LMFDB - Embedded newform 471.2.b.b.313.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [471,2,Mod(313,471)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(471, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("471.313");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 471 = 3 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	471.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:	$3.76095393520$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 24x^{12} + 224x^{10} + 1027x^{8} + 2399x^{6} + 2652x^{4} + 1094x^{2} + 147 $ x^14 + 24x^12 + 224x^10 + 1027x^8 + 2399x^6 + 2652x^4 + 1094x^2 + 147
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			313.8
Root			$0.560879i$ of defining polynomial
Character	$\chi$	$=$	471.313
Dual form			471.2.b.b.313.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.560879i q^{2} +1.00000 q^{3} +1.68542 q^{4} -0.365796i q^{5} +0.560879i q^{6} +4.51711i q^{7} +2.06707i q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.560879i q^{2} +1.00000 q^{3} +1.68542 q^{4} -0.365796i q^{5} +0.560879i q^{6} +4.51711i q^{7} +2.06707i q^{8} +1.00000 q^{9} +0.205167 q^{10} +2.17449 q^{11} +1.68542 q^{12} -6.15454 q^{13} -2.53355 q^{14} -0.365796i q^{15} +2.21146 q^{16} -3.05570 q^{17} +0.560879i q^{18} +1.16956 q^{19} -0.616519i q^{20} +4.51711i q^{21} +1.21962i q^{22} -4.14770i q^{23} +2.06707i q^{24} +4.86619 q^{25} -3.45195i q^{26} +1.00000 q^{27} +7.61321i q^{28} -7.44518i q^{29} +0.205167 q^{30} +3.34405 q^{31} +5.37450i q^{32} +2.17449 q^{33} -1.71387i q^{34} +1.65234 q^{35} +1.68542 q^{36} +0.810496 q^{37} +0.655979i q^{38} -6.15454 q^{39} +0.756127 q^{40} -11.7079i q^{41} -2.53355 q^{42} +2.50206i q^{43} +3.66492 q^{44} -0.365796i q^{45} +2.32636 q^{46} +5.83941 q^{47} +2.21146 q^{48} -13.4043 q^{49} +2.72934i q^{50} -3.05570 q^{51} -10.3730 q^{52} +6.65338i q^{53} +0.560879i q^{54} -0.795421i q^{55} -9.33718 q^{56} +1.16956 q^{57} +4.17584 q^{58} -6.16274i q^{59} -0.616519i q^{60} +8.60279i q^{61} +1.87560i q^{62} +4.51711i q^{63} +1.40847 q^{64} +2.25131i q^{65} +1.21962i q^{66} -5.54532 q^{67} -5.15012 q^{68} -4.14770i q^{69} +0.926764i q^{70} +7.49175 q^{71} +2.06707i q^{72} -5.54258i q^{73} +0.454590i q^{74} +4.86619 q^{75} +1.97119 q^{76} +9.82241i q^{77} -3.45195i q^{78} +3.93279i q^{79} -0.808942i q^{80} +1.00000 q^{81} +6.56672 q^{82} -5.95165i q^{83} +7.61321i q^{84} +1.11776i q^{85} -1.40335 q^{86} -7.44518i q^{87} +4.49482i q^{88} -15.6446 q^{89} +0.205167 q^{90} -27.8007i q^{91} -6.99059i q^{92} +3.34405 q^{93} +3.27520i q^{94} -0.427819i q^{95} +5.37450i q^{96} -14.6619i q^{97} -7.51818i q^{98} +2.17449 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9}+O(q^{10}) $ 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9	$ 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9} + 6 q^{10} - 2 q^{11} - 20 q^{12} + 24 q^{16} + 18 q^{17} - 12 q^{19} - 18 q^{25} + 14 q^{27} + 6 q^{30} - 14 q^{31} - 2 q^{33} + 16 q^{35} - 20 q^{36} - 14 q^{37} - 36 q^{40} + 24 q^{44} - 8 q^{46} + 22 q^{47} + 24 q^{48} - 48 q^{49} + 18 q^{51} - 50 q^{52} - 62 q^{56} - 12 q^{57} + 20 q^{58} - 34 q^{64} + 42 q^{67} - 56 q^{68} + 38 q^{71} - 18 q^{75} + 52 q^{76} + 14 q^{81} + 10 q^{82} + 34 q^{86} - 48 q^{89} + 6 q^{90} - 14 q^{93} - 2 q^{99}+O(q^{100}) $ 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9 + 6 * q^10 - 2 * q^11 - 20 * q^12 + 24 * q^16 + 18 * q^17 - 12 * q^19 - 18 * q^25 + 14 * q^27 + 6 * q^30 - 14 * q^31 - 2 * q^33 + 16 * q^35 - 20 * q^36 - 14 * q^37 - 36 * q^40 + 24 * q^44 - 8 * q^46 + 22 * q^47 + 24 * q^48 - 48 * q^49 + 18 * q^51 - 50 * q^52 - 62 * q^56 - 12 * q^57 + 20 * q^58 - 34 * q^64 + 42 * q^67 - 56 * q^68 + 38 * q^71 - 18 * q^75 + 52 * q^76 + 14 * q^81 + 10 * q^82 + 34 * q^86 - 48 * q^89 + 6 * q^90 - 14 * q^93 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/471\mathbb{Z}\right)^\times$.

$n$	$158$	$319$
$\chi(n)$	$1$	$-1$

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 $

$2$			0.560879i			0.396601i	0.980141	+	0.198301i	$0.0635422\pi$
$2$			0.560879i			0.396601i	−0.980141	+	0.198301i	$0.936458\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	1.68542			0.842708
$5$		−	0.365796i		−	0.163589i	−0.996649	−	0.0817946i	$-0.973935\pi$
$5$		−	0.365796i		−	0.163589i	0.996649	−	0.0817946i	$-0.0260651\pi$
$6$			0.560879i			0.228978i
$7$			4.51711i			1.70731i	0.520841	+	0.853654i	$0.325618\pi$
$7$			4.51711i			1.70731i	−0.520841	+	0.853654i	$0.674382\pi$
$8$			2.06707i			0.730820i
$9$	1.00000			0.333333
$10$	0.205167			0.0648796
$11$	2.17449			0.655633			0.327817	−	0.944741i	$-0.393687\pi$
$11$	2.17449			0.655633			0.327817	+	0.944741i	$0.393687\pi$
$12$	1.68542			0.486537
$13$	−6.15454			−1.70696			−0.853481	−	0.521123i	$-0.825513\pi$
$13$	−6.15454			−1.70696			−0.853481	+	0.521123i	$0.825513\pi$
$14$	−2.53355			−0.677120
$15$		−	0.365796i		−	0.0944482i
$16$	2.21146			0.552864
$17$	−3.05570			−0.741115			−0.370558	−	0.928809i	$-0.620833\pi$
$17$	−3.05570			−0.741115			−0.370558	+	0.928809i	$0.620833\pi$
$18$			0.560879i			0.132200i
$19$	1.16956			0.268315			0.134157	−	0.990960i	$-0.457167\pi$
$19$	1.16956			0.268315			0.134157	+	0.990960i	$0.457167\pi$
$20$		−	0.616519i		−	0.137858i
$21$			4.51711i			0.985714i
$22$			1.21962i			0.260025i
$23$		−	4.14770i		−	0.864855i	−0.901669	−	0.432427i	$-0.857657\pi$
$23$		−	4.14770i		−	0.864855i	0.901669	−	0.432427i	$-0.142343\pi$
$24$			2.06707i			0.421939i
$25$	4.86619			0.973239
$26$		−	3.45195i		−	0.676983i
$27$	1.00000			0.192450
$28$			7.61321i			1.43876i
$29$		−	7.44518i		−	1.38254i	−0.722598	−	0.691268i	$-0.757052\pi$
$29$		−	7.44518i		−	1.38254i	0.722598	−	0.691268i	$-0.242948\pi$
$30$	0.205167			0.0374583
$31$	3.34405			0.600608			0.300304	−	0.953843i	$-0.402912\pi$
$31$	3.34405			0.600608			0.300304	+	0.953843i	$0.402912\pi$
$32$			5.37450i			0.950086i
$33$	2.17449			0.378530
$34$		−	1.71387i		−	0.293927i
$35$	1.65234			0.279297
$36$	1.68542			0.280903
$37$	0.810496			0.133245			0.0666223	−	0.997778i	$-0.478778\pi$
$37$	0.810496			0.133245			0.0666223	+	0.997778i	$0.478778\pi$
$38$			0.655979i			0.106414i
$39$	−6.15454			−0.985515
$40$	0.756127			0.119554
$41$		−	11.7079i		−	1.82847i	−0.405184	−	0.914235i	$-0.632793\pi$
$41$		−	11.7079i		−	1.82847i	0.405184	−	0.914235i	$-0.367207\pi$
$42$	−2.53355			−0.390935
$43$			2.50206i			0.381561i	0.981633	+	0.190781i	$0.0611019\pi$
$43$			2.50206i			0.381561i	−0.981633	+	0.190781i	$0.938898\pi$
$44$	3.66492			0.552507
$45$		−	0.365796i		−	0.0545297i
$46$	2.32636			0.343002
$47$	5.83941			0.851765			0.425883	−	0.904778i	$-0.359964\pi$
