LMFDB - Embedded newform 5.34.b.a.4.10

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			4.10
Root			$20202.3i$ of defining polynomial
Character	$\chi$	$=$	5.4
Dual form			5.34.b.a.4.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+40404.6i q^{2} +1.28550e8i q^{3} +6.95740e9 q^{4} +(3.40199e11 + 2.60749e10i) q^{5} -5.19400e12 q^{6} -4.50276e13i q^{7} +6.28184e14i q^{8} -1.09659e16 q^{9} +O(q^{10})$	\(q+40404.6i q^{2} +1.28550e8i q^{3} +6.95740e9 q^{4} +(3.40199e11 + 2.60749e10i) q^{5} -5.19400e12 q^{6} -4.50276e13i q^{7} +6.28184e14i q^{8} -1.09659e16 q^{9} +(-1.05355e15 + 1.37456e16i) q^{10} +7.97737e16 q^{11} +8.94371e17i q^{12} +2.76246e18i q^{13} +1.81932e18 q^{14} +(-3.35192e18 + 4.37325e19i) q^{15} +3.43821e19 q^{16} -5.61300e19i q^{17} -4.43075e20i q^{18} -1.90278e21 q^{19} +(2.36690e21 + 1.81414e20i) q^{20} +5.78828e21 q^{21} +3.22323e21i q^{22} +4.97743e22i q^{23} -8.07529e22 q^{24} +(1.15056e23 + 1.77413e22i) q^{25} -1.11616e23 q^{26} -6.95053e23i q^{27} -3.13275e23i q^{28} +1.05527e24 q^{29} +(-1.76699e24 - 1.35433e23i) q^{30} -5.13782e24 q^{31} +6.78526e24i q^{32} +1.02549e25i q^{33} +2.26791e24 q^{34} +(1.17409e24 - 1.53183e25i) q^{35} -7.62945e25 q^{36} -1.64642e25i q^{37} -7.68810e25i q^{38} -3.55113e26 q^{39} +(-1.63799e25 + 2.13708e26i) q^{40} -3.83500e26 q^{41} +2.33873e26i q^{42} +6.26547e25i q^{43} +5.55017e26 q^{44} +(-3.73060e27 - 2.85936e26i) q^{45} -2.01111e27 q^{46} -5.32010e27i q^{47} +4.41980e27i q^{48} +5.70351e27 q^{49} +(-7.16832e26 + 4.64878e27i) q^{50} +7.21550e27 q^{51} +1.92195e28i q^{52} -8.17146e27i q^{53} +2.80834e28 q^{54} +(2.71389e28 + 2.08009e27i) q^{55} +2.82856e28 q^{56} -2.44601e29i q^{57} +4.26377e28i q^{58} +2.46982e29 q^{59} +(-2.33207e28 + 3.04264e29i) q^{60} -5.26306e28 q^{61} -2.07592e29i q^{62} +4.93770e29i q^{63} +2.11838e28 q^{64} +(-7.20308e28 + 9.39785e29i) q^{65} -4.14344e29 q^{66} -2.38307e30i q^{67} -3.90519e29i q^{68} -6.39847e30 q^{69} +(6.18932e29 + 4.74387e28i) q^{70} +2.98248e30 q^{71} -6.88863e30i q^{72} +8.89249e30i q^{73} +6.65231e29 q^{74} +(-2.28064e30 + 1.47903e31i) q^{75} -1.32384e31 q^{76} -3.59202e30i q^{77} -1.43482e31i q^{78} +2.50324e31 q^{79} +(1.16967e31 + 8.96509e29i) q^{80} +2.83884e31 q^{81} -1.54952e31i q^{82} -2.29063e31i q^{83} +4.02714e31 q^{84} +(1.46359e30 - 1.90954e31i) q^{85} -2.53154e30 q^{86} +1.35654e32i q^{87} +5.01126e31i q^{88} -6.67430e31 q^{89} +(1.15531e31 - 1.50734e32i) q^{90} +1.24387e32 q^{91} +3.46300e32i q^{92} -6.60464e32i q^{93} +2.14957e32 q^{94} +(-6.47323e32 - 4.96148e31i) q^{95} -8.72242e32 q^{96} +6.85302e32i q^{97} +2.30448e32i q^{98} -8.74794e32 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 $

$2$			40404.6i			0.435950i	0.975954	+	0.217975i	$0.0699451\pi$
$2$			40404.6i			0.435950i	−0.975954	+	0.217975i	$0.930055\pi$
$3$			1.28550e8i			1.72413i	0.506797	+	0.862065i	$0.330829\pi$
$3$			1.28550e8i			1.72413i	−0.506797	+	0.862065i	$0.669171\pi$
$4$	6.95740e9			0.809948
$5$	3.40199e11	+	2.60749e10i	0.997076	+	0.0764219i
$5$	3.40199e11	+	2.60749e10i	0.997076	+	0.0764219i
$6$	−5.19400e12			−0.751634
$7$		−	4.50276e13i		−	0.512107i	−0.966663	−	0.256054i	$-0.917578\pi$
$7$		−	4.50276e13i		−	0.512107i	0.966663	−	0.256054i	$-0.0824224\pi$
$8$			6.28184e14i			0.789046i
$9$	−1.09659e16			−1.97263
$10$	−1.05355e15	+	1.37456e16i	−0.0333161	+	0.434675i
$11$	7.97737e16			0.523456			0.261728	−	0.965142i	$-0.415708\pi$
$11$	7.97737e16			0.523456			0.261728	+	0.965142i	$0.415708\pi$
$12$			8.94371e17i			1.39646i
$13$			2.76246e18i			1.15141i	0.817658	+	0.575705i	$0.195272\pi$
$13$			2.76246e18i			1.15141i	−0.817658	+	0.575705i	$0.804728\pi$
$14$	1.81932e18			0.223253
$15$	−3.35192e18	+	4.37325e19i	−0.131761	+	1.71909i
$16$	3.43821e19			0.465964
$17$		−	5.61300e19i		−	0.279762i	−0.990168	−	0.139881i	$-0.955328\pi$
$17$		−	5.61300e19i		−	0.279762i	0.990168	−	0.139881i	$-0.0446719\pi$
$18$		−	4.43075e20i		−	0.859965i
$19$	−1.90278e21			−1.51340			−0.756700	−	0.653763i	$-0.773190\pi$
$19$	−1.90278e21			−1.51340			−0.756700	+	0.653763i	$0.773190\pi$
$20$	2.36690e21	+	1.81414e20i	0.807579	+	0.0618978i
$21$	5.78828e21			0.882940
$22$			3.22323e21i			0.228200i
$23$			4.97743e22i			1.69237i	0.532888	+	0.846186i	$0.321107\pi$
$23$			4.97743e22i			1.69237i	−0.532888	+	0.846186i	$0.678893\pi$
$24$	−8.07529e22			−1.36042
$25$	1.15056e23	+	1.77413e22i	0.988319	+	0.152397i
$26$	−1.11616e23			−0.501957
$27$		−	6.95053e23i		−	1.67693i
$28$		−	3.13275e23i		−	0.414780i
$29$	1.05527e24			0.783061			0.391530	−	0.920165i	$-0.371946\pi$
$29$	1.05527e24			0.783061			0.391530	+	0.920165i	$0.371946\pi$
$30$	−1.76699e24	−	1.35433e23i	−0.749436	−	0.0574413i
$31$	−5.13782e24			−1.26856			−0.634279	−	0.773104i	$-0.718703\pi$
$31$	−5.13782e24			−1.26856			−0.634279	+	0.773104i	$0.718703\pi$
$32$			6.78526e24i			0.992183i
$33$			1.02549e25i			0.902507i
$34$	2.26791e24			0.121962
$35$	1.17409e24	−	1.53183e25i	0.0391362	−	0.510610i
$36$	−7.62945e25			−1.59772
$37$		−	1.64642e25i		−	0.219388i	−0.993965	−	0.109694i	$-0.965013\pi$
$37$		−	1.64642e25i		−	0.219388i	0.993965	−	0.109694i	$-0.0349871\pi$
$38$		−	7.68810e25i		−	0.659766i
$39$	−3.55113e26			−1.98518
$40$	−1.63799e25	+	2.13708e26i	−0.0603004	+	0.786739i
$41$	−3.83500e26			−0.939359			−0.469680	−	0.882837i	$-0.655631\pi$
$41$	−3.83500e26			−0.939359			−0.469680	+	0.882837i	$0.655631\pi$
$42$			2.33873e26i			0.384917i
$43$			6.26547e25i			0.0699398i	0.999388	+	0.0349699i	$0.0111335\pi$
$43$			6.26547e25i			0.0699398i	−0.999388	+	0.0349699i	$0.988866\pi$
$44$	5.55017e26			0.423972
$45$	−3.73060e27	−	2.85936e26i	−1.96686	−	0.150752i
$46$	−2.01111e27			−0.737789
$47$		−	5.32010e27i		−	1.36869i	−0.729158	−	0.684345i	$-0.760088\pi$
$47$		−	5.32010e27i		−	1.36869i	0.729158	−	0.684345i	$-0.239912\pi$
$48$			4.41980e27i			0.803382i
$49$	5.70351e27			0.737746
$50$	−7.16832e26	+	4.64878e27i	−0.0664374	+	0.430857i
$51$	7.21550e27			0.482346
$52$			1.92195e28i			0.932582i
$53$		−	8.17146e27i		−	0.289566i	−0.989463	−	0.144783i	$-0.953752\pi$
$53$		−	8.17146e27i		−	0.289566i	0.989463	−	0.144783i	$-0.0462484\pi$
$54$	2.80834e28			0.731058
$55$	2.71389e28	+	2.08009e27i	0.521925	+	0.0400035i
$56$	2.82856e28			0.404076
$57$		−	2.44601e29i		−	2.60930i
$58$			4.26377e28i			0.341375i
$59$	2.46982e29			1.49144			0.745721	−	0.666258i	$-0.232105\pi$
$59$	2.46982e29			1.49144			0.745721	+	0.666258i	$0.232105\pi$
$60$	−2.33207e28	+	3.04264e29i	−0.106720	+	1.39237i
$61$	−5.26306e28			−0.183356			−0.0916782	−	0.995789i	$-0.529223\pi$
$61$	−5.26306e28			−0.183356			−0.0916782	+	0.995789i	$0.529223\pi$
$62$		−	2.07592e29i		−	0.553028i
$63$			4.93770e29i			1.01020i
$64$	2.11838e28			0.0334221
$65$	−7.20308e28	+	9.39785e29i	−0.0879930	+	1.14804i
$66$	−4.14344e29			−0.393447
$67$		−	2.38307e30i		−	1.76564i	−0.469708	−	0.882822i	$-0.655641\pi$
$67$		−	2.38307e30i		−	1.76564i	0.469708	−	0.882822i	$-0.344359\pi$
$68$		−	3.90519e29i		−	0.226592i
$69$	−6.39847e30			−2.91787
$70$	6.18932e29	+	4.74387e28i	0.222600	+	0.0170614i
$71$	2.98248e30			0.848818			0.424409	−	0.905471i	$-0.360482\pi$
$71$	2.98248e30			0.848818			0.424409	+	0.905471i	$0.360482\pi$
$72$		−	6.88863e30i		−	1.55649i
$73$			8.89249e30i			1.60028i	0.599813	+	0.800140i	$0.295242\pi$
$73$			8.89249e30i			1.60028i	−0.599813	+	0.800140i	$0.704758\pi$
$74$	6.65231e29			0.0956421
