LMFDB - Embedded newform 5.34.b.a.4.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,34,Mod(4,5)]

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([1]))

N = Newforms(chi, 34, names="a")

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

chi := DirichletCharacter("5.4");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 34 $
Character orbit:	$[\chi]$	$=$	5.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$34.4914144405$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 26286285043 x^{14} + \cdots + 16\!\cdots\!36 $ x^16 + 26286285043x^14 + 277176279803774573548x^12 + 1496006322727341104924267746816x^10 + 4376228902975645752284567792282218577920x^8 + 6785210496827316795155770011788917433647451078656x^6 + 5093319366938751307797338793282286802764384084972313509888x^4 + 1608229292592013531797229664939538769264311330074914543142623510528*x^2 + 163532475457876517394407745867705361011086521692855999713211555842344615936
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{83}\cdot 3^{26}\cdot 5^{53}\cdot 7^{4}\cdot 11^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			4.3
Root			$-78034.2i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.34.b.a.4.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-156068. i q^{2} -6.96239e7i q^{3} -1.57674e10 q^{4} +(-2.14154e11 - 2.65619e11i) q^{5} -1.08661e13 q^{6} +1.55193e14i q^{7} +1.12018e15i q^{8} +7.11573e14 q^{9} +O(q^{10})$	\(q-156068. i q^{2} -6.96239e7i q^{3} -1.57674e10 q^{4} +(-2.14154e11 - 2.65619e11i) q^{5} -1.08661e13 q^{6} +1.55193e14i q^{7} +1.12018e15i q^{8} +7.11573e14 q^{9} +(-4.14548e16 + 3.34226e16i) q^{10} +4.13199e16 q^{11} +1.09779e18i q^{12} -2.38246e18i q^{13} +2.42207e19 q^{14} +(-1.84934e19 + 1.49102e19i) q^{15} +3.93836e19 q^{16} +2.91772e20i q^{17} -1.11054e20i q^{18} +3.61361e20 q^{19} +(3.37665e21 + 4.18813e21i) q^{20} +1.08051e22 q^{21} -6.44874e21i q^{22} +3.81748e22i q^{23} +7.79913e22 q^{24} +(-2.46919e22 + 1.13767e23i) q^{25} -3.71827e23 q^{26} -4.36586e23i q^{27} -2.44699e24i q^{28} -1.65188e24 q^{29} +(2.32701e24 + 2.88624e24i) q^{30} -2.76253e24 q^{31} +3.47573e24i q^{32} -2.87685e24i q^{33} +4.55364e25 q^{34} +(4.12223e25 - 3.32351e25i) q^{35} -1.12197e25 q^{36} +8.70723e24i q^{37} -5.63971e25i q^{38} -1.65876e26 q^{39} +(2.97541e26 - 2.39891e26i) q^{40} +2.69048e26 q^{41} -1.68634e27i q^{42} -1.33984e26i q^{43} -6.51509e26 q^{44} +(-1.52386e26 - 1.89008e26i) q^{45} +5.95788e27 q^{46} +2.88434e27i q^{47} -2.74204e27i q^{48} -1.63539e28 q^{49} +(1.77554e28 + 3.85362e27i) q^{50} +2.03143e28 q^{51} +3.75653e28i q^{52} -2.92563e28i q^{53} -6.81373e28 q^{54} +(-8.84880e27 - 1.09754e28i) q^{55} -1.73844e29 q^{56} -2.51594e28i q^{57} +2.57806e29i q^{58} -1.51134e29 q^{59} +(2.91594e29 - 2.35096e29i) q^{60} +2.88604e29 q^{61} +4.31144e29i q^{62} +1.10431e29i q^{63} +8.80755e29 q^{64} +(-6.32827e29 + 5.10212e29i) q^{65} -4.48986e29 q^{66} +8.72314e29i q^{67} -4.60049e30i q^{68} +2.65788e30 q^{69} +(-5.18696e30 - 6.43349e30i) q^{70} +3.08526e30 q^{71} +7.97090e29i q^{72} +2.41300e30i q^{73} +1.35892e30 q^{74} +(7.92087e30 + 1.71914e30i) q^{75} -5.69774e30 q^{76} +6.41256e30i q^{77} +2.58880e31i q^{78} +3.21352e31 q^{79} +(-8.43414e30 - 1.04610e31i) q^{80} -2.64411e31 q^{81} -4.19898e31i q^{82} +7.79056e31i q^{83} -1.70369e32 q^{84} +(7.75002e31 - 6.24839e31i) q^{85} -2.09107e31 q^{86} +1.15010e32i q^{87} +4.62857e31i q^{88} -1.41115e32 q^{89} +(-2.94981e31 + 2.37826e31i) q^{90} +3.69741e32 q^{91} -6.01918e32i q^{92} +1.92338e32i q^{93} +4.50154e32 q^{94} +(-7.73868e31 - 9.59845e31i) q^{95} +2.41994e32 q^{96} -7.13656e32i q^{97} +2.55232e33i q^{98} +2.94021e31 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 72851326872 q^{4} - 232168160280 q^{5} + 11001777346872 q^{6} - 27\!\cdots\!68 q^{9}+O(q^{10}) $ 16 * q - 72851326872 * q^4 - 232168160280 * q^5 + 11001777346872 * q^6 - 27535156574590368 * q^9	$ 16 q - 72851326872 q^{4} - 232168160280 q^{5} + 11001777346872 q^{6} - 27\!\cdots\!68 q^{9}+ \cdots + 34\!\cdots\!24 q^{99}+O(q^{100}) $ 16 * q - 72851326872 * q^4 - 232168160280 * q^5 + 11001777346872 * q^6 - 27535156574590368 * q^9 - 22271193818331880 * q^10 + 219974590742466912 * q^11 - 10416043581549356184 * q^14 + 9232415497377901440 * q^15 + 133171456389985196576 * q^16 - 2949217257058889591200 * q^19 + 5571772909456424216760 * q^20 + 20126160533851210892592 * q^21 - 236696360036140740492000 * q^24 + 269473151678676722148400 * q^25 + 23043234216449373353232 * q^26 + 2210824656972934579370400 * q^29 - 7438800885032297852420760 * q^30 + 4805180075928582021889472 * q^31 - 106706080442140703440064 * q^34 + 34840114703893102459924320 * q^35 + 150609707516636111776170456 * q^36 - 950668737676648885834065216 * q^39 + 967967034953888345833396000 * q^40 + 960625982433026021733974352 * q^41 - 4300041994750366563328828704 * q^44 + 5959973976670208219568382440 * q^45 + 4030532465737707969346868392 * q^46 - 48902999941413820155855454112 * q^49 + 64132734499011351066825776400 * q^50 + 37677263492556888574173469632 * q^51 - 416785644990759180210455480400 * q^54 + 208827421951347317583761567040 * q^55 + 209868986171565551575474447200 * q^56 - 204679212804521237512362904800 * q^59 - 320542648209593925139588560480 * q^60 - 62902839261738400132019069488 * q^61 + 3273202940251902417009873735808 * q^64 - 1155813780125630532662955267360 * q^65 - 2991219624550267460630717491296 * q^66 + 6899695112224183044828868241904 * q^69 - 5880904834264312779374002982280 * q^70 - 87525095316001019795902439808 * q^71 + 43140282179597200538055251968176 * q^74 - 27726088944293536006405507003200 * q^75 - 38605994956626944020944749752800 * q^76 - 10590745643822309766800662264000 * q^79 + 24913342429758171577982759437920 * q^80 + 126385893984816788804508532470336 * q^81 - 401968339664232685914350670917664 * q^84 + 174616747052458036927895334806720 * q^85 - 18805496634715830052189508032488 * q^86 - 816457769414638729740610145056800 * q^89 + 814730708455223899676092744179240 * q^90 + 572310345418666359618454810906752 * q^91 + 1084618018208246129370832376900296 * q^94 - 960346549067575215463879922304000 * q^95 - 1376269400022374885061468958478208 * q^96 + 3432482025669259323040953857901024 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/5\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$		−	156068.i		−	1.68392i	−0.539544	−	0.841958i	$-0.681403\pi$
$2$		−	156068.i		−	1.68392i	0.539544	−	0.841958i	$-0.318597\pi$
$3$		−	6.96239e7i		−	0.933808i	−0.884308	−	0.466904i	$-0.845369\pi$
$3$		−	6.96239e7i		−	0.933808i	0.884308	−	0.466904i	$-0.154631\pi$
$4$	−1.57674e10			−1.83557
$5$	−2.14154e11	−	2.65619e11i	−0.627654	−	0.778493i
$5$	−2.14154e11	−	2.65619e11i	−0.627654	−	0.778493i
$6$	−1.08661e13			−1.57245
$7$			1.55193e14i			1.76504i	0.470275	+	0.882520i	$0.344155\pi$
$7$			1.55193e14i			1.76504i	−0.470275	+	0.882520i	$0.655845\pi$
$8$			1.12018e15i			1.40703i
$9$	7.11573e14			0.128002
$10$	−4.14548e16	+	3.34226e16i	−1.31092	+	1.05692i
$11$	4.13199e16			0.271132			0.135566	−	0.990768i	$-0.456715\pi$
$11$	4.13199e16			0.271132			0.135566	+	0.990768i	$0.456715\pi$
$12$			1.09779e18i			1.71407i
$13$		−	2.38246e18i		−	0.993025i	−0.868029	−	0.496513i	$-0.834614\pi$
$13$		−	2.38246e18i		−	0.993025i	0.868029	−	0.496513i	$-0.165386\pi$
$14$	2.42207e19			2.97218
$15$	−1.84934e19	+	1.49102e19i	−0.726963	+	0.586108i
$16$	3.93836e19			0.533747
$17$			2.91772e20i			1.45424i	0.686511	+	0.727120i	$0.259142\pi$
$17$			2.91772e20i			1.45424i	−0.686511	+	0.727120i	$0.740858\pi$
$18$		−	1.11054e20i		−	0.215545i
$19$	3.61361e20			0.287414			0.143707	−	0.989620i	$-0.454098\pi$
$19$	3.61361e20			0.287414			0.143707	+	0.989620i	$0.454098\pi$
$20$	3.37665e21	+	4.18813e21i	1.15210	+	1.42898i
$21$	1.08051e22			1.64821
$22$		−	6.44874e21i		−	0.456563i
$23$			3.81748e22i			1.29798i	0.760798	+	0.648989i	$0.224808\pi$
$23$			3.81748e22i			1.29798i	−0.760798	+	0.648989i	$0.775192\pi$
$24$	7.79913e22			1.31390
$25$	−2.46919e22	+	1.13767e23i	−0.212102	+	0.977248i
$26$	−3.71827e23			−1.67217
$27$		−	4.36586e23i		−	1.05334i