$47$	5.83941			0.851765			0.425883	+	0.904778i	$0.359964\pi$
$48$	2.21146			0.319196
$49$	−13.4043			−1.91490
$50$			2.72934i			0.385987i
$51$	−3.05570			−0.427883
$52$	−10.3730			−1.43847
$53$			6.65338i			0.913912i	0.889489	+	0.456956i	$0.151060\pi$
$53$			6.65338i			0.913912i	−0.889489	+	0.456956i	$0.848940\pi$
$54$			0.560879i			0.0763259i
$55$		−	0.795421i		−	0.107254i
$56$	−9.33718			−1.24773
$57$	1.16956			0.154911
$58$	4.17584			0.548315
$59$		−	6.16274i		−	0.802321i	−0.916008	−	0.401160i	$-0.868607\pi$
$59$		−	6.16274i		−	0.802321i	0.916008	−	0.401160i	$-0.131393\pi$
$60$		−	0.616519i		−	0.0795922i
$61$			8.60279i			1.10147i	0.834679	+	0.550737i	$0.185653\pi$
$61$			8.60279i			1.10147i	−0.834679	+	0.550737i	$0.814347\pi$
$62$			1.87560i			0.238202i
$63$			4.51711i			0.569102i
$64$	1.40847			0.176059
$65$			2.25131i			0.279241i
$66$			1.21962i			0.150125i
$67$	−5.54532			−0.677469			−0.338734	−	0.940882i	$-0.609999\pi$
$67$	−5.54532			−0.677469			−0.338734	+	0.940882i	$0.609999\pi$
$68$	−5.15012			−0.624544
$69$		−	4.14770i		−	0.499324i
$70$			0.926764i			0.110769i
$71$	7.49175			0.889107			0.444554	−	0.895752i	$-0.353362\pi$
$71$	7.49175			0.889107			0.444554	+	0.895752i	$0.353362\pi$
$72$			2.06707i			0.243607i
$73$		−	5.54258i		−	0.648709i	−0.945936	−	0.324355i	$-0.894853\pi$
$73$		−	5.54258i		−	0.648709i	0.945936	−	0.324355i	$-0.105147\pi$
$74$			0.454590i			0.0528450i
$75$	4.86619			0.561900
$76$	1.97119			0.226111
$77$			9.82241i			1.11937i
$78$		−	3.45195i		−	0.390856i
$79$			3.93279i			0.442473i	0.975220	+	0.221237i	$0.0710093\pi$
$79$			3.93279i			0.442473i	−0.975220	+	0.221237i	$0.928991\pi$
$80$		−	0.808942i		−	0.0904425i
$81$	1.00000			0.111111
$82$	6.56672			0.725173
$83$		−	5.95165i		−	0.653278i	−0.945149	−	0.326639i	$-0.894084\pi$
$83$		−	5.95165i		−	0.653278i	0.945149	−	0.326639i	$-0.105916\pi$
$84$			7.61321i			0.830669i
$85$			1.11776i			0.121238i
$86$	−1.40335			−0.151328
$87$		−	7.44518i		−	0.798208i
$88$			4.49482i			0.479150i
$89$	−15.6446			−1.65832			−0.829160	−	0.559012i	$-0.811181\pi$
$89$	−15.6446			−1.65832			−0.829160	+	0.559012i	$0.811181\pi$
$90$	0.205167			0.0216265
$91$		−	27.8007i		−	2.91431i
$92$		−	6.99059i		−	0.728820i
$93$	3.34405			0.346761
$94$			3.27520i			0.337811i
$95$		−	0.427819i		−	0.0438933i
$96$			5.37450i			0.548532i
$97$		−	14.6619i		−	1.48869i	−0.667795	−	0.744345i	$-0.732762\pi$
$97$		−	14.6619i		−	1.48869i	0.667795	−	0.744345i	$-0.267238\pi$
$98$		−	7.51818i		−	0.759450i
$99$	2.17449			0.218544
$100$	8.20156			0.820156
$101$	6.44863			0.641663			0.320831	−	0.947136i	$-0.396038\pi$
$101$	6.44863			0.641663			0.320831	+	0.947136i	$0.396038\pi$
$102$		−	1.71387i		−	0.169699i
$103$		−	1.17835i		−	0.116107i	−0.998313	−	0.0580533i	$-0.981511\pi$
$103$		−	1.17835i		−	0.116107i	0.998313	−	0.0580533i	$-0.0184893\pi$
$104$		−	12.7219i		−	1.24748i
$105$	1.65234			0.161252
$106$	−3.73174			−0.362458
$107$		−	2.69599i		−	0.260631i	−0.991473	−	0.130316i	$-0.958401\pi$
$107$		−	2.69599i		−	0.260631i	0.991473	−	0.130316i	$-0.0415990\pi$
$108$	1.68542			0.162179
$109$	10.9989			1.05350			0.526751	−	0.850020i	$-0.323410\pi$
$109$	10.9989			1.05350			0.526751	+	0.850020i	$0.323410\pi$
$110$	0.446134			0.0425372
$111$	0.810496			0.0769289
$112$			9.98939i			0.943908i
$113$	−14.1541			−1.33151			−0.665754	−	0.746171i	$-0.731890\pi$
$113$	−14.1541			−1.33151			−0.665754	+	0.746171i	$0.731890\pi$
$114$			0.655979i			0.0614380i
$115$	−1.51721			−0.141481
$116$		−	12.5482i		−	1.16507i
$117$	−6.15454			−0.568988
$118$	3.45655			0.318201
$119$		−	13.8029i		−	1.26531i
$120$	0.756127			0.0690246
$121$	−6.27159			−0.570145
$122$	−4.82512			−0.436846
$123$		−	11.7079i		−	1.05567i
$124$	5.63611			0.506137
$125$		−	3.60902i		−	0.322800i
$126$	−2.53355			−0.225707
$127$	−10.4510			−0.927378			−0.463689	−	0.885998i	$-0.653474\pi$
$127$	−10.4510			−0.927378			−0.463689	+	0.885998i	$0.653474\pi$
$128$			11.5390i			1.01991i
$129$			2.50206i			0.220295i
$130$	−1.26271			−0.110747
$131$		−	2.18668i		−	0.191051i	−0.995427	−	0.0955257i	$-0.969547\pi$
$131$		−	2.18668i		−	0.191051i	0.995427	−	0.0955257i	$-0.0304532\pi$
$132$	3.66492			0.318990
$133$			5.28301i			0.458095i
$134$		−	3.11025i		−	0.268685i
$135$		−	0.365796i		−	0.0314827i
$136$		−	6.31634i		−	0.541622i
$137$			14.8371i			1.26762i	0.773489	+	0.633810i	$0.218510\pi$
$137$			14.8371i			1.26762i	−0.773489	+	0.633810i	$0.781490\pi$
$138$	2.32636			0.198032
$139$			12.5356i			1.06325i	0.846979	+	0.531627i	$0.178419\pi$
$139$			12.5356i			1.06325i	−0.846979	+	0.531627i	$0.821581\pi$
$140$	2.78488			0.235366
$141$	5.83941			0.491767
$142$			4.20196i			0.352621i
$143$	−13.3830			−1.11914
$144$	2.21146			0.184288
$145$	−2.72342			−0.226168
$146$	3.10871			0.257279
$147$	−13.4043			−1.10557
$148$	1.36602			0.112286
$149$			18.9150i			1.54958i	0.632218	+	0.774790i	$0.282145\pi$
$149$			18.9150i			1.54958i	−0.632218	+	0.774790i	$0.717855\pi$
$150$			2.72934i			0.222850i
$151$		−	5.79236i		−	0.471375i	−0.971829	−	0.235688i	$-0.924266\pi$
$151$		−	5.79236i		−	0.471375i	0.971829	−	0.235688i	$-0.0757342\pi$
$152$			2.41755i			0.196090i
$153$	−3.05570			−0.247038
$154$	−5.50918			−0.443942
$155$		−	1.22324i		−	0.0982530i
$156$	−10.3730			−0.830501
$157$	5.12882	−	11.4322i	0.409325	−	0.912389i
$157$	5.12882	−	11.4322i	0.409325	−	0.912389i
$158$	−2.20582			−0.175485
$159$			6.65338i			0.527647i
$160$	1.96597			0.155424
$161$	18.7356			1.47657
$162$			0.560879i			0.0440668i
$163$		−	22.7161i		−	1.77926i	−0.456679	−	0.889632i	$-0.650961\pi$
$163$		−	22.7161i		−	1.77926i	0.456679	−	0.889632i	$-0.349039\pi$
$164$		−	19.7327i		−	1.54087i
$165$		−	0.795421i		−	0.0619234i
$166$	3.33815			0.259091
$167$	−19.7256			−1.52641			−0.763206	−	0.646156i	$-0.776376\pi$
$167$	−19.7256			−1.52641			−0.763206	+	0.646156i	$0.776376\pi$
$168$	−9.33718			−0.720379
$169$	24.8784			1.91372
$170$	−0.626929			−0.0480833
$171$	1.16956			0.0894382
$172$			4.21702i			0.321545i
$173$	−16.4222			−1.24856			−0.624279	−	0.781201i	$-0.714607\pi$
$173$	−16.4222			−1.24856			−0.624279	+	0.781201i	$0.714607\pi$
$174$	4.17584			0.316570
$175$			21.9811i			1.66162i
$176$	4.80879			0.362476
$177$		−	6.16274i		−	0.463220i
$178$		−	8.77469i		−	0.657691i
$179$			8.01210i			0.598852i	0.954119	+	0.299426i	$0.0967952\pi$
$179$			8.01210i			0.598852i	−0.954119	+	0.299426i	$0.903205\pi$
$180$		−	0.616519i		−	0.0459526i
$181$		−	0.989543i		−	0.0735522i	−0.999324	−	0.0367761i	$-0.988291\pi$
$181$		−	0.989543i		−	0.0735522i	0.999324	−	0.0367761i	$-0.0117088\pi$
$182$	15.5928			1.15582
$183$			8.60279i			0.635936i
$184$	8.57358			0.632053
