LMFDB - Embedded newform 177.7.c.a.58.48

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,7,Mod(58,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 7, names="a")

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

chi := DirichletCharacter("177.58");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	177.c (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:	$40.7195728007$
Analytic rank:	$0$
Dimension:	$60$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			58.48
Character	$\chi$	$=$	177.58
Dual form			177.7.c.a.58.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+10.1526i q^{2} -15.5885 q^{3} -39.0745 q^{4} -104.301 q^{5} -158.263i q^{6} -654.718 q^{7} +253.057i q^{8} +243.000 q^{9} +O(q^{10})$	\(q+10.1526i q^{2} -15.5885 q^{3} -39.0745 q^{4} -104.301 q^{5} -158.263i q^{6} -654.718 q^{7} +253.057i q^{8} +243.000 q^{9} -1058.93i q^{10} +442.991i q^{11} +609.112 q^{12} -3003.02i q^{13} -6647.07i q^{14} +1625.90 q^{15} -5069.95 q^{16} -6614.72 q^{17} +2467.07i q^{18} -2022.49 q^{19} +4075.53 q^{20} +10206.1 q^{21} -4497.50 q^{22} +7860.31i q^{23} -3944.78i q^{24} -4746.22 q^{25} +30488.4 q^{26} -3788.00 q^{27} +25582.8 q^{28} +24340.1 q^{29} +16507.0i q^{30} -13844.9i q^{31} -35277.3i q^{32} -6905.55i q^{33} -67156.4i q^{34} +68288.0 q^{35} -9495.11 q^{36} +73303.9i q^{37} -20533.5i q^{38} +46812.5i q^{39} -26394.2i q^{40} -5255.31 q^{41} +103618. i q^{42} -72295.0i q^{43} -17309.7i q^{44} -25345.2 q^{45} -79802.3 q^{46} +175954. i q^{47} +79032.7 q^{48} +311007. q^{49} -48186.3i q^{50} +103113. q^{51} +117342. i q^{52} -23803.5 q^{53} -38457.9i q^{54} -46204.6i q^{55} -165681. i q^{56} +31527.5 q^{57} +247114. i q^{58} +(-114946. + 170200. i) q^{59} -63531.2 q^{60} -28156.5i q^{61} +140561. q^{62} -159097. q^{63} +33678.3 q^{64} +313219. i q^{65} +70109.0 q^{66} +320803. i q^{67} +258467. q^{68} -122530. i q^{69} +693299. i q^{70} +554734. q^{71} +61493.0i q^{72} -125135. i q^{73} -744223. q^{74} +73986.2 q^{75} +79027.9 q^{76} -290035. i q^{77} -475266. q^{78} -858752. q^{79} +528803. q^{80} +59049.0 q^{81} -53354.8i q^{82} -520126. i q^{83} -398797. q^{84} +689925. q^{85} +733979. q^{86} -379424. q^{87} -112102. q^{88} -300665. i q^{89} -257319. i q^{90} +1.96613e6i q^{91} -307138. i q^{92} +215820. i q^{93} -1.78639e6 q^{94} +210949. q^{95} +549919. i q^{96} +1.22552e6i q^{97} +3.15752e6i q^{98} +107647. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) $ 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9	$ 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9} - 1944 q^{12} - 4536 q^{15} + 56616 q^{16} + 8480 q^{17} + 11376 q^{19} + 40796 q^{20} - 8232 q^{22} + 197940 q^{25} + 147252 q^{26} + 71640 q^{28} + 63456 q^{29} - 364432 q^{35} - 466560 q^{36} + 99632 q^{41} - 470316 q^{46} + 171072 q^{48} + 1737420 q^{49} + 60912 q^{51} + 92240 q^{53} + 186624 q^{57} + 917264 q^{59} + 1063368 q^{60} - 115768 q^{62} - 99144 q^{63} - 1107444 q^{64} + 1172232 q^{66} - 4247232 q^{68} + 1498048 q^{71} + 1161448 q^{74} - 1477440 q^{75} - 1045320 q^{76} - 1060452 q^{78} - 90600 q^{79} + 77096 q^{80} + 3542940 q^{81} - 2225880 q^{84} - 693408 q^{85} - 1567768 q^{86} + 1821528 q^{87} + 62892 q^{88} + 5268696 q^{94} + 296128 q^{95}+O(q^{100}) $ 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9 - 1944 * q^12 - 4536 * q^15 + 56616 * q^16 + 8480 * q^17 + 11376 * q^19 + 40796 * q^20 - 8232 * q^22 + 197940 * q^25 + 147252 * q^26 + 71640 * q^28 + 63456 * q^29 - 364432 * q^35 - 466560 * q^36 + 99632 * q^41 - 470316 * q^46 + 171072 * q^48 + 1737420 * q^49 + 60912 * q^51 + 92240 * q^53 + 186624 * q^57 + 917264 * q^59 + 1063368 * q^60 - 115768 * q^62 - 99144 * q^63 - 1107444 * q^64 + 1172232 * q^66 - 4247232 * q^68 + 1498048 * q^71 + 1161448 * q^74 - 1477440 * q^75 - 1045320 * q^76 - 1060452 * q^78 - 90600 * q^79 + 77096 * q^80 + 3542940 * q^81 - 2225880 * q^84 - 693408 * q^85 - 1567768 * q^86 + 1821528 * q^87 + 62892 * q^88 + 5268696 * q^94 + 296128 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/177\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$1$

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 $

$2$			10.1526i			1.26907i	0.772894	+	0.634535i	$0.218808\pi$
$2$			10.1526i			1.26907i	−0.772894	+	0.634535i	$0.781192\pi$
$3$	−15.5885			−0.577350
$3$	−15.5885			−0.577350
$4$	−39.0745			−0.610539
$5$	−104.301			−0.834411			−0.417206	−	0.908812i	$-0.636990\pi$
$5$	−104.301			−0.834411			−0.417206	+	0.908812i	$0.636990\pi$
$6$		−	158.263i		−	0.732698i
$7$	−654.718			−1.90880			−0.954400	−	0.298531i	$-0.903503\pi$
$7$	−654.718			−1.90880			−0.954400	+	0.298531i	$0.903503\pi$
$8$			253.057i			0.494253i
$9$	243.000			0.333333
$10$		−	1058.93i		−	1.05893i
$11$			442.991i			0.332826i	0.986056	+	0.166413i	$0.0532185\pi$
$11$			442.991i			0.332826i	−0.986056	+	0.166413i	$0.946782\pi$
$12$	609.112			0.352495
$13$		−	3003.02i		−	1.36687i	−0.730010	−	0.683437i	$-0.760485\pi$
$13$		−	3003.02i		−	1.36687i	0.730010	−	0.683437i	$-0.239515\pi$
$14$		−	6647.07i		−	2.42240i
$15$	1625.90			0.481747
$16$	−5069.95			−1.23778
$17$	−6614.72			−1.34637			−0.673186	−	0.739474i	$-0.735074\pi$
$17$	−6614.72			−1.34637			−0.673186	+	0.739474i	$0.735074\pi$
$18$			2467.07i			0.423023i
$19$	−2022.49			−0.294867			−0.147433	−	0.989072i	$-0.547101\pi$
$19$	−2022.49			−0.294867			−0.147433	+	0.989072i	$0.547101\pi$
$20$	4075.53			0.509441
$21$	10206.1			1.10205
$22$	−4497.50			−0.422379
$23$			7860.31i			0.646035i	0.946393	+	0.323018i	$0.104697\pi$
$23$			7860.31i			0.646035i	−0.946393	+	0.323018i	$0.895303\pi$
$24$		−	3944.78i		−	0.285357i
$25$	−4746.22			−0.303758
$26$	30488.4			1.73466
$27$	−3788.00			−0.192450
$28$	25582.8			1.16540
$29$	24340.1			0.997993			0.498997	−	0.866604i	$-0.333702\pi$
$29$	24340.1			0.997993			0.498997	+	0.866604i	$0.333702\pi$
$30$			16507.0i			0.611371i
$31$		−	13844.9i		−	0.464733i	−0.972628	−	0.232367i	$-0.925353\pi$
$31$		−	13844.9i		−	0.464733i	0.972628	−	0.232367i	$-0.0746469\pi$
$32$		−	35277.3i		−	1.07658i
$33$		−	6905.55i		−	0.192157i
$34$		−	67156.4i		−	1.70864i
$35$	68288.0			1.59272
$36$	−9495.11			−0.203513
$37$			73303.9i			1.44718i	0.690231	+	0.723589i	$0.257509\pi$
$37$			73303.9i			1.44718i	−0.690231	+	0.723589i	$0.742491\pi$
$38$		−	20533.5i		−	0.374207i
$39$			46812.5i			0.789165i
$40$		−	26394.2i		−	0.412410i
$41$	−5255.31			−0.0762512			−0.0381256	−	0.999273i	$-0.512139\pi$
$41$	−5255.31			−0.0762512			−0.0381256	+	0.999273i	$0.512139\pi$
$42$			103618.i			1.39857i
$43$		−	72295.0i		−	0.909291i	−0.890673	−	0.454645i	$-0.849766\pi$
$43$		−	72295.0i		−	0.909291i	0.890673	−	0.454645i	$-0.150234\pi$
$44$		−	17309.7i		−	0.203203i
$45$	−25345.2			−0.278137
$46$	−79802.3			−0.819864
$47$			175954.i			1.69475i	0.530993	+	0.847376i	$0.321819\pi$
$47$			175954.i			1.69475i	−0.530993	+	0.847376i	$0.678181\pi$
$48$	79032.7			0.714633
$49$	311007.			2.64352
$50$		−	48186.3i		−	0.385490i