$28$		−	2.44699e24i		−	3.23985i
$29$	−1.65188e24			−1.22577			−0.612887	−	0.790170i	$-0.709992\pi$
$29$	−1.65188e24			−1.22577			−0.612887	+	0.790170i	$0.709992\pi$
$30$	2.32701e24	+	2.88624e24i	0.986956	+	1.22414i
$31$	−2.76253e24			−0.682086			−0.341043	−	0.940048i	$-0.610780\pi$
$31$	−2.76253e24			−0.682086			−0.341043	+	0.940048i	$0.610780\pi$
$32$			3.47573e24i			0.508244i
$33$		−	2.87685e24i		−	0.253185i
$34$	4.55364e25			2.44882
$35$	4.12223e25	−	3.32351e25i	1.37407	−	1.10783i
$36$	−1.12197e25			−0.234957
$37$			8.70723e24i			0.116025i	0.998316	+	0.0580125i	$0.0184763\pi$
$37$			8.70723e24i			0.116025i	−0.998316	+	0.0580125i	$0.981524\pi$
$38$		−	5.63971e25i		−	0.483980i
$39$	−1.65876e26			−0.927295
$40$	2.97541e26	−	2.39891e26i	1.09536	−	0.883127i
$41$	2.69048e26			0.659015			0.329508	−	0.944153i	$-0.393117\pi$
$41$	2.69048e26			0.659015			0.329508	+	0.944153i	$0.393117\pi$
$42$		−	1.68634e27i		−	2.77544i
$43$		−	1.33984e26i		−	0.149563i	−0.997200	−	0.0747815i	$-0.976174\pi$
$43$		−	1.33984e26i		−	0.149563i	0.997200	−	0.0747815i	$-0.0238259\pi$
$44$	−6.51509e26			−0.497681
$45$	−1.52386e26	−	1.89008e26i	−0.0803412	−	0.0996489i
$46$	5.95788e27			2.18568
$47$			2.88434e27i			0.742047i	0.928623	+	0.371024i	$0.120993\pi$
$47$			2.88434e27i			0.742047i	−0.928623	+	0.371024i	$0.879007\pi$
$48$		−	2.74204e27i		−	0.498418i
$49$	−1.63539e28			−2.11537
$50$	1.77554e28	+	3.85362e27i	1.64560	+	0.357161i
$51$	2.03143e28			1.35798
$52$			3.75653e28i			1.82277i
$53$		−	2.92563e28i		−	1.03673i	−0.855158	−	0.518367i	$-0.826540\pi$
$53$		−	2.92563e28i		−	1.03673i	0.855158	−	0.518367i	$-0.173460\pi$
$54$	−6.81373e28			−1.77373
$55$	−8.84880e27	−	1.09754e28i	−0.170177	−	0.211074i
$56$	−1.73844e29			−2.48346
$57$		−	2.51594e28i		−	0.268389i
$58$			2.57806e29i			2.06410i
$59$	−1.51134e29			−0.912650			−0.456325	−	0.889813i	$-0.650834\pi$
$59$	−1.51134e29			−0.912650			−0.456325	+	0.889813i	$0.650834\pi$
$60$	2.91594e29	−	2.35096e29i	1.33439	−	1.07584i
$61$	2.88604e29			1.00545			0.502725	−	0.864446i	$-0.332331\pi$
$61$	2.88604e29			1.00545			0.502725	+	0.864446i	$0.332331\pi$
$62$			4.31144e29i			1.14857i
$63$			1.10431e29i			0.225929i
$64$	8.80755e29			1.38959
$65$	−6.32827e29	+	5.10212e29i	−0.773063	+	0.623276i
$66$	−4.48986e29			−0.426342
$67$			8.72314e29i			0.646307i	0.946347	+	0.323153i	$0.104743\pi$
$67$			8.72314e29i			0.646307i	−0.946347	+	0.323153i	$0.895257\pi$
$68$		−	4.60049e30i		−	2.66936i
$69$	2.65788e30			1.21206
$70$	−5.18696e30	−	6.43349e30i	−1.86550	−	2.31382i
$71$	3.08526e30			0.878069			0.439034	−	0.898470i	$-0.355321\pi$
$71$	3.08526e30			0.878069			0.439034	+	0.898470i	$0.355321\pi$
$72$			7.97090e29i			0.180103i
$73$			2.41300e30i			0.434240i	0.976145	+	0.217120i	$0.0696662\pi$
$73$			2.41300e30i			0.434240i	−0.976145	+	0.217120i	$0.930334\pi$
$74$	1.35892e30			0.195376
$75$	7.92087e30	+	1.71914e30i	0.912562	+	0.198062i
$76$	−5.69774e30			−0.527568
$77$			6.41256e30i			0.478558i
$78$			2.58880e31i			1.56149i
$79$	3.21352e31			1.57085			0.785423	−	0.618960i	$-0.212446\pi$
$79$	3.21352e31			1.57085			0.785423	+	0.618960i	$0.212446\pi$
$80$	−8.43414e30	−	1.04610e31i	−0.335009	−	0.415518i
$81$	−2.64411e31			−0.855613
$82$		−	4.19898e31i		−	1.10973i
$83$			7.79056e31i			1.68570i	0.538148	+	0.842850i	$0.319124\pi$
$83$			7.79056e31i			1.68570i	−0.538148	+	0.842850i	$0.680876\pi$
$84$	−1.70369e32			−3.02540
$85$	7.75002e31	−	6.24839e31i	1.13211	−	0.912759i
$86$	−2.09107e31			−0.251851
$87$			1.15010e32i			1.14464i
$88$			4.62857e31i			0.381490i
$89$	−1.41115e32			−0.965245			−0.482623	−	0.875828i	$-0.660316\pi$
$89$	−1.41115e32			−0.965245			−0.482623	+	0.875828i	$0.660316\pi$
$90$	−2.94981e31	+	2.37826e31i	−0.167800	+	0.135288i
$91$	3.69741e32			1.75273
$92$		−	6.01918e32i		−	2.38253i
$93$			1.92338e32i			0.636937i
$94$	4.50154e32			1.24954
$95$	−7.73868e31	−	9.59845e31i	−0.180396	−	0.223749i
$96$	2.41994e32			0.474602
$97$		−	7.13656e32i		−	1.17966i	−0.807529	−	0.589828i	$-0.799196\pi$
$97$		−	7.13656e32i		−	1.17966i	0.807529	−	0.589828i	$-0.200804\pi$
$98$			2.55232e33i			3.56210i
$99$	2.94021e31			0.0347055
$100$	3.89327e32	−	1.79381e33i	0.389327	−	1.79381i
$101$	−9.02530e32			−0.765877			−0.382939	−	0.923774i	$-0.625088\pi$
$101$	−9.02530e32			−0.765877			−0.382939	+	0.923774i	$0.625088\pi$
$102$		−	3.17042e33i		−	2.28672i
$103$			6.15871e32i			0.378160i	0.981962	+	0.189080i	$0.0605505\pi$
$103$			6.15871e32i			0.378160i	−0.981962	+	0.189080i	$0.939449\pi$
$104$	2.66878e33			1.39722
$105$	−2.31396e33	−	2.87005e33i	−1.03450	−	1.28312i
$106$	−4.56598e33			−1.74577
$107$			4.51029e33i			1.47697i	0.674270	+	0.738485i	$0.264459\pi$
$107$			4.51029e33i			1.47697i	−0.674270	+	0.738485i	$0.735541\pi$
$108$			6.88384e33i			1.93348i
$109$	1.07835e33			0.260149			0.130074	−	0.991504i	$-0.458478\pi$
$109$	1.07835e33			0.260149			0.130074	+	0.991504i	$0.458478\pi$
$110$	−1.71291e33	+	1.38102e33i	−0.355431	+	0.286563i
$111$	6.06231e32			0.108345
$112$			6.11206e33i			0.942085i
$113$			2.37121e31i			0.00315629i	0.999999	+	0.00157814i	$0.000502339\pi$
$113$			2.37121e31i			0.00315629i	−0.999999	+	0.00157814i	$0.999498\pi$
$114$	−3.92659e33			−0.451944
$115$	1.01400e34	−	8.17526e33i	1.01047	−	0.814681i
$116$	2.60458e34			2.24999
$117$		−	1.69529e33i		−	0.127110i
$118$			2.35873e34i			1.53682i
$119$	−4.52809e34			−2.56679
$120$	−1.67021e34	−	2.07160e34i	−0.824671	−	1.02286i
$121$	−2.15178e34			−0.926488
$122$		−	4.50420e34i		−	1.69309i
$123$		−	1.87321e34i		−	0.615394i
$124$	4.35580e34			1.25202
$125$	3.55065e34	−	1.78049e34i	0.893906	−	0.448254i
$126$	1.72348e34			0.380446
$127$			6.78580e34i			1.31474i	0.753568	+	0.657370i	$0.228331\pi$
$127$			6.78580e34i			1.31474i	−0.753568	+	0.657370i	$0.771669\pi$
$128$		−	1.07602e35i		−	1.83170i
$129$	−9.32850e33			−0.139663
$130$	7.96280e34	+	9.87644e34i	1.04954	+	1.30177i
$131$	7.18678e34			0.834753			0.417377	−	0.908734i	$-0.362950\pi$
$131$	7.18678e34			0.834753			0.417377	+	0.908734i	$0.362950\pi$
$132$			4.53606e34i			0.464739i
$133$			5.60808e34i			0.507296i
$134$	1.36141e35			1.08833
$135$	−1.15966e35	+	9.34964e34i	−0.820016	+	0.661131i
$136$	−3.26837e35			−2.04616
$137$			1.24185e34i			0.0688940i	0.999407	+	0.0344470i	$0.0109670\pi$
$137$			1.24185e34i			0.0688940i	−0.999407	+	0.0344470i	$0.989033\pi$
$138$		−	4.14811e35i		−	2.04101i
$139$	−3.36802e34			−0.147106			−0.0735531	−	0.997291i	$-0.523434\pi$
$139$	−3.36802e34			−0.147106			−0.0735531	+	0.997291i	$0.523434\pi$
$140$	−6.49969e35	+	5.24032e35i	−2.52220	+	2.03351i
$141$	2.00819e35			0.692930
$142$		−	4.81511e35i		−	1.47859i
$143$		−	9.84431e34i		−	0.269241i
$144$	2.80243e34			0.0683210
$145$	3.53755e35	+	4.38770e35i	0.769362	+	0.954256i
$146$	3.76593e35			0.731223
$147$			1.13862e36i			1.97535i
$148$		−	1.37291e35i		−	0.212972i
$149$	−7.60967e35			−1.05631			−0.528156	−	0.849147i	$-0.677116\pi$
$149$	−7.60967e35			−1.05631			−0.528156	+	0.849147i	$0.677116\pi$
$150$	2.68304e35	−	1.23620e36i	0.333520	−	1.53668i
$151$	3.06240e35			0.341147			0.170574	−	0.985345i	$-0.445438\pi$
$151$	3.06240e35			0.341147			0.170574	+	0.985345i	$0.445438\pi$
$152$			4.04790e35i			0.404399i
$153$			2.07617e35i			0.186146i
$154$	1.00080e36			0.805851
$155$	5.91605e35	+	7.33781e35i	0.428114	+	0.530999i
$156$	2.61544e36			1.70212
$157$		−	2.10956e36i		−	1.23551i	−0.786370	−	0.617755i	$-0.788042\pi$
$157$		−	2.10956e36i		−	1.23551i	0.786370	−	0.617755i	$-0.211958\pi$
$158$		−	5.01528e36i		−	2.64517i
$159$	−2.03694e36			−0.968110
$160$	9.23222e35	−	7.44341e35i	0.395664	−	0.319001i
$161$	−5.92446e36			−2.29098
$162$			4.12663e36i			1.44078i
$163$			2.09987e36i			0.662365i	0.943567	+	0.331182i	$0.107448\pi$
$163$			2.09987e36i			0.662365i	−0.943567	+	0.331182i	$0.892552\pi$
$164$	−4.24219e36			−1.20967
$165$	−7.64148e35	+	6.16088e35i	−0.197103	+	0.158912i
$166$	1.21586e37			2.83858
$167$		−	4.97146e36i		−	1.05114i	−0.850749	−	0.525572i	$-0.823851\pi$
$167$		−	4.97146e36i		−	1.05114i	0.850749	−	0.525572i	$-0.176149\pi$
$168$			1.21037e37i			2.31908i
$169$	8.00138e34			0.0139006