$185$		−	0.296476i		−	0.0217974i
$186$			1.87560i			0.137526i
$187$	−6.64458			−0.485900
$188$	9.84183			0.717789
$189$			4.51711i			0.328571i
$190$	0.239955			0.0174081
$191$			7.26639i			0.525778i	0.964826	+	0.262889i	$0.0846753\pi$
$191$			7.26639i			0.525778i	−0.964826	+	0.262889i	$0.915325\pi$
$192$	1.40847			0.101648
$193$	15.7238			1.13183			0.565913	−	0.824465i	$-0.308524\pi$
$193$	15.7238			1.13183			0.565913	+	0.824465i	$0.308524\pi$
$194$	8.22354			0.590416
$195$			2.25131i			0.161220i
$196$	−22.5918			−1.61370
$197$	16.6306			1.18488			0.592441	−	0.805614i	$-0.298164\pi$
$197$	16.6306			1.18488			0.592441	+	0.805614i	$0.298164\pi$
$198$			1.21962i			0.0866750i
$199$	−12.8169			−0.908567			−0.454283	−	0.890857i	$-0.650105\pi$
$199$	−12.8169			−0.908567			−0.454283	+	0.890857i	$0.650105\pi$
$200$			10.0588i			0.711262i
$201$	−5.54532			−0.391137
$202$			3.61690i			0.254484i
$203$	33.6307			2.36041
$204$	−5.15012			−0.360580
$205$	−4.28272			−0.299118
$206$	0.660914			0.0460480
$207$		−	4.14770i		−	0.288285i
$208$	−13.6105			−0.943718
$209$	2.54319			0.175916
$210$			0.926764i			0.0639528i
$211$			6.33080i			0.435830i	0.975968	+	0.217915i	$0.0699256\pi$
$211$			6.33080i			0.435830i	−0.975968	+	0.217915i	$0.930074\pi$
$212$			11.2137i			0.770160i
$213$	7.49175			0.513326
$214$	1.51212			0.103367
$215$	0.915246			0.0624193
$216$			2.06707i			0.140646i
$217$			15.1054i			1.02542i
$218$			6.16904i			0.417820i
$219$		−	5.54258i		−	0.374533i
$220$		−	1.34061i		−	0.0903842i
$221$	18.8064			1.26506
$222$			0.454590i			0.0305101i
$223$			8.21262i			0.549958i	0.961450	+	0.274979i	$0.0886709\pi$
$223$			8.21262i			0.549958i	−0.961450	+	0.274979i	$0.911329\pi$
$224$	−24.2772			−1.62209
$225$	4.86619			0.324413
$226$		−	7.93874i		−	0.528077i
$227$			19.4021i			1.28776i	0.765127	+	0.643880i	$0.222676\pi$
$227$			19.4021i			1.28776i	−0.765127	+	0.643880i	$0.777324\pi$
$228$	1.97119			0.130545
$229$			14.9579i			0.988445i	0.869336	+	0.494222i	$0.164547\pi$
$229$			14.9579i			0.988445i	−0.869336	+	0.494222i	$0.835453\pi$
$230$		−	0.850972i		−	0.0561115i
$231$			9.82241i			0.646267i
$232$	15.3897			1.01038
$233$	−10.0171			−0.656245			−0.328123	−	0.944635i	$-0.606416\pi$
$233$	−10.0171			−0.656245			−0.328123	+	0.944635i	$0.606416\pi$
$234$		−	3.45195i		−	0.225661i
$235$		−	2.13603i		−	0.139340i
$236$		−	10.3868i		−	0.676122i
$237$			3.93279i			0.255462i
$238$	7.74176			0.501824
$239$	−19.3135			−1.24929			−0.624643	−	0.780910i	$-0.714756\pi$
$239$	−19.3135			−1.24929			−0.624643	+	0.780910i	$0.714756\pi$
$240$		−	0.808942i		−	0.0522170i
$241$		−	9.34217i		−	0.601782i	−0.953658	−	0.300891i	$-0.902716\pi$
$241$		−	9.34217i		−	0.601782i	0.953658	−	0.300891i	$-0.0972841\pi$
$242$		−	3.51760i		−	0.226120i
$243$	1.00000			0.0641500
$244$			14.4993i			0.928220i
$245$			4.90324i			0.313256i
$246$	6.56672			0.418679
$247$	−7.19808			−0.458003
$248$			6.91238i			0.438936i
$249$		−	5.95165i		−	0.377170i
$250$	2.02422			0.128023
$251$		−	3.31439i		−	0.209202i	−0.994514	−	0.104601i	$-0.966643\pi$
$251$		−	3.31439i		−	0.209202i	0.994514	−	0.104601i	$-0.0333566\pi$
$252$			7.61321i			0.479587i
$253$		−	9.01913i		−	0.567028i
$254$		−	5.86175i		−	0.367799i
$255$			1.11776i			0.0699970i
$256$	−3.65503			−0.228439
$257$	−2.23406			−0.139357			−0.0696783	−	0.997570i	$-0.522197\pi$
$257$	−2.23406			−0.139357			−0.0696783	+	0.997570i	$0.522197\pi$
$258$	−1.40335			−0.0873690
$259$			3.66110i			0.227490i
$260$			3.79439i			0.235318i
$261$		−	7.44518i		−	0.460845i
$262$	1.22646			0.0757712
$263$	−28.9757			−1.78672			−0.893359	−	0.449344i	$-0.851658\pi$
$263$	−28.9757			−1.78672			−0.893359	+	0.449344i	$0.851658\pi$
$264$			4.49482i			0.276637i
$265$	2.43378			0.149506
$266$	−2.96313			−0.181681
$267$	−15.6446			−0.957431
$268$	−9.34617			−0.570908
$269$			12.0127i			0.732426i	0.930531	+	0.366213i	$0.119346\pi$
$269$			12.0127i			0.732426i	−0.930531	+	0.366213i	$0.880654\pi$
$270$	0.205167			0.0124861
$271$			17.4599i			1.06062i	0.847805	+	0.530308i	$0.177924\pi$
$271$			17.4599i			1.06062i	−0.847805	+	0.530308i	$0.822076\pi$
$272$	−6.75754			−0.409736
$273$		−	27.8007i		−	1.68258i
$274$	−8.32182			−0.502740
$275$	10.5815			0.638088
$276$		−	6.99059i		−	0.420784i
$277$	0.340178			0.0204393			0.0102196	−	0.999948i	$-0.496747\pi$
$277$	0.340178			0.0204393			0.0102196	+	0.999948i	$0.496747\pi$
$278$	−7.03093			−0.421687
$279$	3.34405			0.200203
$280$			3.41551i			0.204116i
$281$	−11.4193			−0.681220			−0.340610	−	0.940205i	$-0.610634\pi$
$281$	−11.4193			−0.681220			−0.340610	+	0.940205i	$0.610634\pi$
$282$			3.27520i			0.195035i
$283$	12.1002			0.719285			0.359643	−	0.933090i	$-0.382899\pi$
$283$	12.1002			0.719285			0.359643	+	0.933090i	$0.382899\pi$
$284$	12.6267			0.749257
$285$		−	0.427819i		−	0.0253418i
$286$		−	7.50623i		−	0.443853i
$287$	52.8860			3.12176
$288$			5.37450i			0.316695i
$289$	−7.66271			−0.450748
$290$		−	1.52751i		−	0.0896984i
$291$		−	14.6619i		−	0.859496i
$292$		−	9.34154i		−	0.546672i
$293$			31.5936i			1.84572i	0.385138	+	0.922859i	$0.374154\pi$
$293$			31.5936i			1.84572i	−0.385138	+	0.922859i	$0.625846\pi$
$294$		−	7.51818i		−	0.438469i
$295$	−2.25431			−0.131251
$296$			1.67535i			0.0973778i
$297$	2.17449			0.126177
$298$	−10.6090			−0.614565
$299$			25.5272i			1.47628i
$300$	8.20156			0.473517
$301$	−11.3021			−0.651442
$302$	3.24881			0.186948
$303$	6.44863			0.370464
$304$	2.58642			0.148341
$305$	3.14687			0.180189
$306$		−	1.71387i		−	0.0979757i
$307$		−	23.6587i		−	1.35028i	−0.737692	−	0.675138i	$-0.764084\pi$
$307$		−	23.6587i		−	1.35028i	0.737692	−	0.675138i	$-0.235916\pi$
$308$			16.5548i			0.943300i
$309$		−	1.17835i		−	0.0670342i
$310$	0.686089			0.0389672
$311$	−21.3386			−1.21000			−0.605002	−	0.796224i	$-0.706828\pi$
$311$	−21.3386			−1.21000			−0.605002	+	0.796224i	$0.706828\pi$
$312$		−	12.7219i		−	0.720234i
$313$	9.87715			0.558290			0.279145	−	0.960249i	$-0.409949\pi$
$313$	9.87715			0.558290			0.279145	+	0.960249i	$0.409949\pi$
$314$	6.41208	+	2.87665i	0.361854	+	0.162339i
$315$	1.65234			0.0930990
$316$			6.62838i			0.372876i
$317$	29.2523			1.64297			0.821487	−	0.570227i	$-0.193145\pi$
$317$	29.2523			1.64297			0.821487	+	0.570227i	$0.193145\pi$
$318$	−3.73174			−0.209265
$319$		−	16.1895i		−	0.906437i
$320$		−	0.515213i		−	0.0288013i
$321$		−	2.69599i		−	0.150475i
$322$			10.5084i			0.585610i
$323$	−3.57381			−0.198852
$324$	1.68542			0.0936342
$325$	−29.9492			−1.66128
$326$	12.7410			0.705658
$327$	10.9989			0.608240
$328$	24.2011			1.33628
$329$			26.3773i			1.45422i
$330$	0.446134			0.0245589