$75$	−2.28064e30	+	1.47903e31i	−0.262752	+	1.70399i
$76$	−1.32384e31			−1.22577
$77$		−	3.59202e30i		−	0.268066i
$78$		−	1.43482e31i		−	0.865439i
$79$	2.50324e31			1.22364			0.611822	−	0.790995i	$-0.290437\pi$
$79$	2.50324e31			1.22364			0.611822	+	0.790995i	$0.290437\pi$
$80$	1.16967e31	+	8.96509e29i	0.464601	+	0.0356098i
$81$	2.83884e31			0.918625
$82$		−	1.54952e31i		−	0.409513i
$83$		−	2.29063e31i		−	0.495640i	−0.968806	−	0.247820i	$-0.920286\pi$
$83$		−	2.29063e31i		−	0.495640i	0.968806	−	0.247820i	$-0.0797141\pi$
$84$	4.02714e31			0.715135
$85$	1.46359e30	−	1.90954e31i	0.0213799	−	0.278944i
$86$	−2.53154e30			−0.0304902
$87$			1.35654e32i			1.35010i
$88$			5.01126e31i			0.413031i
$89$	−6.67430e31			−0.456531			−0.228266	−	0.973599i	$-0.573305\pi$
$89$	−6.67430e31			−0.456531			−0.228266	+	0.973599i	$0.573305\pi$
$90$	1.15531e31	−	1.50734e32i	0.0657202	−	0.857450i
$91$	1.24387e32			0.589645
$92$			3.46300e32i			1.37073i
$93$		−	6.60464e32i		−	2.18716i
$94$	2.14957e32			0.596680
$95$	−6.47323e32	−	4.96148e31i	−1.50897	−	0.115657i
$96$	−8.72242e32			−1.71065
$97$			6.85302e32i			1.13279i	0.824135	+	0.566394i	$0.191662\pi$
$97$			6.85302e32i			1.13279i	−0.824135	+	0.566394i	$0.808338\pi$
$98$			2.30448e32i			0.321620i
$99$	−8.74794e32			−1.03258
$100$	8.00487e32	+	1.23434e32i	0.800487	+	0.123434i
$101$	8.51430e32			0.722514			0.361257	−	0.932466i	$-0.382348\pi$
$101$	8.51430e32			0.722514			0.361257	+	0.932466i	$0.382348\pi$
$102$			2.91539e32i			0.210278i
$103$		−	8.72065e32i		−	0.535469i	−0.963493	−	0.267735i	$-0.913725\pi$
$103$		−	8.72065e32i		−	0.535469i	0.963493	−	0.267735i	$-0.0862750\pi$
$104$	−1.73533e33			−0.908515
$105$	1.96917e33	+	1.50929e32i	0.880358	+	0.0674760i
$106$	3.30165e32			0.126236
$107$		−	4.32409e32i		−	0.141600i	−0.997491	−	0.0707999i	$-0.977445\pi$
$107$		−	4.32409e32i		−	0.141600i	0.997491	−	0.0707999i	$-0.0225552\pi$
$108$		−	4.83576e33i		−	1.35823i
$109$	3.03313e33			0.731734			0.365867	−	0.930667i	$-0.380773\pi$
$109$	3.03313e33			0.731734			0.365867	+	0.930667i	$0.380773\pi$
$110$	−8.40454e31	+	1.09654e33i	−0.0174395	+	0.227533i
$111$	2.11647e33			0.378253
$112$		−	1.54814e33i		−	0.238623i
$113$			1.08556e34i			1.44497i	0.691385	+	0.722487i	$0.257001\pi$
$113$			1.08556e34i			1.44497i	−0.691385	+	0.722487i	$0.742999\pi$
$114$	9.88303e33			1.13752
$115$	−1.29786e33	+	1.69332e34i	−0.129334	+	1.68742i
$116$	7.34192e33			0.634239
$117$		−	3.02929e34i		−	2.27130i
$118$			9.97920e33i			0.650194i
$119$	−2.52740e33			−0.143268
$120$	−2.74720e34	−	2.10562e33i	−1.35644	−	0.103966i
$121$	−1.68613e34			−0.725994
$122$		−	2.12652e33i		−	0.0799341i
$123$		−	4.92988e34i		−	1.61958i
$124$	−3.57458e34			−1.02747
$125$	3.86792e34	+	9.03565e33i	0.973783	+	0.227480i
$126$	−1.99506e34			−0.440394
$127$			3.44816e34i			0.668076i	0.942560	+	0.334038i	$0.108411\pi$
$127$			3.44816e34i			0.668076i	−0.942560	+	0.334038i	$0.891589\pi$
$128$			5.91408e34i			1.00675i
$129$	−8.05424e33			−0.120585
$130$	−3.79717e34	−	2.91038e33i	−0.500489	−	0.0383605i
$131$	−2.82091e34			−0.327652			−0.163826	−	0.986489i	$-0.552384\pi$
$131$	−2.82091e34			−0.327652			−0.163826	+	0.986489i	$0.552384\pi$
$132$			7.13473e34i			0.730983i
$133$			8.56775e34i			0.775023i
$134$	9.62872e34			0.769732
$135$	1.81234e34	−	2.36456e35i	0.128154	−	1.67203i
$136$	3.52600e34			0.220745
$137$			2.60993e34i			0.144790i	0.997376	+	0.0723951i	$0.0230643\pi$
$137$			2.60993e34i			0.144790i	−0.997376	+	0.0723951i	$0.976936\pi$
$138$		−	2.58528e35i		−	1.27204i
$139$	−1.24199e34			−0.0542467			−0.0271234	−	0.999632i	$-0.508635\pi$
$139$	−1.24199e34			−0.0542467			−0.0271234	+	0.999632i	$0.508635\pi$
$140$	8.16862e33	−	1.06576e35i	0.0316983	−	0.413567i
$141$	6.83897e35			2.35980
$142$			1.20506e35i			0.370042i
$143$			2.20371e35i			0.602712i
$144$	−3.77032e35			−0.919172
$145$	3.59001e35	+	2.75160e34i	0.780771	+	0.0598430i
$146$	−3.59298e35			−0.697642
$147$			7.33184e35i			1.27197i
$148$		−	1.14548e35i		−	0.177693i
$149$	5.29769e34			0.0735382			0.0367691	−	0.999324i	$-0.488293\pi$
$149$	5.29769e34			0.0735382			0.0367691	+	0.999324i	$0.488293\pi$
$150$	−5.97598e35	−	9.21485e34i	−0.742854	−	0.114547i
$151$	5.38877e35			0.600303			0.300151	−	0.953892i	$-0.402963\pi$
$151$	5.38877e35			0.600303			0.300151	+	0.953892i	$0.402963\pi$
$152$		−	1.19529e36i		−	1.19414i
$153$			6.15519e35i			0.551865i
$154$	1.45134e35			0.116863
$155$	−1.74788e36	−	1.33968e35i	−1.26485	−	0.0969457i
$156$	−2.47066e36			−1.60789
$157$		−	2.16103e36i		−	1.26566i	−0.774291	−	0.632829i	$-0.781893\pi$
$157$		−	2.16103e36i		−	1.26566i	0.774291	−	0.632829i	$-0.218107\pi$
$158$			1.01142e36i			0.533447i
$159$	1.05044e36			0.499250
$160$	−1.76925e35	+	2.30834e36i	−0.0758245	+	0.989281i
$161$	2.24122e36			0.866676
$162$			1.14702e36i			0.400474i
$163$		−	1.17374e36i		−	0.370233i	−0.982717	−	0.185116i	$-0.940734\pi$
$163$		−	1.17374e36i		−	0.370233i	0.982717	−	0.185116i	$-0.0592662\pi$
$164$	−2.66816e36			−0.760832
$165$	−2.67395e35	+	3.48870e36i	−0.0689713	+	0.899867i
$166$	9.25520e35			0.216074
$167$		−	8.30333e36i		−	1.75562i	−0.479009	−	0.877810i	$-0.659004\pi$
$167$		−	8.30333e36i		−	1.75562i	0.479009	−	0.877810i	$-0.340996\pi$
$168$			3.63611e36i			0.696680i
$169$	−1.87503e36			−0.325744
$170$	7.71542e35	+	5.91357e34i	0.121605	+	0.00932057i
$171$	2.08658e37			2.98537
$172$			4.35914e35i			0.0566476i
$173$		−	1.09567e37i		−	1.29396i	−0.762509	−	0.646978i	$-0.776033\pi$
$173$		−	1.09567e37i		−	1.29396i	0.762509	−	0.646978i	$-0.223967\pi$
$174$	−5.48106e36			−0.588575
$175$	7.98849e35	−	5.18067e36i	0.0780435	−	0.506126i
$176$	2.74278e36			0.243912
$177$			3.17494e37i			2.57144i
$178$		−	2.69673e36i		−	0.199025i
$179$	1.51833e37			1.02163			0.510813	−	0.859692i	$-0.329345\pi$
$179$	1.51833e37			1.02163			0.510813	+	0.859692i	$0.329345\pi$
$180$	−2.59553e37	−	1.98937e36i	−1.59305	−	0.122101i
$181$	−1.72911e35			−0.00968559			−0.00484279	−	0.999988i	$-0.501542\pi$
$181$	−1.72911e35			−0.00968559			−0.00484279	+	0.999988i	$0.501542\pi$
$182$			5.02580e36i			0.257056i
$183$		−	6.76564e36i		−	0.316130i
$184$	−3.12674e37			−1.33536
$185$	4.29303e35	−	5.60111e36i	0.0167660	−	0.218746i
$186$	2.66858e37			0.953492
$187$		−	4.47770e36i		−	0.146443i
$188$		−	3.70141e37i		−	1.10857i
$189$	−3.12965e37			−0.858770
$190$	2.00467e36	−	2.61549e37i	0.0504206	−	0.657836i
$191$	−9.66754e36			−0.222980			−0.111490	−	0.993766i	$-0.535562\pi$
$191$	−9.66754e36			−0.222980			−0.111490	+	0.993766i	$0.535562\pi$
$192$			2.72317e36i			0.0576241i
$193$			9.54292e37i			1.85347i	0.375715	+	0.926735i	$0.377397\pi$
$193$			9.54292e37i			1.85347i	−0.375715	+	0.926735i	$0.622603\pi$
$194$	−2.76894e37			−0.493838
$195$	−1.20809e38	−	9.25953e36i	−1.97937	−	0.151711i
$196$	3.96816e37			0.597536
$197$			4.71590e37i			0.652938i	0.945208	+	0.326469i	$0.105859\pi$
$197$			4.71590e37i			0.652938i	−0.945208	+	0.326469i	$0.894141\pi$
$198$		−	3.53457e37i		−	0.450154i
$199$	5.80769e37			0.680656			0.340328	−	0.940307i	$-0.389462\pi$
$199$	5.80769e37			0.680656			0.340328	+	0.940307i	$0.389462\pi$
$200$	−1.11448e37	+	7.22761e37i	−0.120248	+	0.779829i
$201$	3.06343e38			3.04420
$202$			3.44017e37i			0.314980i
$203$		−	4.75161e37i		−	0.401011i
$204$	5.02011e37			0.390675
$205$	−1.30466e38	−	9.99973e36i	−0.936612	−	0.0717876i
$206$	3.52355e37			0.233438
$207$		−	5.45822e38i		−	3.33842i