$170$	−9.75177e36	−	1.20953e37i	−1.53701	−	1.90639i
$171$	2.57135e35			0.0367896
$172$			2.11259e36i			0.274533i
$173$			1.51427e37i			1.78831i	0.447753	+	0.894157i	$0.352224\pi$
$173$			1.51427e37i			1.78831i	−0.447753	+	0.894157i	$0.647776\pi$
$174$	1.79494e37			1.92747
$175$	−1.76558e37	−	3.83201e36i	−1.72488	−	0.374368i
$176$	1.62733e36			0.144716
$177$			1.05225e37i			0.852240i
$178$			2.20236e37i			1.62539i
$179$	−9.15862e36			−0.616247			−0.308124	−	0.951346i	$-0.599701\pi$
$179$	−9.15862e36			−0.616247			−0.308124	+	0.951346i	$0.599701\pi$
$180$	2.40273e36	+	2.98016e36i	0.147472	+	0.182913i
$181$	1.09431e37			0.612975			0.306488	−	0.951875i	$-0.400846\pi$
$181$	1.09431e37			0.612975			0.306488	+	0.951875i	$0.400846\pi$
$182$		−	5.77049e37i		−	2.95145i
$183$		−	2.00938e37i		−	0.938898i
$184$	−4.27626e37			−1.82629
$185$	2.31281e36	−	1.86468e36i	0.0903246	−	0.0728235i
$186$	3.00179e37			1.07255
$187$			1.20560e37i			0.394290i
$188$		−	4.54786e37i		−	1.36208i
$189$	6.77551e37			1.85918
$190$	−1.49802e37	+	1.20776e37i	−0.376775	+	0.303772i
$191$	−2.18522e37			−0.504016			−0.252008	−	0.967725i	$-0.581091\pi$
$191$	−2.18522e37			−0.504016			−0.252008	+	0.967725i	$0.581091\pi$
$192$		−	6.13216e37i		−	1.29761i
$193$			7.41572e37i			1.44032i	0.693810	+	0.720158i	$0.255931\pi$
$193$			7.41572e37i			1.44032i	−0.693810	+	0.720158i	$0.744069\pi$
$194$	−1.11379e38			−1.98644
$195$	3.55230e37	+	4.40599e37i	0.582020	+	0.721892i
$196$	2.57859e38			3.88290
$197$			9.94695e37i			1.37720i	0.725141	+	0.688601i	$0.241775\pi$
$197$			9.94695e37i			1.37720i	−0.725141	+	0.688601i	$0.758225\pi$
$198$		−	4.58875e36i		−	0.0584411i
$199$	−1.85341e37			−0.217217			−0.108609	−	0.994085i	$-0.534640\pi$
$199$	−1.85341e37			−0.217217			−0.108609	+	0.994085i	$0.534640\pi$
$200$	−1.27439e38	−	2.76593e37i	−1.37502	−	0.298433i
$201$	6.07339e37			0.603526
$202$			1.40857e38i			1.28967i
$203$		−	2.56360e38i		−	2.16354i
$204$	−3.20304e38			−2.49267
$205$	−5.76175e37	−	7.14642e37i	−0.413633	−	0.513038i
$206$	9.61180e37			0.636789
$207$			2.71642e37i			0.166144i
$208$		−	9.38299e37i		−	0.530025i
$209$	1.49314e37			0.0779269
$210$	−4.47925e38	+	3.61136e38i	−2.16066	+	1.74202i
$211$	−2.61345e38			−1.16561			−0.582805	−	0.812612i	$-0.698045\pi$
$211$	−2.61345e38			−1.16561			−0.582805	+	0.812612i	$0.698045\pi$
$212$			4.61296e38i			1.90300i
$213$		−	2.14808e38i		−	0.819948i
$214$	7.03914e38			2.48709
$215$	−3.55888e37	+	2.86932e37i	−0.116434	+	0.0938738i
$216$	4.89055e38			1.48208
$217$		−	4.28725e38i		−	1.20391i
$218$		−	1.68296e38i		−	0.438068i
$219$	1.68002e38			0.405496
$220$	1.39523e38	+	1.73053e38i	0.312371	+	0.387441i
$221$	6.95134e38			1.44410
$222$		−	9.46135e37i		−	0.182444i
$223$		−	2.67594e38i		−	0.479122i	−0.970881	−	0.239561i	$-0.922997\pi$
$223$		−	2.67594e38i		−	0.479122i	0.970881	−	0.239561i	$-0.0770035\pi$
$224$	−5.39410e38			−0.897070
$225$	−1.75701e37	+	8.09533e37i	−0.0271495	+	0.125090i
$226$	3.70072e36			0.00531492
$227$			3.53241e38i			0.471677i	0.971792	+	0.235838i	$0.0757836\pi$
$227$			3.53241e38i			0.471677i	−0.971792	+	0.235838i	$0.924216\pi$
$228$			3.96699e38i			0.492647i
$229$	−1.17673e39			−1.35954			−0.679769	−	0.733427i	$-0.737920\pi$
$229$	−1.17673e39			−1.35954			−0.679769	+	0.733427i	$0.737920\pi$
$230$	−1.27590e39	−	1.58253e39i	−1.37185	−	1.70154i
$231$	4.46468e38			0.446881
$232$		−	1.85040e39i		−	1.72470i
$233$			1.12975e38i			0.0980870i	0.998797	+	0.0490435i	$0.0156173\pi$
$233$			1.12975e38i			0.0980870i	−0.998797	+	0.0490435i	$0.984383\pi$
$234$	−2.64582e38			−0.214042
$235$	7.66136e38	−	6.17691e38i	0.577678	−	0.465749i
$236$	2.38299e39			1.67523
$237$		−	2.23738e39i		−	1.46687i
$238$			7.06692e39i			4.32226i
$239$	−9.43852e38			−0.538690			−0.269345	−	0.963044i	$-0.586807\pi$
$239$	−9.43852e38			−0.538690			−0.269345	+	0.963044i	$0.586807\pi$
$240$	−7.28339e38	+	5.87218e38i	−0.388015	+	0.312834i
$241$	7.67029e38			0.381532			0.190766	−	0.981636i	$-0.438903\pi$
$241$	7.67029e38			0.381532			0.190766	+	0.981636i	$0.438903\pi$
$242$			3.35825e39i			1.56013i
$243$		−	5.86073e38i		−	0.254359i
$244$	−4.55055e39			−1.84558
$245$	3.50224e39	+	4.34390e39i	1.32772	+	1.64680i
$246$	−2.92350e39			−1.03627
$247$		−	8.60929e38i		−	0.285409i
$248$		−	3.09453e39i		−	0.959714i
$249$	5.42409e39			1.57412
$250$	−2.77878e39	−	5.54144e39i	−0.754821	−	1.50526i
$251$	−2.55001e39			−0.648524			−0.324262	−	0.945967i	$-0.605116\pi$
$251$	−2.55001e39			−0.648524			−0.324262	+	0.945967i	$0.605116\pi$
$252$		−	1.74122e39i		−	0.414709i
$253$			1.57738e39i			0.351923i
$254$	1.05905e40			2.21391
$255$	−4.35038e39	−	5.39587e39i	−0.852342	−	1.05718i
$256$	−9.22761e39			−1.69484
$257$			7.67124e39i			1.32120i	0.750737	+	0.660601i	$0.229698\pi$
$257$			7.67124e39i			1.32120i	−0.750737	+	0.660601i	$0.770302\pi$
$258$			1.45588e39i			0.235181i
$259$	−1.35130e39			−0.204789
$260$	9.97806e39	−	8.04473e39i	1.41901	−	1.14407i
$261$	−1.17543e39			−0.156902
$262$		−	1.12163e40i		−	1.40565i
$263$		−	1.76090e39i		−	0.207236i	−0.994617	−	0.103618i	$-0.966958\pi$
$263$		−	1.76090e39i		−	0.207236i	0.994617	−	0.103618i	$-0.0330419\pi$
$264$	3.22259e39			0.356238
$265$	−7.77103e39	+	6.26533e39i	−0.807089	+	0.650710i
$266$	8.75244e39			0.854244
$267$			9.82497e39i			0.901354i
$268$		−	1.37541e40i		−	1.18634i
$269$	−1.37145e38			−0.0111241			−0.00556206	−	0.999985i	$-0.501770\pi$
$269$	−1.37145e38			−0.0111241			−0.00556206	+	0.999985i	$0.501770\pi$
$270$	1.45918e40	+	1.80986e40i	1.11329	+	1.38084i
$271$	1.20503e40			0.864978			0.432489	−	0.901639i	$-0.357635\pi$
$271$	1.20503e40			0.864978			0.432489	+	0.901639i	$0.357635\pi$
$272$			1.14910e40i			0.776197i
$273$		−	2.57428e40i		−	1.63671i
$274$	1.93814e39			0.116012
$275$	−1.02027e39	+	4.70083e39i	−0.0575074	+	0.264963i
$276$	−4.19079e40			−2.22483
$277$			1.15971e40i			0.580005i	0.957026	+	0.290002i	$0.0936561\pi$
$277$			1.15971e40i			0.580005i	−0.957026	+	0.290002i	$0.906344\pi$
$278$			5.25642e39i			0.247714i
$279$	−1.96574e39			−0.0873086
$280$	3.72293e40	+	4.61763e40i	1.55875	+	1.93336i
$281$	−3.63872e40			−1.43646			−0.718232	−	0.695804i	$-0.755048\pi$
$281$	−3.63872e40			−1.43646			−0.718232	+	0.695804i	$0.755048\pi$
$282$		−	3.13415e40i		−	1.16684i
$283$		−	1.87432e40i		−	0.658213i	−0.944293	−	0.329107i	$-0.893252\pi$
$283$		−	1.87432e40i		−	0.658213i	0.944293	−	0.329107i	$-0.106748\pi$
$284$	−4.86466e40			−1.61176
$285$	−6.68282e39	+	5.38797e39i	−0.208939	+	0.168455i
$286$	−1.53639e40			−0.453378
$287$			4.17543e40i			1.16319i
$288$			2.47324e39i			0.0650564i
$289$	−4.48762e40			−1.11481
$290$	6.84782e40	−	5.52100e40i	1.60689	−	1.29554i
$291$	−4.96875e40			−1.10157
$292$		−	3.80467e40i		−	0.797077i
$293$		−	2.34908e40i		−	0.465139i	−0.972580	−	0.232569i	$-0.925287\pi$
$293$		−	2.34908e40i		−	0.465139i	0.972580	−	0.232569i	$-0.0747132\pi$
$294$	1.77703e41			3.32631
$295$	3.23659e40	+	4.01441e40i	0.572828	+	0.710491i
$296$	−9.75366e39			−0.163250
$297$		−	1.80397e40i		−	0.285593i
$298$			1.18763e41i			1.77874i
$299$	9.09499e40			1.28893
$300$	−1.24892e41	−	2.71065e40i	−1.67507	−	0.363557i
$301$	2.07934e40			0.263985
$302$		−	4.77944e40i		−	0.574463i
$303$			6.28377e40i			0.715182i
$304$	1.42317e40			0.153406
$305$	−6.18057e40	−	7.66589e40i	−0.631075	−	0.782736i
$306$	3.24024e40			0.313454
$307$			2.12921e40i			0.195180i	0.995227	+	0.0975901i	$0.0311134\pi$
$307$			2.12921e40i			0.195180i	−0.995227	+	0.0975901i	$0.968887\pi$
$308$		−	1.01110e41i		−	0.878427i
$309$	4.28793e40			0.353129
$310$	1.14520e41	−	9.23309e40i	0.894157	−	0.720907i
$311$	9.65601e40			0.714910			0.357455	−	0.933930i	$-0.383645\pi$
$311$	9.65601e40			0.714910			0.357455	+	0.933930i	$0.383645\pi$
$312$		−	1.85811e41i		−	1.30473i
$313$		−	2.25901e40i		−	0.150465i	−0.997166	−	0.0752327i	$-0.976030\pi$
$313$		−	2.25901e40i		−	0.150465i	0.997166	−	0.0752327i	$-0.0239700\pi$
$314$	−3.29235e41			−2.08050
$315$	2.93326e40	−	2.36492e40i	0.175884	−	0.141805i
$316$	−5.06689e41			−2.88340
$317$			1.90392e40i			0.102842i	0.998677	+	0.0514209i	$0.0163750\pi$
$317$			1.90392e40i			0.102842i	−0.998677	+	0.0514209i	$0.983625\pi$