$331$	34.5329			1.89810			0.949049	−	0.315130i	$-0.102048\pi$
$331$	34.5329			1.89810			0.949049	+	0.315130i	$0.102048\pi$
$332$		−	10.0310i		−	0.550522i
$333$	0.810496			0.0444149
$334$		−	11.0637i		−	0.605376i
$335$			2.02846i			0.110827i
$336$			9.98939i			0.544966i
$337$			13.8370i			0.753749i	0.926264	+	0.376875i	$0.123001\pi$
$337$			13.8370i			0.753749i	−0.926264	+	0.376875i	$0.876999\pi$
$338$			13.9538i			0.758984i
$339$	−14.1541			−0.768746
$340$			1.88390i			0.102169i
$341$	7.27159			0.393779
$342$			0.655979i			0.0354713i
$343$		−	28.9289i		−	1.56201i
$344$	−5.17194			−0.278853
$345$	−1.51721			−0.0816840
$346$		−	9.21087i		−	0.495179i
$347$	10.6864			0.573673			0.286837	−	0.957979i	$-0.407396\pi$
$347$	10.6864			0.573673			0.286837	+	0.957979i	$0.407396\pi$
$348$		−	12.5482i		−	0.672656i
$349$	−5.62351			−0.301020			−0.150510	−	0.988609i	$-0.548092\pi$
$349$	−5.62351			−0.301020			−0.150510	+	0.988609i	$0.548092\pi$
$350$	−12.3287			−0.658999
$351$	−6.15454			−0.328505
$352$			11.6868i			0.622908i
$353$	31.4357			1.67315			0.836577	−	0.547849i	$-0.184553\pi$
$353$	31.4357			1.67315			0.836577	+	0.547849i	$0.184553\pi$
$354$	3.45655			0.183714
$355$		−	2.74046i		−	0.145448i
$356$	−26.3676			−1.39748
$357$		−	13.8029i		−	0.730528i
$358$	−4.49381			−0.237505
$359$		−	12.5226i		−	0.660916i	−0.943821	−	0.330458i	$-0.892797\pi$
$359$		−	12.5226i		−	0.660916i	0.943821	−	0.330458i	$-0.107203\pi$
$360$	0.756127			0.0398514
$361$	−17.6321			−0.928007
$362$	0.555013			0.0291709
$363$	−6.27159			−0.329173
$364$		−	46.8558i		−	2.45591i
$365$	−2.02745			−0.106122
$366$	−4.82512			−0.252213
$367$			27.6457i			1.44309i	0.692365	+	0.721547i	$0.256569\pi$
$367$			27.6457i			1.44309i	−0.692365	+	0.721547i	$0.743431\pi$
$368$		−	9.17245i		−	0.478147i
$369$		−	11.7079i		−	0.609490i
$370$	0.166287			0.00864486
$371$	−30.0540			−1.56033
$372$	5.63611			0.292218
$373$		−	30.3124i		−	1.56952i	−0.619801	−	0.784759i	$-0.712787\pi$
$373$		−	30.3124i		−	1.56952i	0.619801	−	0.784759i	$-0.287213\pi$
$374$		−	3.72680i		−	0.192708i
$375$		−	3.60902i		−	0.186369i
$376$			12.0705i			0.622487i
$377$			45.8217i			2.35994i
$378$	−2.53355			−0.130312
$379$		−	29.2751i		−	1.50376i	−0.659300	−	0.751880i	$-0.729147\pi$
$379$		−	29.2751i		−	1.50376i	0.659300	−	0.751880i	$-0.270853\pi$
$380$		−	0.721053i		−	0.0369893i
$381$	−10.4510			−0.535422
$382$	−4.07556			−0.208524
$383$		−	31.1227i		−	1.59030i	−0.606416	−	0.795148i	$-0.707393\pi$
$383$		−	31.1227i		−	1.59030i	0.606416	−	0.795148i	$-0.292607\pi$
$384$			11.5390i			0.588846i
$385$	3.59300			0.183116
$386$			8.81916i			0.448884i
$387$			2.50206i			0.127187i
$388$		−	24.7114i		−	1.25453i
$389$	10.2932			0.521888			0.260944	−	0.965354i	$-0.415966\pi$
$389$	10.2932			0.521888			0.260944	+	0.965354i	$0.415966\pi$
$390$	−1.26271			−0.0639399
$391$			12.6741i			0.640957i
$392$		−	27.7076i		−	1.39945i
$393$		−	2.18668i		−	0.110304i
$394$			9.32775i			0.469925i
$395$	1.43860			0.0723838
$396$	3.66492			0.184169
$397$			11.5945i			0.581909i	0.956737	+	0.290955i	$0.0939729\pi$
$397$			11.5945i			0.581909i	−0.956737	+	0.290955i	$0.906027\pi$
$398$		−	7.18873i		−	0.360339i
$399$			5.28301i			0.264481i
$400$	10.7614			0.538068
$401$			27.2218i			1.35939i	0.733493	+	0.679697i	$0.237889\pi$
$401$			27.2218i			1.35939i	−0.733493	+	0.679697i	$0.762111\pi$
$402$		−	3.11025i		−	0.155125i
$403$	−20.5811			−1.02522
$404$	10.8686			0.540734
$405$		−	0.365796i		−	0.0181766i
$406$			18.8627i			0.936142i
$407$	1.76241			0.0873597
$408$		−	6.31634i		−	0.312705i
$409$		−	35.0949i		−	1.73533i	−0.497148	−	0.867666i	$-0.665619\pi$
$409$		−	35.0949i		−	1.73533i	0.497148	−	0.867666i	$-0.334381\pi$
$410$		−	2.40208i		−	0.118630i
$411$			14.8371i			0.731861i
$412$		−	1.98602i		−	0.0978440i
$413$	27.8378			1.36981
$414$	2.32636			0.114334
$415$	−2.17709			−0.106869
$416$		−	33.0776i		−	1.62176i
$417$			12.5356i			0.613870i
$418$			1.42642i			0.0697685i
$419$	2.03155			0.0992478			0.0496239	−	0.998768i	$-0.484198\pi$
$419$	2.03155			0.0992478			0.0496239	+	0.998768i	$0.484198\pi$
$420$	2.78488			0.135888
$421$			30.2131i			1.47250i	0.676710	+	0.736249i	$0.263405\pi$
$421$			30.2131i			1.47250i	−0.676710	+	0.736249i	$0.736595\pi$
$422$	−3.55081			−0.172851
$423$	5.83941			0.283922
$424$	−13.7530			−0.667905
$425$	−14.8696			−0.721282
$426$			4.20196i			0.203586i
$427$	−38.8597			−1.88055
$428$		−	4.54386i		−	0.219636i
$429$	−13.3830			−0.646137
$430$			0.513342i			0.0247556i
$431$	6.45266			0.310814			0.155407	−	0.987851i	$-0.450331\pi$
$431$	6.45266			0.310814			0.155407	+	0.987851i	$0.450331\pi$
$432$	2.21146			0.106399
$433$			20.6483i			0.992296i	0.868238	+	0.496148i	$0.165253\pi$
$433$			20.6483i			0.992296i	−0.868238	+	0.496148i	$0.834747\pi$
$434$	−8.47231			−0.406684
$435$	−2.72342			−0.130578
$436$	18.5377			0.887794
$437$		−	4.85097i		−	0.232053i
$438$	3.10871			0.148540
$439$			26.3457i			1.25741i	0.777643	+	0.628706i	$0.216415\pi$
$439$			26.3457i			1.25741i	−0.777643	+	0.628706i	$0.783585\pi$
$440$	1.64419			0.0783837
$441$	−13.4043			−0.638299
$442$			10.5481i			0.501723i
$443$		−	23.3702i		−	1.11035i	−0.831733	−	0.555176i	$-0.812651\pi$
$443$		−	23.3702i		−	1.11035i	0.831733	−	0.555176i	$-0.187349\pi$
$444$	1.36602			0.0648285
$445$			5.72272i			0.271283i
$446$	−4.60628			−0.218114
$447$			18.9150i			0.894651i
$448$			6.36221i			0.300586i
$449$		−	25.8896i		−	1.22181i	−0.791706	−	0.610903i	$-0.790807\pi$
$449$		−	25.8896i		−	1.22181i	0.791706	−	0.610903i	$-0.209193\pi$
$450$			2.72934i			0.128662i
$451$		−	25.4588i		−	1.19881i
$452$	−23.8556			−1.12207
$453$		−	5.79236i		−	0.272149i
$454$	−10.8822			−0.510727
$455$	−10.1694			−0.476749
$456$			2.41755i			0.113212i
$457$	10.6096			0.496294			0.248147	−	0.968722i	$-0.420178\pi$
$457$	10.6096			0.496294			0.248147	+	0.968722i	$0.420178\pi$
$458$	−8.38956			−0.392018
$459$	−3.05570			−0.142628
$460$	−2.55713			−0.119227
$461$	27.0068			1.25783			0.628916	−	0.777473i	$-0.283499\pi$
$461$	27.0068			1.25783			0.628916	+	0.777473i	$0.283499\pi$
$462$	−5.50918			−0.256310
$463$		−	13.9024i		−	0.646099i	−0.946382	−	0.323050i	$-0.895292\pi$
$463$		−	13.9024i		−	0.646099i	0.946382	−	0.323050i	$-0.104708\pi$
$464$		−	16.4647i		−	0.764354i
$465$		−	1.22324i		−	0.0567264i
$466$		−	5.61840i		−	0.260268i
$467$	19.4726			0.901083			0.450541	−	0.892756i	$-0.351231\pi$
$467$	19.4726			0.901083			0.450541	+	0.892756i	$0.351231\pi$
$468$	−10.3730			−0.479490
$469$		−	25.0488i		−	1.15665i
$470$	1.19806			0.0552622
$471$	5.12882	−	11.4322i	0.236324	−	0.526768i
$472$	12.7388			0.586352
$473$			5.44071i			0.250164i
$474$	−2.20582			−0.101316