$208$			9.49789e37i			0.536515i
$209$	−1.51792e38			−0.792198
$210$	−6.09823e36	+	7.95635e37i	−0.0294161	+	0.383791i
$211$	2.04970e38			0.914177			0.457088	−	0.889421i	$-0.348892\pi$
$211$	2.04970e38			0.914177			0.457088	+	0.889421i	$0.348892\pi$
$212$		−	5.68521e37i		−	0.234533i
$213$			3.83396e38i			1.46347i
$214$	1.74713e37			0.0617304
$215$	−1.63372e36	+	2.13151e37i	−0.00534493	+	0.0697353i
$216$	4.36621e38			1.32318
$217$			2.31343e38i			0.649638i
$218$			1.22552e38i			0.318999i
$219$	−1.14313e39			−2.75909
$220$	1.88816e38	+	1.44720e37i	0.422732	+	0.0324008i
$221$	1.55057e38			0.322120
$222$			8.55152e37i			0.164899i
$223$		−	9.58767e37i		−	0.171665i	−0.996310	−	0.0858327i	$-0.972645\pi$
$223$		−	9.58767e37i		−	0.171665i	0.996310	−	0.0858327i	$-0.0273551\pi$
$224$	3.05524e38			0.508104
$225$	−1.26169e39	−	1.94550e38i	−1.94958	−	0.300622i
$226$	−4.38617e38			−0.629935
$227$			2.43307e38i			0.324884i	0.986718	+	0.162442i	$0.0519370\pi$
$227$			2.43307e38i			0.324884i	−0.986718	+	0.162442i	$0.948063\pi$
$228$		−	1.70179e39i		−	2.11340i
$229$	1.55024e38			0.179107			0.0895536	−	0.995982i	$-0.471456\pi$
$229$	1.55024e38			0.179107			0.0895536	+	0.995982i	$0.471456\pi$
$230$	−6.84179e38	−	5.24396e37i	−0.735631	−	0.0563833i
$231$	4.61752e38			0.462180
$232$			6.62902e38i			0.617871i
$233$			5.99322e38i			0.520340i	0.965563	+	0.260170i	$0.0837786\pi$
$233$			5.99322e38i			0.520340i	−0.965563	+	0.260170i	$0.916221\pi$
$234$	1.22397e39			0.990172
$235$	1.38721e38	−	1.80989e39i	0.104598	−	1.36469i
$236$	1.71835e39			1.20799
$237$			3.21790e39i			2.10972i
$238$		−	1.02119e38i		−	0.0624576i
$239$	−1.00905e39			−0.575898			−0.287949	−	0.957646i	$-0.592973\pi$
$239$	−1.00905e39			−0.575898			−0.287949	+	0.957646i	$0.592973\pi$
$240$	−1.15246e38	+	1.50361e39i	−0.0613960	+	0.801033i
$241$	7.17231e38			0.356761			0.178381	−	0.983962i	$-0.442914\pi$
$241$	7.17231e38			0.356761			0.178381	+	0.983962i	$0.442914\pi$
$242$		−	6.81275e38i		−	0.316497i
$243$		−	2.14519e38i		−	0.0931029i
$244$	−3.66172e38			−0.148509
$245$	1.94033e39	+	1.48719e38i	0.735589	+	0.0563800i
$246$	1.99190e39			0.706054
$247$		−	5.25634e39i		−	1.74254i
$248$		−	3.22750e39i		−	1.00095i
$249$	2.94459e39			0.854547
$250$	−3.65082e38	+	1.56282e39i	−0.0991700	+	0.424520i
$251$	−4.78159e39			−1.21606			−0.608031	−	0.793913i	$-0.708041\pi$
$251$	−4.78159e39			−1.21606			−0.608031	+	0.793913i	$0.708041\pi$
$252$			3.43535e39i			0.818206i
$253$			3.97068e39i			0.885883i
$254$	−1.39322e39			−0.291248
$255$	2.45471e39	+	1.88144e38i	0.480935	+	0.0368618i
$256$	−2.20760e39			−0.405471
$257$		−	6.14408e39i		−	1.05818i	−0.848565	−	0.529091i	$-0.822533\pi$
$257$		−	6.14408e39i		−	1.05818i	0.848565	−	0.529091i	$-0.177467\pi$
$258$		−	3.25429e38i		−	0.0525691i
$259$	−7.41344e38			−0.112350
$260$	−5.01147e38	+	6.53846e39i	−0.0712697	+	0.929855i
$261$	−1.15720e40			−1.54469
$262$		−	1.13978e39i		−	0.142840i
$263$			1.16782e40i			1.37437i	0.726481	+	0.687187i	$0.241155\pi$
$263$			1.16782e40i			1.37437i	−0.726481	+	0.687187i	$0.758845\pi$
$264$	−6.44195e39			−0.712119
$265$	2.13070e38	−	2.77992e39i	0.0221292	−	0.288719i
$266$	−3.46177e39			−0.337871
$267$		−	8.57978e39i		−	0.787119i
$268$		−	1.65800e40i		−	1.43008i
$269$	−1.55042e39			−0.125758			−0.0628791	−	0.998021i	$-0.520028\pi$
$269$	−1.55042e39			−0.125758			−0.0628791	+	0.998021i	$0.520028\pi$
$270$	9.55393e39	+	7.32271e38i	0.728920	+	0.0558689i
$271$	1.82806e40			1.31219			0.656095	−	0.754678i	$-0.272207\pi$
$271$	1.82806e40			1.31219			0.656095	+	0.754678i	$0.272207\pi$
$272$		−	1.92987e39i		−	0.130359i
$273$			1.59899e40i			1.01663i
$274$	−1.05453e39			−0.0631213
$275$	9.17840e39	+	1.41529e39i	0.517342	+	0.0797731i
$276$	−4.45167e40			−2.36332
$277$			3.66520e39i			0.183308i	0.995791	+	0.0916541i	$0.0292154\pi$
$277$			3.66520e39i			0.183308i	−0.995791	+	0.0916541i	$0.970785\pi$
$278$		−	5.01821e38i		−	0.0236488i
$279$	5.63410e40			2.50239
$280$	9.62274e39	+	7.37545e38i	0.402895	+	0.0308803i
$281$	−2.60347e39			−0.102777			−0.0513887	−	0.998679i	$-0.516365\pi$
$281$	−2.60347e39			−0.102777			−0.0513887	+	0.998679i	$0.516365\pi$
$282$			2.76326e40i			1.02875i
$283$			3.40904e40i			1.19717i	0.801059	+	0.598585i	$0.204270\pi$
$283$			3.40904e40i			1.19717i	−0.801059	+	0.598585i	$0.795730\pi$
$284$	2.07503e40			0.687498
$285$	6.37796e39	−	8.32131e40i	0.199408	−	2.60167i
$286$	−8.90402e39			−0.262752
$287$			1.72681e40i			0.481053i
$288$		−	7.44067e40i		−	1.95720i
$289$	3.71039e40			0.921733
$290$	−1.11177e39	+	1.45053e40i	−0.0260885	+	0.340377i
$291$	−8.80953e40			−1.95307
$292$			6.18686e40i			1.29614i
$293$		−	1.88928e40i		−	0.374094i	−0.982351	−	0.187047i	$-0.940108\pi$
$293$		−	1.88928e40i		−	0.374094i	0.982351	−	0.187047i	$-0.0598916\pi$
$294$	−2.96240e40			−0.554515
$295$	8.40229e40	+	6.44003e39i	1.48708	+	0.113979i
$296$	1.03426e40			0.173107
$297$		−	5.54469e40i		−	0.877801i
$298$			2.14051e39i			0.0320589i
$299$	−1.37499e41			−1.94861
$300$	−1.58673e40	+	1.02902e41i	−0.212816	+	1.38014i
$301$	2.82119e39			0.0358167
$302$			2.17731e40i			0.261702i
$303$			1.09451e41i			1.24571i
$304$	−6.54214e40			−0.705189
$305$	−1.79049e40	−	1.37234e39i	−0.182820	−	0.0140124i
$306$	−2.48698e40			−0.240585
$307$		−	3.68552e40i		−	0.337843i	−0.985629	−	0.168922i	$-0.945972\pi$
$307$		−	3.68552e40i		−	0.337843i	0.985629	−	0.168922i	$-0.0540285\pi$
$308$		−	2.49911e40i		−	0.217119i
$309$	1.12104e41			0.923219
$310$	5.41294e39	−	7.06225e40i	0.0422634	−	0.551410i
$311$	−1.22261e41			−0.905197			−0.452599	−	0.891714i	$-0.649503\pi$
$311$	−1.22261e41			−0.905197			−0.452599	+	0.891714i	$0.649503\pi$
$312$		−	2.23076e41i		−	1.56640i
$313$		−	1.04888e41i		−	0.698626i	−0.937006	−	0.349313i	$-0.886415\pi$
$313$		−	1.04888e41i		−	0.698626i	0.937006	−	0.349313i	$-0.113585\pi$
$314$	8.73156e40			0.551763
$315$	−1.28750e40	+	1.67980e41i	−0.0772011	+	1.00724i
$316$	1.74160e41			0.991088
$317$		−	1.38670e41i		−	0.749042i	−0.927218	−	0.374521i	$-0.877807\pi$
$317$		−	1.38670e41i		−	0.749042i	0.927218	−	0.374521i	$-0.122193\pi$
$318$			4.24426e40i			0.217648i
$319$	8.41825e40			0.409898
$320$	7.20670e39	+	5.52366e38i	0.0333244	+	0.00255418i
$321$	5.55861e40			0.244137
$322$			9.05555e40i			0.377827i
$323$			1.06803e41i			0.423391i
$324$	1.97510e41			0.744039
$325$	−4.90096e40	+	3.17836e41i	−0.175471	+	1.13796i
$326$	4.74244e40			0.161403
$327$			3.89907e41i			1.26160i
$328$		−	2.40909e41i		−	0.741198i
$329$	−2.39551e41			−0.700917
$330$	−1.40960e41	−	1.08040e40i	−0.392297	−	0.0300680i
$331$	4.76787e41			1.26230			0.631150	−	0.775661i	$-0.282583\pi$
$331$	4.76787e41			1.26230			0.631150	+	0.775661i	$0.282583\pi$
$332$		−	1.59368e41i		−	0.401442i
$333$			1.80546e41i			0.432770i
$334$	3.35493e41			0.765362
$335$	6.21385e40	−	8.10719e41i	0.134934	−	1.76048i
$336$	1.99013e41			0.411418
$337$		−	2.81601e41i		−	0.554294i	−0.960828	−	0.277147i	$-0.910611\pi$
$337$		−	2.81601e41i		−	0.554294i	0.960828	−	0.277147i	$-0.0893889\pi$
$338$		−	7.57598e40i		−	0.142008i
$339$	−1.39548e42			−2.49132
$340$	1.01828e40	−	1.32854e41i	0.0173166	−	0.225930i
$341$	−4.09863e41			−0.664035
$342$			8.43073e41i			1.30147i
$343$		−	6.04923e41i		−	0.889912i
$344$	−3.93587e40			−0.0551857
$345$	−2.17675e42	−	1.66840e41i	−2.90934	−	0.222989i
$346$	4.42702e41			0.564099
$347$			4.64811e41i			0.564729i	0.959307	+	0.282364i	$0.0911188\pi$