$51$	103113.			0.777328
$52$			117342.i			0.834530i
$53$	−23803.5			−0.159887			−0.0799435	−	0.996799i	$-0.525474\pi$
$53$	−23803.5			−0.159887			−0.0799435	+	0.996799i	$0.525474\pi$
$54$		−	38457.9i		−	0.244233i
$55$		−	46204.6i		−	0.277714i
$56$		−	165681.i		−	0.943430i
$57$	31527.5			0.170242
$58$			247114.i			1.26652i
$59$	−114946.	+	170200.i	−0.559676	+	0.828711i
$59$	−114946.	+	170200.i	−0.559676	+	0.828711i
$60$	−63531.2			−0.294126
$61$		−	28156.5i		−	0.124048i	−0.998075	−	0.0620240i	$-0.980244\pi$
$61$		−	28156.5i		−	0.124048i	0.998075	−	0.0620240i	$-0.0197555\pi$
$62$	140561.			0.589779
$63$	−159097.			−0.636267
$64$	33678.3			0.128473
$65$			313219.i			1.14053i
$66$	70109.0			0.243861
$67$			320803.i			1.06663i	0.845917	+	0.533315i	$0.179054\pi$
$67$			320803.i			1.06663i	−0.845917	+	0.533315i	$0.820946\pi$
$68$	258467.			0.822013
$69$		−	122530.i		−	0.372989i
$70$			693299.i			2.02128i
$71$	554734.			1.54992			0.774961	−	0.632009i	$-0.217769\pi$
$71$	554734.			1.54992			0.774961	+	0.632009i	$0.217769\pi$
$72$			61493.0i			0.164751i
$73$		−	125135.i		−	0.321671i	−0.986981	−	0.160835i	$-0.948581\pi$
$73$		−	125135.i		−	0.321671i	0.986981	−	0.160835i	$-0.0514188\pi$
$74$	−744223.			−1.83657
$75$	73986.2			0.175375
$76$	79027.9			0.180028
$77$		−	290035.i		−	0.635298i
$78$	−475266.			−1.00151
$79$	−858752.			−1.74175			−0.870877	−	0.491501i	$-0.836448\pi$
$79$	−858752.			−1.74175			−0.870877	+	0.491501i	$0.836448\pi$
$80$	528803.			1.03282
$81$	59049.0			0.111111
$82$		−	53354.8i		−	0.0967681i
$83$		−	520126.i		−	0.909650i	−0.890581	−	0.454825i	$-0.849702\pi$
$83$		−	520126.i		−	0.909650i	0.890581	−	0.454825i	$-0.150298\pi$
$84$	−398797.			−0.672843
$85$	689925.			1.12343
$86$	733979.			1.15395
$87$	−379424.			−0.576192
$88$	−112102.			−0.164500
$89$		−	300665.i		−	0.426495i	−0.976998	−	0.213247i	$-0.931596\pi$
$89$		−	300665.i		−	0.426495i	0.976998	−	0.213247i	$-0.0684040\pi$
$90$		−	257319.i		−	0.352975i
$91$			1.96613e6i			2.60909i
$92$		−	307138.i		−	0.394430i
$93$			215820.i			0.268314i
$94$	−1.78639e6			−2.15076
$95$	210949.			0.246040
$96$			549919.i			0.621563i
$97$			1.22552e6i			1.34278i	0.741103	+	0.671391i	$0.234303\pi$
$97$			1.22552e6i			1.34278i	−0.741103	+	0.671391i	$0.765697\pi$
$98$			3.15752e6i			3.35481i
$99$			107647.i			0.110942i
$100$	185456.			0.185456
$101$		−	927913.i		−	0.900624i	−0.892871	−	0.450312i	$-0.851313\pi$
$101$		−	927913.i		−	0.900624i	0.892871	−	0.450312i	$-0.148687\pi$
$102$			1.04686e6i			0.986484i
$103$		−	412082.i		−	0.377114i	−0.982062	−	0.188557i	$-0.939619\pi$
$103$		−	412082.i		−	0.377114i	0.982062	−	0.188557i	$-0.0603809\pi$
$104$	759937.			0.675581
$105$	−1.06451e6			−0.919560
$106$		−	241666.i		−	0.202908i
$107$	−879511.			−0.717943			−0.358971	−	0.933349i	$-0.616872\pi$
$107$	−879511.			−0.717943			−0.358971	+	0.933349i	$0.616872\pi$
$108$	148014.			0.117498
$109$		−	1.22209e6i		−	0.943676i	−0.881685	−	0.471838i	$-0.843591\pi$
$109$		−	1.22209e6i		−	0.943676i	0.881685	−	0.471838i	$-0.156409\pi$
$110$	469095.			0.352438
$111$		−	1.14270e6i		−	0.835529i
$112$	3.31939e6			2.36268
$113$		−	1.16448e6i		−	0.807040i	−0.914971	−	0.403520i	$-0.867787\pi$
$113$		−	1.16448e6i		−	0.807040i	0.914971	−	0.403520i	$-0.132213\pi$
$114$			320085.i			0.216048i
$115$		−	819841.i		−	0.539059i
$116$	−951076.			−0.609314
$117$		−	729734.i		−	0.455624i
$118$	−1.72796e6	−	1.16699e6i	−1.05169	−	0.710269i
$119$	4.33078e6			2.56995
$120$			411446.i			0.238105i
$121$	1.57532e6			0.889227
$122$	285861.			0.157426
$123$	81922.1			0.0440236
$124$			540982.i			0.283738i
$125$	2.12475e6			1.08787
$126$		−	1.61524e6i		−	0.807467i
$127$	−1.36949e6			−0.668571			−0.334285	−	0.942472i	$-0.608495\pi$
$127$	−1.36949e6			−0.668571			−0.334285	+	0.942472i	$0.608495\pi$
$128$		−	1.91583e6i		−	0.913538i
$129$			1.12697e6i			0.524979i
$130$	−3.17998e6			−1.44742
$131$		−	3.89962e6i		−	1.73464i	−0.497754	−	0.867318i	$-0.665842\pi$
$131$		−	3.89962e6i		−	1.73464i	0.497754	−	0.867318i	$-0.334158\pi$
$132$			269831.i			0.117319i
$133$	1.32416e6			0.562842
$134$	−3.25697e6			−1.35363
$135$	395093.			0.160582
$136$		−	1.67390e6i		−	0.665448i
$137$	−538204.			−0.209308			−0.104654	−	0.994509i	$-0.533373\pi$
$137$	−538204.			−0.209308			−0.104654	+	0.994509i	$0.533373\pi$
$138$	1.24399e6			0.473349
$139$	3.79961e6			1.41480			0.707400	−	0.706813i	$-0.249868\pi$
$139$	3.79961e6			1.41480			0.707400	+	0.706813i	$0.249868\pi$
$140$	−2.66832e6			−0.972421
$141$		−	2.74286e6i		−	0.978466i
$142$			5.63198e6i			1.96696i
$143$	1.33031e6			0.454931
$144$	−1.23200e6			−0.412594
$145$	−2.53870e6			−0.832737
$146$	1.27044e6			0.408223
$147$	−4.84812e6			−1.52624
$148$		−	2.86432e6i		−	0.883560i
$149$		−	2.19953e6i		−	0.664921i	−0.943117	−	0.332461i	$-0.892121\pi$
$149$		−	2.19953e6i		−	0.664921i	0.943117	−	0.332461i	$-0.107879\pi$
$150$			751150.i			0.222563i
$151$			5.72520e6i			1.66288i	0.555617	+	0.831438i	$0.312482\pi$
$151$			5.72520e6i			1.66288i	−0.555617	+	0.831438i	$0.687518\pi$
$152$		−	511807.i		−	0.145739i
$153$	−1.60738e6			−0.448790
$154$	2.94459e6			0.806238
$155$			1.44404e6i			0.387779i
$156$		−	1.82917e6i		−	0.481816i
$157$		−	332770.i		−	0.0859893i	−0.999075	−	0.0429947i	$-0.986310\pi$
$157$		−	332770.i		−	0.0859893i	0.999075	−	0.0429947i	$-0.0136898\pi$
$158$		−	8.71854e6i		−	2.21041i
$159$	371060.			0.0923108
$160$			3.67947e6i			0.898309i
$161$		−	5.14629e6i		−	1.23315i
$162$			599499.i			0.141008i
$163$	3.50429e6			0.809165			0.404582	−	0.914502i	$-0.367417\pi$
$163$	3.50429e6			0.809165			0.404582	+	0.914502i	$0.367417\pi$
$164$	205349.			0.0465544
$165$			720258.i			0.160338i
$166$	5.28061e6			1.15441
$167$	4.97745e6			1.06870			0.534352	−	0.845262i	$-0.320556\pi$
$167$	4.97745e6			1.06870			0.534352	+	0.845262i	$0.320556\pi$
$168$			2.58272e6i			0.544690i
$169$	−4.19132e6			−0.868343
$170$			7.00450e6i			1.42571i
$171$	−491466.			−0.0982890
$172$			2.82489e6i			0.555158i
$173$		−	7.61411e6i		−	1.47055i	−0.677767	−	0.735276i	$-0.737052\pi$
$173$		−	7.61411e6i		−	1.47055i	0.677767	−	0.735276i	$-0.262948\pi$
$174$		−	3.85213e6i		−	0.731228i
$175$	3.10744e6			0.579813
$176$		−	2.24594e6i		−	0.411966i
$177$	1.79183e6	−	2.65315e6i	0.323129	−	0.478457i
$178$	3.05252e6			0.541252
$179$			1.59663e6i			0.278384i	0.990265	+	0.139192i	$0.0444505\pi$
$179$			1.59663e6i			0.278384i	−0.990265	+	0.139192i	$0.955549\pi$
$180$	990353.			0.169814
$181$	−1.02310e7			−1.72537			−0.862686	−	0.505741i	$-0.831219\pi$
$181$	−1.02310e7			−1.72537			−0.862686	+	0.505741i	$0.831219\pi$
$182$	−1.99613e7			−3.31112
$183$			438917.i			0.0716191i
$184$	−1.98911e6			−0.319305
$185$		−	7.64570e6i		−	1.20754i
$186$	−2.19113e6			−0.340509
$187$		−	2.93026e6i		−	0.448107i
$188$		−	6.87533e6i		−	1.03471i
$189$	2.48007e6			0.367349
$190$			2.14167e6i			0.312242i
$191$			1.13201e7i			1.62462i	0.583227	+	0.812309i	$0.301790\pi$