$475$	5.69129			0.261134
$476$		−	23.2637i		−	1.06629i
$477$			6.65338i			0.304637i
$478$		−	10.8325i		−	0.495468i
$479$		−	26.8241i		−	1.22562i	−0.790229	−	0.612812i	$-0.790038\pi$
$479$		−	26.8241i		−	1.22562i	0.790229	−	0.612812i	$-0.209962\pi$
$480$	1.96597			0.0897339
$481$	−4.98823			−0.227444
$482$	5.23982			0.238667
$483$	18.7356			0.852500
$484$	−10.5702			−0.480465
$485$	−5.36327			−0.243534
$486$			0.560879i			0.0254420i
$487$	−14.5081			−0.657425			−0.328713	−	0.944430i	$-0.606615\pi$
$487$	−14.5081			−0.657425			−0.328713	+	0.944430i	$0.606615\pi$
$488$	−17.7826			−0.804979
$489$		−	22.7161i		−	1.02726i
$490$	−2.75012			−0.124238
$491$			3.05844i			0.138025i	0.997616	+	0.0690127i	$0.0219849\pi$
$491$			3.05844i			0.138025i	−0.997616	+	0.0690127i	$0.978015\pi$
$492$		−	19.7327i		−	0.889619i
$493$			22.7502i			1.02462i
$494$		−	4.03725i		−	0.181644i
$495$		−	0.795421i		−	0.0357515i
$496$	7.39521			0.332055
$497$			33.8411i			1.51798i
$498$	3.33815			0.149586
$499$		−	14.3133i		−	0.640752i	−0.947291	−	0.320376i	$-0.896191\pi$
$499$		−	14.3133i		−	0.640752i	0.947291	−	0.320376i	$-0.103809\pi$
$500$		−	6.08269i		−	0.272026i
$501$	−19.7256			−0.881274
$502$	1.85897			0.0829699
$503$		−	14.9035i		−	0.664516i	−0.943188	−	0.332258i	$-0.892189\pi$
$503$		−	14.9035i		−	0.664516i	0.943188	−	0.332258i	$-0.107811\pi$
$504$	−9.33718			−0.415911
$505$		−	2.35889i		−	0.104969i
$506$	5.05864			0.224884
$507$	24.8784			1.10489
$508$	−17.6143			−0.781508
$509$		−	21.2829i		−	0.943349i	−0.881773	−	0.471675i	$-0.843650\pi$
$509$		−	21.2829i		−	0.943349i	0.881773	−	0.471675i	$-0.156350\pi$
$510$	−0.626929			−0.0277609
$511$	25.0364			1.10755
$512$			21.0279i			0.929312i
$513$	1.16956			0.0516372
$514$		−	1.25303i		−	0.0552689i
$515$	−0.431038			−0.0189938
$516$			4.21702i			0.185644i
$517$	12.6977			0.558446
$518$	−2.05343			−0.0902226
$519$	−16.4222			−0.720855
$520$	−4.65361			−0.204074
$521$			0.660265i			0.0289267i	0.999895	+	0.0144634i	$0.00460399\pi$
$521$			0.660265i			0.0289267i	−0.999895	+	0.0144634i	$0.995396\pi$
$522$	4.17584			0.182772
$523$	−20.6068			−0.901071			−0.450535	−	0.892759i	$-0.648767\pi$
$523$	−20.6068			−0.901071			−0.450535	+	0.892759i	$0.648767\pi$
$524$		−	3.68547i		−	0.161000i
$525$			21.9811i			0.959335i
$526$		−	16.2518i		−	0.708614i
$527$	−10.2184			−0.445120
$528$	4.80879			0.209276
$529$	5.79660			0.252026
$530$			1.36506i			0.0592942i
$531$		−	6.16274i		−	0.267440i
$532$			8.90407i			0.386040i
$533$			72.0569i			3.12113i
$534$		−	8.77469i		−	0.379718i
$535$	−0.986183			−0.0426364
$536$		−	11.4626i		−	0.495107i
$537$			8.01210i			0.345748i
$538$	−6.73765			−0.290481
$539$	−29.1475			−1.25547
$540$		−	0.616519i		−	0.0265307i
$541$			34.4198i			1.47982i	0.672703	+	0.739912i	$0.265133\pi$
$541$			34.4198i			1.47982i	−0.672703	+	0.739912i	$0.734867\pi$
$542$	−9.79291			−0.420642
$543$		−	0.989543i		−	0.0424654i
$544$		−	16.4228i		−	0.704123i
$545$		−	4.02335i		−	0.172341i
$546$	15.5928			0.667312
$547$	40.2646			1.72159			0.860794	−	0.508953i	$-0.169967\pi$
$547$	40.2646			1.72159			0.860794	+	0.508953i	$0.169967\pi$
$548$			25.0067i			1.06823i
$549$			8.60279i			0.367158i
$550$			5.93493i			0.253066i
$551$		−	8.70756i		−	0.370955i
$552$	8.57358			0.364916
$553$	−17.7648			−0.755438
$554$			0.190798i			0.00810624i
$555$		−	0.296476i		−	0.0125847i
$556$			21.1276i			0.896012i
$557$	−1.65743			−0.0702277			−0.0351139	−	0.999383i	$-0.511179\pi$
$557$	−1.65743			−0.0702277			−0.0351139	+	0.999383i	$0.511179\pi$
$558$			1.87560i			0.0794006i
$559$		−	15.3991i		−	0.651311i
$560$	3.65408			0.154413
$561$	−6.64458			−0.280535
$562$		−	6.40486i		−	0.270173i
$563$		−	41.3614i		−	1.74317i	−0.490241	−	0.871587i	$-0.663091\pi$
$563$		−	41.3614i		−	1.74317i	0.490241	−	0.871587i	$-0.336909\pi$
$564$	9.84183			0.414416
$565$			5.17753i			0.217820i
$566$			6.78677i			0.285269i
$567$			4.51711i			0.189701i
$568$			15.4860i			0.649777i
$569$		−	4.19194i		−	0.175735i	−0.996132	−	0.0878677i	$-0.971995\pi$
$569$		−	4.19194i		−	0.175735i	0.996132	−	0.0878677i	$-0.0280053\pi$
$570$	0.239955			0.0100506
$571$	25.7648			1.07822			0.539112	−	0.842234i	$-0.318760\pi$
$571$	25.7648			1.07822			0.539112	+	0.842234i	$0.318760\pi$
$572$	−22.5559			−0.943109
$573$			7.26639i			0.303558i
$574$			29.6626i			1.23809i
$575$		−	20.1835i		−	0.841710i
$576$	1.40847			0.0586862
$577$	7.71723			0.321272			0.160636	−	0.987014i	$-0.448645\pi$
$577$	7.71723			0.321272			0.160636	+	0.987014i	$0.448645\pi$
$578$		−	4.29785i		−	0.178767i
$579$	15.7238			0.653461
$580$	−4.59010			−0.190593
$581$	26.8842			1.11535
$582$	8.22354			0.340877
$583$			14.4677i			0.599191i
$584$	11.4569			0.474090
$585$			2.25131i			0.0930802i
$586$	−17.7202			−0.732014
$587$			10.9115i			0.450366i	0.974316	+	0.225183i	$0.0722980\pi$
$587$			10.9115i			0.450366i	−0.974316	+	0.225183i	$0.927702\pi$
$588$	−22.5918			−0.931670
$589$	3.91105			0.161152
$590$		−	1.26439i		−	0.0520543i
$591$	16.6306			0.684092
$592$	1.79238			0.0736662
$593$	−12.5155			−0.513948			−0.256974	−	0.966418i	$-0.582725\pi$
$593$	−12.5155			−0.513948			−0.256974	+	0.966418i	$0.582725\pi$
$594$			1.21962i			0.0500418i
$595$	−5.04906			−0.206991
$596$			31.8797i			1.30584i
$597$	−12.8169			−0.524561
$598$	−14.3176			−0.585492
$599$			6.45722i			0.263835i	0.991261	+	0.131917i	$0.0421134\pi$
$599$			6.45722i			0.263835i	−0.991261	+	0.131917i	$0.957887\pi$
$600$			10.0588i			0.410647i
$601$	−0.0129257			−0.000527251			−0.000263625	−	1.00000i	$-0.500084\pi$
$601$	−0.0129257			−0.000527251			−0.000263625		1.00000i	$0.500084\pi$
$602$		−	6.33911i		−	0.258363i
$603$	−5.54532			−0.225823
$604$		−	9.76253i		−	0.397232i
$605$			2.29413i			0.0932695i
$606$			3.61690i			0.146926i
$607$			26.2901i			1.06708i	0.845774	+	0.533541i	$0.179139\pi$
$607$			26.2901i			1.06708i	−0.845774	+	0.533541i	$0.820861\pi$
$608$			6.28578i			0.254922i
$609$	33.6307			1.36279
$610$			1.76501i			0.0714632i
$611$	−35.9389			−1.45393
$612$	−5.15012			−0.208181
$613$		−	10.4050i		−	0.420255i	−0.977674	−	0.210127i	$-0.932612\pi$
$613$		−	10.4050i		−	0.420255i	0.977674	−	0.210127i	$-0.0673879\pi$
$614$	13.2697			0.535521
$615$	−4.28272			−0.172696
$616$	−20.3036			−0.818056
$617$	−25.0440			−1.00823			−0.504117	−	0.863635i	$-0.668182\pi$
$617$	−25.0440			−1.00823			−0.504117	+	0.863635i	$0.668182\pi$
$618$	0.660914			0.0265858
$619$	−20.9591			−0.842418			−0.421209	−	0.906964i	$-0.638394\pi$
$619$	−20.9591			−0.842418			−0.421209	+	0.906964i	$0.638394\pi$
$620$		−	2.06167i		−	0.0827986i
$621$		−	4.14770i		−	0.166441i
$622$		−	11.9684i		−	0.479889i