$318$			3.17901e41i			1.63021i
$319$	−6.82554e40			−0.332346
$320$	−1.88617e41	−	2.33946e41i	−0.872179	−	1.08178i
$321$	3.14024e41			1.37921
$322$			9.24621e41i			3.85782i
$323$			1.05435e41i			0.417968i
$324$	4.16909e41			1.57054
$325$	2.71044e41	+	5.88274e40i	0.970432	+	0.210622i
$326$	3.27724e41			1.11537
$327$		−	7.50788e40i		−	0.242929i
$328$			3.01382e41i			0.927253i
$329$	−4.47629e41			−1.30974
$330$	9.61519e40	+	1.19259e41i	0.267595	+	0.331904i
$331$	8.34163e39			0.0220846			0.0110423	−	0.999939i	$-0.496485\pi$
$331$	8.34163e39			0.0220846			0.0110423	+	0.999939i	$0.496485\pi$
$332$		−	1.22837e42i		−	3.09422i
$333$			6.19583e39i			0.0148515i
$334$	−7.75889e41			−1.77004
$335$	2.31703e41	−	1.86809e41i	0.503145	−	0.405657i
$336$	4.25546e41			0.879727
$337$		−	1.27475e41i		−	0.250918i	−0.992099	−	0.125459i	$-0.959960\pi$
$337$		−	1.27475e41i		−	0.250918i	0.992099	−	0.125459i	$-0.0400404\pi$
$338$		−	1.24876e40i		−	0.0234075i
$339$	1.65093e39			0.00294737
$340$	−1.22198e42	+	9.85211e41i	−2.07808	+	1.67543i
$341$	−1.14147e41			−0.184935
$342$		−	4.01307e40i		−	0.0619506i
$343$		−	1.33821e42i		−	1.96866i
$344$	1.50086e41			0.210439
$345$	−5.69194e41	−	7.05983e41i	−0.760756	−	0.943582i
$346$	2.36330e42			3.01137
$347$			2.90496e41i			0.352943i	0.984306	+	0.176471i	$0.0564683\pi$
$347$			2.90496e41i			0.352943i	−0.984306	+	0.176471i	$0.943532\pi$
$348$		−	1.81341e42i		−	2.10106i
$349$	1.05476e42			1.16556			0.582779	−	0.812631i	$-0.301965\pi$
$349$	1.05476e42			1.16556			0.582779	+	0.812631i	$0.301965\pi$
$350$	−5.98055e41	+	2.75551e42i	−0.630403	+	2.90455i
$351$	−1.04015e42			−1.04599
$352$			1.43617e41i			0.137801i
$353$		−	1.42033e42i		−	1.30049i	−0.759724	−	0.650246i	$-0.774666\pi$
$353$		−	1.42033e42i		−	1.30049i	0.759724	−	0.650246i	$-0.225334\pi$
$354$	1.64224e42			1.43510
$355$	−6.60719e41	−	8.19504e41i	−0.551123	−	0.683570i
$356$	2.22502e42			1.77177
$357$			3.15263e42i			2.39689i
$358$			1.42937e42i			1.03771i
$359$	3.15371e41			0.218657			0.109329	−	0.994006i	$-0.465130\pi$
$359$	3.15371e41			0.218657			0.109329	+	0.994006i	$0.465130\pi$
$360$	2.11722e41	−	1.70700e41i	0.140209	−	0.113042i
$361$	−1.45019e42			−0.917393
$362$		−	1.70787e42i		−	1.03220i
$363$			1.49815e42i			0.865162i
$364$	−5.82987e42			−3.21726
$365$	6.40938e41	−	5.16752e41i	0.338052	−	0.272552i
$366$	−3.13600e42			−1.58102
$367$			3.83973e41i			0.185059i	0.995710	+	0.0925297i	$0.0294953\pi$
$367$			3.83973e41i			0.185059i	−0.995710	+	0.0925297i	$0.970505\pi$
$368$			1.50346e42i			0.692792i
$369$	1.91447e41			0.0843555
$370$	−2.91018e41	−	3.60956e41i	−0.122629	−	0.152099i
$371$	4.54037e42			1.82988
$372$		−	3.03268e42i		−	1.16914i
$373$			2.58713e42i			0.954164i	0.878859	+	0.477082i	$0.158305\pi$
$373$			2.58713e42i			0.954164i	−0.878859	+	0.477082i	$0.841695\pi$
$374$	1.88156e42			0.663951
$375$	−1.23965e42	−	2.47210e42i	−0.418583	−	0.834737i
$376$	−3.23098e42			−1.04408
$377$			3.93553e42i			1.21723i
$378$		−	1.05744e43i		−	3.13071i
$379$	−1.90182e42			−0.539042			−0.269521	−	0.962994i	$-0.586865\pi$
$379$	−1.90182e42			−0.539042			−0.269521	+	0.962994i	$0.586865\pi$
$380$	1.22019e42	+	1.51343e42i	0.331130	+	0.410708i
$381$	4.72454e42			1.22771
$382$			3.41044e42i			0.848720i
$383$			6.82259e42i			1.62618i	0.582135	+	0.813092i	$0.302217\pi$
$383$			6.82259e42i			1.62618i	−0.582135	+	0.813092i	$0.697783\pi$
$384$	−7.49165e42			−1.71046
$385$	1.70330e42	−	1.37327e42i	0.372554	−	0.300369i
$386$	1.15736e43			2.42537
$387$		−	9.53396e40i		−	0.0191444i
$388$			1.12525e43i			2.16534i
$389$	2.03241e42			0.374837			0.187419	−	0.982280i	$-0.439988\pi$
$389$	2.03241e42			0.374837			0.187419	+	0.982280i	$0.439988\pi$
$390$	6.87636e42	−	5.54401e42i	1.21561	−	0.980073i
$391$	−1.11383e43			−1.88757
$392$		−	1.83193e43i		−	2.97638i
$393$		−	5.00372e42i		−	0.779499i
$394$	1.55241e43			2.31909
$395$	−6.88186e42	−	8.53572e42i	−0.985947	−	1.22289i
$396$	−4.63596e41			−0.0637044
$397$			7.63461e42i			1.00634i	0.864188	+	0.503168i	$0.167832\pi$
$397$			7.63461e42i			1.00634i	−0.864188	+	0.503168i	$0.832168\pi$
$398$			2.89258e42i			0.365776i
$399$	3.90456e42			0.473717
$400$	−9.72455e41	+	4.48054e42i	−0.113209	+	0.521603i
$401$	−1.09608e43			−1.22450			−0.612250	−	0.790664i	$-0.709736\pi$
$401$	−1.09608e43			−1.22450			−0.612250	+	0.790664i	$0.709736\pi$
$402$		−	9.47864e42i		−	1.01629i
$403$			6.58162e42i			0.677328i
$404$	1.42306e43			1.40582
$405$	5.66246e42	+	7.02328e42i	0.537029	+	0.666088i
$406$	−4.00097e43			−3.64322
$407$			3.59782e41i			0.0314580i
$408$			2.27557e43i			1.91072i
$409$	−1.27736e43			−1.03010			−0.515050	−	0.857160i	$-0.672227\pi$
$409$	−1.27736e43			−1.03010			−0.515050	+	0.857160i	$0.672227\pi$
$410$	−1.11533e43	+	8.99227e42i	−0.863913	+	0.696523i
$411$	8.64628e41			0.0643338
$412$		−	9.71070e42i		−	0.694139i
$413$		−	2.34549e43i		−	1.61086i
$414$	4.23947e42			0.279773
$415$	2.06932e43	−	1.66838e43i	1.31231	−	1.05804i
$416$	8.28080e42			0.504699
$417$			2.34495e42i			0.137369i
$418$		−	2.33032e42i		−	0.131222i
$419$	−1.81304e43			−0.981467			−0.490734	−	0.871310i	$-0.663271\pi$
$419$	−1.81304e43			−0.981467			−0.490734	+	0.871310i	$0.663271\pi$
$420$	3.64852e43	+	4.52534e43i	1.89891	+	2.35525i
$421$	1.35628e43			0.678724			0.339362	−	0.940656i	$-0.389789\pi$
$421$	1.35628e43			0.678724			0.339362	+	0.940656i	$0.389789\pi$
$422$			4.07877e43i			1.96279i
$423$			2.05242e42i			0.0949839i
$424$	3.27723e43			1.45871
$425$	−3.31939e43	−	7.20439e42i	−1.42115	−	0.308446i
$426$	−3.35247e43			−1.38072
$427$			4.47894e43i			1.77466i
$428$		−	7.11156e43i		−	2.71108i
$429$	−6.85399e42			−0.251419
$430$	4.47810e42	+	5.55429e42i	0.158075	+	0.196064i
$431$	4.12465e43			1.40124			0.700620	−	0.713535i	$-0.252907\pi$
$431$	4.12465e43			1.40124			0.700620	+	0.713535i	$0.252907\pi$
$432$		−	1.71943e43i		−	0.562216i
$433$		−	5.05620e43i		−	1.59138i	−0.605704	−	0.795690i	$-0.707108\pi$
$433$		−	5.05620e43i		−	1.59138i	0.605704	−	0.795690i	$-0.292892\pi$
$434$	−6.69105e43			−2.02728
$435$	3.05489e43	−	2.46298e43i	0.891092	−	0.718436i
$436$	−1.70028e43			−0.477521
$437$			1.37949e43i			0.373056i
$438$		−	2.62198e43i		−	0.682822i
$439$	2.66416e43			0.668182			0.334091	−	0.942541i	$-0.391571\pi$
$439$	2.66416e43			0.668182			0.334091	+	0.942541i	$0.391571\pi$
$440$	1.22944e43	−	9.91226e42i	0.296987	−	0.239444i
$441$	−1.16370e43			−0.270772
$442$		−	1.08489e44i		−	2.43174i
$443$		−	1.04497e43i		−	0.225653i	−0.993615	−	0.112826i	$-0.964010\pi$
$443$		−	1.04497e43i		−	0.225653i	0.993615	−	0.112826i	$-0.0359904\pi$
$444$	−9.55870e42			−0.198875
$445$	3.02202e43	+	3.74828e43i	0.605840	+	0.751436i
$446$	−4.17630e43			−0.806800
$447$			5.29815e43i			0.986393i
$448$			1.36687e44i			2.45268i
$449$	5.66906e43			0.980497			0.490248	−	0.871583i	$-0.336906\pi$
$449$	5.66906e43			0.980497			0.490248	+	0.871583i	$0.336906\pi$
$450$	1.26342e43	+	2.74213e42i	0.210641	+	0.0457175i
$451$	1.11170e43			0.178680
$452$		−	3.73879e41i		−	0.00579358i
$453$		−	2.13216e43i		−	0.318566i
$454$	5.51298e43			0.794264
$455$	−7.91814e43	−	9.82104e43i	−1.10011	−	1.36449i
$456$	2.81830e43			0.377631
$457$			1.11812e44i			1.44501i	0.691366	+	0.722505i	$0.257009\pi$
$457$			1.11812e44i			1.44501i	−0.691366	+	0.722505i	$0.742991\pi$
$458$			1.83650e44i			2.28935i
$459$	1.27383e44			1.53181
$460$	−1.59881e44	+	1.28903e44i	−1.85478	+	1.49540i
$461$	−2.91705e43			−0.326496			−0.163248	−	0.986585i	$-0.552197\pi$
$461$	−2.91705e43			−0.326496			−0.163248	+	0.986585i	$0.552197\pi$
$462$		−	6.96795e43i		−	0.752510i
$463$		−	1.20018e44i		−	1.25072i	−0.780335	−	0.625362i	$-0.784952\pi$
$463$		−	1.20018e44i		−	1.25072i	0.780335	−	0.625362i	$-0.215048\pi$
$464$	−6.50569e43			−0.654254
$465$	5.10887e43	−	4.11899e43i	0.495851	−	0.399776i
$466$	1.76319e43			0.165170
$467$		−	2.20756e43i		−	0.199611i	−0.995007	−	0.0998054i	$-0.968178\pi$
$467$		−	2.20756e43i		−	0.199611i	0.995007	−	0.0998054i	$-0.0318220\pi$
$468$			2.67304e43i			0.233319i
$469$	−1.35377e44			−1.14076
$470$	−9.64021e43	−	1.19570e44i	−0.784281	−	0.972761i
$471$	−1.46875e44			−1.15373