$347$			4.64811e41i			0.564729i	−0.959307	+	0.282364i	$0.908881\pi$
$348$			9.43801e41i			1.09351i
$349$	9.10831e41			1.00651			0.503255	−	0.864138i	$-0.332136\pi$
$349$	9.10831e41			1.00651			0.503255	+	0.864138i	$0.332136\pi$
$350$	2.09323e41	+	3.22772e40i	0.220645	+	0.0340230i
$351$	1.92005e42			1.93084
$352$			5.41285e41i			0.519364i
$353$			1.14490e41i			0.104830i	0.998625	+	0.0524150i	$0.0166919\pi$
$353$			1.14490e41i			0.104830i	−0.998625	+	0.0524150i	$0.983308\pi$
$354$	−1.28282e42			−1.12102
$355$	1.01464e42	+	7.77679e40i	0.846336	+	0.0648683i
$356$	−4.64358e41			−0.369767
$357$		−	3.24896e41i		−	0.247013i
$358$			6.13476e41i			0.445377i
$359$	−2.42615e42			−1.68213			−0.841064	−	0.540935i	$-0.818070\pi$
$359$	−2.42615e42			−1.68213			−0.841064	+	0.540935i	$0.818070\pi$
$360$	1.79621e41	−	2.34351e42i	0.118950	−	1.55194i
$361$	2.03979e42			1.29038
$362$		−	6.98640e39i		−	0.00422243i
$363$		−	2.16752e42i		−	1.25171i
$364$	8.65408e41			0.477582
$365$	−2.31871e41	+	3.02522e42i	−0.122297	+	1.59560i
$366$	2.73363e41			0.137817
$367$		−	2.93662e42i		−	1.41533i	−0.706549	−	0.707664i	$-0.749749\pi$
$367$		−	2.93662e42i		−	1.41533i	0.706549	−	0.707664i	$-0.250251\pi$
$368$			1.71134e42i			0.788584i
$369$	4.20544e42			1.85300
$370$	2.26311e41	+	1.73458e40i	0.0953624	+	0.00730915i
$371$	−3.67941e41			−0.148289
$372$		−	4.59512e42i		−	1.77149i
$373$			2.96590e42i			1.09386i	0.837180	+	0.546928i	$0.184203\pi$
$373$			2.96590e42i			1.09386i	−0.837180	+	0.546928i	$0.815797\pi$
$374$	1.80920e41			0.0638417
$375$	−1.16153e42	+	4.97219e42i	−0.392206	+	1.67893i
$376$	3.34201e42			1.07996
$377$			2.91513e42i			0.901624i
$378$		−	1.26453e42i		−	0.374380i
$379$	2.82552e42			0.800852			0.400426	−	0.916329i	$-0.368862\pi$
$379$	2.82552e42			0.800852			0.400426	+	0.916329i	$0.368862\pi$
$380$	−4.50369e42	−	3.45190e41i	−1.22219	−	0.0936761i
$381$	−4.43260e42			−1.15185
$382$		−	3.90613e41i		−	0.0972079i
$383$		−	5.03031e42i		−	1.19899i	−0.800379	−	0.599494i	$-0.795369\pi$
$383$		−	5.03031e42i		−	1.19899i	0.800379	−	0.599494i	$-0.204631\pi$
$384$	−7.60253e42			−1.73577
$385$	9.36615e40	−	1.22200e42i	0.0204861	−	0.267282i
$386$	−3.85578e42			−0.808020
$387$		−	6.87068e41i		−	0.137965i
$388$			4.76792e42i			0.917499i
$389$	3.04513e42			0.561612			0.280806	−	0.959764i	$-0.409398\pi$
$389$	3.04513e42			0.561612			0.280806	+	0.959764i	$0.409398\pi$
$390$	3.74128e41	−	4.88124e42i	0.0661385	−	0.862908i
$391$	2.79383e42			0.473461
$392$			3.58286e42i			0.582116i
$393$		−	3.62627e42i		−	0.564915i
$394$	−1.90544e42			−0.284648
$395$	8.51600e42	+	6.52718e41i	1.22007	+	0.0935133i
$396$	−6.08629e42			−0.836338
$397$			5.66877e42i			0.747215i	0.927587	+	0.373607i	$0.121879\pi$
$397$			5.66877e42i			0.747215i	−0.927587	+	0.373607i	$0.878121\pi$
$398$			2.34657e42i			0.296732i
$399$	−1.10138e43			−1.33624
$400$	3.95585e42	+	6.09983e41i	0.460521	+	0.0710114i
$401$	−8.89547e42			−0.993773			−0.496886	−	0.867816i	$-0.665523\pi$
$401$	−8.89547e42			−0.993773			−0.496886	+	0.867816i	$0.665523\pi$
$402$			1.23777e43i			1.32712i
$403$		−	1.41930e43i		−	1.46063i
$404$	5.92374e42			0.585199
$405$	9.65772e42	+	7.40226e41i	0.915939	+	0.0702031i
$406$	1.91987e42			0.174821
$407$		−	1.31341e42i		−	0.114840i
$408$			4.53266e42i			0.380593i
$409$	1.61063e43			1.29885			0.649427	−	0.760424i	$-0.275009\pi$
$409$	1.61063e43			1.29885			0.649427	+	0.760424i	$0.275009\pi$
$410$	4.04036e41	−	5.27144e42i	0.0312958	−	0.408316i
$411$	−3.35505e42			−0.249637
$412$		−	6.06730e42i		−	0.433702i
$413$		−	1.11210e43i		−	0.763779i
$414$	2.20537e43			1.45538
$415$	5.97280e41	−	7.79270e42i	0.0378777	−	0.494190i
$416$	−1.87440e43			−1.14241
$417$		−	1.59657e42i		−	0.0935284i
$418$		−	6.13308e42i		−	0.345358i
$419$	−7.91126e41			−0.0428267			−0.0214133	−	0.999771i	$-0.506817\pi$
$419$	−7.91126e41			−0.0428267			−0.0214133	+	0.999771i	$0.506817\pi$
$420$	1.37003e43	+	1.05007e42i	0.713044	+	0.0546520i
$421$	1.27306e43			0.637079			0.318540	−	0.947910i	$-0.396808\pi$
$421$	1.27306e43			0.637079			0.318540	+	0.947910i	$0.396808\pi$
$422$			8.28174e42i			0.398535i
$423$			5.83399e43i			2.69991i
$424$	5.13318e42			0.228481
$425$	9.95822e41	−	6.45807e42i	0.0426348	−	0.276494i
$426$	−1.54910e43			−0.638000
$427$			2.36983e42i			0.0938981i
$428$		−	3.00844e42i		−	0.114688i
$429$	−2.83286e43			−1.03915
$430$	−8.61228e41	−	6.60098e40i	−0.0304011	−	0.00233012i
$431$	−3.83641e43			−1.30332			−0.651658	−	0.758513i	$-0.725926\pi$
$431$	−3.83641e43			−1.30332			−0.651658	+	0.758513i	$0.725926\pi$
$432$		−	2.38973e43i		−	0.781390i
$433$			1.42983e43i			0.450022i	0.974356	+	0.225011i	$0.0722417\pi$
$433$			1.42983e43i			0.450022i	−0.974356	+	0.225011i	$0.927758\pi$
$434$	−9.34735e42			−0.283210
$435$	−3.53717e42	+	4.61494e43i	−0.103177	+	1.34615i
$436$	2.11027e43			0.592666
$437$		−	9.47094e43i		−	2.56124i
$438$		−	4.61876e43i		−	1.20283i
$439$	1.76341e43			0.442270			0.221135	−	0.975243i	$-0.429024\pi$
$439$	1.76341e43			0.442270			0.221135	+	0.975243i	$0.429024\pi$
$440$	−1.30668e42	+	1.70483e43i	−0.0315646	+	0.411823i
$441$	−6.25444e43			−1.45530
$442$			6.26501e42i			0.140428i
$443$			2.12703e43i			0.459317i	0.973271	+	0.229659i	$0.0737610\pi$
$443$			2.12703e43i			0.459317i	−0.973271	+	0.229659i	$0.926239\pi$
$444$	1.47251e43			0.306366
$445$	−2.27059e43	−	1.74032e42i	−0.455196	−	0.0348890i
$446$	3.87386e42			0.0748375
$447$			6.81016e42i			0.126789i
$448$		−	9.53855e41i		−	0.0171157i
$449$	1.42398e43			0.246286			0.123143	−	0.992389i	$-0.460703\pi$
$449$	1.42398e43			0.246286			0.123143	+	0.992389i	$0.460703\pi$
$450$	7.86074e42	−	5.09782e43i	0.131056	−	0.849920i
$451$	−3.05932e43			−0.491713
$452$			7.55268e43i			1.17035i
$453$			6.92725e43i			1.03500i
$454$	−9.83073e42			−0.141633
$455$	4.23162e43	+	3.24337e42i	0.587921	+	0.0450618i
$456$	1.53655e44			2.05886
$457$			2.10542e43i			0.272095i	0.990702	+	0.136048i	$0.0434400\pi$
$457$			2.10542e43i			0.272095i	−0.990702	+	0.136048i	$0.956560\pi$
$458$			6.26368e42i			0.0780817i
$459$	−3.90133e43			−0.469142
$460$	−9.02974e42	+	1.17811e44i	−0.104754	+	1.36672i
$461$	6.19842e43			0.693770			0.346885	−	0.937908i	$-0.387239\pi$
$461$	6.19842e43			0.693770			0.346885	+	0.937908i	$0.387239\pi$
$462$			1.86569e43i			0.201487i
$463$		−	9.99008e43i		−	1.04108i	−0.853838	−	0.520538i	$-0.825731\pi$
$463$		−	9.99008e43i		−	1.04108i	0.853838	−	0.520538i	$-0.174269\pi$
$464$	3.62823e43			0.364878
$465$	1.72216e43	−	2.24689e44i	0.167147	−	2.18076i
$466$	−2.42154e43			−0.226842
$467$			1.73459e43i			0.156844i	0.996920	+	0.0784221i	$0.0249882\pi$
$467$			1.73459e43i			0.156844i	−0.996920	+	0.0784221i	$0.975012\pi$
$468$		−	2.10760e44i		−	1.83963i
$469$	−1.07304e44			−0.904199
$470$	7.31281e43	+	5.60498e42i	0.594935	+	0.0455994i
$471$	2.77800e44			2.18216
$472$			1.55150e44i			1.17682i
$473$			4.99820e42i			0.0366104i
$474$	−1.30018e44			−0.919733
$475$	−2.18925e44	−	3.37578e43i	−1.49572	−	0.230637i
$476$	−1.75841e43			−0.116040
$477$			8.96077e43i			0.571205i
$478$		−	4.07701e43i		−	0.251062i
$479$	1.40068e44			0.833303			0.416652	−	0.909066i	$-0.363204\pi$
$479$	1.40068e44			0.833303			0.416652	+	0.909066i	$0.363204\pi$
$480$	−2.96736e44	−	2.27436e43i	−1.70565	−	0.130731i
$481$	4.54817e43			0.252605
$482$			2.89795e43i			0.155530i
$483$			2.88107e44i			1.49426i
$484$	−1.17311e44			−0.588017