$191$			1.13201e7i			1.62462i	−0.583227	+	0.812309i	$0.698210\pi$
$192$	−524993.			−0.0741736
$193$	1.96778e6			0.273719			0.136860	−	0.990590i	$-0.456299\pi$
$193$	1.96778e6			0.273719			0.136860	+	0.990590i	$0.456299\pi$
$194$	−1.24422e7			−1.70409
$195$		−	4.88260e6i		−	0.658488i
$196$	−1.21525e7			−1.61397
$197$	−6.29328e6			−0.823149			−0.411574	−	0.911376i	$-0.635021\pi$
$197$	−6.29328e6			−0.823149			−0.411574	+	0.911376i	$0.635021\pi$
$198$	−1.09289e6			−0.140793
$199$	8.10498e6			1.02847			0.514236	−	0.857649i	$-0.328076\pi$
$199$	8.10498e6			1.02847			0.514236	+	0.857649i	$0.328076\pi$
$200$		−	1.20107e6i		−	0.150133i
$201$		−	5.00082e6i		−	0.615819i
$202$	9.42070e6			1.14295
$203$	−1.59359e7			−1.90497
$204$	−4.02910e6			−0.474589
$205$	548136.			0.0636248
$206$	4.18369e6			0.478584
$207$			1.91006e6i			0.215345i
$208$			1.52252e7i			1.69189i
$209$		−	895947.i		−	0.0981394i
$210$		−	1.08075e7i		−	1.16699i
$211$		−	1.19788e7i		−	1.27516i	−0.770382	−	0.637582i	$-0.779935\pi$
$211$		−	1.19788e7i		−	1.27516i	0.770382	−	0.637582i	$-0.220065\pi$
$212$	930110.			0.0976173
$213$	−8.64745e6			−0.894848
$214$		−	8.92929e6i		−	0.911120i
$215$			7.54047e6i			0.758722i
$216$		−	958580.i		−	0.0951190i
$217$			9.06449e6i			0.887083i
$218$	1.24073e7			1.19759
$219$			1.95067e6i			0.185717i
$220$			1.80542e6i			0.169555i
$221$			1.98641e7i			1.84032i
$222$	1.16013e7			1.06035
$223$	−6.83511e6			−0.616355			−0.308178	−	0.951329i	$-0.599719\pi$
$223$	−6.83511e6			−0.616355			−0.308178	+	0.951329i	$0.599719\pi$
$224$			2.30967e7i			2.05497i
$225$	−1.15333e6			−0.101253
$226$	1.18224e7			1.02419
$227$		−	9.63771e6i		−	0.823941i	−0.911197	−	0.411971i	$-0.864841\pi$
$227$		−	9.63771e6i		−	0.823941i	0.911197	−	0.411971i	$-0.135159\pi$
$228$	−1.23192e6			−0.103939
$229$		−	1.02822e7i		−	0.856212i	−0.903728	−	0.428106i	$-0.859181\pi$
$229$		−	1.02822e7i		−	0.856212i	0.903728	−	0.428106i	$-0.140819\pi$
$230$	8.32349e6			0.684104
$231$			4.52119e6i			0.366790i
$232$			6.15943e6i			0.493261i
$233$			195801.i			0.0154791i	0.999970	+	0.00773956i	$0.00246360\pi$
$233$			195801.i			0.0154791i	−0.999970	+	0.00773956i	$0.997536\pi$
$234$	7.40867e6			0.578219
$235$		−	1.83523e7i		−	1.41412i
$236$	4.49145e6	−	6.65048e6i	0.341705	−	0.505961i
$237$	1.33866e7			1.00560
$238$			4.39685e7i			3.26145i
$239$	3.73985e6			0.273943			0.136972	−	0.990575i	$-0.456263\pi$
$239$	3.73985e6			0.273943			0.136972	+	0.990575i	$0.456263\pi$
$240$	−8.24322e6			−0.596298
$241$	−3.69307e6			−0.263837			−0.131919	−	0.991261i	$-0.542114\pi$
$241$	−3.69307e6			−0.263837			−0.131919	+	0.991261i	$0.542114\pi$
$242$			1.59935e7i			1.12849i
$243$	−920483.			−0.0641500
$244$			1.10020e6i			0.0757362i
$245$	−3.24385e7			−2.20578
$246$			831720.i			0.0558691i
$247$			6.07359e6i			0.403046i
$248$	3.50355e6			0.229696
$249$			8.10797e6i			0.525187i
$250$			2.15716e7i			1.38058i
$251$	1.05621e7			0.667928			0.333964	−	0.942586i	$-0.391614\pi$
$251$	1.05621e7			0.667928			0.333964	+	0.942586i	$0.391614\pi$
$252$	6.21662e6			0.388466
$253$	−3.48205e6			−0.215017
$254$		−	1.39038e7i		−	0.848463i
$255$	−1.07549e7			−0.648611
$256$	2.16060e7			1.28782
$257$	1.61502e6			0.0951432			0.0475716	−	0.998868i	$-0.484852\pi$
$257$	1.61502e6			0.0951432			0.0475716	+	0.998868i	$0.484852\pi$
$258$	−1.14416e7			−0.666236
$259$		−	4.79934e7i		−	2.76237i
$260$		−	1.22389e7i		−	0.696341i
$261$	5.91463e6			0.332664
$262$	3.95911e7			2.20138
$263$	−3.39349e6			−0.186543			−0.0932715	−	0.995641i	$-0.529732\pi$
$263$	−3.39349e6			−0.186543			−0.0932715	+	0.995641i	$0.529732\pi$
$264$	1.74750e6			0.0949742
$265$	2.48274e6			0.133411
$266$			1.34437e7i			0.714286i
$267$			4.68691e6i			0.246237i
$268$		−	1.25352e7i		−	0.651219i
$269$			669790.i			0.0344098i	0.999852	+	0.0172049i	$0.00547676\pi$
$269$			669790.i			0.0344098i	−0.999852	+	0.0172049i	$0.994523\pi$
$270$			4.01121e6i			0.203790i
$271$	−9.11749e6			−0.458107			−0.229054	−	0.973414i	$-0.573563\pi$
$271$	−9.11749e6			−0.458107			−0.229054	+	0.973414i	$0.573563\pi$
$272$	3.35363e7			1.66651
$273$		−	3.06490e7i		−	1.50636i
$274$		−	5.46415e6i		−	0.265626i
$275$		−	2.10253e6i		−	0.101099i
$276$			4.78781e6i			0.227724i
$277$	2.33110e7			1.09679			0.548393	−	0.836221i	$-0.315240\pi$
$277$	2.33110e7			1.09679			0.548393	+	0.836221i	$0.315240\pi$
$278$			3.85758e7i			1.79548i
$279$		−	3.36430e6i		−	0.154911i
$280$			1.72808e7i			0.787208i
$281$	−1.64403e7			−0.740954			−0.370477	−	0.928842i	$-0.620806\pi$
$281$	−1.64403e7			−0.740954			−0.370477	+	0.928842i	$0.620806\pi$
$282$	2.78470e7			1.24174
$283$			2.24174e7i			0.989066i	0.869159	+	0.494533i	$0.164661\pi$
$283$			2.24174e7i			0.989066i	−0.869159	+	0.494533i	$0.835339\pi$
$284$	−2.16760e7			−0.946289
$285$	−3.28837e6			−0.142051
$286$			1.35061e7i			0.577339i
$287$	3.44075e6			0.145548
$288$		−	8.57239e6i		−	0.358859i
$289$	1.96170e7			0.812715
$290$		−	2.57743e7i		−	1.05680i
$291$		−	1.91040e7i		−	0.775256i
$292$			4.88960e6i			0.196393i
$293$	3.78032e7			1.50289			0.751443	−	0.659798i	$-0.229358\pi$
$293$	3.78032e7			1.50289			0.751443	+	0.659798i	$0.229358\pi$
$294$		−	4.92209e7i		−	1.93690i
$295$	1.19890e7	−	1.77521e7i	0.467000	−	0.691486i
$296$	−1.85501e7			−0.715272
$297$		−	1.67805e6i		−	0.0640524i
$298$	2.23308e7			0.843832
$299$	2.36047e7			0.883048
$300$	−2.89098e6			−0.107073
$301$			4.73329e7i			1.73565i
$302$	−5.81255e7			−2.11031
$303$			1.44647e7i			0.519975i
$304$	1.02539e7			0.364981
$305$			2.93677e6i			0.103507i
$306$		−	1.63190e7i		−	0.569547i
$307$	−1.78309e7			−0.616252			−0.308126	−	0.951345i	$-0.599702\pi$
$307$	−1.78309e7			−0.616252			−0.308126	+	0.951345i	$0.599702\pi$
$308$			1.13330e7i			0.387875i
$309$			6.42372e6i			0.217727i
$310$	−1.46607e7			−0.492118
$311$	−4.32981e7			−1.43942			−0.719710	−	0.694274i	$-0.755725\pi$
$311$	−4.32981e7			−1.43942			−0.719710	+	0.694274i	$0.755725\pi$
$312$	−1.18462e7			−0.390047
$313$			3.12259e7i			1.01831i	0.860674	+	0.509157i	$0.170043\pi$
$313$			3.12259e7i			1.01831i	−0.860674	+	0.509157i	$0.829957\pi$
$314$	3.37846e6			0.109127
$315$	1.65940e7			0.530908
$316$	3.35553e7			1.06341
$317$	344531.			0.0108156			0.00540780	−	0.999985i	$-0.498279\pi$
$317$	344531.			0.0108156			0.00540780	+	0.999985i	$0.498279\pi$
$318$			3.76721e6i			0.117149i
$319$			1.07824e7i			0.332158i
$320$	−3.51269e6			−0.107199
$321$	1.37102e7			0.414505
$322$	5.22480e7			1.56496
$323$	1.33782e7			0.397000
$324$	−2.30731e6			−0.0678377
$325$			1.42530e7i			0.415199i
$326$			3.55775e7i			1.02689i
$327$			1.90505e7i			0.544831i
$328$		−	1.32989e6i		−	0.0376874i
$329$		−	1.15201e8i		−	3.23494i
$330$	−7.31247e6			−0.203480
$331$	1.63978e7			0.452171			0.226086	−	0.974107i	$-0.427407\pi$
$331$	1.63978e7			0.452171			0.226086	+	0.974107i	$0.427407\pi$
$332$			2.03237e7i			0.555377i
$333$			1.78129e7i			0.482393i
$334$			5.05339e7i			1.35626i
$335$		−	3.34602e7i		−	0.890007i
$336$	−5.17442e7			−1.36409
