LMFDB - Embedded newform 49.7.f.a.6.17

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [49,7,Mod(6,49)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("49.6"); S:= CuspForms(chi, 7); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(49, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([9])) N = Newforms(chi, 7, names="a")

Level:	$ N $	$=$	$ 49 = 7^{2} $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	49.f (of order $14$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.2726500974$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			6.17
Character	$\chi$	$=$	49.6
Dual form			49.7.f.a.41.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.86787 - 2.34223i) q^{2} +(13.7924 - 28.6402i) q^{3} +(12.2442 + 53.6454i) q^{4} +(17.8467 - 37.0591i) q^{5} +(-41.3197 - 85.8012i) q^{6} +(329.864 - 94.0163i) q^{7} +(321.266 + 154.714i) q^{8} +(-175.506 - 220.078i) q^{9} +(-53.4657 - 111.023i) q^{10} +(711.951 - 892.758i) q^{11} +(1705.29 + 389.222i) q^{12} +(-594.892 - 474.411i) q^{13} +(395.934 - 948.228i) q^{14} +(-815.230 - 1022.27i) q^{15} +(-2210.39 + 1064.47i) q^{16} +(-1951.36 - 445.385i) q^{17} -843.298 q^{18} -10553.8i q^{19} +(2206.57 + 503.635i) q^{20} +(1856.96 - 10744.1i) q^{21} +(-761.217 - 3335.11i) q^{22} +(364.092 + 1595.19i) q^{23} +(8862.06 - 7067.26i) q^{24} +(8687.16 + 10893.4i) q^{25} +(-2222.36 + 507.240i) q^{26} +(13868.9 - 3165.48i) q^{27} +(9082.46 + 16544.5i) q^{28} +(-1340.62 + 5873.65i) q^{29} -3917.13 q^{30} -33072.8i q^{31} +(-6713.65 + 29414.4i) q^{32} +(-15749.3 - 32703.7i) q^{33} +(-4688.09 + 3738.62i) q^{34} +(2402.82 - 13902.3i) q^{35} +(9657.24 - 12109.8i) q^{36} +(-10955.1 + 47997.6i) q^{37} +(-24719.4 - 19713.1i) q^{38} +(-21792.2 + 10494.6i) q^{39} +(11467.1 - 9144.70i) q^{40} +(-54169.5 + 112484. i) q^{41} +(-21696.6 - 24418.0i) q^{42} +(-57947.3 + 27906.0i) q^{43} +(56609.6 + 27261.8i) q^{44} +(-11288.1 + 2576.44i) q^{45} +(4416.39 + 2126.82i) q^{46} +(24234.2 + 19326.2i) q^{47} +77987.6i q^{48} +(99970.9 - 62025.1i) q^{49} +41741.3 q^{50} +(-39669.9 + 49744.4i) q^{51} +(18166.0 - 37722.0i) q^{52} +(48916.9 + 214319. i) q^{53} +(18490.9 - 38396.8i) q^{54} +(-20378.8 - 42317.0i) q^{55} +(120520. + 20830.1i) q^{56} +(-302262. - 145562. i) q^{57} +(11253.4 + 14111.3i) q^{58} +(78994.6 + 164034. i) q^{59} +(44858.1 - 56250.2i) q^{60} +(-49353.0 - 11264.5i) q^{61} +(-77464.3 - 61775.7i) q^{62} +(-78584.1 - 56095.3i) q^{63} +(-41541.7 - 52091.6i) q^{64} +(-28198.1 + 13579.5i) q^{65} +(-106017. - 