$485$	−1.78692e43	+	2.33139e44i	−0.0865698	+	1.12947i
$486$	8.66758e42			0.0405882
$487$		−	6.30878e43i		−	0.285573i	−0.989754	−	0.142787i	$-0.954394\pi$
$487$		−	6.30878e43i		−	0.285573i	0.989754	−	0.142787i	$-0.0456063\pi$
$488$		−	3.30617e43i		−	0.144677i
$489$	1.50883e44			0.638330
$490$	−6.00892e42	+	7.83983e43i	−0.0245788	+	0.320680i
$491$	−3.14086e44			−1.24223			−0.621117	−	0.783718i	$-0.713321\pi$
$491$	−3.14086e44			−1.24223			−0.621117	+	0.783718i	$0.713321\pi$
$492$		−	3.42991e44i		−	1.31177i
$493$		−	5.92322e43i		−	0.219070i
$494$	2.12380e44			0.759661
$495$	−2.97604e44	−	2.28102e43i	−1.02956	−	0.0789120i
$496$	−1.76649e44			−0.591102
$497$		−	1.34294e44i		−	0.434686i
$498$			1.18975e44i			0.372540i
$499$	−4.89217e44			−1.48198			−0.740990	−	0.671516i	$-0.765644\pi$
$499$	−4.89217e44			−1.48198			−0.740990	+	0.671516i	$0.765644\pi$
$500$	2.69107e44	+	6.28646e43i	0.788713	+	0.184247i
$501$	1.06739e45			3.02692
$502$		−	1.93198e44i		−	0.530142i
$503$		−	4.01818e44i		−	1.06698i	−0.845805	−	0.533492i	$-0.820879\pi$
$503$		−	4.01818e44i		−	1.06698i	0.845805	−	0.533492i	$-0.179121\pi$
$504$	−3.10179e44			−0.797091
$505$	2.89656e44	+	2.22010e43i	0.720401	+	0.0552159i
$506$	−1.60434e44			−0.386200
$507$		−	2.41034e44i		−	0.561626i
$508$			2.39902e44i			0.541107i
$509$	−1.77493e44			−0.387560			−0.193780	−	0.981045i	$-0.562075\pi$
$509$	−1.77493e44			−0.387560			−0.193780	+	0.981045i	$0.562075\pi$
$510$	−7.60187e42	+	9.91815e43i	−0.0160699	+	0.209663i
$511$	4.00407e44			0.819515
$512$			4.18819e44i			0.829988i
$513$			1.32253e45i			2.53787i
$514$	2.48249e44			0.461314
$515$	2.27390e43	−	2.96676e44i	0.0409216	−	0.533903i
$516$	−5.60366e43			−0.0976678
$517$		−	4.24404e44i		−	0.716450i
$518$		−	2.99537e43i		−	0.0489790i
$519$	1.40848e45			2.23095
$520$	−5.90358e44	−	4.52486e43i	−0.905858	−	0.0694305i
$521$	6.44372e44			0.957887			0.478944	−	0.877846i	$-0.341020\pi$
$521$	6.44372e44			0.957887			0.478944	+	0.877846i	$0.341020\pi$
$522$		−	4.67562e44i		−	0.673405i
$523$		−	1.01493e45i		−	1.41631i	−0.706057	−	0.708155i	$-0.749528\pi$
$523$		−	1.01493e45i		−	1.41631i	0.706057	−	0.708155i	$-0.250472\pi$
$524$	−1.96262e44			−0.265381
$525$	6.65973e44	+	1.02692e44i	0.872626	+	0.134557i
$526$	−4.71852e44			−0.599158
$527$			2.88386e44i			0.354894i
$528$			3.52584e44i			0.420535i
$529$	−1.61248e45			−1.86412
$530$	1.12322e44	+	8.60902e42i	0.125867	+	0.00964721i
$531$	−2.70839e45			−2.94206
$532$			5.96092e44i			0.627728i
$533$		−	1.05940e45i		−	1.08159i
$534$	3.46663e44			0.343144
$535$	1.12750e43	−	1.47105e44i	0.0108213	−	0.141186i
$536$	1.49701e45			1.39317
$537$			1.95181e45i			1.76142i
$538$		−	6.26441e43i		−	0.0548242i
$539$	4.54990e44			0.386178
$540$	1.26092e44	−	1.64512e45i	0.103798	−	1.35426i
$541$	−2.19276e45			−1.75080			−0.875398	−	0.483402i	$-0.839401\pi$
$541$	−2.19276e45			−1.75080			−0.875398	+	0.483402i	$0.839401\pi$
$542$			7.38620e44i			0.572049i
$543$		−	2.22276e43i		−	0.0166992i
$544$	3.80857e44			0.277575
$545$	1.03187e45	+	7.90885e43i	0.729594	+	0.0559205i
$546$	−6.46064e44			−0.443197
$547$			2.39160e45i			1.59183i	0.605406	+	0.795917i	$0.293011\pi$
$547$			2.39160e45i			1.59183i	−0.605406	+	0.795917i	$0.706989\pi$
$548$			1.81583e44i			0.117273i
$549$	5.77144e44			0.361693
$550$	−5.71843e43	+	3.70850e44i	−0.0347770	+	0.225535i
$551$	−2.00794e45			−1.18508
$552$		−	4.01942e45i		−	2.30233i
$553$		−	1.12715e45i		−	0.626637i
$554$	−1.48091e44			−0.0799131
$555$	7.20021e44	+	5.51868e43i	0.377147	+	0.0289069i
$556$	−8.64101e43			−0.0439370
$557$		−	8.28307e44i		−	0.408866i	−0.978881	−	0.204433i	$-0.934465\pi$
$557$		−	8.28307e44i		−	0.408866i	0.978881	−	0.204433i	$-0.0655350\pi$
$558$			2.27644e45i			1.09092i
$559$	−1.73081e44			−0.0805294
$560$	4.03677e43	−	5.26676e44i	0.0182361	−	0.237926i
$561$	5.75607e44			0.252487
$562$		−	1.05192e44i		−	0.0448058i
$563$		−	2.75942e45i		−	1.14138i	−0.821166	−	0.570689i	$-0.806676\pi$
$563$		−	2.75942e45i		−	1.14138i	0.821166	−	0.570689i	$-0.193324\pi$
$564$	4.75815e45			1.91132
$565$	−2.83059e44	+	3.69307e45i	−0.110428	+	1.44075i
$566$	−1.37741e45			−0.521906
$567$		−	1.27826e45i		−	0.470435i
$568$			1.87355e45i			0.669756i
$569$	3.85974e45			1.34031			0.670156	−	0.742220i	$-0.266227\pi$
$569$	3.85974e45			1.34031			0.670156	+	0.742220i	$0.266227\pi$
$570$	3.36220e45	+	2.57699e44i	1.13420	+	0.0869316i
$571$	3.14573e45			1.03092			0.515461	−	0.856913i	$-0.327621\pi$
$571$	3.14573e45			1.03092			0.515461	+	0.856913i	$0.327621\pi$
$572$			1.53321e45i			0.488166i
$573$		−	1.24276e45i		−	0.384446i
$574$	−6.97710e44			−0.209715
$575$	−8.83062e44	+	5.72681e45i	−0.257912	+	1.67260i
$576$	−2.32300e44			−0.0659293
$577$		−	3.38645e45i		−	0.933994i	−0.884259	−	0.466997i	$-0.845336\pi$
$577$		−	3.38645e45i		−	0.933994i	0.884259	−	0.466997i	$-0.154664\pi$
$578$			1.49917e45i			0.401829i
$579$	−1.22674e46			−3.19563
$580$	2.49771e45	+	1.91440e44i	0.632384	+	0.0484697i
$581$	−1.03141e45			−0.253821
$582$		−	3.55946e45i		−	0.851442i
$583$		−	6.51867e44i		−	0.151575i
$584$	−5.58612e45			−1.26270
$585$	7.89886e44	−	1.03056e46i	0.173577	−	2.26466i
$586$	7.63357e44			0.163086
$587$		−	4.55046e44i		−	0.0945206i	−0.998883	−	0.0472603i	$-0.984951\pi$
$587$		−	4.55046e44i		−	0.0945206i	0.998883	−	0.0472603i	$-0.0150490\pi$
$588$			5.10106e45i			1.03023i
$589$	9.77612e45			1.91984
$590$	−2.60207e44	+	3.39492e45i	−0.0496891	+	0.648292i
$591$	−6.06227e45			−1.12575
$592$		−	5.66074e44i		−	0.102227i
$593$		−	6.04073e45i		−	1.06093i	−0.847707	−	0.530465i	$-0.822017\pi$
$593$		−	6.04073e45i		−	1.06093i	0.847707	−	0.530465i	$-0.177983\pi$
$594$	2.24031e45			0.382677
$595$	−8.59819e44	−	6.59018e43i	−0.142849	−	0.0109488i
$596$	3.68581e44			0.0595621
$597$			7.46576e45i			1.17354i
$598$		−	5.55561e45i		−	0.849497i
$599$	−6.89493e45			−1.02562			−0.512811	−	0.858501i	$-0.671396\pi$
$599$	−6.89493e45			−1.02562			−0.512811	+	0.858501i	$0.671396\pi$
$600$	−9.29106e45	−	1.43266e45i	−1.34453	−	0.207323i
$601$	1.70804e44			0.0240474			0.0120237	−	0.999928i	$-0.496173\pi$
$601$	1.70804e44			0.0240474			0.0120237	+	0.999928i	$0.496173\pi$
$602$			1.13989e44i			0.0156143i
$603$			2.61326e46i			3.48295i
$604$	3.74919e45			0.486214
$605$	−5.73620e45	−	4.39658e44i	−0.723871	−	0.0554818i
$606$	−4.42233e45			−0.543066
$607$			1.12811e46i			1.34815i	0.738662	+	0.674076i	$0.235458\pi$
$607$			1.12811e46i			1.34815i	−0.738662	+	0.674076i	$0.764542\pi$
$608$		−	1.29108e46i		−	1.50157i
$609$	6.10818e45			0.691395
$610$	5.54488e43	−	7.23440e44i	0.00610872	−	0.0797004i
$611$	1.46965e46			1.57592
$612$			4.28241e45i			0.446982i
$613$		−	1.40624e46i		−	1.42877i	−0.699754	−	0.714383i	$-0.746707\pi$
$613$		−	1.40624e46i		−	1.42877i	0.699754	−	0.714383i	$-0.253293\pi$
$614$	1.48912e45			0.147283
$615$	1.28546e45	−	1.67714e46i	0.123771	−	1.61484i
$616$	2.25645e45			0.211516
$617$		−	1.29589e45i		−	0.118267i	−0.998250	−	0.0591335i	$-0.981166\pi$
$617$		−	1.29589e45i		−	0.118267i	0.998250	−	0.0591335i	$-0.0188338\pi$
$618$			4.52950e45i			0.402477i
$619$	−3.31478e45			−0.286787			−0.143393	−	0.989666i	$-0.545801\pi$
$619$	−3.31478e45			−0.286787			−0.143393	+	0.989666i	$0.545801\pi$
$620$	−1.21607e46	−	9.32070e44i	−1.02446	−	0.0785210i
$621$	3.45958e46			2.83799
$622$		−	4.93993e45i		−	0.394620i
$623$			3.00527e45i			0.233793i
$624$	−1.22095e46			−0.925022