$472$		−	1.69297e44i		−	1.28412i
$473$		−	5.53622e42i		−	0.0405512i
$474$	−3.49184e44			−2.47008
$475$	−8.92269e42	+	4.11108e43i	−0.0609609	+	0.280874i
$476$	7.13964e44			4.71152
$477$		−	2.08180e43i		−	0.132704i
$478$			1.47306e44i			0.907108i
$479$	−7.80915e43			−0.464588			−0.232294	−	0.972646i	$-0.574623\pi$
$479$	−7.80915e43			−0.464588			−0.232294	+	0.972646i	$0.574623\pi$
$480$	−5.18239e43	−	6.42783e43i	−0.297886	−	0.369474i
$481$	2.07446e43			0.115216
$482$		−	1.19709e44i		−	0.642467i
$483$			4.12484e44i			2.13934i
$484$	3.39281e44			1.70063
$485$	−1.89561e44	+	1.52832e44i	−0.918353	+	0.740415i
$486$	−9.14674e43			−0.428320
$487$		−	4.19385e44i		−	1.89839i	−0.314693	−	0.949194i	$-0.601901\pi$
$487$		−	4.19385e44i		−	1.89839i	0.314693	−	0.949194i	$-0.398099\pi$
$488$			3.23289e44i			1.41470i
$489$	1.46201e44			0.618522
$490$	6.77947e44	−	5.46589e44i	2.77307	−	2.23576i
$491$	4.24412e44			1.67859			0.839293	−	0.543680i	$-0.182969\pi$
$491$	4.24412e44			1.67859			0.839293	+	0.543680i	$0.182969\pi$
$492$			2.95358e44i			1.12960i
$493$		−	4.81971e44i		−	1.78257i
$494$	−1.34364e44			−0.480604
$495$	−6.29657e42	−	7.80978e42i	−0.0217830	−	0.0270180i
$496$	−1.08798e44			−0.364061
$497$			4.78810e44i			1.54983i
$498$		−	8.46530e44i		−	2.65069i
$499$	−6.09953e44			−1.84772			−0.923862	−	0.382726i	$-0.874985\pi$
$499$	−6.09953e44			−1.84772			−0.923862	+	0.382726i	$0.874985\pi$
$500$	−5.59845e44	+	2.80737e44i	−1.64083	+	0.822801i
$501$	−3.46133e44			−0.981567
$502$			3.97976e44i			1.09206i
$503$			3.00762e44i			0.798639i	0.916812	+	0.399320i	$0.130754\pi$
$503$			3.00762e44i			0.798639i	−0.916812	+	0.399320i	$0.869246\pi$
$504$	−1.23703e44			−0.317889
$505$	1.93280e44	+	2.39729e44i	0.480706	+	0.596230i
$506$	2.46179e44			0.592608
$507$		−	5.57087e42i		−	0.0129805i
$508$		−	1.06995e45i		−	2.41330i
$509$	−1.45444e44			−0.317578			−0.158789	−	0.987313i	$-0.550759\pi$
$509$	−1.45444e44			−0.317578			−0.158789	+	0.987313i	$0.550759\pi$
$510$	−8.42124e44	+	6.78956e44i	−1.78020	+	1.43527i
$511$	−3.74480e44			−0.766450
$512$			5.15847e44i			1.02227i
$513$		−	1.57765e44i		−	0.302744i
$514$	1.19724e45			2.22479
$515$	1.63587e44	−	1.31891e44i	0.294395	−	0.237353i
$516$	1.47086e44			0.256361
$517$			1.19181e44i			0.201192i
$518$			2.10895e44i			0.344847i
$519$	1.05430e45			1.66994
$520$	−5.71530e44	−	7.08881e44i	−0.876968	−	1.08772i
$521$	3.35096e44			0.498135			0.249067	−	0.968486i	$-0.419876\pi$
$521$	3.35096e44			0.498135			0.249067	+	0.968486i	$0.419876\pi$
$522$			1.83448e44i			0.264210i
$523$			7.95243e44i			1.10974i	0.831937	+	0.554871i	$0.187232\pi$
$523$			7.95243e44i			1.10974i	−0.831937	+	0.554871i	$0.812768\pi$
$524$	−1.13317e45			−1.53225
$525$	−2.66799e44	+	1.22926e45i	−0.349588	+	1.61071i
$526$	−2.74821e44			−0.348967
$527$		−	8.06028e44i		−	0.991916i
$528$		−	1.13301e44i		−	0.135137i
$529$	−5.92309e44			−0.684747
$530$	9.77821e44	+	1.21281e45i	1.09574	+	1.35907i
$531$	−1.07543e44			−0.116821
$532$		−	8.84249e44i		−	0.931178i
$533$		−	6.40995e44i		−	0.654419i
$534$	1.53337e45			1.51780
$535$	1.19802e45	−	9.65894e44i	1.14981	−	0.927026i
$536$	−9.77149e44			−0.909372
$537$			6.37659e44i			0.575457i
$538$			2.14039e43i			0.0187321i
$539$	−6.75741e44			−0.573542
$540$	1.82848e45	−	1.47420e45i	1.50520	−	1.21355i
$541$	1.21161e45			0.967402			0.483701	−	0.875233i	$-0.339292\pi$
$541$	1.21161e45			0.967402			0.483701	+	0.875233i	$0.339292\pi$
$542$		−	1.88067e45i		−	1.45655i
$543$		−	7.61900e44i		−	0.572401i
$544$	−1.01412e45			−0.739108
$545$	−2.30932e44	−	2.86430e44i	−0.163283	−	0.202524i
$546$	−4.01764e45			−2.75609
$547$		−	1.99236e45i		−	1.32610i	−0.748573	−	0.663052i	$-0.769261\pi$
$547$		−	1.99236e45i		−	1.32610i	0.748573	−	0.663052i	$-0.230739\pi$
$548$		−	1.95808e44i		−	0.126460i
$549$	2.05363e44			0.128700
$550$	7.33651e44	+	1.59231e44i	0.446175	+	0.0968376i
$551$	−5.96924e44			−0.352304
$552$			2.97730e45i			1.70541i
$553$			4.98715e45i			2.77260i
$554$	1.80993e45			0.976679
$555$	−1.29827e44	−	1.61027e44i	−0.0680032	−	0.0843458i
$556$	5.31051e44			0.270024
$557$		−	1.74444e45i		−	0.861082i	−0.902571	−	0.430541i	$-0.858323\pi$
$557$		−	1.74444e45i		−	0.861082i	0.902571	−	0.430541i	$-0.141677\pi$
$558$			3.06790e44i			0.147020i
$559$	−3.19212e44			−0.148520
$560$	1.62348e45	−	1.30892e45i	0.733407	−	0.591303i
$561$	8.39384e44			0.368191
$562$			5.67890e45i			2.41888i
$563$		−	1.30371e45i		−	0.539251i	−0.962965	−	0.269626i	$-0.913100\pi$
$563$		−	1.30371e45i		−	0.539251i	0.962965	−	0.269626i	$-0.0868999\pi$
$564$	−3.16640e45			−1.27192
$565$	6.29840e42	−	5.07804e42i	0.00245715	−	0.00198105i
$566$	−2.92522e45			−1.10838
$567$		−	4.10348e45i		−	1.51019i
$568$			3.45604e45i			1.23547i
$569$	−8.99757e43			−0.0312445			−0.0156222	−	0.999878i	$-0.504973\pi$
$569$	−8.99757e43			−0.0312445			−0.0156222	+	0.999878i	$0.504973\pi$
$570$	8.40892e44	+	1.04298e45i	0.283665	+	0.351835i
$571$	2.85011e45			0.934039			0.467020	−	0.884247i	$-0.345328\pi$
$571$	2.85011e45			0.934039			0.467020	+	0.884247i	$0.345328\pi$
$572$			1.55219e45i			0.494210i
$573$			1.52143e45i			0.470654i
$574$	6.51653e45			1.95871
$575$	−4.34302e45	−	9.42607e44i	−1.26845	−	0.275303i
$576$	6.26722e44			0.177870
$577$		−	6.49472e45i		−	1.79126i	−0.444797	−	0.895632i	$-0.646724\pi$
$577$		−	6.49472e45i		−	1.79126i	0.444797	−	0.895632i	$-0.353276\pi$
$578$			7.00376e45i			1.87725i
$579$	5.16312e45			1.34498
$580$	−5.57781e45	−	6.91828e45i	−1.41222	−	1.75160i
$581$	−1.20904e46			−2.97533
$582$			7.75465e45i			1.85495i
$583$		−	1.20887e45i		−	0.281091i
$584$	−2.70299e45			−0.610988
$585$	−4.50303e44	+	3.63053e44i	−0.0989539	+	0.0797808i
$586$	−3.66618e45			−0.783254
$587$			5.04614e44i			0.104817i	0.998626	+	0.0524084i	$0.0166898\pi$
$587$			5.04614e44i			0.104817i	−0.998626	+	0.0524084i	$0.983310\pi$
$588$		−	1.79531e46i		−	3.62588i
$589$	−9.98271e44			−0.196041
$590$	6.26523e45	−	5.05129e45i	1.19641	−	0.964594i
$591$	6.92546e45			1.28604
$592$			3.42922e44i			0.0619280i
$593$			1.38106e45i			0.242555i	0.992619	+	0.121277i	$0.0386990\pi$
$593$			1.38106e45i			0.242555i	−0.992619	+	0.121277i	$0.961301\pi$
$594$	−2.81543e45			−0.480915
$595$	9.69707e45	+	1.20275e46i	1.61106	+	1.99823i
$596$	1.19985e46			1.93894
$597$			1.29041e45i			0.202839i
$598$		−	1.41944e46i		−	2.17044i
$599$	7.75620e45			1.15374			0.576868	−	0.816837i	$-0.304275\pi$
$599$	7.75620e45			1.15374			0.576868	+	0.816837i	$0.304275\pi$
$600$	−1.92575e45	+	8.87281e45i	−0.278679	+	1.28400i
$601$	−1.97032e45			−0.277400			−0.138700	−	0.990334i	$-0.544292\pi$
$601$	−1.97032e45			−0.277400			−0.138700	+	0.990334i	$0.544292\pi$
$602$		−	3.24520e45i		−	0.444528i
$603$			6.20715e44i			0.0827288i
$604$	−4.82861e45			−0.626200
$605$	4.60812e45	+	5.71555e45i	0.581513	+	0.721264i
$606$	9.80698e45			1.20431
$607$			3.36784e45i			0.402474i	0.979543	+	0.201237i	$0.0644962\pi$
$607$			3.36784e45i			0.402474i	−0.979543	+	0.201237i	$0.935504\pi$
$608$			1.25600e45i			0.146076i
$609$	−1.78488e46			−2.02033
$610$	−1.19640e46	+	9.64591e45i	−1.31806	+	1.06268i
$611$	6.87182e45			0.736872
$612$		−	3.27358e45i		−	0.341684i
$613$			9.87239e45i			1.00305i	0.865142	+	0.501527i	$0.167228\pi$
$613$			9.87239e45i			1.00305i	−0.865142	+	0.501527i	$0.832772\pi$
$614$	3.32303e45			0.328667
$615$	−4.97562e45	+	4.01155e45i	−0.479079	+	0.386254i
$616$	−7.18322e45			−0.673345
$617$		−	3.29814e45i		−	0.300998i	−0.988610	−	0.150499i	$-0.951912\pi$
$617$		−	3.29814e45i		−	0.300998i	0.988610	−	0.150499i	$-0.0480880\pi$
$618$		−	6.69211e45i		−	0.594639i
$619$	−1.65886e46			−1.43521			−0.717604	−	0.696451i	$-0.754761\pi$
$619$	−1.65886e46			−1.43521			−0.717604	+	0.696451i	$0.754761\pi$
$620$	−9.32809e45	−	1.15698e46i	−0.785832	−	0.974685i
$621$	1.66666e46			1.36721
$622$		−	1.50700e46i		−	1.20385i
$623$		−	2.19000e46i		−	1.70370i
$624$	−6.53280e45			−0.494941
$625$	−1.23332e46	−	5.61822e45i	−0.910026	−	0.414551i
$626$	−3.52560e45			−0.253371
$627$		−	1.03958e45i		−	0.0727688i
$628$			3.32623e46i			2.26787i
$629$	−2.54052e45			−0.168728
$630$	−3.69090e45	−	4.57790e45i	−0.238788	−	0.296174i