24197.7i) q^{66} -85238.5 q^{67} -110135. i q^{68} +(50708.3 + 11573.8i) q^{69} +(-28074.3 - 31595.7i) q^{70} +(-97742.1 - 428236. i) q^{71} +(-22335.2 - 97857.0i) q^{72} +(-204204. + 162847. i) q^{73} +(91958.9 + 115313. i) q^{74} +(431804. - 98556.5i) q^{75} +(566162. - 129223. i) q^{76} +(150913. - 361423. i) q^{77} +(-16124.2 + 70644.9i) q^{78} +104397. q^{79} +100912. i q^{80} +(146288. - 640928. i) q^{81} +(162283. + 336983. i) q^{82} +(157840. - 125873. i) q^{83} +(599107. - 31935.2i) q^{84} +(-51331.0 + 64367.0i) q^{85} +(-42875.8 + 187851. i) q^{86} +(149732. + 119407. i) q^{87} +(366848. - 176665. i) q^{88} +(-546739. + 436010. i) q^{89} +(-15050.1 + 31251.8i) q^{90} +(-240836. - 100561. i) q^{91} +(-81116.7 + 39063.7i) q^{92} +(-947211. - 456153. i) q^{93} +(90532.8 - 20663.5i) q^{94} +(-391114. - 188350. i) q^{95} +(749837. + 597975. i) q^{96} -1.17877e6i q^{97} +(41455.3 - 350010. i) q^{98} -321428. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q - 5 q^{2} - 7 q^{3} - 837 q^{4} - 7 q^{5} - 791 q^{6} + 70 q^{7} - 843 q^{8} + 2990 q^{9} - 7 q^{10} + 1171 q^{11} - 13482 q^{12} - 7 q^{13} + 22533 q^{14} + 6181 q^{15} - 17901 q^{16} - 3143 q^{17}+ \cdots + 4449580 q^{99}+O(q^{100}) $ 162 * q - 5 * q^2 - 7 * q^3 - 837 * q^4 - 7 * q^5 - 791 * q^6 + 70 * q^7 - 843 * q^8 + 2990 * q^9 - 7 * q^10 + 1171 * q^11 - 13482 * q^12 - 7 * q^13 + 22533 * q^14 + 6181 * q^15 - 17901 * q^16 - 3143 * q^17 - 22692 * q^18 + 50169 * q^20 + 28553 * q^21 - 33057 * q^22 - 49677 * q^23 - 119077 * q^24 + 30038 * q^25 + 59577 * q^26 + 11753 * q^27 + 42994 * q^28 + 80383 * q^29 + 27328 * q^30 + 253875 * q^32 - 7 * q^33 + 54677 * q^34 - 74067 * q^35 - 193099 * q^36 + 118463 * q^37 - 121079 * q^38 - 304143 * q^39 - 702079 * q^40 - 58023 * q^41 - 1137479 * q^42 + 93963 * q^43 + 352505 * q^44 + 1333577 * q^45 + 782877 * q^46 + 408261 * q^47 - 149338 * q^49 + 1164004 * q^50 - 911743 * q^51 + 721273 * q^52 - 992325 * q^53 - 576646 * q^54 - 1502935 * q^55 + 1368514 * q^56 + 116032 * q^57 + 2610717 * q^58 + 24493 * q^59 - 1027131 * q^60 + 563101 * q^61 - 262199 * q^62 - 966154 * q^63 - 2839067 * q^64 - 140287 * q^65 - 1523319 * q^66 - 1313660 * q^67 + 2216753 * q^69 + 1806959 * q^70 + 1031011 * q^71 - 3123354 * q^72 - 846727 * q^73 + 1270357 * q^74 + 873173 * q^75 + 5463990 * q^76 + 1565235 * q^77 + 1006005 * q^78 + 82420 * q^79 + 2259538 * q^81 - 7672672 * q^82 - 3860031 * q^83 - 9104942 * q^84 + 1596833 * q^85 + 224039 * q^86 + 2590525 * q^87 + 4179421 * q^88 + 5417433 * q^89 + 6759578 * q^90 - 6163507 * q^91 - 7060306 * q^92 + 1903160 * q^93 + 4029998 * q^94 + 2115400 * q^95 + 957950 * q^96 - 1546783 * q^98 + 4449580 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/49\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{9}{14}\right)$