$623$		−	70.6682i		−	2.83126i
$624$	−13.6105			−0.544856
$625$	23.0108			0.920432
$626$			5.53988i			0.221418i
$627$	2.54319			0.101565
$628$	8.64420	−	19.2680i	0.344941	−	0.768877i
$629$	−2.47663			−0.0987497
$630$			0.926764i			0.0369231i
$631$	24.0024			0.955521			0.477761	−	0.878490i	$-0.341449\pi$
$631$	24.0024			0.955521			0.477761	+	0.878490i	$0.341449\pi$
$632$	−8.12935			−0.323368
$633$			6.33080i			0.251627i
$634$			16.4070i			0.651605i
$635$			3.82294i			0.151709i
$636$			11.2137i			0.444652i
$637$	82.4972			3.26866
$638$	9.08033			0.359494
$639$	7.49175			0.296369
$640$	4.22092			0.166846
$641$	−36.3004			−1.43378			−0.716891	−	0.697186i	$-0.754435\pi$
$641$	−36.3004			−1.43378			−0.716891	+	0.697186i	$0.754435\pi$
$642$	1.51212			0.0596787
$643$			6.55712i			0.258587i	0.991606	+	0.129294i	$0.0412710\pi$
$643$			6.55712i			0.258587i	−0.991606	+	0.129294i	$0.958729\pi$
$644$	31.5773			1.24432
$645$	0.915246			0.0360378
$646$		−	2.00447i		−	0.0788649i
$647$	−17.0971			−0.672157			−0.336078	−	0.941834i	$-0.609101\pi$
$647$	−17.0971			−0.672157			−0.336078	+	0.941834i	$0.609101\pi$
$648$			2.06707i			0.0812022i
$649$		−	13.4008i		−	0.526028i
$650$		−	16.7979i		−	0.658866i
$651$			15.1054i			0.592028i
$652$		−	38.2861i		−	1.49940i
$653$	21.0409			0.823392			0.411696	−	0.911321i	$-0.364937\pi$
$653$	21.0409			0.823392			0.411696	+	0.911321i	$0.364937\pi$
$654$			6.16904i			0.241228i
$655$	−0.799881			−0.0312539
$656$		−	25.8915i		−	1.01090i
$657$		−	5.54258i		−	0.216236i
$658$	−14.7944			−0.576747
$659$	−20.6397			−0.804009			−0.402005	−	0.915638i	$-0.631686\pi$
$659$	−20.6397			−0.804009			−0.402005	+	0.915638i	$0.631686\pi$
$660$		−	1.34061i		−	0.0521833i
$661$	−18.0517			−0.702129			−0.351064	−	0.936351i	$-0.614180\pi$
$661$	−18.0517			−0.702129			−0.351064	+	0.936351i	$0.614180\pi$
$662$			19.3687i			0.752787i
$663$	18.8064			0.730381
$664$	12.3025			0.477428
$665$	1.93251			0.0749394
$666$			0.454590i			0.0176150i
$667$	−30.8804			−1.19569
$668$	−33.2458			−1.28632
$669$			8.21262i			0.317518i
$670$	−1.13772			−0.0439539
$671$			18.7067i			0.722163i
$672$	−24.2772			−0.936513
$673$			19.0131i			0.732900i	0.930438	+	0.366450i	$0.119427\pi$
$673$			19.0131i			0.732900i	−0.930438	+	0.366450i	$0.880573\pi$
$674$	−7.76087			−0.298938
$675$	4.86619			0.187300
$676$	41.9304			1.61271
$677$	33.1239			1.27305			0.636527	−	0.771255i	$-0.280370\pi$
$677$	33.1239			1.27305			0.636527	+	0.771255i	$0.280370\pi$
$678$		−	7.93874i		−	0.304886i
$679$	66.2294			2.54165
$680$	−2.31049			−0.0886034
$681$			19.4021i			0.743488i
$682$			4.07848i			0.156173i
$683$			29.0811i			1.11276i	0.830929	+	0.556378i	$0.187809\pi$
$683$			29.0811i			1.11276i	−0.830929	+	0.556378i	$0.812191\pi$
$684$	1.97119			0.0753702
$685$	5.42736			0.207369
$686$	16.2256			0.619495
$687$			14.9579i			0.570679i
$688$			5.53320i			0.210951i
$689$		−	40.9485i		−	1.56001i
$690$		−	0.850972i		−	0.0323960i
$691$			0.978379i			0.0372193i	0.999827	+	0.0186096i	$0.00592397\pi$
$691$			0.978379i			0.0372193i	−0.999827	+	0.0186096i	$0.994076\pi$
$692$	−27.6783			−1.05217
$693$			9.82241i			0.373123i
$694$			5.99375i			0.227519i
$695$	4.58547			0.173937
$696$	15.3897			0.583346
$697$			35.7759i			1.35511i
$698$		−	3.15411i		−	0.119385i
$699$	−10.0171			−0.378883
$700$			37.0473i			1.40026i
$701$		−	2.69957i		−	0.101962i	−0.998700	−	0.0509808i	$-0.983765\pi$
$701$		−	2.69957i		−	0.101962i	0.998700	−	0.0509808i	$-0.0162347\pi$
$702$		−	3.45195i		−	0.130285i
$703$	0.947920			0.0357515
$704$	3.06270			0.115430
$705$		−	2.13603i		−	0.0804477i
$706$			17.6316i			0.663575i
$707$			29.1292i			1.09552i
$708$		−	10.3868i		−	0.390359i
$709$	−41.3830			−1.55417			−0.777086	−	0.629394i	$-0.783303\pi$
$709$	−41.3830			−1.55417			−0.777086	+	0.629394i	$0.783303\pi$
$710$	1.53706			0.0576849
$711$			3.93279i			0.147491i
$712$		−	32.3384i		−	1.21193i
$713$		−	13.8701i		−	0.519439i
$714$	7.74176			0.289728
$715$			4.89545i			0.183079i
$716$			13.5037i			0.504658i
$717$	−19.3135			−0.721276
$718$	7.02365			0.262120
$719$			34.0299i			1.26910i	0.772882	+	0.634550i	$0.218815\pi$
$719$			34.0299i			1.26910i	−0.772882	+	0.634550i	$0.781185\pi$
$720$		−	0.808942i		−	0.0301475i
$721$	5.32276			0.198230
$722$		−	9.88949i		−	0.368049i
$723$		−	9.34217i		−	0.347439i
$724$		−	1.66779i		−	0.0619830i
$725$		−	36.2297i		−	1.34554i
$726$		−	3.51760i		−	0.130550i
$727$	1.00621			0.0373183			0.0186592	−	0.999826i	$-0.494060\pi$
$727$	1.00621			0.0373183			0.0186592	+	0.999826i	$0.494060\pi$
$728$	57.4661			2.12983
$729$	1.00000			0.0370370
$730$		−	1.13716i		−	0.0420880i
$731$		−	7.64555i		−	0.282781i
$732$			14.4993i			0.535908i
$733$	−27.9708			−1.03312			−0.516562	−	0.856250i	$-0.672789\pi$
$733$	−27.9708			−1.03312			−0.516562	+	0.856250i	$0.672789\pi$
$734$	−15.5059			−0.572333
$735$			4.90324i			0.180859i
$736$	22.2918			0.821687
$737$	−12.0582			−0.444171
$738$	6.56672			0.241724
$739$	47.5127			1.74778			0.873891	−	0.486122i	$-0.161589\pi$
$739$	47.5127			1.74778			0.873891	+	0.486122i	$0.161589\pi$
$740$		−	0.499686i		−	0.0183688i
$741$	−7.19808			−0.264428
$742$		−	16.8567i		−	0.618828i
$743$	19.0946			0.700511			0.350256	−	0.936654i	$-0.386095\pi$
$743$	19.0946			0.700511			0.350256	+	0.936654i	$0.386095\pi$
$744$			6.91238i			0.253420i
$745$	6.91905			0.253495
$746$	17.0016			0.622472
$747$		−	5.95165i		−	0.217759i
$748$	−11.1989			−0.409472
$749$	12.1781			0.444977
$750$	2.02422			0.0739141
$751$		−	51.5600i		−	1.88145i	−0.339170	−	0.940725i	$-0.610146\pi$
$751$		−	51.5600i		−	1.88145i	0.339170	−	0.940725i	$-0.389854\pi$
$752$	12.9136			0.470910
$753$		−	3.31439i		−	0.120783i
$754$	−25.7004			−0.935954
$755$	−2.11882			−0.0771119
$756$			7.61321i			0.276890i
$757$			45.0900i			1.63883i	0.573204	+	0.819413i	$0.305700\pi$
$757$			45.0900i			1.63883i	−0.573204	+	0.819413i	$0.694300\pi$
$758$	16.4198			0.596393
$759$		−	9.01913i		−	0.327374i
$760$	0.884333			0.0320781
$761$			15.1840i			0.550419i	0.961384	+	0.275209i	$0.0887472\pi$
$761$			15.1840i			0.550419i	−0.961384	+	0.275209i	$0.911253\pi$
$762$		−	5.86175i		−	0.212349i
$763$			49.6832i			1.79865i
$764$			12.2469i			0.443077i
$765$			1.11776i			0.0404128i
$766$	17.4561			0.630713
$767$			37.9289i			1.36953i
$768$	−3.65503			−0.131889
$769$	−42.2841			−1.52480			−0.762401	−	0.647104i	$-0.775980\pi$
$769$	−42.2841			−1.52480			−0.762401	+	0.647104i	$0.775980\pi$
$770$			2.01524i			0.0726241i
$771$	−2.23406			−0.0804575
$772$	26.5012			0.953799
$773$	−44.0157			−1.58313			−0.791567	−	0.611083i	$-0.790734\pi$
$773$	−44.0157			−1.58313			−0.791567	+	0.611083i	$0.790734\pi$