$337$			7.51217e7i			1.96280i	0.191976	+	0.981400i	$0.438510\pi$
$337$			7.51217e7i			1.96280i	−0.191976	+	0.981400i	$0.561490\pi$
$338$		−	4.25527e7i		−	1.10199i
$339$			1.81524e7i			0.465945i
$340$	−2.69585e7			−0.685896
$341$	6.13315e6			0.154675
$342$		−	4.98964e6i		−	0.124736i
$343$	−1.26595e8			−3.13715
$344$	1.82948e7			0.449420
$345$			1.27801e7i			0.311226i
$346$	7.73027e7			1.86623
$347$			5.29666e7i			1.26769i	0.773459	+	0.633846i	$0.218525\pi$
$347$			5.29666e7i			1.26769i	−0.773459	+	0.633846i	$0.781475\pi$
$348$	1.48258e7			0.351788
$349$		−	7.42339e7i		−	1.74633i	−0.487426	−	0.873164i	$-0.662064\pi$
$349$		−	7.42339e7i		−	1.74633i	0.487426	−	0.873164i	$-0.337936\pi$
$350$			3.15485e7i			0.735824i
$351$			1.13754e7i			0.263055i
$352$	1.56275e7			0.358313
$353$		−	6.31527e6i		−	0.143571i	−0.997420	−	0.0717857i	$-0.977130\pi$
$353$		−	6.31527e6i		−	0.143571i	0.997420	−	0.0717857i	$-0.0228698\pi$
$354$	2.69363e7	+	1.81916e7i	0.607195	+	0.410074i
$355$	−5.78596e7			−1.29327
$356$			1.17484e7i			0.260392i
$357$	−6.75102e7			−1.48376
$358$	−1.62099e7			−0.353289
$359$	−3.59250e7			−0.776450			−0.388225	−	0.921565i	$-0.626912\pi$
$359$	−3.59250e7			−0.776450			−0.388225	+	0.921565i	$0.626912\pi$
$360$		−	6.41380e6i		−	0.137470i
$361$	−4.29554e7			−0.913053
$362$		−	1.03871e8i		−	2.18962i
$363$	−2.45568e7			−0.513395
$364$		−	7.68257e7i		−	1.59295i
$365$			1.30518e7i			0.268405i
$366$	−4.45613e6			−0.0908897
$367$		−	1.84700e7i		−	0.373653i	−0.982393	−	0.186827i	$-0.940180\pi$
$367$		−	1.84700e7i		−	0.373653i	0.982393	−	0.186827i	$-0.0598203\pi$
$368$		−	3.98514e7i		−	0.799650i
$369$	−1.27704e6			−0.0254171
$370$	7.76235e7			1.53246
$371$	1.55846e7			0.305192
$372$		−	8.43307e6i		−	0.163816i
$373$	−7.31675e7			−1.40991			−0.704955	−	0.709252i	$-0.749033\pi$
$373$	−7.31675e7			−1.40991			−0.704955	+	0.709252i	$0.749033\pi$
$374$	2.97497e7			0.568679
$375$	−3.31215e7			−0.628082
$376$	−4.45266e7			−0.837636
$377$		−	7.30937e7i		−	1.36413i
$378$			2.51791e7i			0.466191i
$379$	−2.43432e7			−0.447157			−0.223579	−	0.974686i	$-0.571774\pi$
$379$	−2.43432e7			−0.447157			−0.223579	+	0.974686i	$0.571774\pi$
$380$	−8.24272e6			−0.150217
$381$	2.13482e7			0.386000
$382$	−1.14928e8			−2.06176
$383$	3.71024e7			0.660399			0.330199	−	0.943911i	$-0.392884\pi$
$383$	3.71024e7			0.660399			0.330199	+	0.943911i	$0.392884\pi$
$384$			2.98648e7i			0.527431i
$385$			3.02510e7i			0.530100i
$386$			1.99781e7i			0.347369i
$387$		−	1.75677e7i		−	0.303097i
$388$		−	4.78867e7i		−	0.819822i
$389$	−3.94013e7			−0.669362			−0.334681	−	0.942331i	$-0.608629\pi$
$389$	−3.94013e7			−0.669362			−0.334681	+	0.942331i	$0.608629\pi$
$390$	4.95709e7			0.835667
$391$		−	5.19938e7i		−	0.869803i
$392$			7.87027e7i			1.30657i
$393$			6.07891e7i			1.00149i
$394$		−	6.38929e7i		−	1.04463i
$395$	8.95691e7			1.45334
$396$		−	4.20625e6i		−	0.0677344i
$397$		−	8.86748e7i		−	1.41719i	−0.705614	−	0.708596i	$-0.749329\pi$
$397$		−	8.86748e7i		−	1.41719i	0.705614	−	0.708596i	$-0.250671\pi$
$398$			8.22863e7i			1.30520i
$399$	−2.06417e7			−0.324957
$400$	2.40631e7			0.375986
$401$			1.10931e8i			1.72036i	0.509990	+	0.860181i	$0.329649\pi$
$401$			1.10931e8i			1.72036i	−0.509990	+	0.860181i	$0.670351\pi$
$402$	5.07711e7			0.781517
$403$	−4.15764e7			−0.635231
$404$			3.62578e7i			0.549866i
$405$	−6.15889e6			−0.0927123
$406$		−	1.61790e8i		−	2.41754i
$407$	−3.24730e7			−0.481658
$408$			2.60936e7i			0.384196i
$409$			4.60916e7i			0.673677i	0.941562	+	0.336839i	$0.109358\pi$
$409$			4.60916e7i			0.673677i	−0.941562	+	0.336839i	$0.890642\pi$
$410$			5.56498e6i			0.0807444i
$411$	8.38977e6			0.120844
$412$			1.61019e7i			0.230243i
$413$	7.52571e7	−	1.11433e8i	1.06831	−	1.58184i
$414$	−1.93920e7			−0.273288
$415$			5.42499e7i			0.759022i
$416$	−1.05939e8			−1.47155
$417$	−5.92301e7			−0.816835
$418$	9.09615e6			0.124546
$419$			6.43202e7i			0.874390i	0.899367	+	0.437195i	$0.144028\pi$
$419$			6.43202e7i			0.874390i	−0.899367	+	0.437195i	$0.855972\pi$
$420$	4.15950e7			0.561427
$421$			1.80783e7i			0.242276i	0.992636	+	0.121138i	$0.0386543\pi$
$421$			1.80783e7i			0.242276i	−0.992636	+	0.121138i	$0.961346\pi$
$422$	1.21616e8			1.61827
$423$			4.27569e7i			0.564918i
$424$		−	6.02365e6i		−	0.0790246i
$425$	3.13949e7			0.408971
$426$		−	8.77938e7i		−	1.13563i
$427$			1.84346e7i			0.236783i
$428$	3.43665e7			0.438333
$429$	−2.07375e7			−0.262654
$430$	−7.65551e7			−0.962872
$431$		−	1.40777e7i		−	0.175833i	−0.996128	−	0.0879166i	$-0.971979\pi$
$431$		−	1.40777e7i		−	0.175833i	0.996128	−	0.0879166i	$-0.0280209\pi$
$432$	1.92050e7			0.238211
$433$	−9.56225e7			−1.17787			−0.588934	−	0.808181i	$-0.700452\pi$
$433$	−9.56225e7			−1.17787			−0.588934	+	0.808181i	$0.700452\pi$
$434$	−9.20278e7			−1.12577
$435$	3.95744e7			0.480781
$436$			4.77525e7i			0.576151i
$437$		−	1.58974e7i		−	0.190494i
$438$	−1.98043e7			−0.235687
$439$	8.07733e7			0.954716			0.477358	−	0.878709i	$-0.341595\pi$
$439$	8.07733e7			0.954716			0.477358	+	0.878709i	$0.341595\pi$
$440$	1.16924e7			0.137261
$441$	7.55748e7			0.881173
$442$	−2.01672e8			−2.33549
$443$		−	8.66157e7i		−	0.996290i	−0.867094	−	0.498145i	$-0.834015\pi$
$443$		−	8.66157e7i		−	0.996290i	0.867094	−	0.498145i	$-0.165985\pi$
$444$			4.46503e7i			0.510123i
$445$			3.13598e7i			0.355872i
$446$		−	6.93939e7i		−	0.782198i
$447$			3.42872e7i			0.383892i
$448$	−2.20498e7			−0.245228
$449$	1.10404e8			1.21968			0.609841	−	0.792524i	$-0.291233\pi$
$449$	1.10404e8			1.21968			0.609841	+	0.792524i	$0.291233\pi$
$450$		−	1.17093e7i		−	0.128497i
$451$		−	2.32806e6i		−	0.0253784i
$452$			4.55013e7i			0.492730i
$453$		−	8.92471e7i		−	0.960062i
$454$	9.78474e7			1.04564
$455$		−	2.05070e8i		−	2.17705i
$456$			7.97828e6i			0.0841424i
$457$		−	1.11206e8i		−	1.16514i	−0.812779	−	0.582572i	$-0.802047\pi$
$457$		−	1.11206e8i		−	1.16514i	0.812779	−	0.582572i	$-0.197953\pi$
$458$	1.04391e8			1.08659
$459$	2.50565e7			0.259109
$460$			3.20349e7i			0.329117i
$461$	8.07065e7			0.823770			0.411885	−	0.911236i	$-0.364871\pi$
$461$	8.07065e7			0.823770			0.411885	+	0.911236i	$0.364871\pi$
$462$	−4.59017e7			−0.465482
$463$		−	1.13852e8i		−	1.14709i	−0.819173	−	0.573547i	$-0.805567\pi$
$463$		−	1.13852e8i		−	1.14709i	0.819173	−	0.573547i	$-0.194433\pi$
$464$	−1.23403e8			−1.23530
$465$		−	2.25103e7i		−	0.223884i
$466$	−1.98788e6			−0.0196441
$467$			1.34224e8i			1.31789i	0.752192	+	0.658944i	$0.228997\pi$
$467$			1.34224e8i			1.31789i	−0.752192	+	0.658944i	$0.771003\pi$
$468$			2.85140e7i			0.278177i
$469$		−	2.10035e8i		−	2.03598i
$470$	1.86323e8			1.79462
$471$			5.18736e6i			0.0496460i
$472$	−4.30704e7	−	2.90879e7i	−0.409593	−	0.276622i
$473$	3.20260e7			0.302635
$474$			1.35909e8i			1.27618i
$475$	9.59920e6			0.0895682
$476$	−1.69223e8			−1.56906
$477$	−5.78425e6			−0.0532957
$478$			3.79691e7i			0.347653i
$479$	1.89590e8			1.72508			0.862538	−	0.505992i	$-0.168874\pi$