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 $

$2$	1.86787	−	2.34223i	0.233484	−	0.292779i	−0.651262	−	0.758853i	$-0.725760\pi$
$2$	1.86787	−	2.34223i	0.233484	−	0.292779i	0.884746	+	0.466073i	$0.154332\pi$
$3$	13.7924	−	28.6402i	0.510829	−	1.06075i	−0.472904	−	0.881114i	$-0.656794\pi$
$3$	13.7924	−	28.6402i	0.510829	−	1.06075i	0.983734	−	0.179634i	$-0.0574913\pi$
$4$	12.2442	+	53.6454i	0.191316	+	0.838209i
$5$	17.8467	−	37.0591i	0.142774	−	0.296473i	−0.817304	−	0.576207i	$-0.804532\pi$
$5$	17.8467	−	37.0591i	0.142774	−	0.296473i	0.960077	+	0.279734i	$0.0902464\pi$
$6$	−41.3197	−	85.8012i	−0.191295	−	0.397228i
$7$	329.864	−	94.0163i	0.961701	−	0.274100i
$7$	329.864	−	94.0163i	0.961701	−	0.274100i
$8$	321.266	+	154.714i	0.627473	+	0.302175i
$9$	−175.506	−	220.078i	−0.240750	−	0.301890i
$10$	−53.4657	−	111.023i	−0.0534657	−	0.111023i
$11$	711.951	−	892.758i	0.534899	−	0.670742i	−0.438799	−	0.898585i	$-0.644596\pi$
$11$	711.951	−	892.758i	0.534899	−	0.670742i	0.973698	+	0.227843i	$0.0731673\pi$
$12$	1705.29	+	389.222i	0.986859	+	0.225244i
$13$	−594.892	−	474.411i	−0.270775	−	0.215936i	0.478683	−	0.877988i	$-0.341114\pi$
$13$	−594.892	−	474.411i	−0.270775	−	0.215936i	−0.749458	+	0.662052i	$0.769686\pi$
$14$	395.934	−	948.228i	0.144291	−	0.345564i
$15$	−815.230	−	1022.27i	−0.241550	−	0.302894i
$16$	−2210.39	+	1064.47i	−0.539647	+	0.259880i
$17$	−1951.36	−	445.385i	−0.397183	−	0.0906545i	0.0192639	−	0.999814i	$-0.493868\pi$
$17$	−1951.36	−	445.385i	−0.397183	−	0.0906545i	−0.416447	+	0.909160i	$0.636725\pi$
$18$	−843.298			−0.144598
$19$		−	10553.8i		−	1.53868i	−0.638842	−	0.769338i	$-0.720586\pi$
$19$		−	10553.8i		−	1.53868i	0.638842	−	0.769338i	$-0.279414\pi$
$20$	2206.57	+	503.635i	0.275821	+	0.0629544i
$21$	1856.96	−	10744.1i	0.200514	−	1.16014i
$22$	−761.217	−	3335.11i	−0.0714892	−	0.313215i
$23$	364.092	+	1595.19i	0.0299245	+	0.131108i	0.987684	−	0.156463i	$-0.0500093\pi$
$23$	364.092	+	1595.19i	0.0299245	+	0.131108i	−0.957759	+	0.287571i	$0.907152\pi$
$24$	8862.06	−	7067.26i	0.641063	−	0.511231i
$25$	8687.16	+	10893.4i	0.555978	+	0.697174i
$26$	−2222.36	+	507.240i	−0.126443	+	0.0288598i
$27$	13868.9	−	3165.48i	0.704611	−	0.160823i
$28$	9082.46	+	16544.5i	0.413742	+	0.753667i
