^67 - 104178000188 * q^68 - 14601399408 * q^69 - 67948872984 * q^70 - 5573287168 * q^71 - 24062143544 * q^72 + 39661511924 * q^73 + 28506052056 * q^74 + 81845109044 * q^75 + 166950090320 * q^76 + 38773567192 * q^77 + 54249159006 * q^78 + 105565209020 * q^79 + 146242150550 * q^80 + 170581084750 * q^81 + 47345182756 * q^82 + 127846064024 * q^83 + 215311861496 * q^84 + 83883234552 * q^85 - 103162039382 * q^86 - 9763306924 * q^87 + 418253082102 * q^88 + 187826099404 * q^89 + 96335639960 * q^90 + 58390389864 * q^91 - 259645875396 * q^92 + 394641636020 * q^93 + 117694719934 * q^94 + 69935059424 * q^95 + 12533631786 * q^96 + 137285937500 * q^97 - 484896369168 * q^98 + 235419947204 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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