$625$	1.29230e46	+	4.08248e45i	0.953550	+	0.301234i
$626$	4.23797e45			0.304566
$627$		−	1.95127e46i		−	1.36585i
$628$		−	1.50352e46i		−	1.02512i
$629$	−9.24137e44			−0.0613763
$630$	−6.78717e45	−	5.20210e44i	−0.439106	−	0.0336558i
$631$	1.94858e45			0.122810			0.0614050	−	0.998113i	$-0.480442\pi$
$631$	1.94858e45			0.122810			0.0614050	+	0.998113i	$0.480442\pi$
$632$			1.57250e46i			0.965512i
$633$			2.63488e46i			1.57616i
$634$	5.60293e45			0.326545
$635$	−8.99105e44	+	1.17306e46i	−0.0510557	+	0.666122i
$636$	7.30832e45			0.404366
$637$			1.57557e46i			0.849448i
$638$			3.40136e45i			0.178695i
$639$	−3.27057e46			−1.67440
$640$	−1.54209e45	+	2.01197e46i	−0.0769380	+	1.00381i
$641$	−5.77896e45			−0.280991			−0.140495	−	0.990081i	$-0.544869\pi$
$641$	−5.77896e45			−0.280991			−0.140495	+	0.990081i	$0.544869\pi$
$642$			2.24593e45i			0.106431i
$643$		−	3.42017e46i		−	1.57967i	−0.613320	−	0.789835i	$-0.710166\pi$
$643$		−	3.42017e46i		−	1.57967i	0.613320	−	0.789835i	$-0.289834\pi$
$644$	1.55930e46			0.701963
$645$	−2.74005e45	−	2.10014e44i	−0.120233	−	0.00921536i
$646$	−4.31534e45			−0.184577
$647$		−	3.03331e46i		−	1.26473i	−0.774672	−	0.632363i	$-0.782085\pi$
$647$		−	3.03331e46i		−	1.26473i	0.774672	−	0.632363i	$-0.217915\pi$
$648$			1.78332e46i			0.724838i
$649$	1.97026e46			0.780705
$650$	−1.28420e46	−	1.98022e45i	−0.496093	−	0.0764966i
$651$	−2.97391e46			−1.12006
$652$		−	8.16615e45i		−	0.299869i
$653$			2.24480e46i			0.803732i	0.915699	+	0.401866i	$0.131638\pi$
$653$			2.24480e46i			0.803732i	−0.915699	+	0.401866i	$0.868362\pi$
$654$	−1.57541e46			−0.549996
$655$	−9.59672e45	−	7.35551e44i	−0.326694	−	0.0250398i
$656$	−1.31855e46			−0.437707
$657$		−	9.75145e46i		−	3.15675i
$658$		−	9.67898e45i		−	0.305564i
$659$	−5.25928e46			−1.61926			−0.809630	−	0.586940i	$-0.800332\pi$
$659$	−5.25928e46			−1.61926			−0.809630	+	0.586940i	$0.800332\pi$
$660$	−1.86037e45	+	2.42723e46i	−0.0558632	+	0.728846i
$661$	5.50373e46			1.61188			0.805941	−	0.591996i	$-0.201660\pi$
$661$	5.50373e46			1.61188			0.805941	+	0.591996i	$0.201660\pi$
$662$			1.92644e46i			0.550299i
$663$			1.99325e46i			0.555377i
$664$	1.43894e46			0.391083
$665$	−2.23403e45	+	2.91474e46i	−0.0592287	+	0.772756i
$666$	−7.29488e45			−0.188666
$667$			5.25252e46i			1.32523i
$668$		−	5.77696e46i		−	1.42196i
$669$	1.23249e46			0.295974
$670$	3.27568e46	+	2.51068e45i	0.767481	+	0.0588244i
$671$	−4.19854e45			−0.0959790
$672$			3.92750e46i			0.876037i
$673$			3.89204e46i			0.847089i	0.905875	+	0.423544i	$0.139214\pi$
$673$			3.89204e46i			0.847089i	−0.905875	+	0.423544i	$0.860786\pi$
$674$	1.13780e46			0.241644
$675$	1.23312e46	−	7.99697e46i	0.255559	−	1.65735i
$676$	−1.30453e46			−0.263836
$677$			9.82090e46i			1.93838i	0.246321	+	0.969188i	$0.420778\pi$
$677$			9.82090e46i			1.93838i	−0.246321	+	0.969188i	$0.579222\pi$
$678$		−	5.63840e46i		−	1.08609i
$679$	3.08575e46			0.580109
$680$	1.19954e46	+	9.19402e44i	0.220099	+	0.0168697i
$681$	−3.12770e46			−0.560142
$682$		−	1.65603e46i		−	0.289486i
$683$		−	3.34300e46i		−	0.570420i	−0.958465	−	0.285210i	$-0.907937\pi$
$683$		−	3.34300e46i		−	0.570420i	0.958465	−	0.285210i	$-0.0920633\pi$
$684$	1.45171e47			2.41799
$685$	−6.80537e44	+	8.87896e45i	−0.0110652	+	0.144367i
$686$	2.44417e46			0.387957
$687$			1.99283e46i			0.308804i
$688$			2.15420e45i			0.0325894i
$689$	2.25733e46			0.333409
$690$	6.74109e45	−	8.79509e46i	0.0972121	−	1.26832i
$691$	−7.86716e46			−1.10772			−0.553860	−	0.832610i	$-0.686846\pi$
$691$	−7.86716e46			−1.10772			−0.553860	+	0.832610i	$0.686846\pi$
$692$		−	7.62302e46i		−	1.04804i
$693$			3.93898e46i			0.528793i
$694$	−1.87805e46			−0.246193
$695$	−4.22523e45	−	3.23848e44i	−0.0540881	−	0.00414564i
$696$	−8.52158e46			−1.06529
$697$			2.15259e46i			0.262797i
$698$			3.68018e46i			0.438788i
$699$	−7.70426e46			−0.897134
$700$	5.55791e45	−	3.60440e46i	0.0632112	−	0.409935i
$701$	1.57034e45			0.0174440			0.00872199	−	0.999962i	$-0.497224\pi$
$701$	1.57034e45			0.0174440			0.00872199	+	0.999962i	$0.497224\pi$
$702$			7.75790e46i			0.841747i
$703$			3.13277e46i			0.332022i
$704$	1.68991e45			0.0174950
$705$	2.32661e47	+	1.78326e46i	2.35290	+	0.180341i
$706$	−4.62594e45			−0.0457006
$707$		−	3.83378e46i		−	0.370005i
$708$			2.20893e47i			2.08273i
$709$	−1.61122e47			−1.48420			−0.742099	−	0.670291i	$-0.766169\pi$
$709$	−1.61122e47			−1.48420			−0.742099	+	0.670291i	$0.766169\pi$
$710$	−3.14218e45	+	4.09960e46i	−0.0282793	+	0.368960i
$711$	−2.74504e47			−2.41379
$712$		−	4.19269e46i		−	0.360224i
$713$		−	2.55731e47i		−	2.14687i
$714$	1.31273e46			0.107685
$715$	−5.74616e45	+	7.49701e46i	−0.0460604	+	0.600950i
$716$	1.05636e47			0.827463
$717$		−	1.29712e47i		−	0.992923i
$718$		−	9.80277e46i		−	0.733323i
$719$	−4.48895e46			−0.328185			−0.164092	−	0.986445i	$-0.552469\pi$
$719$	−4.48895e46			−0.328185			−0.164092	+	0.986445i	$0.552469\pi$
$720$	−1.28266e47	−	9.83107e45i	−0.916484	−	0.0702449i
$721$	−3.92670e46			−0.274218
$722$			8.24170e46i			0.562540i
$723$			9.21998e46i			0.615103i
$724$	−1.20301e45			−0.00784482
$725$	1.21414e47	+	1.87218e46i	0.773914	+	0.119336i
$726$	8.75777e46			0.545681
$727$		−	1.37452e47i		−	0.837210i	−0.908168	−	0.418605i	$-0.862519\pi$
$727$		−	1.37452e47i		−	0.837210i	0.908168	−	0.418605i	$-0.137481\pi$
$728$			7.81378e46i			0.465257i
$729$	1.85389e47			1.07915
$730$	−1.22233e47	−	9.36866e45i	−0.695601	−	0.0533151i
$731$	3.51681e45			0.0195665
$732$		−	4.70713e46i		−	0.256049i
$733$			7.11867e46i			0.378603i	0.981919	+	0.189301i	$0.0606223\pi$
$733$			7.11867e46i			0.378603i	−0.981919	+	0.189301i	$0.939378\pi$
$734$	1.18653e47			0.617012
$735$	−1.91177e46	+	2.49429e47i	−0.0972064	+	1.26825i
$736$	−3.37731e47			−1.67914
$737$		−	1.90107e47i		−	0.924237i
$738$			1.69919e47i			0.807816i
$739$	6.60143e45			0.0306905			0.0153453	−	0.999882i	$-0.495115\pi$
$739$	6.60143e45			0.0306905			0.0153453	+	0.999882i	$0.495115\pi$
$740$	2.98683e45	−	3.89692e46i	0.0135796	−	0.177173i
$741$	6.75700e47			3.00437
$742$		−	1.48665e46i		−	0.0646465i
$743$		−	3.76363e46i		−	0.160063i	−0.996792	−	0.0800315i	$-0.974498\pi$
$743$		−	3.76363e46i		−	0.160063i	0.996792	−	0.0800315i	$-0.0255021\pi$
$744$	4.14893e47			1.72577
$745$	1.80227e46	+	1.38137e45i	0.0733231	+	0.00561993i
$746$	−1.19836e47			−0.476866
$747$			2.51189e47i			0.977711i
$748$		−	3.11532e46i		−	0.118611i
$749$	−1.94703e46			−0.0725143
$750$	−2.00900e47	−	4.69312e46i	−0.731928	−	0.170982i
$751$	1.65143e47			0.588574			0.294287	−	0.955717i	$-0.404918\pi$
$751$	1.65143e47			0.588574			0.294287	+	0.955717i	$0.404918\pi$
$752$		−	1.82916e47i		−	0.637760i
$753$		−	6.14672e47i		−	2.09665i
$754$	−1.17785e47			−0.393063
$755$	1.83326e47	+	1.40512e46i	0.598547	+	0.0458763i
$756$	−2.17743e47			−0.695559
$757$			2.98191e47i			0.931993i	0.884786	+	0.465997i	$0.154304\pi$
$757$			2.98191e47i			0.931993i	−0.884786	+	0.465997i	$0.845696\pi$
$758$			1.14164e47i			0.349131i
$759$	−5.10429e47			−1.52738
$760$	3.11672e46	−	4.06638e47i	0.0912586	−	1.19065i
$761$	−3.71671e46			−0.106491			−0.0532453	−	0.998581i	$-0.516957\pi$
$761$	−3.71671e46			−0.106491			−0.0532453	+	0.998581i	$0.516957\pi$
$762$		−	1.79097e47i		−	0.502149i
$763$		−	1.36574e47i		−	0.374726i
$764$	−6.72609e46			−0.180602
$765$	−1.60496e46	+	2.09399e47i	−0.0421746	+	0.550251i
$766$	2.03248e47			0.522698
$767$			6.82276e47i			1.71726i