$29$	−1340.62	+	5873.65i	−0.0549683	+	0.240832i	−0.994947	−	0.100401i	$-0.967987\pi$
$29$	−1340.62	+	5873.65i	−0.0549683	+	0.240832i	0.939979	+	0.341233i	$0.110845\pi$
$30$	−3917.13			−0.145079
$31$		−	33072.8i		−	1.11016i	−0.831797	−	0.555080i	$-0.812688\pi$
$31$		−	33072.8i		−	1.11016i	0.831797	−	0.555080i	$-0.187312\pi$
$32$	−6713.65	+	29414.4i	−0.204884	+	0.897657i
$33$	−15749.3	−	32703.7i	−0.438246	−	0.910028i
$34$	−4688.09	+	3738.62i	−0.119278	+	0.0951207i
$35$	2402.82	−	13902.3i	0.0560425	−	0.324252i
$36$	9657.24	−	12109.8i	0.206988	−	0.259555i
$37$	−10955.1	+	47997.6i	−0.216278	+	0.947577i	0.743922	+	0.668266i	$0.232963\pi$
$37$	−10955.1	+	47997.6i	−0.216278	+	0.947577i	−0.960201	+	0.279311i	$0.909894\pi$
$38$	−24719.4	−	19713.1i	−0.450493	−	0.359256i
$39$	−21792.2	+	10494.6i	−0.367373	+	0.176918i
$40$	11467.1	−	9144.70i	0.179173	−	0.142886i
$41$	−54169.5	+	112484.i	−0.785965	+	1.63207i	−0.0111054	+	0.999938i	$0.503535\pi$
$41$	−54169.5	+	112484.i	−0.785965	+	1.63207i	−0.774859	+	0.632134i	$0.782179\pi$
$42$	−21696.6	−	24418.0i	−0.292848	−	0.329580i
$43$	−57947.3	+	27906.0i	−0.728833	+	0.350988i	−0.761225	−	0.648488i	$-0.775402\pi$
$43$	−57947.3	+	27906.0i	−0.728833	+	0.350988i	0.0323920	+	0.999475i	$0.489687\pi$
$44$	56609.6	+	27261.8i	0.664557	+	0.320034i
$45$	−11288.1	+	2576.44i	−0.123875	+	0.0282737i
$46$	4416.39	+	2126.82i	0.0453726	+	0.0218503i
$47$	24234.2	+	19326.2i	0.233419	+	0.186145i	0.733213	−	0.679999i	$-0.238020\pi$
$47$	24234.2	+	19326.2i	0.233419	+	0.186145i	−0.499794	+	0.866144i	$0.666591\pi$
$48$			77987.6i			0.705183i
$49$	99970.9	−	62025.1i	0.849738	−	0.527205i
$50$	41741.3			0.333930
$51$	−39669.9	+	49744.4i	−0.299054	+	0.375002i
$52$	18166.0	−	37722.0i	0.129196	−	0.268278i
$53$	48916.9	+	214319.i	0.328573	+	1.43957i	0.821852	+	0.569701i	$0.192941\pi$
$53$	48916.9	+	214319.i	0.328573	+	1.43957i	−0.493280	+	0.869871i	$0.664202\pi$
$54$	18490.9	−	38396.8i	0.117430	−	0.243845i
$55$	−20378.8	−	42317.0i	−0.122487	−	0.254347i
$56$	120520.	+	20830.1i	0.686268	+	0.118612i
$57$	−302262.	−	145562.i	−1.63215	−	0.786001i
$58$	11253.4	+	14111.3i	0.0576764	+	0.0723239i
$59$	78994.6	+	164034.i	0.384628	+	0.798689i	0.999946	+	0.0104096i	$0.00331353\pi$
$59$	78994.6	+	164034.i	0.384628	+	0.798689i	−0.615317	+	0.788279i	$0.710972\pi$
$60$	44858.1	−	56250.2i	0.207676	−	0.260418i
$61$	−49353.0	−	11264.5i	−0.217432	−	0.0496275i	0.112417	−	0.993661i	$-0.464141\pi$
$61$	−49353.0	−	11264.5i	−0.217432	−	0.0496275i	−0.329849	+	0.944034i	$0.606998\pi$