$631$	5.39111e45			0.339777			0.169888	−	0.985463i	$-0.445659\pi$
$631$	5.39111e45			0.339777			0.169888	+	0.985463i	$0.445659\pi$
$632$			3.59972e46i			2.21023i
$633$			1.81958e46i			1.08846i
$634$	2.97141e45			0.173177
$635$	1.80244e46	−	1.45320e46i	1.02352	−	0.825201i
$636$	3.21172e46			1.77703
$637$			3.89625e46i			2.10061i
$638$			1.06525e46i			0.559643i
$639$	2.19539e45			0.112395
$640$	−2.85811e46	+	2.30433e46i	−1.42597	+	1.14967i
$641$	−3.59612e46			−1.74854			−0.874271	−	0.485438i	$-0.838660\pi$
$641$	−3.59612e46			−1.74854			−0.874271	+	0.485438i	$0.838660\pi$
$642$		−	4.90092e46i		−	2.32247i
$643$		−	3.23556e46i		−	1.49441i	−0.664596	−	0.747203i	$-0.731396\pi$
$643$		−	3.23556e46i		−	1.49441i	0.664596	−	0.747203i	$-0.268604\pi$
$644$	9.34135e46			4.20526
$645$	1.99773e45	+	2.47783e45i	0.0876601	+	0.108727i
$646$	1.64551e46			0.703823
$647$			5.30852e45i			0.221336i	0.993857	+	0.110668i	$0.0352991\pi$
$647$			5.30852e45i			0.221336i	−0.993857	+	0.110668i	$0.964701\pi$
$648$		−	2.96188e46i		−	1.20387i
$649$	−6.24485e45			−0.247448
$650$	9.18110e45	−	4.23015e46i	0.354670	−	1.63412i
$651$	−2.98495e46			−1.12422
$652$		−	3.31096e46i		−	1.21582i
$653$			2.38611e46i			0.854326i	0.904175	+	0.427163i	$0.140487\pi$
$653$			2.38611e46i			0.854326i	−0.904175	+	0.427163i	$0.859513\pi$
$654$	−1.17174e46			−0.409072
$655$	−1.53907e46	−	1.90895e46i	−0.523936	−	0.649849i
$656$	1.05961e46			0.351748
$657$			1.71702e45i			0.0555837i
$658$			6.98608e46i			2.20550i
$659$	−2.81962e46			−0.868122			−0.434061	−	0.900883i	$-0.642920\pi$
$659$	−2.81962e46			−0.868122			−0.434061	+	0.900883i	$0.642920\pi$
$660$	1.20486e46	−	9.71413e45i	0.361796	−	0.291695i
$661$	3.38643e46			0.991786			0.495893	−	0.868384i	$-0.334841\pi$
$661$	3.38643e46			0.991786			0.495893	+	0.868384i	$0.334841\pi$
$662$		−	1.30187e45i		−	0.0371886i
$663$		−	4.83980e46i		−	1.34851i
$664$	−8.72683e46			−2.37183
$665$	1.48961e46	−	1.20099e46i	0.394926	−	0.318406i
$666$	9.66973e44			0.0250086
$667$		−	6.30600e46i		−	1.59103i
$668$			7.83872e46i			1.92945i
$669$	−1.86309e46			−0.447408
$670$	−2.91550e46	−	3.61616e46i	−0.683091	−	0.847253i
$671$	1.19251e46			0.272609
$672$			3.75558e46i			0.837692i
$673$			3.57808e46i			0.778756i	0.921078	+	0.389378i	$0.127310\pi$
$673$			3.57808e46i			0.778756i	−0.921078	+	0.389378i	$0.872690\pi$
$674$	−1.98949e46			−0.422525
$675$	4.96689e46	+	1.07801e46i	1.02937	+	0.223415i
$676$	−1.26161e45			−0.0255156
$677$			6.06906e46i			1.19787i	0.800799	+	0.598933i	$0.204409\pi$
$677$			6.06906e46i			1.19787i	−0.800799	+	0.598933i	$0.795591\pi$
$678$		−	2.57658e44i		−	0.00496311i
$679$	1.10754e47			2.08214
$680$	6.99933e46	+	8.68142e46i	1.28428	+	1.59292i
$681$	2.45940e46			0.440456
$682$			1.78148e46i			0.311415i
$683$		−	6.22121e46i		−	1.06153i	−0.847518	−	0.530766i	$-0.821904\pi$
$683$		−	6.22121e46i		−	1.06153i	0.847518	−	0.530766i	$-0.178096\pi$
$684$	−4.05436e45			−0.0675299
$685$	3.29860e45	−	2.65947e45i	0.0536335	−	0.0432416i
$686$	−2.08853e47			−3.31506
$687$			8.19285e46i			1.26955i
$688$		−	5.27678e45i		−	0.0798289i
$689$	−6.97019e46			−1.02950
$690$	−1.10182e47	+	8.88332e46i	−1.58891	+	1.28105i
$691$	1.23978e47			1.74565			0.872825	−	0.488033i	$-0.162285\pi$
$691$	1.23978e47			1.74565			0.872825	+	0.488033i	$0.162285\pi$
$692$		−	2.38762e47i		−	3.28258i
$693$			4.56301e45i			0.0612566i
$694$	4.53373e46			0.594326
$695$	7.21274e45	+	8.94612e45i	0.0923317	+	0.114521i
$696$	−1.28832e47			−1.61054
$697$			7.85005e46i			0.958366i
$698$		−	1.64615e47i		−	1.96270i
$699$	7.86579e45			0.0915944
$700$	2.78386e47	+	6.04209e46i	3.16614	+	0.687178i
$701$	−7.57725e46			−0.841713			−0.420857	−	0.907127i	$-0.638270\pi$
$701$	−7.57725e46			−0.841713			−0.420857	+	0.907127i	$0.638270\pi$
$702$			1.62334e47i			1.76136i
$703$			3.14645e45i			0.0333471i
$704$	3.63927e46			0.376761
$705$	−4.30061e46	−	5.33414e46i	−0.434920	−	0.539441i
$706$	−2.21669e47			−2.18992
$707$		−	1.40066e47i		−	1.35180i
$708$		−	1.65913e47i		−	1.56435i
$709$	9.15900e46			0.843694			0.421847	−	0.906667i	$-0.361382\pi$
$709$	9.15900e46			0.843694			0.421847	+	0.906667i	$0.361382\pi$
$710$	−1.27899e47	+	1.03117e47i	−1.15107	+	0.928045i
$711$	2.28665e46			0.201072
$712$		−	1.58074e47i		−	1.35813i
$713$		−	1.05459e47i		−	0.885332i
$714$	4.92027e47			4.03616
$715$	−2.61484e46	+	2.10819e46i	−0.209602	+	0.168990i
$716$	1.44408e47			1.13117
$717$			6.57147e46i			0.503033i
$718$		−	4.92195e46i		−	0.368200i
$719$	−1.43667e47			−1.05034			−0.525169	−	0.850998i	$-0.675998\pi$
$719$	−1.43667e47			−1.05034			−0.525169	+	0.850998i	$0.675998\pi$
$720$	−6.00151e45	−	7.44380e45i	−0.0428819	−	0.0531874i
$721$	−9.55788e46			−0.667467
$722$			2.26329e47i			1.54481i
$723$		−	5.34036e46i		−	0.356277i
$724$	−1.72544e47			−1.12516
$725$	4.07879e46	−	1.87928e47i	0.259989	−	1.19789i
$726$	2.33815e47			1.45686
$727$			9.62263e46i			0.586106i	0.956096	+	0.293053i	$0.0946712\pi$
$727$			9.62263e46i			0.586106i	−0.956096	+	0.293053i	$0.905329\pi$
$728$			4.14177e47i			2.46614i
$729$	−1.87793e47			−1.09314
$730$	−8.06486e46	−	1.00030e47i	−0.458955	−	0.569251i
$731$	3.90928e46			0.217500
$732$			3.16827e47i			1.72341i
$733$			1.83322e47i			0.974988i	0.873126	+	0.487494i	$0.162089\pi$
$733$			1.83322e47i			0.974988i	−0.873126	+	0.487494i	$0.837911\pi$
$734$	5.99261e46			0.311624
$735$	3.02440e47	−	2.43840e47i	1.53779	−	1.23983i
$736$	−1.32685e47			−0.659689
$737$			3.60439e46i			0.175234i
$738$		−	2.98788e46i		−	0.142048i
$739$	−2.28000e47			−1.05999			−0.529996	−	0.848000i	$-0.677806\pi$
$739$	−2.28000e47			−1.05999			−0.529996	+	0.848000i	$0.677806\pi$
$740$	−3.64670e46	+	2.94013e46i	−0.165797	+	0.133673i
$741$	−5.99412e46			−0.266517
$742$		−	7.08608e47i		−	3.08135i
$743$			4.61345e46i			0.196205i	0.995176	+	0.0981026i	$0.0312773\pi$
$743$			4.61345e46i			0.196205i	−0.995176	+	0.0981026i	$0.968723\pi$
$744$	−2.15453e47			−0.896189
$745$	1.62964e47	+	2.02128e47i	0.662999	+	0.822332i
$746$	4.03770e47			1.60673
$747$			5.54356e46i			0.215774i
$748$		−	1.90092e47i		−	0.723747i
$749$	−6.99965e47			−2.60691
$750$	−3.85816e47	+	1.93470e47i	−1.40563	+	0.704858i
$751$	−3.50719e46			−0.124997			−0.0624986	−	0.998045i	$-0.519907\pi$
$751$	−3.50719e46			−0.124997			−0.0624986	+	0.998045i	$0.519907\pi$
$752$			1.13596e47i			0.396066i
$753$			1.77542e47i			0.605597i
$754$	6.14212e47			2.04970
$755$	−6.55823e46	−	8.13432e46i	−0.214122	−	0.265581i
$756$	−1.06832e48			−3.41266
$757$			1.87145e47i			0.584921i	0.956278	+	0.292460i	$0.0944739\pi$
$757$			1.87145e47i			0.584921i	−0.956278	+	0.292460i	$0.905526\pi$
$758$			2.96814e47i			0.907701i
$759$	1.09823e47			0.328628
$760$	1.07520e47	−	8.66872e46i	0.314822	−	0.253823i
$761$	2.20228e47			0.630994			0.315497	−	0.948927i	$-0.397829\pi$
$761$	2.20228e47			0.630994			0.315497	+	0.948927i	$0.397829\pi$
$762$		−	7.37352e47i		−	2.06737i
$763$			1.67352e47i			0.459173i
$764$	3.44553e47			0.925157
$765$	5.51470e46	−	4.44619e46i	0.144913	−	0.116835i
$766$	1.06479e48			2.73836
$767$			3.60071e47i			0.906284i
$768$			6.42462e47i			1.58266i
$769$	2.66239e47			0.641928			0.320964	−	0.947091i	$-0.395993\pi$
$769$	2.66239e47			0.641928			0.320964	+	0.947091i	$0.395993\pi$
$770$	−2.14325e47	−	2.65831e47i	−0.505795	−	0.627349i
$771$	5.34102e47			1.23375
$772$		−	1.16927e48i		−	2.64380i
$773$			5.04292e45i			0.0111614i	0.999984	+	0.00558072i	$0.00177641\pi$
$773$			5.04292e45i			0.0111614i	−0.999984	+	0.00558072i	$0.998224\pi$
$774$	−1.48795e46			−0.0322376
$775$	6.82120e46	−	3.14284e47i	0.144671	−	0.666567i
$776$	7.99423e47			1.65981
$777$			9.40828e46i			0.191233i
$778$		−	3.17195e47i		−	0.631194i
$779$	9.72234e46			0.189410
$780$	−5.60106e47	−	6.94711e47i	−1.06834	−	1.32508i
$781$	1.27483e47			0.238072
$782$			1.73834e48i			3.17851i
$783$			7.21186e47i			1.29115i
$784$	−6.44075e47			−1.12907
$785$	−5.60338e47	+	4.51769e47i	−0.961836	+	0.775473i
$786$	−7.80922e47			−1.31261
$787$		−	1.14740e48i		−	1.88857i	−0.329133	−	0.944283i	$-0.606757\pi$
$787$		−	1.14740e48i		−	1.88857i	0.329133	−	0.944283i	$-0.393243\pi$