$774$	−1.40335			−0.0504425
$775$	16.2728			0.584535
$776$	30.3072			1.08796
$777$			3.66110i			0.131341i
$778$			5.77325i			0.206981i
$779$		−	13.6931i		−	0.490605i
$780$			3.79439i			0.135861i
$781$	16.2907			0.582928
$782$	−7.10864			−0.254204
$783$		−	7.44518i		−	0.266069i
$784$	−29.6430			−1.05868
$785$	−4.18186	−	1.87610i	−0.149257	−	0.0669611i
$786$	1.22646			0.0437465
$787$			15.7093i			0.559975i	0.960004	+	0.279988i	$0.0903304\pi$
$787$			15.7093i			0.559975i	−0.960004	+	0.279988i	$0.909670\pi$
$788$	28.0295			0.998509
$789$	−28.9757			−1.03156
$790$			0.806880i			0.0287075i
$791$		−	63.9357i		−	2.27329i
$792$			4.49482i			0.159717i
$793$		−	52.9462i		−	1.88017i
$794$	−6.50308			−0.230786
$795$	2.43378			0.0863174
$796$	−21.6018			−0.765656
$797$	−11.0410			−0.391091			−0.195545	−	0.980695i	$-0.562648\pi$
$797$	−11.0410			−0.391091			−0.195545	+	0.980695i	$0.562648\pi$
$798$	−2.96313			−0.104894
$799$	−17.8435			−0.631256
$800$			26.1533i			0.924660i
$801$	−15.6446			−0.552773
$802$	−15.2681			−0.539137
$803$		−	12.0523i		−	0.425316i
$804$	−9.34617			−0.329614
$805$		−	6.85342i		−	0.241551i
$806$		−	11.5435i		−	0.406602i
$807$			12.0127i			0.422866i
$808$			13.3298i			0.468940i
$809$			16.5703i			0.582581i	0.956635	+	0.291290i	$0.0940846\pi$
$809$			16.5703i			0.582581i	−0.956635	+	0.291290i	$0.905915\pi$
$810$	0.205167			0.00720885
$811$			46.6598i			1.63845i	0.573475	+	0.819223i	$0.305595\pi$
$811$			46.6598i			1.63845i	−0.573475	+	0.819223i	$0.694405\pi$
$812$	56.6817			1.98914
$813$			17.4599i			0.612347i
$814$			0.988501i			0.0346469i
$815$	−8.30947			−0.291068
$816$	−6.75754			−0.236561
$817$			2.92631i			0.102378i
$818$	19.6840			0.688234
$819$		−	27.8007i		−	0.971437i
$820$	−7.21816			−0.252069
$821$	−50.0671			−1.74735			−0.873677	−	0.486507i	$-0.838271\pi$
$821$	−50.0671			−1.74735			−0.873677	+	0.486507i	$0.838271\pi$
$822$	−8.32182			−0.290257
$823$			17.7388i			0.618337i	0.951007	+	0.309168i	$0.100051\pi$
$823$			17.7388i			0.618337i	−0.951007	+	0.309168i	$0.899949\pi$
$824$	2.43574			0.0848531
$825$	10.5815			0.368400
$826$			15.6136i			0.543267i
$827$	−18.7547			−0.652166			−0.326083	−	0.945341i	$-0.605729\pi$
$827$	−18.7547			−0.652166			−0.326083	+	0.945341i	$0.605729\pi$
$828$		−	6.99059i		−	0.242940i
$829$	16.5226			0.573855			0.286927	−	0.957952i	$-0.407366\pi$
$829$	16.5226			0.573855			0.286927	+	0.957952i	$0.407366\pi$
$830$		−	1.22108i		−	0.0423844i
$831$	0.340178			0.0118006
$832$	−8.66849			−0.300526
$833$	40.9594			1.41916
$834$	−7.03093			−0.243461
$835$			7.21555i			0.249704i
$836$	4.28633			0.148246
$837$	3.34405			0.115587
$838$			1.13945i			0.0393618i
$839$			31.4391i			1.08540i	0.839927	+	0.542699i	$0.182597\pi$
$839$			31.4391i			1.08540i	−0.839927	+	0.542699i	$0.817403\pi$
$840$			3.41551i			0.117846i
$841$	−26.4308			−0.911406
$842$	−16.9459			−0.583994
$843$	−11.4193			−0.393303
$844$			10.6700i			0.367278i
$845$		−	9.10042i		−	0.313064i
$846$			3.27520i			0.112604i
$847$		−	28.3295i		−	0.973412i
$848$			14.7136i			0.505269i
$849$	12.1002			0.415279
$850$		−	8.34005i		−	0.286061i
$851$		−	3.36169i		−	0.115237i
$852$	12.6267			0.432584
$853$	−14.1906			−0.485878			−0.242939	−	0.970042i	$-0.578112\pi$
$853$	−14.1906			−0.485878			−0.242939	+	0.970042i	$0.578112\pi$
$854$		−	21.7956i		−	0.745830i
$855$		−	0.427819i		−	0.0146311i
$856$	5.57280			0.190474
$857$		−	35.3406i		−	1.20721i	−0.797283	−	0.603605i	$-0.793730\pi$
$857$		−	35.3406i		−	1.20721i	0.797283	−	0.603605i	$-0.206270\pi$
$858$		−	7.50623i		−	0.256258i
$859$			50.0606i			1.70805i	0.520235	+	0.854023i	$0.325844\pi$
$859$			50.0606i			1.70805i	−0.520235	+	0.854023i	$0.674156\pi$
$860$	1.54257			0.0526012
$861$	52.8860			1.80235
$862$			3.61916i			0.123269i
$863$		−	0.365226i		−	0.0124324i	−0.999981	−	0.00621622i	$-0.998021\pi$
$863$		−	0.365226i		−	0.0124324i	0.999981	−	0.00621622i	$-0.00197870\pi$
$864$			5.37450i			0.182844i
$865$			6.00719i			0.204251i
$866$	−11.5812			−0.393546
$867$	−7.66271			−0.260239
$868$			25.4589i			0.864132i
$869$			8.55181i			0.290100i
$870$		−	1.52751i		−	0.0517874i
$871$	34.1289			1.15641
$872$			22.7355i			0.769920i
$873$		−	14.6619i		−	0.496230i
$874$	2.72080			0.0920325
$875$	16.3023			0.551119
$876$		−	9.34154i		−	0.315621i
$877$		−	24.5711i		−	0.829706i	−0.909888	−	0.414853i	$-0.863833\pi$
$877$		−	24.5711i		−	0.829706i	0.909888	−	0.414853i	$-0.136167\pi$
$878$	−14.7768			−0.498691
$879$			31.5936i			1.06563i
$880$		−	1.75904i		−	0.0592971i
$881$		−	14.8740i		−	0.501116i	−0.968102	−	0.250558i	$-0.919386\pi$
$881$		−	14.8740i		−	0.501116i	0.968102	−	0.250558i	$-0.0806141\pi$
$882$		−	7.51818i		−	0.253150i
$883$		−	47.5278i		−	1.59944i	−0.600375	−	0.799718i	$-0.704982\pi$
$883$		−	47.5278i		−	1.59944i	0.600375	−	0.799718i	$-0.295018\pi$
$884$	31.6966			1.06607
$885$	−2.25431			−0.0757778
$886$	13.1078			0.440367
$887$			21.4708i			0.720919i	0.932775	+	0.360459i	$0.117380\pi$
$887$			21.4708i			0.720919i	−0.932775	+	0.360459i	$0.882620\pi$
$888$			1.67535i			0.0562211i
$889$		−	47.2084i		−	1.58332i
$890$	−3.20975			−0.107591
$891$	2.17449			0.0728482
$892$			13.8417i			0.463454i
$893$	6.82952			0.228541
$894$	−10.6090			−0.354819
$895$	2.93080			0.0979658
$896$	−52.1228			−1.74130
$897$			25.5272i			0.852328i
$898$	14.5209			0.484569
$899$		−	24.8970i		−	0.830363i
$900$	8.20156			0.273385
$901$		−	20.3307i		−	0.677314i
$902$	14.2793			0.475448
$903$	−11.3021			−0.376110
$904$		−	29.2576i		−	0.973092i
$905$	−0.361971			−0.0120323
$906$	3.24881			0.107934
$907$	−34.6201			−1.14954			−0.574770	−	0.818315i	$-0.694908\pi$
$907$	−34.6201			−1.14954			−0.574770	+	0.818315i	$0.694908\pi$
$908$			32.7005i			1.08521i
$909$	6.44863			0.213888
$910$		−	5.70380i		−	0.189079i
$911$	−17.9023			−0.593129			−0.296564	−	0.955013i	$-0.595841\pi$
$911$	−17.9023			−0.593129			−0.296564	+	0.955013i	$0.595841\pi$
$912$	2.58642			0.0856449
$913$		−	12.9418i		−	0.428311i
$914$			5.95068i			0.196831i
$915$	3.14687			0.104032
$916$			25.2102i			0.832970i
$917$	9.87749			0.326183
$918$		−	1.71387i		−	0.0565663i
$919$		−	34.3880i		−	1.13435i	−0.823596	−	0.567177i	$-0.808035\pi$
$919$		−	34.3880i		−	1.13435i	0.823596	−	0.567177i	$-0.191965\pi$
$920$		−	3.13619i		−	0.103397i
$921$		−	23.6587i		−	0.779582i
$922$			15.1475i			0.498858i
$923$	−46.1083			−1.51767
$924$			16.5548i			0.544614i
$925$	3.94403			0.129679
$926$	7.79756			0.256244
$927$		−	1.17835i		−	0.0387022i
$928$	40.0141			1.31353
$929$	−0.0899649			−0.00295165			−0.00147583	−	0.999999i	$-0.500470\pi$
$929$	−0.0899649			−0.00295165			−0.00147583	+	0.999999i	$0.500470\pi$