$62$	−77464.3	−	61775.7i	−0.325032	−	0.259204i
$63$	−78584.1	−	56095.3i	−0.314277	−	0.224339i
$64$	−41541.7	−	52091.6i	−0.158469	−	0.198714i
$65$	−28198.1	+	13579.5i	−0.102679	+	0.0494474i
$66$	−106017.	−	24197.7i	−0.368761	−	0.0841672i
$67$	−85238.5			−0.283408			−0.141704	−	0.989909i	$-0.545258\pi$
$67$	−85238.5			−0.283408			−0.141704	+	0.989909i	$0.545258\pi$
$68$		−	110135.i		−	0.350266i
$69$	50708.3	+	11573.8i	0.154359	+	0.0352314i
$70$	−28074.3	−	31595.7i	−0.0818494	−	0.0921157i
$71$	−97742.1	−	428236.i	−0.273091	−	1.19649i	−0.906343	−	0.422543i	$-0.861138\pi$
$71$	−97742.1	−	428236.i	−0.273091	−	1.19649i	0.633252	−	0.773945i	$-0.281720\pi$
$72$	−22335.2	−	97857.0i	−0.0598401	−	0.262177i
$73$	−204204.	+	162847.i	−0.524924	+	0.418613i	−0.849770	−	0.527154i	$-0.823259\pi$
$73$	−204204.	+	162847.i	−0.524924	+	0.418613i	0.324846	+	0.945767i	$0.394688\pi$
$74$	91958.9	+	115313.i	0.226934	+	0.284566i
$75$	431804.	−	98556.5i	1.02354	−	0.233615i
$76$	566162.	−	129223.i	1.28973	−	0.294373i
$77$	150913.	−	361423.i	0.330563	−	0.791669i
$78$	−16124.2	+	70644.9i	−0.0339778	+	0.148867i
$79$	104397.			0.211743			0.105871	−	0.994380i	$-0.466237\pi$
$79$	104397.			0.211743			0.105871	+	0.994380i	$0.466237\pi$
$80$			100912.i			0.197095i
$81$	146288.	−	640928.i	0.275266	−	1.20602i
$82$	162283.	+	336983.i	0.294327	+	0.611176i
$83$	157840.	−	125873.i	0.276047	−	0.220140i	−0.475673	−	0.879622i	$-0.657796\pi$
$83$	157840.	−	125873.i	0.276047	−	0.220140i	0.751721	+	0.659482i	$0.229224\pi$
$84$	599107.	−	31935.2i	1.01080	−	0.0538805i
$85$	−51331.0	+	64367.0i	−0.0835839	+	0.104811i
$86$	−42875.8	+	187851.i	−0.0674088	+	0.295337i
$87$	149732.	+	119407.i	0.227382	+	0.181331i
$88$	366848.	−	176665.i	0.538317	−	0.259240i
$89$	−546739.	+	436010.i	−0.775550	+	0.618480i	−0.929171	−	0.369649i	$-0.879478\pi$
$89$	−546739.	+	436010.i	−0.775550	+	0.618480i	0.153621	+	0.988130i	$0.450906\pi$
$90$	−15050.1	+	31251.8i	−0.0206449	+	0.0428695i
$91$	−240836.	−	100561.i	−0.319592	−	0.133446i
$92$	−81116.7	+	39063.7i	−0.104171	+	0.0501661i
$93$	−947211.	−	456153.i	−1.17760	−	0.567103i
$94$	90532.8	−	20663.5i	0.108999	−	0.0248783i
$95$	−391114.	−	188350.i	−0.456176	−	0.219683i
$96$	749837.	+	597975.i	0.847526	+	0.675880i
$97$		−	1.17877e6i		−	1.29156i	−0.763525	−	0.645778i	$-0.776533\pi$
$97$		−	1.17877e6i		−	1.29156i	0.763525	−	0.645778i	$-0.223467\pi$
$98$	41455.3	−	350010.i	0.0440455	−	0.371880i
$99$	−321428.			−0.331267
$100$	−478011.	+	599407.i	−0.478011	+	0.599407i