$788$		−	1.56838e48i		−	2.52795i
$789$	−1.22601e47			−0.193518
$790$	−1.33216e48	+	1.07404e48i	−2.05925	+	1.66025i
$791$	−3.67996e45			−0.00557097
$792$			3.29357e46i			0.0488316i
$793$		−	6.87589e47i		−	0.998438i
$794$	1.19152e48			1.69459
$795$	4.36217e47	+	5.41049e47i	0.607638	+	0.753666i
$796$	2.92234e47			0.398718
$797$		−	1.04385e48i		−	1.39501i	−0.716582	−	0.697503i	$-0.754294\pi$
$797$		−	1.04385e48i		−	1.39501i	0.716582	−	0.697503i	$-0.245706\pi$
$798$		−	6.09379e47i		−	0.797700i
$799$	−8.41568e47			−1.07911
$800$	−3.95423e47	−	8.58224e46i	−0.496680	−	0.107799i
$801$	−1.00414e47			−0.123554
$802$			1.71063e48i			2.06196i
$803$			9.97048e46i			0.117736i
$804$	−9.57617e47			−1.10781
$805$	1.26874e48	+	1.57365e48i	1.43794	+	1.78351i
$806$	1.02718e48			1.14056
$807$			9.54854e45i			0.0103878i
$808$		−	1.01100e48i		−	1.07761i
$809$	−1.19411e48			−1.24707			−0.623537	−	0.781794i	$-0.714305\pi$
$809$	−1.19411e48			−1.24707			−0.623537	+	0.781794i	$0.714305\pi$
$810$	1.09611e48	−	8.83732e47i	1.12164	−	0.904311i
$811$	−1.04748e48			−1.05027			−0.525134	−	0.851019i	$-0.675985\pi$
$811$	−1.04748e48			−1.05027			−0.525134	+	0.851019i	$0.675985\pi$
$812$			4.04213e48i			3.97133i
$813$		−	8.38990e47i		−	0.807723i
$814$	5.61506e46			0.0529727
$815$	5.57766e47	−	4.49695e47i	0.515646	−	0.415736i
$816$	8.00050e47			0.724819
$817$		−	4.84167e46i		−	0.0429864i
$818$			1.99356e48i			1.73460i
$819$	2.63098e47			0.224354
$820$	9.08479e47	+	1.12681e48i	0.759253	+	0.941718i
$821$	8.56741e47			0.701758			0.350879	−	0.936421i	$-0.385883\pi$
$821$	8.56741e47			0.701758			0.350879	+	0.936421i	$0.385883\pi$
$822$		−	1.34941e47i		−	0.108333i
$823$			4.60629e47i			0.362455i	0.983441	+	0.181228i	$0.0580070\pi$
$823$			4.60629e47i			0.362455i	−0.983441	+	0.181228i	$0.941993\pi$
$824$	−6.89886e47			−0.532082
$825$	3.27290e47	+	7.10349e46i	0.247424	+	0.0537009i
$826$	−3.66058e48			−2.71256
$827$		−	2.09756e48i		−	1.52361i	−0.647808	−	0.761803i	$-0.724314\pi$
$827$		−	2.09756e48i		−	1.52361i	0.647808	−	0.761803i	$-0.275686\pi$
$828$		−	4.28309e47i		−	0.304970i
$829$	2.34867e48			1.63935			0.819675	−	0.572828i	$-0.194154\pi$
$829$	2.34867e48			1.63935			0.819675	+	0.572828i	$0.194154\pi$
$830$	−2.60381e48	−	3.22956e48i	−1.78164	−	2.20981i
$831$	8.07432e47			0.541613
$832$		−	2.09836e48i		−	1.37989i
$833$		−	4.77160e48i		−	3.07625i
$834$	3.65973e47			0.231318
$835$	−1.32052e48	+	1.06466e48i	−0.818308	+	0.659755i
$836$	−2.35430e47			−0.143040
$837$			1.20608e48i			0.718467i
$838$			2.82958e48i			1.65271i
$839$	−3.05667e48			−1.75056			−0.875279	−	0.483618i	$-0.839322\pi$
$839$	−3.05667e48			−1.75056			−0.875279	+	0.483618i	$0.839322\pi$
$840$	3.21498e48	−	2.59205e48i	1.80538	−	1.45558i
$841$	9.12620e47			0.502523
$842$		−	2.11672e48i		−	1.14291i
$843$			2.53342e48i			1.34138i
$844$	4.12074e48			2.13956
$845$	−1.71352e46	−	2.12532e46i	−0.00872478	−	0.0108215i
$846$	3.20318e47			0.159945
$847$		−	3.33942e48i		−	1.63529i
$848$		−	1.15222e48i		−	0.553354i
$849$	−1.30497e48			−0.614645
$850$	−1.12438e48	+	5.18052e48i	−0.519398	+	2.39310i
$851$	−3.32397e47			−0.150598
$852$			3.38696e48i			1.50507i
$853$			3.72611e48i			1.62404i	0.583629	+	0.812021i	$0.301632\pi$
$853$			3.72611e48i			1.62404i	−0.583629	+	0.812021i	$0.698368\pi$
$854$	6.99021e48			2.98838
$855$	−5.50664e46	−	6.83000e46i	−0.0230911	−	0.0286405i
$856$	−5.05233e48			−2.07814
$857$			6.05125e47i			0.244153i	0.992521	+	0.122076i	$0.0389553\pi$
$857$			6.05125e47i			0.244153i	−0.992521	+	0.122076i	$0.961045\pi$
$858$			1.06969e48i			0.423368i
$859$	−2.95430e48			−1.14701			−0.573505	−	0.819202i	$-0.694417\pi$
$859$	−2.95430e48			−1.14701			−0.573505	+	0.819202i	$0.694417\pi$
$860$	5.61144e47	−	4.52418e47i	0.213722	−	0.172312i
$861$	2.90710e48			1.08619
$862$		−	6.43728e48i		−	2.35957i
$863$			5.76096e47i			0.207165i	0.994621	+	0.103583i	$0.0330306\pi$
$863$			5.76096e47i			0.207165i	−0.994621	+	0.103583i	$0.966969\pi$
$864$	1.51746e48			0.535352
$865$	4.02221e48	−	3.24287e48i	1.39219	−	1.12244i
$866$	−7.89113e48			−2.67975
$867$			3.12446e48i			1.04102i
$868$			6.75989e48i			2.20986i
$869$	1.32782e48			0.425906
$870$	−3.84394e48	−	4.76772e48i	−1.20979	−	1.50052i
$871$	2.07825e48			0.641799
$872$			1.20794e48i			0.366037i
$873$		−	5.07818e47i		−	0.150999i
$874$	2.15295e48			0.628195
$875$	2.76319e48	+	5.51035e48i	0.791186	+	1.57778i
$876$	−2.64896e48			−0.744317
$877$		−	1.47230e48i		−	0.405980i	−0.979181	−	0.202990i	$-0.934934\pi$
$877$		−	1.47230e48i		−	0.405980i	0.979181	−	0.202990i	$-0.0650658\pi$
$878$		−	4.15791e48i		−	1.12516i
$879$	−1.63552e48			−0.434350
$880$	−3.48498e47	−	4.32250e47i	−0.0908314	−	0.112660i
$881$	−6.01645e48			−1.53900			−0.769499	−	0.638648i	$-0.779494\pi$
$881$	−6.01645e48			−1.53900			−0.769499	+	0.638648i	$0.779494\pi$
$882$			1.81617e48i			0.455957i
$883$			1.72340e48i			0.424654i	0.977199	+	0.212327i	$0.0681041\pi$
$883$			1.72340e48i			0.424654i	−0.977199	+	0.212327i	$0.931896\pi$
$884$	−1.09605e49			−2.65074
$885$	2.79499e48	−	2.25344e48i	0.663462	−	0.534911i
$886$	−1.63086e48			−0.379980
$887$			4.24957e48i			0.971863i	0.873997	+	0.485931i	$0.161520\pi$
$887$			4.24957e48i			0.971863i	−0.873997	+	0.485931i	$0.838480\pi$
$888$			6.79088e47i			0.152445i
$889$	−1.05311e49			−2.32057
$890$	5.84989e48	−	4.71643e48i	1.26535	−	1.02018i
$891$	−1.09255e48			−0.231984
$892$			4.21927e48i			0.879462i
$893$			1.04229e48i			0.213274i
$894$	8.26874e48			1.66100
$895$	1.96135e48	+	2.43271e48i	0.386790	+	0.479744i
$896$	1.66990e49			3.23303
$897$		−	6.33229e48i		−	1.20361i
$898$		−	8.84761e48i		−	1.65107i
$899$	4.56336e48			0.836083
$900$	2.77035e47	−	1.27642e48i	0.0498348	−	0.229612i
$901$	8.53615e48			1.50766
$902$		−	1.73502e48i		−	0.300882i
$903$		−	1.44772e48i		−	0.246511i
$904$	−2.65619e46			−0.00444099
$905$	−2.34350e48	−	2.90669e48i	−0.384736	−	0.477197i
$906$	−3.32763e48			−0.536438
$907$			1.37448e48i			0.217579i	0.994065	+	0.108789i	$0.0346974\pi$
$907$			1.37448e48i			0.217579i	−0.994065	+	0.108789i	$0.965303\pi$
$908$		−	5.56970e48i		−	0.865796i
$909$	−6.42216e47			−0.0980341
$910$	−1.53275e49	+	1.23577e49i	−2.29768	+	1.85249i
$911$	−6.36073e48			−0.936383			−0.468192	−	0.883627i	$-0.655094\pi$
$911$	−6.36073e48			−0.936383			−0.468192	+	0.883627i	$0.655094\pi$
$912$		−	9.90867e47i		−	0.143252i
$913$			3.21905e48i			0.457047i
$914$	1.74503e49			2.43327
$915$	−5.33729e48	+	4.30315e48i	−0.730925	+	0.589303i
$916$	1.85540e49			2.49553
$917$			1.11534e49i			1.47337i
$918$		−	1.98805e49i		−	2.57943i
$919$	−1.02620e49			−1.30775			−0.653876	−	0.756601i	$-0.726858\pi$
$919$	−1.02620e49			−1.30775			−0.653876	+	0.756601i	$0.726858\pi$
$920$	9.15777e48	+	1.13586e49i	1.14628	+	1.42176i
$921$	1.48244e48			0.182261
$922$			4.55259e48i			0.549792i
$923$		−	7.35050e48i		−	0.871945i
$924$	−7.03965e48			−0.820282
$925$	−9.90592e47	−	2.14998e47i	−0.113385	−	0.0246091i
$926$	−1.87311e49			−2.10611
$927$			4.38237e47i			0.0484054i
$928$		−	5.74148e48i		−	0.622992i
$929$	8.18502e48			0.872490			0.436245	−	0.899828i	$-0.356308\pi$
$929$	8.18502e48			0.872490			0.436245	+	0.899828i	$0.356308\pi$
$930$	−6.42844e48	−	7.97333e48i	−0.673189	−	0.834971i
$931$	−5.90966e48			−0.607985
$932$		−	1.78133e48i		−	0.180046i
$933$		−	6.72289e48i		−	0.667589i
$934$	−3.44530e48			−0.336128
$935$	3.20230e48	−	2.58183e48i	0.306952	−	0.247478i
$936$	1.89904e48			0.178847
$937$		−	2.10406e49i		−	1.94695i	−0.228800	−	0.973474i	$-0.573480\pi$
$937$		−	2.10406e49i		−	1.94695i	0.228800	−	0.973474i	$-0.426520\pi$
$938$			2.11281e49i			1.92094i
$939$	−1.57281e48			−0.140506
$940$	−1.20800e49	+	9.73940e48i	−1.06037	+	0.854915i
$941$	1.12511e49			0.970434			0.485217	−	0.874394i	$-0.338741\pi$
$941$	1.12511e49			0.970434			0.485217	+	0.874394i	$0.338741\pi$
$942$			2.29226e49i			1.94278i
$943$			1.02708e49i			0.855387i
$944$	−5.95220e48			−0.487124
$945$	−1.45100e49	−	1.79971e49i	−1.16692	−	1.44736i
$946$	−8.64029e47			−0.0682849
$947$			1.47061e49i			1.14215i	0.820898	+	0.571075i	$0.193474\pi$
$947$			1.47061e49i			1.14215i	−0.820898	+	0.571075i	$0.806526\pi$