$479$	1.89590e8			1.72508			0.862538	+	0.505992i	$0.168874\pi$
$480$		−	5.73573e7i		−	0.518639i
$481$	2.20133e8			1.97811
$482$		−	3.74941e7i		−	0.334828i
$483$			8.02227e7i			0.711961i
$484$	−6.15549e7			−0.542908
$485$		−	1.27824e8i		−	1.12043i
$486$		−	9.34526e6i		−	0.0814109i
$487$	−1.40587e7			−0.121719			−0.0608595	−	0.998146i	$-0.519384\pi$
$487$	−1.40587e7			−0.121719			−0.0608595	+	0.998146i	$0.519384\pi$
$488$	7.12522e6			0.0613111
$489$	−5.46264e7			−0.467171
$490$		−	3.29334e8i		−	2.79929i
$491$	1.36388e8			1.15221			0.576104	−	0.817377i	$-0.304572\pi$
$491$	1.36388e8			1.15221			0.576104	+	0.817377i	$0.304572\pi$
$492$	−3.20107e6			−0.0268782
$493$	−1.61003e8			−1.34367
$494$	−6.16625e7			−0.511493
$495$		−	1.12277e7i		−	0.0925712i
$496$			7.01928e7i			0.575238i
$497$	−3.63195e8			−2.95849
$498$	−8.23166e7			−0.666499
$499$	1.80444e8			1.45225			0.726123	−	0.687565i	$-0.241320\pi$
$499$	1.80444e8			1.45225			0.726123	+	0.687565i	$0.241320\pi$
$500$	−8.30235e7			−0.664188
$501$	−7.75907e7			−0.617016
$502$			1.07232e8i			0.847647i
$503$			4.39678e7i			0.345486i	0.984967	+	0.172743i	$0.0552631\pi$
$503$			4.39678e7i			0.345486i	−0.984967	+	0.172743i	$0.944737\pi$
$504$		−	4.02606e7i		−	0.314477i
$505$			9.67827e7i			0.751490i
$506$		−	3.53517e7i		−	0.272872i
$507$	6.53363e7			0.501338
$508$	5.35121e7			0.408189
$509$		−	4.22630e7i		−	0.320484i	−0.987078	−	0.160242i	$-0.948773\pi$
$509$		−	4.22630e7i		−	0.320484i	0.987078	−	0.160242i	$-0.0512275\pi$
$510$		−	1.09189e8i		−	0.823133i
$511$			8.19284e7i			0.614005i
$512$			9.67430e7i			0.720791i
$513$	7.66119e6			0.0567472
$514$			1.63966e7i			0.120743i
$515$			4.29807e7i			0.314668i
$516$		−	4.40357e7i		−	0.320521i
$517$	−7.79462e7			−0.564058
$518$	4.87256e8			3.50565
$519$			1.18692e8i			0.849024i
$520$	−7.92625e7			−0.563712
$521$	2.74322e7			0.193976			0.0969880	−	0.995286i	$-0.469079\pi$
$521$	2.74322e7			0.193976			0.0969880	+	0.995286i	$0.469079\pi$
$522$			6.00487e7i			0.422175i
$523$	7.55469e7			0.528095			0.264047	−	0.964510i	$-0.414943\pi$
$523$	7.55469e7			0.528095			0.264047	+	0.964510i	$0.414943\pi$
$524$			1.52376e8i			1.05906i
$525$	−4.84402e7			−0.334755
$526$		−	3.44526e7i		−	0.236736i
$527$			9.15799e7i			0.625703i
$528$			3.50108e7i			0.237848i
$529$	8.62514e7			0.582638
$530$			2.52061e7i			0.169309i
$531$	−2.79318e7	+	4.13586e7i	−0.186559	+	0.276237i
$532$	−5.17410e7			−0.343637
$533$			1.57818e7i			0.104226i
$534$	−4.75842e7			−0.312492
$535$	9.17342e7			0.599060
$536$	−8.11815e7			−0.527185
$537$		−	2.48890e7i		−	0.160725i
$538$	−6.80009e6			−0.0436684
$539$			1.37773e8i			0.879831i
$540$	−1.54381e7			−0.0980419
$541$			2.82600e8i			1.78476i	0.451285	+	0.892380i	$0.350966\pi$
$541$			2.82600e8i			1.78476i	−0.451285	+	0.892380i	$0.649034\pi$
$542$		−	9.25659e7i		−	0.581371i
$543$	1.59486e8			0.996143
$544$			2.33350e8i			1.44947i
$545$			1.27465e8i			0.787414i
$546$	3.11166e8			1.91167
$547$	7.30113e7			0.446095			0.223048	−	0.974808i	$-0.428399\pi$
$547$	7.30113e7			0.446095			0.223048	+	0.974808i	$0.428399\pi$
$548$	2.10301e7			0.127791
$549$		−	6.84204e6i		−	0.0413493i
$550$	2.13461e7			0.128301
$551$	−4.92276e7			−0.294275
$552$	3.10072e7			0.184351
$553$	5.62241e8			3.32466
$554$			2.36667e8i			1.39190i
$555$			1.19185e8i			0.697175i
$556$	−1.48468e8			−0.863791
$557$	−3.01043e8			−1.74206			−0.871031	−	0.491229i	$-0.836548\pi$
$557$	−3.01043e8			−1.74206			−0.871031	+	0.491229i	$0.836548\pi$
$558$	3.41563e7			0.196593
$559$	−2.17103e8			−1.24289
$560$	−3.46217e8			−1.97144
$561$			4.56783e7i			0.258715i
$562$		−	1.66911e8i		−	0.940323i
$563$		−	1.26927e7i		−	0.0711262i	−0.999367	−	0.0355631i	$-0.988678\pi$
$563$		−	1.26927e7i		−	0.0711262i	0.999367	−	0.0355631i	$-0.0113225\pi$
$564$			1.07176e8i			0.597392i
$565$			1.21456e8i			0.673403i
$566$	−2.27594e8			−1.25519
$567$	−3.86605e7			−0.212089
$568$			1.40380e8i			0.766054i
$569$		−	2.72018e8i		−	1.47659i	−0.674476	−	0.738297i	$-0.735630\pi$
$569$		−	2.72018e8i		−	1.47659i	0.674476	−	0.738297i	$-0.264370\pi$
$570$		−	3.33853e7i		−	0.180273i
$571$		−	2.66755e8i		−	1.43286i	−0.697658	−	0.716431i	$-0.745774\pi$
$571$		−	2.66755e8i		−	1.43286i	0.697658	−	0.716431i	$-0.254226\pi$
$572$	−5.19813e7			−0.277753
$573$		−	1.76463e8i		−	0.937974i
$574$			3.49324e7i			0.184711i
$575$		−	3.73068e7i		−	0.196238i
$576$	8.18383e6			0.0428242
$577$	−2.29588e8			−1.19515			−0.597575	−	0.801813i	$-0.703869\pi$
$577$	−2.29588e8			−1.19515			−0.597575	+	0.801813i	$0.703869\pi$
$578$			1.99162e8i			1.03139i
$579$	−3.06747e7			−0.158032
$580$	9.91986e7			0.508419
$581$			3.40536e8i			1.73634i
$582$	1.93954e8			0.983854
$583$		−	1.05447e7i		−	0.0532145i
$584$	3.16664e7			0.158987
$585$			7.61123e7i			0.380178i
$586$			3.83800e8i			1.90727i
$587$			3.03353e8i			1.49980i	0.661550	+	0.749901i	$0.269899\pi$
$587$			3.03353e8i			1.49980i	−0.661550	+	0.749901i	$0.730101\pi$
$588$	1.89438e8			0.931827
$589$			2.80011e7i			0.137034i
$590$	1.80229e8	+	1.21719e8i	0.877544	+	0.592656i
$591$	9.81025e7			0.475245
$592$		−	3.71647e8i		−	1.79129i
$593$	3.40728e7			0.163397			0.0816985	−	0.996657i	$-0.473966\pi$
$593$	3.40728e7			0.163397			0.0816985	+	0.996657i	$0.473966\pi$
$594$	1.70365e7			0.0812870
$595$	−4.51706e8			−2.14440
$596$			8.59454e7i			0.405961i
$597$	−1.26344e8			−0.593789
$598$			2.39648e8i			1.12065i
$599$	2.96815e8			1.38104			0.690520	−	0.723314i	$-0.257382\pi$
$599$	2.96815e8			1.38104			0.690520	+	0.723314i	$0.257382\pi$
$600$			1.87228e7i			0.0866795i
$601$		−	1.19578e8i		−	0.550845i	−0.961323	−	0.275423i	$-0.911182\pi$
$601$		−	1.19578e8i		−	0.550845i	0.961323	−	0.275423i	$-0.0888178\pi$
$602$	−4.80550e8			−2.20267
$603$			7.79550e7i			0.355543i
$604$		−	2.23710e8i		−	1.01525i
$605$	−1.64308e8			−0.741981
$606$	−1.46854e8			−0.659885
$607$	−4.34360e8			−1.94216			−0.971078	−	0.238763i	$-0.923258\pi$
$607$	−4.34360e8			−1.94216			−0.971078	+	0.238763i	$0.923258\pi$
$608$			7.13481e7i			0.317447i
$609$	2.48416e8			1.09983
$610$	−2.98157e7			−0.131358
$611$	5.28394e8			2.31651
$612$	6.28075e7			0.274004
$613$			1.91315e8i			0.830552i	0.909696	+	0.415276i	$0.136315\pi$
$613$			1.91315e8i			0.830552i	−0.909696	+	0.415276i	$0.863685\pi$
$614$		−	1.81030e8i		−	0.782068i
$615$	−8.54459e6			−0.0367338
$616$	7.33954e7			0.313998
$617$	1.22851e8			0.523027			0.261513	−	0.965200i	$-0.415778\pi$
$617$	1.22851e8			0.523027			0.261513	+	0.965200i	$0.415778\pi$
$618$	−6.52173e7			−0.276310
$619$	2.76299e8			1.16495			0.582474	−	0.812849i	$-0.302085\pi$
$619$	2.76299e8			1.16495			0.582474	+	0.812849i	$0.302085\pi$
$620$		−	5.64251e7i		−	0.236754i
$621$		−	2.97748e7i		−	0.124330i
$622$		−	4.39587e8i		−	1.82673i
$623$			1.96851e8i			0.814093i
$624$		−	2.37337e8i		−	0.976813i
$625$	−1.47454e8			−0.603973
$626$	−3.17022e8			−1.29231
$627$			1.39664e7i			0.0566608i
$628$			1.30028e7i			0.0524999i
$629$		−	4.84885e8i		−	1.94844i