$768$		−	2.83786e47i		−	0.699086i
$769$	−7.77065e47			−1.87358			−0.936792	−	0.349888i	$-0.886220\pi$
$769$	−7.77065e47			−1.87358			−0.936792	+	0.349888i	$0.886220\pi$
$770$	4.93745e46	+	3.78436e45i	0.116521	+	0.00893090i
$771$	7.89819e47			1.82444
$772$			6.63939e47i			1.50121i
$773$			6.54527e47i			1.44866i	0.689454	+	0.724330i	$0.257851\pi$
$773$			6.54527e47i			1.44866i	−0.689454	+	0.724330i	$0.742149\pi$
$774$	2.77607e46			0.0601458
$775$	−5.91134e47	−	9.11517e46i	−1.25374	−	0.193324i
$776$	−4.30496e47			−0.893822
$777$		−	9.52995e46i		−	0.193706i
$778$			1.23037e47i			0.244835i
$779$	7.29715e47			1.42163
$780$	−8.40516e47	−	6.44223e46i	−1.60319	−	0.122878i
$781$	2.37923e47			0.444319
$782$			1.12884e47i			0.206405i
$783$		−	7.33466e47i		−	1.31314i
$784$	1.96098e47			0.343763
$785$	5.63487e46	−	7.35181e47i	0.0967241	−	1.26196i
$786$	1.46518e47			0.246275
$787$		−	1.48230e46i		−	0.0243980i	−0.999926	−	0.0121990i	$-0.996117\pi$
$787$		−	1.48230e46i		−	0.0243980i	0.999926	−	0.0121990i	$-0.00388316\pi$
$788$			3.28104e47i			0.528846i
$789$	−1.50122e48			−2.36960
$790$	−2.63728e46	+	3.44086e47i	−0.0407671	+	0.531887i
$791$	4.88802e47			0.739981
$792$		−	5.49532e47i		−	0.814755i
$793$		−	1.45390e47i		−	0.211118i
$794$	−2.29045e47			−0.325748
$795$	3.57358e47	+	2.73901e46i	0.497790	+	0.0381536i
$796$	4.04064e47			0.551296
$797$		−	1.05939e48i		−	1.41577i	−0.706326	−	0.707887i	$-0.749649\pi$
$797$		−	1.05939e48i		−	1.41577i	0.706326	−	0.707887i	$-0.250351\pi$
$798$		−	4.45009e47i		−	0.582533i
$799$	−2.98618e47			−0.382907
$800$	−1.20379e47	+	7.80681e47i	−0.151206	+	0.980593i
$801$	7.31900e47			0.900565
$802$		−	3.59418e47i		−	0.433235i
$803$			7.09387e47i			0.837677i
$804$	2.13135e48			2.46564
$805$	7.62460e47	+	5.84395e46i	0.864142	+	0.0662331i
$806$	5.73462e47			0.636762
$807$		−	1.99306e47i		−	0.216824i
$808$			5.34855e47i			0.570097i
$809$	4.84112e47			0.505587			0.252793	−	0.967520i	$-0.418651\pi$
$809$	4.84112e47			0.505587			0.252793	+	0.967520i	$0.418651\pi$
$810$	−2.99086e46	+	3.90216e47i	−0.0306050	+	0.399303i
$811$	−9.65779e47			−0.968353			−0.484176	−	0.874970i	$-0.660881\pi$
$811$	−9.65779e47			−0.968353			−0.484176	+	0.874970i	$0.660881\pi$
$812$		−	3.30589e47i		−	0.324798i
$813$			2.34996e48i			2.26239i
$814$	5.30679e46			0.0500644
$815$	3.06051e46	−	3.99304e47i	0.0282939	−	0.369150i
$816$	2.48084e47			0.224756
$817$		−	1.19218e47i		−	0.105847i
$818$			6.50768e47i			0.566235i
$819$	−1.36402e48			−1.16315
$820$	−9.07707e47	−	6.95721e46i	−0.758607	−	0.0581443i
$821$	−1.81523e48			−1.48686			−0.743428	−	0.668816i	$-0.766801\pi$
$821$	−1.81523e48			−1.48686			−0.743428	+	0.668816i	$0.766801\pi$
$822$		−	1.35560e47i		−	0.108829i
$823$		−	1.53424e47i		−	0.120725i	−0.998177	−	0.0603625i	$-0.980774\pi$
$823$		−	1.53424e47i		−	0.120725i	0.998177	−	0.0603625i	$-0.0192257\pi$
$824$	5.47817e47			0.422510
$825$	−1.81935e47	+	1.17988e48i	−0.137539	+	0.891965i
$826$	4.49339e47			0.332969
$827$		−	1.63967e48i		−	1.19101i	−0.803350	−	0.595507i	$-0.796951\pi$
$827$		−	1.63967e48i		−	1.19101i	0.803350	−	0.595507i	$-0.203049\pi$
$828$		−	3.79750e48i		−	2.70394i
$829$	2.26341e48			1.57984			0.789922	−	0.613207i	$-0.210121\pi$
$829$	2.26341e48			1.57984			0.789922	+	0.613207i	$0.210121\pi$
$830$	3.14861e47	+	2.41329e46i	0.215442	+	0.0165128i
$831$	−4.71160e47			−0.316047
$832$			5.85193e46i			0.0384826i
$833$		−	3.20138e47i		−	0.206393i
$834$	6.45089e46			0.0407737
$835$	2.16509e47	−	2.82478e48i	0.134168	−	1.75049i
$836$	−1.05607e48			−0.641639
$837$			3.57105e48i			2.12729i
$838$		−	3.19651e46i		−	0.0186703i
$839$	−2.77504e48			−1.58927			−0.794633	−	0.607090i	$-0.792337\pi$
$839$	−2.77504e48			−1.58927			−0.794633	+	0.607090i	$0.792337\pi$
$840$	−9.48112e46	+	1.23700e48i	−0.0532416	+	0.694643i
$841$	−7.02487e47			−0.386816
$842$			5.14374e47i			0.277734i
$843$		−	3.34674e47i		−	0.177202i
$844$	1.42606e48			0.740436
$845$	−6.37883e47	−	4.88912e46i	−0.324792	−	0.0248940i
$846$	−2.35720e48			−1.17703
$847$			7.59224e47i			0.371787i
$848$		−	2.80952e47i		−	0.134927i
$849$	−4.38231e48			−2.06408
$850$	2.60936e47	+	4.02358e46i	0.120537	+	0.0185866i
$851$	8.19495e47			0.371286
$852$			2.66744e48i			1.18534i
$853$			3.64584e48i			1.58905i	0.607229	+	0.794527i	$0.292281\pi$
$853$			3.64584e48i			1.58905i	−0.607229	+	0.794527i	$0.707719\pi$
$854$	−9.57520e46			−0.0409348
$855$	7.09851e48	+	5.44073e47i	2.97664	+	0.228148i
$856$	2.71633e47			0.111729
$857$		−	2.97756e48i		−	1.20137i	−0.799486	−	0.600685i	$-0.794895\pi$
$857$		−	2.97756e48i		−	1.20137i	0.799486	−	0.600685i	$-0.205105\pi$
$858$		−	1.14461e48i		−	0.453019i
$859$	−8.30251e47			−0.322346			−0.161173	−	0.986926i	$-0.551528\pi$
$859$	−8.30251e47			−0.322346			−0.161173	+	0.986926i	$0.551528\pi$
$860$	−1.13664e46	+	1.48298e47i	−0.00432912	+	0.0564819i
$861$	−2.21980e48			−0.829397
$862$		−	1.55009e48i		−	0.568180i
$863$		−	2.22843e48i		−	0.801347i	−0.916221	−	0.400674i	$-0.868776\pi$
$863$		−	2.22843e48i		−	0.801347i	0.916221	−	0.400674i	$-0.131224\pi$
$864$	4.71611e48			1.66382
$865$	2.85695e47	−	3.72746e48i	0.0988866	−	1.29017i
$866$	−5.77717e47			−0.196187
$867$			4.76969e48i			1.58919i
$868$			1.60955e48i			0.526173i
$869$	1.99693e48			0.640524
$870$	−1.86465e48	−	1.42918e47i	−0.586854	−	0.0449800i
$871$	6.58313e48			2.03298
$872$			1.90536e48i			0.577372i
$873$		−	7.51499e48i		−	2.23457i
$874$	3.82670e48			1.11657
$875$	4.06853e47	−	1.74163e48i	0.116494	−	0.498681i
$876$	−7.95319e48			−2.23472
$877$		−	1.79023e47i		−	0.0493647i	−0.999695	−	0.0246824i	$-0.992143\pi$
$877$		−	1.79023e47i		−	0.0493647i	0.999695	−	0.0246824i	$-0.00785743\pi$
$878$			7.12498e47i			0.192808i
$879$	2.42866e48			0.644986
$880$	9.33092e47	+	7.15179e46i	0.243198	+	0.0186402i
$881$	−4.77018e48			−1.22020			−0.610102	−	0.792323i	$-0.708872\pi$
$881$	−4.77018e48			−1.22020			−0.610102	+	0.792323i	$0.708872\pi$
$882$		−	2.52708e48i		−	0.634436i
$883$		−	7.30531e47i		−	0.180006i	−0.995941	−	0.0900030i	$-0.971312\pi$
$883$		−	7.30531e47i		−	0.180006i	0.995941	−	0.0900030i	$-0.0286877\pi$
$884$	1.07879e48			0.260901
$885$	−8.27863e47	+	1.08011e49i	−0.196515	+	2.56392i
$886$	−8.59420e47			−0.200239
$887$			1.12115e48i			0.256404i	0.991748	+	0.128202i	$0.0409205\pi$
$887$			1.12115e48i			0.256404i	−0.991748	+	0.128202i	$0.959079\pi$
$888$			1.32953e48i			0.298459i
$889$	1.55262e48			0.342127
$890$	7.03169e46	−	9.17424e47i	0.0152098	−	0.198443i
$891$	2.26465e48			0.480860
$892$		−	6.67053e47i		−	0.139040i
$893$			1.01230e49i			2.07138i
$894$	−2.75162e47			−0.0552738
$895$	5.16535e48	+	3.95904e47i	1.01864	+	0.0780746i
$896$	2.66297e48			0.515566
$897$		−	1.76755e49i		−	3.35966i
$898$			5.75355e47i			0.107368i
$899$	−5.42177e48			−0.993359
$900$	−8.77810e48	−	1.35357e48i	−1.57906	−	0.243488i
$901$	−4.58664e47			−0.0810095
$902$		−	1.23611e48i		−	0.214362i
$903$			3.62663e47i			0.0617526i
$904$	−6.81932e48			−1.14015
$905$	−5.88241e46	−	4.50864e45i	−0.00965726	−	0.000740191i
$906$	−2.79893e48			−0.451208
$907$			8.50271e48i			1.34598i	0.739653	+	0.672988i	$0.234989\pi$
$907$			8.50271e48i			1.34598i	−0.739653	+	0.672988i	$0.765011\pi$
$908$			1.69278e48i			0.263139i
$909$	−9.33673e48			−1.42525
$910$	−1.31047e47	+	1.70977e48i	−0.0196447	+	0.256304i
$911$	5.96361e48			0.877922			0.438961	−	0.898506i	$-0.355347\pi$