$948$			3.52777e49i			2.69254i
$949$	5.74887e48			0.431211
$950$	6.41611e48	+	1.39255e48i	0.472968	+	0.102653i
$951$	1.32558e48			0.0960346
$952$		−	5.07228e49i		−	3.61155i
$953$			6.20681e47i			0.0434346i	0.999764	+	0.0217173i	$0.00691338\pi$
$953$			6.20681e47i			0.0434346i	−0.999764	+	0.0217173i	$0.993087\pi$
$954$	−3.24903e48			−0.223463
$955$	4.67972e48	+	5.80436e48i	0.316348	+	0.392373i
$956$	1.48821e49			0.988803
$957$			4.75221e48i			0.310348i
$958$			1.21876e49i			0.782327i
$959$	−1.92727e48			−0.121601
$960$	−1.62882e49	+	1.31322e49i	−1.01018	+	0.814448i
$961$	−8.77191e48			−0.534759
$962$		−	3.23758e48i		−	0.194013i
$963$			3.20940e48i			0.189056i
$964$	−1.20941e49			−0.700328
$965$	1.96976e49	−	1.58810e49i	1.12128	−	0.904020i
$966$	6.43757e49			3.60246
$967$		−	1.22644e49i		−	0.674699i	−0.941379	−	0.337350i	$-0.890470\pi$
$967$		−	1.22644e49i		−	0.674699i	0.941379	−	0.337350i	$-0.109530\pi$
$968$		−	2.41038e49i		−	1.30360i
$969$	7.34080e48			0.390302
$970$	2.38522e49	+	2.95845e49i	1.24680	+	1.54643i
$971$	1.12879e49			0.580090			0.290045	−	0.957013i	$-0.406330\pi$
$971$	1.12879e49			0.580090			0.290045	+	0.957013i	$0.406330\pi$
$972$			9.24086e48i			0.466895i
$973$		−	5.22694e48i		−	0.259648i
$974$	−6.54527e49			−3.19672
$975$	4.09579e48	−	1.88712e49i	0.196681	−	0.906197i
$976$	1.13663e49			0.536657
$977$			4.11771e49i			1.91159i	0.294029	+	0.955796i	$0.405004\pi$
$977$			4.11771e49i			1.91159i	−0.294029	+	0.955796i	$0.594996\pi$
$978$		−	2.28174e49i		−	1.04154i
$979$	−5.83085e48			−0.261708
$980$	−5.52213e49	−	6.84922e49i	−2.43712	−	3.02281i
$981$	7.67323e47			0.0332996
$982$		−	6.62374e49i		−	2.82660i
$983$			1.02350e49i			0.429494i	0.976670	+	0.214747i	$0.0688926\pi$
$983$			1.02350e49i			0.429494i	−0.976670	+	0.214747i	$0.931107\pi$
$984$	2.09834e49			0.865877
$985$	2.64210e49	−	2.13018e49i	1.07214	−	0.864405i
$986$	−7.52204e49			−3.00170
$987$			3.11657e49i			1.22305i
$988$			1.35746e49i			0.523888i
$989$	5.11482e48			0.194129
$990$	−1.21886e48	+	9.82696e47i	−0.0454960	+	0.0366808i
$991$	1.68749e49			0.619478			0.309739	−	0.950822i	$-0.399758\pi$
$991$	1.68749e49			0.619478			0.309739	+	0.950822i	$0.399758\pi$
$992$		−	9.60182e48i		−	0.346666i
$993$		−	5.80777e47i		−	0.0206228i
$994$	7.47272e49			2.60978
$995$	3.96913e48	+	4.92300e48i	0.136337	+	0.169102i
$996$	−8.55240e49			−2.88941
$997$			1.90551e49i			0.633200i	0.948559	+	0.316600i	$0.102541\pi$
$997$			1.90551e49i			0.633200i	−0.948559	+	0.316600i	$0.897459\pi$
$998$			9.51944e49i			3.11141i
$999$	3.80145e48			0.122213

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.b.a.4.3	✓	16
5.2	odd	4		25.34.a.f.1.14		16
5.3	odd	4		25.34.a.f.1.3		16
5.4	even	2	inner	5.34.b.a.4.14	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.b.a.4.3	✓	16	1.1	even	1	trivial
5.34.b.a.4.14	yes	16	5.4	even	2	inner
25.34.a.f.1.3		16	5.3	odd	4
25.34.a.f.1.14		16	5.2	odd	4

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:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	5.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-156068. i q^{2} -6.96239e7i q^{3} -1.57674e10 q^{4} +(-2.14154e11 - 2.65619e11i) q^{5} -1.08661e13 q^{6} +1.55193e14i q^{7} +1.12018e15i q^{8} +7.11573e14 q^{9} +O(q^{10})\)	\(q-156068. i q^{2} -6.96239e7i q^{3} -1.57674e10 q^{4} +(-2.14154e11 - 2.65619e11i) q^{5} -1.08661e13 q^{6} +1.55193e14i q^{7} +1.12018e15i q^{8} +7.11573e14 q^{9} +(-4.14548e16 + 3.34226e16i) q^{10} +4.13199e16 q^{11} +1.09779e18i q^{12} -2.38246e18i q^{13} +2.42207e19 q^{14} +(-1.84934e19 + 1.49102e19i) q^{15} +3.93836e19 q^{16} +2.91772e20i q^{17} -1.11054e20i q^{18} +3.61361e20 q^{19} +(3.37665e21 + 4.18813e21i) q^{20} +1.08051e22 q^{21} -6.44874e21i q^{22} +3.81748e22i q^{23} +7.79913e22 q^{24} +(-2.46919e22 + 1.13767e23i) q^{25} -3.71827e23 q^{26} -4.36586e23i q^{27} -2.44699e24i q^{28} -1.65188e24 q^{29} +(2.32701e24 + 2.88624e24i) q^{30} -2.76253e24 q^{31} +3.47573e24i q^{32} -2.87685e24i q^{33} +4.55364e25 q^{34} +(4.12223e25 - 3.32351e25i) q^{35} -1.12197e25 q^{36} +8.70723e24i q^{37} -5.63971e25i q^{38} -1.65876e26 q^{39} +(2.97541e26 - 2.39891e26i) q^{40} +2.69048e26 q^{41} -1.68634e27i q^{42} -1.33984e26i q^{43} -6.51509e26 q^{44} +(-1.52386e26 - 1.89008e26i) q^{45} +5.95788e27 q^{46} +2.88434e27i q^{47} -2.74204e27i q^{48} -1.63539e28 q^{49} +(1.77554e28 + 3.85362e27i) q^{50} +2.03143e28 q^{51} +3.75653e28i q^{52} -2.92563e28i q^{53} -6.81373e28 q^{54} +(-8.84880e27 - 1.09754e28i) q^{55} -1.73844e29 q^{56} -2.51594e28i q^{57} +2.57806e29i q^{58} -1.51134e29 q^{59} +(2.91594e29 - 2.35096e29i) q^{60} +2.88604e29 q^{61} +4.31144e29i q^{62} +1.10431e29i q^{63} +8.80755e29 q^{64} +(-6.32827e29 + 5.10212e29i) q^{65} -4.48986e29 q^{66} +8.72314e29i q^{67} -4.60049e30i q^{68} +2.65788e30 q^{69} +(-5.18696e30 - 6.43349e30i) q^{70} +3.08526e30 q^{71} +7.97090e29i q^{72} +2.41300e30i q^{73} +1.35892e30 q^{74} +(7.92087e30 + 1.71914e30i) q^{75} -5.69774e30 q^{76} +6.41256e30i q^{77} +2.58880e31i q^{78} +3.21352e31 q^{79} +(-8.43414e30 - 1.04610e31i) q^{80} -2.64411e31 q^{81} -4.19898e31i q^{82} +7.79056e31i q^{83} -1.70369e32 q^{84} +(7.75002e31 - 6.24839e31i) q^{85} -2.09107e31 q^{86} +1.15010e32i q^{87} +4.62857e31i q^{88} -1.41115e32 q^{89} +(-2.94981e31 + 2.37826e31i) q^{90} +3.69741e32 q^{91} -6.01918e32i q^{92} +1.92338e32i q^{93} +4.50154e32 q^{94} +(-7.73868e31 - 9.59845e31i) q^{95} +2.41994e32 q^{96} -7.13656e32i q^{97} +2.55232e33i q^{98} +2.94021e31 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 72851326872 q^{4} - 232168160280 q^{5} + 11001777346872 q^{6} - 27\!\cdots\!68 q^{9}+O(q^{10}) \) 16 * q - 72851326872 * q^4 - 232168160280 * q^5 + 11001777346872 * q^6 - 27535156574590368 * q^9	\( 16 q - 72851326872 q^{4} - 232168160280 q^{5} + 11001777346872 q^{6} - 27\!\cdots\!68 q^{9}+ \cdots + 34\!\cdots\!24 q^{99}+O(q^{100}) \) 16 * q - 72851326872 * q^4 - 232168160280 * q^5 + 11001777346872 * q^6 - 27535156574590368 * q^9 - 22271193818331880 * q^10 + 219974590742466912 * q^11 - 10416043581549356184 * q^14 + 9232415497377901440 * q^15 + 133171456389985196576 * q^16 - 2949217257058889591200 * q^19 + 5571772909456424216760 * q^20 + 20126160533851210892592 * q^21 - 236696360036140740492000 * q^24 + 269473151678676722148400 * q^25 + 23043234216449373353232 * q^26 + 2210824656972934579370400 * q^29 - 7438800885032297852420760 * q^30 + 4805180075928582021889472 * q^31 - 106706080442140703440064 * q^34 + 34840114703893102459924320 * q^35 + 150609707516636111776170456 * q^36 - 950668737676648885834065216 * q^39 + 967967034953888345833396000 * q^40 + 960625982433026021733974352 * q^41 - 4300041994750366563328828704 * q^44 + 5959973976670208219568382440 * q^45 + 4030532465737707969346868392 * q^46 - 48902999941413820155855454112 * q^49 + 64132734499011351066825776400 * q^50 + 37677263492556888574173469632 * q^51 - 416785644990759180210455480400 * q^54 + 208827421951347317583761567040 * q^55 + 209868986171565551575474447200 * q^56 - 204679212804521237512362904800 * q^59 - 320542648209593925139588560480 * q^60 - 62902839261738400132019069488 * q^61 + 3273202940251902417009873735808 * q^64 - 1155813780125630532662955267360 * q^65 - 2991219624550267460630717491296 * q^66 + 6899695112224183044828868241904 * q^69 - 5880904834264312779374002982280 * q^70 - 87525095316001019795902439808 * q^71 + 43140282179597200538055251968176 * q^74 - 27726088944293536006405507003200 * q^75 - 38605994956626944020944749752800 * q^76 - 10590745643822309766800662264000 * q^79 + 24913342429758171577982759437920 * q^80 + 126385893984816788804508532470336 * q^81 - 401968339664232685914350670917664 * q^84 + 174616747052458036927895334806720 * q^85 - 18805496634715830052189508032488 * q^86 - 816457769414638729740610145056800 * q^89 + 814730708455223899676092744179240 * q^90 + 572310345418666359618454810906752 * q^91 + 1084618018208246129370832376900296 * q^94 - 960346549067575215463879922304000 * q^95 - 1376269400022374885061468958478208 * q^96 + 3432482025669259323040953857901024 * q^99

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