$630$			1.68472e8i			0.673760i
$631$	−4.17250e7			−0.166077			−0.0830383	−	0.996546i	$-0.526462\pi$
$631$	−4.17250e7			−0.166077			−0.0830383	+	0.996546i	$0.526462\pi$
$632$		−	2.17314e8i		−	0.860867i
$633$			1.86731e8i			0.736217i
$634$			3.49787e6i			0.0137258i
$635$	1.42840e8			0.557863
$636$	−1.44990e7			−0.0563594
$637$		−	9.33961e8i		−	3.61335i
$638$	−1.09469e8			−0.421532
$639$	1.34800e8			0.516641
$640$			1.99823e8i			0.762266i
$641$	4.30270e8			1.63368			0.816840	−	0.576864i	$-0.195724\pi$
$641$	4.30270e8			1.63368			0.816840	+	0.576864i	$0.195724\pi$
$642$			1.39194e8i			0.526035i
$643$	5.22591e7			0.196575			0.0982877	−	0.995158i	$-0.468663\pi$
$643$	5.22591e7			0.196575			0.0982877	+	0.995158i	$0.468663\pi$
$644$			2.01089e8i			0.752888i
$645$		−	1.17544e8i		−	0.438048i
$646$			1.35823e8i			0.503821i
$647$	1.95145e8			0.720516			0.360258	−	0.932853i	$-0.382689\pi$
$647$	1.95145e8			0.720516			0.360258	+	0.932853i	$0.382689\pi$
$648$			1.49428e7i			0.0549170i
$649$	−7.53971e7	−	5.09200e7i	−0.275817	−	0.186275i
$650$	−1.44704e8			−0.526916
$651$		−	1.41301e8i		−	0.512157i
$652$	−1.36928e8			−0.494027
$653$	−2.87811e8			−1.03364			−0.516818	−	0.856095i	$-0.672884\pi$
$653$	−2.87811e8			−1.03364			−0.516818	+	0.856095i	$0.672884\pi$
$654$	−1.93411e8			−0.691429
$655$			4.06736e8i			1.44740i
$656$	2.66442e7			0.0943823
$657$		−	3.04079e7i		−	0.107224i
$658$	1.16958e9			4.10537
$659$			4.19404e8i			1.46547i	0.680516	+	0.732734i	$0.261756\pi$
$659$			4.19404e8i			1.46547i	−0.680516	+	0.732734i	$0.738244\pi$
$660$		−	2.81438e7i		−	0.0978927i
$661$	−1.64917e8			−0.571032			−0.285516	−	0.958374i	$-0.592165\pi$
$661$	−1.64917e8			−0.571032			−0.285516	+	0.958374i	$0.592165\pi$
$662$			1.66480e8i			0.573837i
$663$		−	3.09651e8i		−	1.06251i
$664$	1.31622e8			0.449597
$665$	−1.38112e8			−0.469642
$666$	−1.80846e8			−0.612190
$667$			1.91320e8i			0.644739i
$668$	−1.94491e8			−0.652486
$669$	1.06549e8			0.355853
$670$	3.39706e8			1.12948
$671$	1.24731e7			0.0412864
$672$		−	3.60042e8i		−	1.18644i
$673$		−	4.61298e8i		−	1.51334i	−0.653796	−	0.756671i	$-0.726825\pi$
$673$		−	4.61298e8i		−	1.51334i	0.653796	−	0.756671i	$-0.273175\pi$
$674$	−7.62678e8			−2.49093
$675$	1.79787e7			0.0584583
$676$	1.63774e8			0.530157
$677$	4.24564e7			0.136829			0.0684143	−	0.997657i	$-0.478206\pi$
$677$	4.24564e7			0.136829			0.0684143	+	0.997657i	$0.478206\pi$
$678$	−1.84293e8			−0.591317
$679$		−	8.02371e8i		−	2.56310i
$680$			1.74591e8i			0.555257i
$681$			1.50237e8i			0.475703i
$682$			6.22672e7i			0.196294i
$683$			6.61697e7i			0.207681i	0.994594	+	0.103841i	$0.0331132\pi$
$683$			6.61697e7i			0.207681i	−0.994594	+	0.103841i	$0.966887\pi$
$684$	1.92038e7			0.0600093
$685$	5.61355e7			0.174649
$686$		−	1.28527e9i		−	3.98126i
$687$			1.60284e8i			0.494334i
$688$			3.66532e8i			1.12550i
$689$			7.14824e7i			0.218545i
$690$	−1.29750e8			−0.394968
$691$			9.68980e7i			0.293684i	0.989160	+	0.146842i	$0.0469109\pi$
$691$			9.68980e7i			0.293684i	−0.989160	+	0.146842i	$0.953089\pi$
$692$			2.97518e8i			0.897830i
$693$		−	7.04784e7i		−	0.211766i
$694$	−5.37747e8			−1.60879
$695$	−3.96305e8			−1.18053
$696$		−	9.60161e7i		−	0.284784i
$697$	3.47624e7			0.102662
$698$	7.53664e8			2.21621
$699$		−	3.05223e6i		−	0.00893688i
$700$	−1.21422e8			−0.353999
$701$		−	5.03940e8i		−	1.46294i	−0.681876	−	0.731468i	$-0.738836\pi$
$701$		−	5.03940e8i		−	1.46294i	0.681876	−	0.731468i	$-0.261164\pi$
$702$	−1.15490e8			−0.333835
$703$		−	1.48257e8i		−	0.426725i
$704$			1.49192e7i			0.0427590i
$705$			2.86084e8i			0.816443i
$706$	6.41162e7			0.182202
$707$			6.07522e8i			1.71911i
$708$	−7.00148e7	+	1.03671e8i	−0.197283	+	0.292117i
$709$	1.17112e8			0.328596			0.164298	−	0.986411i	$-0.447464\pi$
$709$	1.17112e8			0.328596			0.164298	+	0.986411i	$0.447464\pi$
$710$		−	5.87423e8i		−	1.64125i
$711$	−2.08677e8			−0.580585
$712$	7.60856e7			0.210796
$713$	1.08825e8			0.300234
$714$		−	6.85401e8i		−	1.88300i
$715$	−1.38753e8			−0.379599
$716$		−	6.23874e7i		−	0.169964i
$717$	−5.82985e7			−0.158161
$718$		−	3.64731e8i		−	0.985369i
$719$			5.86668e8i			1.57836i	0.614162	+	0.789180i	$0.289494\pi$
$719$			5.86668e8i			1.57836i	−0.614162	+	0.789180i	$0.710506\pi$
$720$	1.28499e8			0.344273
$721$			2.69798e8i			0.719834i
$722$		−	4.36107e8i		−	1.15873i
$723$	5.75693e7			0.152327
$724$	3.99772e8			1.05341
$725$	−1.15523e8			−0.303149
$726$		−	2.49314e8i		−	0.651535i
$727$	−1.83589e8			−0.477797			−0.238898	−	0.971045i	$-0.576786\pi$
$727$	−1.83589e8			−0.477797			−0.238898	+	0.971045i	$0.576786\pi$
$728$	−4.97545e8			−1.28955
$729$	1.43489e7			0.0370370
$730$	−1.32509e8			−0.340625
$731$			4.78211e8i			1.22424i
$732$		−	1.71505e7i		−	0.0437263i
$733$	−1.27061e8			−0.322626			−0.161313	−	0.986903i	$-0.551573\pi$
$733$	−1.27061e8			−0.322626			−0.161313	+	0.986903i	$0.551573\pi$
$734$	1.87518e8			0.474192
$735$	5.05666e8			1.27351
$736$	2.77291e8			0.695508
$737$	−1.42113e8			−0.355002
$738$		−	1.29652e7i		−	0.0322560i
$739$			6.00659e8i			1.48831i	0.668005	+	0.744157i	$0.267149\pi$
$739$			6.00659e8i			1.48831i	−0.668005	+	0.744157i	$0.732851\pi$
$740$			2.98752e8i			0.737252i
$741$		−	9.46779e7i		−	0.232699i
$742$			1.58223e8i			0.387310i
$743$	3.85539e8			0.939944			0.469972	−	0.882681i	$-0.344264\pi$
$743$	3.85539e8			0.939944			0.469972	+	0.882681i	$0.344264\pi$
$744$	−5.46149e7			−0.132615
$745$			2.29414e8i			0.554818i
$746$		−	7.42838e8i		−	1.78928i
$747$		−	1.26391e8i		−	0.303217i
$748$			1.14499e8i			0.273587i
$749$	5.75832e8			1.37041
$750$		−	3.36268e8i		−	0.797080i
$751$		−	1.49633e8i		−	0.353270i	−0.984276	−	0.176635i	$-0.943479\pi$
$751$		−	1.49633e8i		−	0.353270i	0.984276	−	0.176635i	$-0.0565213\pi$
$752$		−	8.92080e8i		−	2.09773i
$753$	−1.64647e8			−0.385628
$754$	7.42088e8			1.73118
$755$		−	5.97147e8i		−	1.38752i
$756$	−9.69076e7			−0.224281
$757$	3.76913e7			0.0868868			0.0434434	−	0.999056i	$-0.486167\pi$
$757$	3.76913e7			0.0868868			0.0434434	+	0.999056i	$0.486167\pi$
$758$		−	2.47146e8i		−	0.567474i
$759$	5.42798e7			0.124140
$760$			5.33822e7i			0.121606i
$761$	−3.09488e8			−0.702248			−0.351124	−	0.936329i	$-0.614200\pi$
$761$	−3.09488e8			−0.702248			−0.351124	+	0.936329i	$0.614200\pi$
$762$			2.16739e8i			0.489861i
$763$			8.00123e8i			1.80129i
$764$		−	4.42329e8i		−	0.991894i
$765$	1.67652e8			0.374476
$766$			3.76685e8i			0.838092i
$767$	5.11114e8	+	3.45185e8i	1.13274	+	0.765007i
$768$	−3.36804e8			−0.743521
$769$		−	1.14414e8i		−	0.251594i	−0.992056	−	0.125797i	$-0.959851\pi$
$769$		−	1.14414e8i		−	0.251594i	0.992056	−	0.125797i	$-0.0401488\pi$
$770$	−3.07125e8			−0.672734
$771$	−2.51756e7			−0.0549310
$772$	−7.68902e7			−0.167116
$773$		−	3.74267e8i		−	0.810294i	−0.914252	−	0.405147i	$-0.867220\pi$
$773$		−	3.74267e8i		−	0.810294i	0.914252	−	0.405147i	$-0.132780\pi$
$774$	1.78357e8			0.384651
$775$			6.57108e7i			0.141166i
$776$	−3.10127e8			−0.663674