$930$	0.686089			0.0224977
$931$	−15.6771			−0.513795
$932$	−16.8831			−0.553023
$933$	−21.3386			−0.698596
$934$			10.9217i			0.357370i
$935$			2.43056i			0.0794880i
$936$		−	12.7219i		−	0.415827i
$937$			6.79383i			0.221945i	0.993823	+	0.110972i	$0.0353965\pi$
$937$			6.79383i			0.221945i	−0.993823	+	0.110972i	$0.964603\pi$
$938$	14.0493			0.458727
$939$	9.87715			0.322329
$940$		−	3.60011i		−	0.117422i
$941$	−34.0881			−1.11124			−0.555620	−	0.831436i	$-0.687519\pi$
$941$	−34.0881			−1.11124			−0.555620	+	0.831436i	$0.687519\pi$
$942$	6.41208	+	2.87665i	0.208917	+	0.0937262i
$943$	−48.5609			−1.58136
$944$		−	13.6286i		−	0.443574i
$945$	1.65234			0.0537507
$946$	−3.05158			−0.0992154
$947$		−	33.5392i		−	1.08988i	−0.838476	−	0.544939i	$-0.816553\pi$
$947$		−	33.5392i		−	1.08988i	0.838476	−	0.544939i	$-0.183447\pi$
$948$			6.62838i			0.215280i
$949$			34.1120i			1.10732i
$950$			3.19212i			0.103566i
$951$	29.2523			0.948572
$952$	28.5316			0.924715
$953$	10.8451			0.351308			0.175654	−	0.984452i	$-0.443796\pi$
$953$	10.8451			0.351308			0.175654	+	0.984452i	$0.443796\pi$
$954$	−3.73174			−0.120819
$955$	2.65802			0.0860115
$956$	−32.5513			−1.05278
$957$		−	16.1895i		−	0.523331i
$958$	15.0451			0.486084
$959$	−67.0209			−2.16422
$960$		−	0.515213i		−	0.0166284i
$961$	−19.8174			−0.639270
$962$		−	2.79779i		−	0.0902044i
$963$		−	2.69599i		−	0.0868771i
$964$		−	15.7454i		−	0.507127i
$965$		−	5.75172i		−	0.185155i
$966$			10.5084i			0.338102i
$967$	−13.6967			−0.440455			−0.220227	−	0.975449i	$-0.570680\pi$
$967$	−13.6967			−0.440455			−0.220227	+	0.975449i	$0.570680\pi$
$968$		−	12.9638i		−	0.416673i
$969$	−3.57381			−0.114807
$970$		−	3.00814i		−	0.0965857i
$971$		−	58.0294i		−	1.86225i	−0.364699	−	0.931125i	$-0.618828\pi$
$971$		−	58.0294i		−	1.86225i	0.364699	−	0.931125i	$-0.381172\pi$
$972$	1.68542			0.0540597
$973$	−56.6246			−1.81530
$974$		−	8.13729i		−	0.260735i
$975$	−29.9492			−0.959142
$976$			19.0247i			0.608965i
$977$	43.5675			1.39385			0.696924	−	0.717145i	$-0.254552\pi$
$977$	43.5675			1.39385			0.696924	+	0.717145i	$0.254552\pi$
$978$	12.7410			0.407412
$979$	−34.0189			−1.08725
$980$			8.26399i			0.263984i
$981$	10.9989			0.351167
$982$	−1.71541			−0.0547410
$983$		−	54.0276i		−	1.72321i	−0.507576	−	0.861607i	$-0.669458\pi$
$983$		−	54.0276i		−	1.72321i	0.507576	−	0.861607i	$-0.330542\pi$
$984$	24.2011			0.771503
$985$		−	6.08342i		−	0.193834i
$986$	−12.7601			−0.406365
$987$			26.3773i			0.839597i
$988$	−12.1318			−0.385963
$989$	10.3778			0.329995
$990$	0.446134			0.0141791
$991$	42.8041			1.35972			0.679858	−	0.733344i	$-0.262041\pi$
$991$	42.8041			1.35972			0.679858	+	0.733344i	$0.262041\pi$
$992$			17.9726i			0.570630i
$993$	34.5329			1.09587
$994$	−18.9807			−0.602032
$995$			4.68838i			0.148632i
$996$		−	10.0310i		−	0.317844i
$997$		−	25.6250i		−	0.811553i	−0.913972	−	0.405776i	$-0.867001\pi$
$997$		−	25.6250i		−	0.811553i	0.913972	−	0.405776i	$-0.132999\pi$
$998$	8.02803			0.254123
$999$	0.810496			0.0256430

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	471.2.b.b.313.8	yes	14
3.2	odd	2		1413.2.b.e.784.7		14
157.156	even	2	inner	471.2.b.b.313.7	✓	14
471.470	odd	2		1413.2.b.e.784.8		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
471.2.b.b.313.7	✓	14	157.156	even	2	inner
471.2.b.b.313.8	yes	14	1.1	even	1	trivial
1413.2.b.e.784.7		14	3.2	odd	2
1413.2.b.e.784.8		14	471.470	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 471 = 3 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	471.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+0.560879i q^{2} +1.00000 q^{3} +1.68542 q^{4} -0.365796i q^{5} +0.560879i q^{6} +4.51711i q^{7} +2.06707i q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.560879i q^{2} +1.00000 q^{3} +1.68542 q^{4} -0.365796i q^{5} +0.560879i q^{6} +4.51711i q^{7} +2.06707i q^{8} +1.00000 q^{9} +0.205167 q^{10} +2.17449 q^{11} +1.68542 q^{12} -6.15454 q^{13} -2.53355 q^{14} -0.365796i q^{15} +2.21146 q^{16} -3.05570 q^{17} +0.560879i q^{18} +1.16956 q^{19} -0.616519i q^{20} +4.51711i q^{21} +1.21962i q^{22} -4.14770i q^{23} +2.06707i q^{24} +4.86619 q^{25} -3.45195i q^{26} +1.00000 q^{27} +7.61321i q^{28} -7.44518i q^{29} +0.205167 q^{30} +3.34405 q^{31} +5.37450i q^{32} +2.17449 q^{33} -1.71387i q^{34} +1.65234 q^{35} +1.68542 q^{36} +0.810496 q^{37} +0.655979i q^{38} -6.15454 q^{39} +0.756127 q^{40} -11.7079i q^{41} -2.53355 q^{42} +2.50206i q^{43} +3.66492 q^{44} -0.365796i q^{45} +2.32636 q^{46} +5.83941 q^{47} +2.21146 q^{48} -13.4043 q^{49} +2.72934i q^{50} -3.05570 q^{51} -10.3730 q^{52} +6.65338i q^{53} +0.560879i q^{54} -0.795421i q^{55} -9.33718 q^{56} +1.16956 q^{57} +4.17584 q^{58} -6.16274i q^{59} -0.616519i q^{60} +8.60279i q^{61} +1.87560i q^{62} +4.51711i q^{63} +1.40847 q^{64} +2.25131i q^{65} +1.21962i q^{66} -5.54532 q^{67} -5.15012 q^{68} -4.14770i q^{69} +0.926764i q^{70} +7.49175 q^{71} +2.06707i q^{72} -5.54258i q^{73} +0.454590i q^{74} +4.86619 q^{75} +1.97119 q^{76} +9.82241i q^{77} -3.45195i q^{78} +3.93279i q^{79} -0.808942i q^{80} +1.00000 q^{81} +6.56672 q^{82} -5.95165i q^{83} +7.61321i q^{84} +1.11776i q^{85} -1.40335 q^{86} -7.44518i q^{87} +4.49482i q^{88} -15.6446 q^{89} +0.205167 q^{90} -27.8007i q^{91} -6.99059i q^{92} +3.34405 q^{93} +3.27520i q^{94} -0.427819i q^{95} +5.37450i q^{96} -14.6619i q^{97} -7.51818i q^{98} +2.17449 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9}+O(q^{10}) \) 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9	\( 14 q + 14 q^{3} - 20 q^{4} + 14 q^{9} + 6 q^{10} - 2 q^{11} - 20 q^{12} + 24 q^{16} + 18 q^{17} - 12 q^{19} - 18 q^{25} + 14 q^{27} + 6 q^{30} - 14 q^{31} - 2 q^{33} + 16 q^{35} - 20 q^{36} - 14 q^{37} - 36 q^{40} + 24 q^{44} - 8 q^{46} + 22 q^{47} + 24 q^{48} - 48 q^{49} + 18 q^{51} - 50 q^{52} - 62 q^{56} - 12 q^{57} + 20 q^{58} - 34 q^{64} + 42 q^{67} - 56 q^{68} + 38 q^{71} - 18 q^{75} + 52 q^{76} + 14 q^{81} + 10 q^{82} + 34 q^{86} - 48 q^{89} + 6 q^{90} - 14 q^{93} - 2 q^{99}+O(q^{100}) \) 14 * q + 14 * q^3 - 20 * q^4 + 14 * q^9 + 6 * q^10 - 2 * q^11 - 20 * q^12 + 24 * q^16 + 18 * q^17 - 12 * q^19 - 18 * q^25 + 14 * q^27 + 6 * q^30 - 14 * q^31 - 2 * q^33 + 16 * q^35 - 20 * q^36 - 14 * q^37 - 36 * q^40 + 24 * q^44 - 8 * q^46 + 22 * q^47 + 24 * q^48 - 48 * q^49 + 18 * q^51 - 50 * q^52 - 62 * q^56 - 12 * q^57 + 20 * q^58 - 34 * q^64 + 42 * q^67 - 56 * q^68 + 38 * q^71 - 18 * q^75 + 52 * q^76 + 14 * q^81 + 10 * q^82 + 34 * q^86 - 48 * q^89 + 6 * q^90 - 14 * q^93 - 2 * q^99

Introduction

L-functions

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