$911$	5.96361e48			0.877922			0.438961	+	0.898506i	$0.355347\pi$
$912$		−	8.40990e48i		−	1.21584i
$913$		−	1.82732e48i		−	0.259446i
$914$	−8.50687e47			−0.118620
$915$	1.76414e47	−	2.30167e48i	0.0241593	−	0.315206i
$916$	1.07856e48			0.145067
$917$			1.27019e48i			0.167793i
$918$		−	1.57632e48i		−	0.204522i
$919$	9.13256e48			1.16382			0.581911	−	0.813252i	$-0.302305\pi$
$919$	9.13256e48			1.16382			0.581911	+	0.813252i	$0.302305\pi$
$920$	−1.06372e49	−	8.15296e47i	−1.33145	−	0.102051i
$921$	4.73772e48			0.582486
$922$			2.50445e48i			0.302449i
$923$			8.23896e48i			0.977337i
$924$	3.21259e48			0.374342
$925$	2.92097e47	−	1.89430e48i	0.0334340	−	0.216825i
$926$	4.03646e48			0.453857
$927$			9.56301e48i			1.05628i
$928$			7.16026e48i			0.776939i
$929$	−9.34290e48			−0.995916			−0.497958	−	0.867201i	$-0.665917\pi$
$929$	−9.34290e48			−0.995916			−0.497958	+	0.867201i	$0.665917\pi$
$930$	9.07849e48	+	6.95831e47i	0.950703	+	0.0728677i
$931$	−1.08525e49			−1.11650
$932$			4.16972e48i			0.421448i
$933$		−	1.57167e49i		−	1.56068i
$934$	−7.00855e47			−0.0683762
$935$	1.16756e47	−	1.52331e48i	0.0111915	−	0.146015i
$936$	1.90295e49			1.79216
$937$			1.11454e47i			0.0103132i	0.999987	+	0.00515660i	$0.00164140\pi$
$937$			1.11454e47i			0.0103132i	−0.999987	+	0.00515660i	$0.998359\pi$
$938$		−	4.33558e48i		−	0.394185i
$939$	1.34833e49			1.20452
$940$	9.65139e47	−	1.25922e49i	0.0847189	−	1.10533i
$941$	1.31523e49			1.13442			0.567208	−	0.823575i	$-0.308024\pi$
$941$	1.31523e49			1.13442			0.567208	+	0.823575i	$0.308024\pi$
$942$			1.12244e49i			0.951312i
$943$		−	1.90884e49i		−	1.58975i
$944$	8.49174e48			0.694958
$945$	−1.06471e49	−	8.16055e47i	−0.856258	−	0.0656288i
$946$	−2.01950e47			−0.0159603
$947$		−	2.52879e48i		−	0.196399i	−0.995167	−	0.0981993i	$-0.968692\pi$
$947$		−	2.52879e48i		−	0.196399i	0.995167	−	0.0981993i	$-0.0313083\pi$
$948$			2.23882e49i			1.70877i
$949$	−2.45651e49			−1.84258
$950$	1.36397e48	−	8.84559e48i	0.100546	−	0.652059i
$951$	1.78260e49			1.29145
$952$		−	1.58767e48i		−	0.113045i
$953$		−	1.36754e49i		−	0.956992i	−0.878090	−	0.478496i	$-0.841182\pi$
$953$		−	1.36754e49i		−	0.956992i	0.878090	−	0.478496i	$-0.158818\pi$
$954$	−3.62057e48			−0.249017
$955$	−3.28889e48	−	2.52080e47i	−0.222328	−	0.0170405i
$956$	−7.02033e48			−0.466447
$957$			1.08216e49i			0.706717i
$958$			5.65940e48i			0.363278i
$959$	1.17519e48			0.0741482
$960$	−7.10064e46	+	9.26419e47i	−0.00440374	+	0.0574556i
$961$	9.99369e48			0.609242
$962$			1.83767e48i			0.110123i
$963$			4.74178e48i			0.279323i
$964$	4.99006e48			0.288958
$965$	−2.48831e48	+	3.24649e49i	−0.141646	+	1.84805i
$966$	−1.16409e49			−0.651423
$967$			1.19899e49i			0.659598i	0.944051	+	0.329799i	$0.106981\pi$
$967$			1.19899e49i			0.659598i	−0.944051	+	0.329799i	$0.893019\pi$
$968$		−	1.05920e49i		−	0.572842i
$969$	−1.37295e49			−0.729982
$970$	−9.41990e48	−	7.21999e47i	−0.492394	−	0.0377401i
$971$	1.76280e49			0.905910			0.452955	−	0.891533i	$-0.350370\pi$
$971$	1.76280e49			0.905910			0.452955	+	0.891533i	$0.350370\pi$
$972$		−	1.49250e48i		−	0.0754085i
$973$			5.59237e47i			0.0277801i
$974$	2.54904e48			0.124495
$975$	−4.08577e49	−	6.30017e48i	−1.96199	−	0.302535i
$976$	−1.80955e48			−0.0854374
$977$		−	2.65563e49i		−	1.23284i	−0.787417	−	0.616421i	$-0.788582\pi$
$977$		−	2.65563e49i		−	1.23284i	0.787417	−	0.616421i	$-0.211418\pi$
$978$			6.09639e48i			0.278280i
$979$	−5.32433e48			−0.238974
$980$	1.34996e49	+	1.03469e48i	0.595789	+	0.0456649i
$981$	−3.32611e49			−1.44344
$982$		−	1.26905e49i		−	0.541551i
$983$			4.24873e48i			0.178289i	0.996019	+	0.0891447i	$0.0284134\pi$
$983$			4.24873e48i			0.178289i	−0.996019	+	0.0891447i	$0.971587\pi$
$984$	3.09687e49			1.27792
$985$	−1.22967e48	+	1.60435e49i	−0.0498988	+	0.651029i
$986$	2.39326e48			0.0955036
$987$		−	3.07942e49i		−	1.20847i
$988$		−	3.65704e49i		−	1.41137i
$989$	−3.11860e48			−0.118364
$990$	9.21637e47	−	1.20246e49i	0.0344016	−	0.448838i
$991$	−5.19907e49			−1.90858			−0.954290	−	0.298882i	$-0.903386\pi$
$991$	−5.19907e49			−1.90858			−0.954290	+	0.298882i	$0.903386\pi$
$992$		−	3.48614e49i		−	1.25864i
$993$			6.12908e49i			2.17637i
$994$	5.42609e48			0.189501
$995$	1.97577e49	+	1.51435e48i	0.678665	+	0.0520170i
$996$	2.04867e49			0.692139
$997$			1.65839e49i			0.551082i	0.961289	+	0.275541i	$0.0888570\pi$
$997$			1.65839e49i			0.551082i	−0.961289	+	0.275541i	$0.911143\pi$
$998$		−	1.97666e49i		−	0.646069i
$999$	−1.14435e49			−0.367899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.b.a.4.10	yes	16
5.2	odd	4		25.34.a.f.1.7		16
5.3	odd	4		25.34.a.f.1.10		16
5.4	even	2	inner	5.34.b.a.4.7	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.b.a.4.7	✓	16	5.4	even	2	inner
5.34.b.a.4.10	yes	16	1.1	even	1	trivial
25.34.a.f.1.7		16	5.2	odd	4
25.34.a.f.1.10		16	5.3	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)

\(f(q)\)	\(=\)	\(q+40404.6i q^{2} +1.28550e8i q^{3} +6.95740e9 q^{4} +(3.40199e11 + 2.60749e10i) q^{5} -5.19400e12 q^{6} -4.50276e13i q^{7} +6.28184e14i q^{8} -1.09659e16 q^{9} +O(q^{10})\)	\(q+40404.6i q^{2} +1.28550e8i q^{3} +6.95740e9 q^{4} +(3.40199e11 + 2.60749e10i) q^{5} -5.19400e12 q^{6} -4.50276e13i q^{7} +6.28184e14i q^{8} -1.09659e16 q^{9} +(-1.05355e15 + 1.37456e16i) q^{10} +7.97737e16 q^{11} +8.94371e17i q^{12} +2.76246e18i q^{13} +1.81932e18 q^{14} +(-3.35192e18 + 4.37325e19i) q^{15} +3.43821e19 q^{16} -5.61300e19i q^{17} -4.43075e20i q^{18} -1.90278e21 q^{19} +(2.36690e21 + 1.81414e20i) q^{20} +5.78828e21 q^{21} +3.22323e21i q^{22} +4.97743e22i q^{23} -8.07529e22 q^{24} +(1.15056e23 + 1.77413e22i) q^{25} -1.11616e23 q^{26} -6.95053e23i q^{27} -3.13275e23i q^{28} +1.05527e24 q^{29} +(-1.76699e24 - 1.35433e23i) q^{30} -5.13782e24 q^{31} +6.78526e24i q^{32} +1.02549e25i q^{33} +2.26791e24 q^{34} +(1.17409e24 - 1.53183e25i) q^{35} -7.62945e25 q^{36} -1.64642e25i q^{37} -7.68810e25i q^{38} -3.55113e26 q^{39} +(-1.63799e25 + 2.13708e26i) q^{40} -3.83500e26 q^{41} +2.33873e26i q^{42} +6.26547e25i q^{43} +5.55017e26 q^{44} +(-3.73060e27 - 2.85936e26i) q^{45} -2.01111e27 q^{46} -5.32010e27i q^{47} +4.41980e27i q^{48} +5.70351e27 q^{49} +(-7.16832e26 + 4.64878e27i) q^{50} +7.21550e27 q^{51} +1.92195e28i q^{52} -8.17146e27i q^{53} +2.80834e28 q^{54} +(2.71389e28 + 2.08009e27i) q^{55} +2.82856e28 q^{56} -2.44601e29i q^{57} +4.26377e28i q^{58} +2.46982e29 q^{59} +(-2.33207e28 + 3.04264e29i) q^{60} -5.26306e28 q^{61} -2.07592e29i q^{62} +4.93770e29i q^{63} +2.11838e28 q^{64} +(-7.20308e28 + 9.39785e29i) q^{65} -4.14344e29 q^{66} -2.38307e30i q^{67} -3.90519e29i q^{68} -6.39847e30 q^{69} +(6.18932e29 + 4.74387e28i) q^{70} +2.98248e30 q^{71} -6.88863e30i q^{72} +8.89249e30i q^{73} +6.65231e29 q^{74} +(-2.28064e30 + 1.47903e31i) q^{75} -1.32384e31 q^{76} -3.59202e30i q^{77} -1.43482e31i q^{78} +2.50324e31 q^{79} +(1.16967e31 + 8.96509e29i) q^{80} +2.83884e31 q^{81} -1.54952e31i q^{82} -2.29063e31i q^{83} +4.02714e31 q^{84} +(1.46359e30 - 1.90954e31i) q^{85} -2.53154e30 q^{86} +1.35654e32i q^{87} +5.01126e31i q^{88} -6.67430e31 q^{89} +(1.15531e31 - 1.50734e32i) q^{90} +1.24387e32 q^{91} +3.46300e32i q^{92} -6.60464e32i q^{93} +2.14957e32 q^{94} +(-6.47323e32 - 4.96148e31i) q^{95} -8.72242e32 q^{96} +6.85302e32i q^{97} +2.30448e32i q^{98} -8.74794e32 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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