$777$			7.48144e8i			1.59486i
$778$		−	4.00024e8i		−	0.849468i
$779$	1.06288e7			0.0224840
$780$			1.90785e8i			0.402033i
$781$			2.45742e8i			0.515854i
$782$	5.27870e8			1.10384
$783$	−9.22000e7			−0.192064
$784$	−1.57679e9			−3.27210
$785$			3.47083e7i			0.0717505i
$786$	−6.17165e8			−1.27097
$787$	3.10295e8			0.636576			0.318288	−	0.947994i	$-0.396892\pi$
$787$	3.10295e8			0.636576			0.318288	+	0.947994i	$0.396892\pi$
$788$	2.45907e8			0.502565
$789$	5.28992e7			0.107701
$790$			9.09356e8i			1.84439i
$791$			7.62404e8i			1.54048i
$792$	−2.72408e7			−0.0548334
$793$	−8.45546e7			−0.169558
$794$	9.00277e8			1.79852
$795$	−3.87020e7			−0.0770252
$796$	−3.16698e8			−0.627923
$797$			2.02748e8i			0.400481i	0.979747	+	0.200241i	$0.0641724\pi$
$797$			2.02748e8i			0.400481i	−0.979747	+	0.200241i	$0.935828\pi$
$798$		−	2.09566e8i		−	0.412393i
$799$		−	1.16389e9i		−	2.28177i
$800$			1.67434e8i			0.327019i
$801$		−	7.30617e7i		−	0.142165i
$802$	−1.12623e9			−2.18326
$803$	5.54338e7			0.107060
$804$			1.95405e8i			0.375982i
$805$			5.36765e8i			1.02896i
$806$		−	4.22107e8i		−	0.806153i
$807$		−	1.04410e7i		−	0.0198665i
$808$	2.34815e8			0.445136
$809$			4.06009e8i			0.766814i	0.923579	+	0.383407i	$0.125249\pi$
$809$			4.06009e8i			0.766814i	−0.923579	+	0.383407i	$0.874751\pi$
$810$		−	6.25285e7i		−	0.117658i
$811$		−	3.85652e8i		−	0.722991i	−0.932374	−	0.361495i	$-0.882266\pi$
$811$		−	3.85652e8i		−	0.722991i	0.932374	−	0.361495i	$-0.117734\pi$
$812$	6.22687e8			1.16306
$813$	1.42128e8			0.264488
$814$		−	3.29684e8i		−	0.611258i
$815$	−3.65502e8			−0.675176
$816$	−5.22779e8			−0.962161
$817$			1.46216e8i			0.268120i
$818$	−4.67948e8			−0.854944
$819$			4.77770e8i			0.869696i
$820$	−2.14181e7			−0.0388455
$821$		−	3.26756e8i		−	0.590464i	−0.955426	−	0.295232i	$-0.904603\pi$
$821$		−	3.26756e8i		−	0.590464i	0.955426	−	0.295232i	$-0.0953970\pi$
$822$			8.51777e7i			0.153359i
$823$		−	1.04134e8i		−	0.186807i	−0.995628	−	0.0934037i	$-0.970225\pi$
$823$		−	1.04134e8i		−	0.186807i	0.995628	−	0.0934037i	$-0.0297747\pi$
$824$	1.04280e8			0.186389
$825$			3.27753e7i			0.0583693i
$826$	1.13133e9	+	7.64053e8i	2.00747	+	1.35576i
$827$	3.71972e8			0.657649			0.328824	−	0.944391i	$-0.393348\pi$
$827$	3.71972e8			0.657649			0.328824	+	0.944391i	$0.393348\pi$
$828$		−	7.46345e7i		−	0.131477i
$829$	−1.59639e8			−0.280204			−0.140102	−	0.990137i	$-0.544743\pi$
$829$	−1.59639e8			−0.280204			−0.140102	+	0.990137i	$0.544743\pi$
$830$	−5.50775e8			−0.963253
$831$	−3.63383e8			−0.633230
$832$		−	1.01137e8i		−	0.175606i
$833$	−2.05723e9			−3.55916
$834$		−	6.01338e8i		−	1.03662i
$835$	−5.19155e8			−0.891738
$836$			3.50087e7i			0.0599180i
$837$			5.24443e7i			0.0894379i
$838$	−6.53015e8			−1.10966
$839$		−	1.08978e9i		−	1.84524i	−0.385710	−	0.922620i	$-0.626043\pi$
$839$		−	1.08978e9i		−	1.84524i	0.385710	−	0.922620i	$-0.373957\pi$
$840$		−	2.69381e8i		−	0.454495i
$841$	−2.38493e6			−0.00400947
$842$	−1.83541e8			−0.307465
$843$	2.56279e8			0.427790
$844$			4.68066e8i			0.778538i
$845$	4.37161e8			0.724555
$846$	−4.34092e8			−0.716920
$847$	−1.03139e9			−1.69736
$848$	1.20683e8			0.197905
$849$		−	3.49452e8i		−	0.571038i
$850$			3.18739e8i			0.519013i
$851$	−5.76192e8			−0.934928
$852$	3.37895e8			0.546340
$853$	−2.70522e7			−0.0435869			−0.0217934	−	0.999762i	$-0.506938\pi$
$853$	−2.70522e7			−0.0435869			−0.0217934	+	0.999762i	$0.506938\pi$
$854$	−1.87158e8			−0.300494
$855$	5.12606e7			0.0820134
$856$		−	2.22567e8i		−	0.354845i
$857$			1.58739e8i			0.252197i	0.992018	+	0.126099i	$0.0402456\pi$
$857$			1.58739e8i			0.252197i	−0.992018	+	0.126099i	$0.959754\pi$
$858$		−	2.10539e8i		−	0.333327i
$859$		−	2.29626e8i		−	0.362278i	−0.983457	−	0.181139i	$-0.942022\pi$
$859$		−	2.29626e8i		−	0.362278i	0.983457	−	0.181139i	$-0.0579785\pi$
$860$		−	2.94640e8i		−	0.463230i
$861$	−5.36359e7			−0.0840323
$862$	1.42925e8			0.223145
$863$			7.49840e8i			1.16664i	0.812243	+	0.583319i	$0.198246\pi$
$863$			7.49840e8i			1.16664i	−0.812243	+	0.583319i	$0.801754\pi$
$864$			1.33630e8i			0.207188i
$865$			7.94162e8i			1.22705i
$866$		−	9.70814e8i		−	1.49480i
$867$	−3.05798e8			−0.469221
$868$		−	3.54191e8i		−	0.541599i
$869$		−	3.80420e8i		−	0.579701i
$870$			4.01782e8i			0.610145i
$871$	9.63377e8			1.45795
$872$	3.09258e8			0.466414
$873$			2.97802e8i			0.447594i
$874$	1.61400e8			0.241751
$875$	−1.39111e9			−2.07653
$876$		−	7.62214e7i		−	0.113387i
$877$	4.50870e8			0.668425			0.334213	−	0.942498i	$-0.391530\pi$
$877$	4.50870e8			0.668425			0.334213	+	0.942498i	$0.391530\pi$
$878$			8.20056e8i			1.21160i
$879$	−5.89294e8			−0.867692
$880$			2.34255e8i			0.343749i
$881$		−	6.10080e8i		−	0.892194i	−0.894985	−	0.446097i	$-0.852814\pi$
$881$		−	6.10080e8i		−	0.892194i	0.894985	−	0.446097i	$-0.147186\pi$
$882$			7.67277e8i			1.11827i
$883$	1.34868e9			1.95897			0.979484	−	0.201524i	$-0.0645894\pi$
$883$	1.34868e9			1.95897			0.979484	+	0.201524i	$0.0645894\pi$
$884$		−	7.76182e8i		−	1.12359i
$885$	−1.86890e8	+	2.76728e8i	−0.269623	+	0.399230i
$886$	8.79372e8			1.26436
$887$		−	4.31159e8i		−	0.617827i	−0.951090	−	0.308913i	$-0.900035\pi$
$887$		−	4.31159e8i		−	0.617827i	0.951090	−	0.308913i	$-0.0999653\pi$
$888$	2.89168e8			0.412963
$889$	8.96630e8			1.27617
$890$	−3.18383e8			−0.451626
$891$			2.61582e7i			0.0369807i
$892$	2.67079e8			0.376309
$893$		−	3.55866e8i		−	0.499727i
$894$	−3.48103e8			−0.487187
$895$		−	1.66530e8i		−	0.232287i
$896$			1.25433e9i			1.74376i
$897$	−3.67960e8			−0.509828
$898$			1.12088e9i			1.54786i
$899$		−	3.36985e8i		−	0.463801i
$900$	4.50659e7			0.0618188
$901$	1.57453e8			0.215267
$902$	2.36357e7			0.0322069
$903$		−	7.37846e8i		−	1.00208i
$904$	2.94679e8			0.398882
$905$	1.06711e9			1.43967
$906$	9.06086e8			1.21839
$907$	−9.35019e8			−1.25314			−0.626569	−	0.779366i	$-0.715541\pi$
$907$	−9.35019e8			−1.25314			−0.626569	+	0.779366i	$0.715541\pi$
$908$			3.76589e8i			0.503049i
$909$		−	2.25483e8i		−	0.300208i
$910$	2.08199e9			2.76283
$911$	−3.30454e8			−0.437075			−0.218538	−	0.975829i	$-0.570129\pi$
$911$	−3.30454e8			−0.437075			−0.218538	+	0.975829i	$0.570129\pi$
$912$	−1.59843e8			−0.210722
$913$	2.30411e8			0.302755
$914$	1.12903e9			1.47865
$915$		−	4.57796e7i		−	0.0597598i
$916$			4.01774e8i			0.522751i
$917$			2.55315e9i			3.31107i
$918$			2.54388e8i			0.328828i
$919$			1.09828e9i			1.41503i	0.706696	+	0.707517i	$0.250185\pi$
$919$			1.09828e9i			1.41503i	−0.706696	+	0.707517i	$0.749815\pi$
$920$	2.07467e8			0.266431
$921$	2.77957e8			0.355793
$922$			8.19378e8i			1.04542i
$923$		−	1.66588e9i		−	2.11855i
$924$		−	1.76663e8i		−	0.223939i
$925$		−	3.47917e8i		−	0.439592i
$926$	1.15589e9			1.45574
$927$		−	1.00136e8i		−	0.125705i
$928$		−	8.58652e8i		−	1.07442i
$929$			5.88270e8i			0.733718i	0.930277	+	0.366859i	$0.119567\pi$
$929$			5.88270e8i			0.733718i	−0.930277	+	0.366859i	$0.880433\pi$
$930$	2.28538e8			0.284125
$931$	−6.29010e8			−0.779486
$932$		−	7.65082e6i		−	0.00945062i
$933$	6.74951e8			0.831050
$934$	−1.36271e9			−1.67249
$935$			3.05631e8i			0.373906i
$936$	1.84665e8			0.225194
$937$			1.30988e9i			1.59226i	0.605129	+	0.796128i	$0.293122\pi$
$937$			1.30988e9i			1.59226i	−0.605129	+	0.796128i	$0.706878\pi$
$938$	2.13240e9			2.58380
$939$		−	4.86763e8i		−	0.587923i
$940$			7.17107e8i			0.863376i
$941$			1.68549e8i			0.202282i	0.994872	+	0.101141i	$0.0322494\pi$
$941$			1.68549e8i			0.202282i	−0.994872	+	0.101141i	$0.967751\pi$
$942$	−5.26650e7			−0.0630042
$943$		−	4.13084e7i		−	0.0492610i
$944$	5.82769e8	−	8.62905e8i	0.692757	−	1.02576i
$945$	−2.58675e8			−0.306520
$946$			3.25146e8i			0.384066i
$947$	1.74904e8			0.205944			0.102972	−	0.994684i	$-0.467165\pi$
$947$	1.74904e8			0.205944			0.102972	+	0.994684i	$0.467165\pi$
$948$	−5.23076e8			−0.613960
$949$	−3.75784e8			−0.439683
$950$			9.74564e7i			0.113668i
$951$	−5.37071e6			−0.00624439
$952$			1.09594e9i			1.27021i
$953$	9.23321e8			1.06678			0.533389	−	0.845870i	$-0.320918\pi$
$953$	9.23321e8			1.06678			0.533389	+	0.845870i	$0.320918\pi$
$954$		−	5.87249e7i		−	0.0676359i
$955$		−	1.18071e9i		−	1.35560i
$956$	−1.46133e8			−0.167253
$957$		−	1.68081e8i		−	0.191771i
$958$			1.92482e9i			2.18924i
$959$	3.52372e8			0.399527
$960$	5.47575e7			0.0618913
$961$	6.95823e8			0.784023
$962$			2.23492e9i			2.51036i
$963$	−2.13721e8			−0.239314
$964$	1.44305e8			0.161083
$965$	−2.05243e8			−0.228394
$966$	−8.14466e8			−0.903528
$967$		−	6.06347e7i		−	0.0670567i	−0.999438	−	0.0335283i	$-0.989326\pi$
$967$		−	6.06347e7i		−	0.0670567i	0.999438	−	0.0335283i	$-0.0106744\pi$
$968$			3.98646e8i			0.439503i
$969$	−2.08546e8			−0.229208
$970$	1.29774e9			1.42191
$971$	4.03846e8			0.441121			0.220561	−	0.975373i	$-0.429211\pi$
$971$	4.03846e8			0.441121			0.220561	+	0.975373i	$0.429211\pi$
$972$	3.59674e7			0.0391661
$973$	−2.48768e9			−2.70057
$974$		−	1.42732e8i		−	0.154470i
$975$		−	2.22182e8i		−	0.239715i
$976$			1.42752e8i			0.153544i
$977$		−	1.34243e9i		−	1.43949i	−0.694241	−	0.719743i	$-0.744260\pi$
$977$		−	1.34243e9i		−	1.43949i	0.694241	−	0.719743i	$-0.255740\pi$
$978$		−	5.54598e8i		−	0.592873i
$979$	1.33192e8			0.141948
$980$	1.26752e9			1.34672
$981$		−	2.96967e8i		−	0.314559i
$982$			1.38468e9i			1.46223i
$983$		−	7.90094e8i		−	0.831798i	−0.909411	−	0.415899i	$-0.863467\pi$
$983$		−	7.90094e8i		−	0.831798i	0.909411	−	0.415899i	$-0.136533\pi$
$984$			2.07310e7i			0.0217588i
$985$	6.56398e8			0.686845
$986$		−	1.63459e9i		−	1.70521i
$987$			1.79580e9i			1.86770i
$988$		−	2.37323e8i		−	0.246075i
$989$	5.68261e8			0.587434
$990$	1.13990e8			0.117479
$991$		−	1.73959e9i		−	1.78742i	−0.448650	−	0.893708i	$-0.648095\pi$
$991$		−	1.73959e9i		−	1.78742i	0.448650	−	0.893708i	$-0.351905\pi$
$992$	−4.88410e8			−0.500322
$993$	−2.55617e8			−0.261061
$994$		−	3.68736e9i		−	3.75454i
$995$	−8.45360e8			−0.858169
$996$		−	3.16815e8i		−	0.320647i
$997$	−1.77731e9			−1.79340			−0.896700	−	0.442638i	$-0.854043\pi$
$997$	−1.77731e9			−1.79340			−0.896700	+	0.442638i	$0.854043\pi$
$998$			1.83197e9i			1.84300i
$999$		−	2.77675e8i		−	0.278510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.7.c.a.58.48	yes	60
59.58	odd	2	inner	177.7.c.a.58.13	✓	60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.7.c.a.58.13	✓	60	59.58	odd	2	inner
177.7.c.a.58.48	yes	60	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	177.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+10.1526i q^{2} -15.5885 q^{3} -39.0745 q^{4} -104.301 q^{5} -158.263i q^{6} -654.718 q^{7} +253.057i q^{8} +243.000 q^{9} +O(q^{10})\)	\(q+10.1526i q^{2} -15.5885 q^{3} -39.0745 q^{4} -104.301 q^{5} -158.263i q^{6} -654.718 q^{7} +253.057i q^{8} +243.000 q^{9} -1058.93i q^{10} +442.991i q^{11} +609.112 q^{12} -3003.02i q^{13} -6647.07i q^{14} +1625.90 q^{15} -5069.95 q^{16} -6614.72 q^{17} +2467.07i q^{18} -2022.49 q^{19} +4075.53 q^{20} +10206.1 q^{21} -4497.50 q^{22} +7860.31i q^{23} -3944.78i q^{24} -4746.22 q^{25} +30488.4 q^{26} -3788.00 q^{27} +25582.8 q^{28} +24340.1 q^{29} +16507.0i q^{30} -13844.9i q^{31} -35277.3i q^{32} -6905.55i q^{33} -67156.4i q^{34} +68288.0 q^{35} -9495.11 q^{36} +73303.9i q^{37} -20533.5i q^{38} +46812.5i q^{39} -26394.2i q^{40} -5255.31 q^{41} +103618. i q^{42} -72295.0i q^{43} -17309.7i q^{44} -25345.2 q^{45} -79802.3 q^{46} +175954. i q^{47} +79032.7 q^{48} +311007. q^{49} -48186.3i q^{50} +103113. q^{51} +117342. i q^{52} -23803.5 q^{53} -38457.9i q^{54} -46204.6i q^{55} -165681. i q^{56} +31527.5 q^{57} +247114. i q^{58} +(-114946. + 170200. i) q^{59} -63531.2 q^{60} -28156.5i q^{61} +140561. q^{62} -159097. q^{63} +33678.3 q^{64} +313219. i q^{65} +70109.0 q^{66} +320803. i q^{67} +258467. q^{68} -122530. i q^{69} +693299. i q^{70} +554734. q^{71} +61493.0i q^{72} -125135. i q^{73} -744223. q^{74} +73986.2 q^{75} +79027.9 q^{76} -290035. i q^{77} -475266. q^{78} -858752. q^{79} +528803. q^{80} +59049.0 q^{81} -53354.8i q^{82} -520126. i q^{83} -398797. q^{84} +689925. q^{85} +733979. q^{86} -379424. q^{87} -112102. q^{88} -300665. i q^{89} -257319. i q^{90} +1.96613e6i q^{91} -307138. i q^{92} +215820. i q^{93} -1.78639e6 q^{94} +210949. q^{95} +549919. i q^{96} +1.22552e6i q^{97} +3.15752e6i q^{98} +107647. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9}+O(q^{10}) \) 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9	\( 60 q - 1920 q^{4} - 408 q^{7} + 14580 q^{9} - 1944 q^{12} - 4536 q^{15} + 56616 q^{16} + 8480 q^{17} + 11376 q^{19} + 40796 q^{20} - 8232 q^{22} + 197940 q^{25} + 147252 q^{26} + 71640 q^{28} + 63456 q^{29} - 364432 q^{35} - 466560 q^{36} + 99632 q^{41} - 470316 q^{46} + 171072 q^{48} + 1737420 q^{49} + 60912 q^{51} + 92240 q^{53} + 186624 q^{57} + 917264 q^{59} + 1063368 q^{60} - 115768 q^{62} - 99144 q^{63} - 1107444 q^{64} + 1172232 q^{66} - 4247232 q^{68} + 1498048 q^{71} + 1161448 q^{74} - 1477440 q^{75} - 1045320 q^{76} - 1060452 q^{78} - 90600 q^{79} + 77096 q^{80} + 3542940 q^{81} - 2225880 q^{84} - 693408 q^{85} - 1567768 q^{86} + 1821528 q^{87} + 62892 q^{88} + 5268696 q^{94} + 296128 q^{95}+O(q^{100}) \) 60 * q - 1920 * q^4 - 408 * q^7 + 14580 * q^9 - 1944 * q^12 - 4536 * q^15 + 56616 * q^16 + 8480 * q^17 + 11376 * q^19 + 40796 * q^20 - 8232 * q^22 + 197940 * q^25 + 147252 * q^26 + 71640 * q^28 + 63456 * q^29 - 364432 * q^35 - 466560 * q^36 + 99632 * q^41 - 470316 * q^46 + 171072 * q^48 + 1737420 * q^49 + 60912 * q^51 + 92240 * q^53 + 186624 * q^57 + 917264 * q^59 + 1063368 * q^60 - 115768 * q^62 - 99144 * q^63 - 1107444 * q^64 + 1172232 * q^66 - 4247232 * q^68 + 1498048 * q^71 + 1161448 * q^74 - 1477440 * q^75 - 1045320 * q^76 - 1060452 * q^78 - 90600 * q^79 + 77096 * q^80 + 3542940 * q^81 - 2225880 * q^84 - 693408 * q^85 - 1567768 * q^86 + 1821528 * q^87 + 62892 * q^88 + 5268696 * q^94 + 296128 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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