$101$	−689735.	+	1.43225e6i	−0.669450	+	1.39013i	0.238539	+	0.971133i	$0.423332\pi$
$101$	−689735.	+	1.43225e6i	−0.669450	+	1.39013i	−0.907989	+	0.418994i	$0.862383\pi$
$102$	42415.0	+	185832.i	0.0399686	+	0.175114i
$103$	−349424.	+	725586.i	−0.319772	+	0.664014i	−0.997452	−	0.0713431i	$-0.977271\pi$
$103$	−349424.	+	725586.i	−0.319772	+	0.664014i	0.677679	+	0.735358i	$0.262986\pi$
$104$	−117721.	−	244450.i	−0.104654	−	0.217315i
$105$	−365024.	−	260563.i	−0.315322	−	0.225085i
$106$	593356.	+	285745.i	0.498193	+	0.239917i
$107$	−893323.	−	1.12019e6i	−0.729218	−	0.914410i	0.269602	−	0.962972i	$-0.413108\pi$
$107$	−893323.	−	1.12019e6i	−0.729218	−	0.914410i	−0.998820	+	0.0485614i	$0.984536\pi$
$108$	339627.	+	705242.i	0.269607	+	0.559844i
$109$	−680934.	+	853864.i	−0.525806	+	0.659340i	−0.971830	−	0.235681i	$-0.924268\pi$
$109$	−680934.	+	853864.i	−0.525806	+	0.659340i	0.446025	+	0.895021i	$0.352839\pi$
$110$	−137181.	−	31310.8i	−0.103066	−	0.0235242i
$111$	1.22356e6	+	975759.i	0.894659	+	0.713467i
$112$	−629050.	+	558942.i	−0.447746	+	0.397844i
$113$	−236245.	−	296242.i	−0.163730	−	0.205311i	0.693198	−	0.720747i	$-0.256201\pi$
$113$	−236245.	−	296242.i	−0.163730	−	0.205311i	−0.856928	+	0.515437i	$0.827630\pi$
$114$	−905527.	+	436079.i	−0.611205	+	0.294341i
$115$	65614.2	+	14976.0i	0.0431424	+	0.00984697i
$116$	−331509.			−0.212384
$117$			214185.i			0.133731i
$118$	531758.	+	121370.i	0.323644	+	0.0738696i
$119$	−685556.	+	36543.3i	−0.406820	+	0.0216854i
$120$	−103747.	−	454547.i	−0.0600390	−	0.263048i
$121$	104066.	+	455945.i	0.0587428	+	0.257369i
$122$	−118569.	+	94555.6i	−0.0652968	+	0.0520724i
$123$	2.47444e6	+	3.10285e6i	1.32972	+	1.66742i
$124$	1.77420e6	−	404950.i	0.930547	−	0.212391i
$125$	1.18532e6	−	270541.i	0.606882	−	0.138517i
$126$	−278173.	+	79283.7i	−0.139060	+	0.0396344i
$127$	544820.	−	2.38701e6i	0.265976	−	1.16531i	−0.648674	−	0.761067i	$-0.724676\pi$
$127$	544820.	−	2.38701e6i	0.265976	−	1.16531i	0.914649	−	0.404248i	$-0.132467\pi$
$128$	−2.13054e6			−1.01592
$129$			2.04451e6i			0.952403i
$130$	−20864.0	+	91411.3i	−0.00949660	+	0.0416073i
$131$	458827.	+	952764.i	0.204096	+	0.423810i	0.977743	−	0.209807i	$-0.0672837\pi$
$131$	458827.	+	952764.i	0.204096	+	0.423810i	−0.773647	+	0.633617i	$0.781569\pi$
$132$	1.56156e6	−	1.24531e6i	0.678950	−	0.541445i
$133$	−992228.	−	3.48131e6i	−0.421751	−	1.47975i
$134$	−159214.	+	199649.i	−0.0661711	+	0.0829759i
$135$	130204.	−	570461.i	0.0529204	−	0.231859i
$136$	−557999.	−	444990.i	−0.221828	−	0.176902i
$137$	−434536.	+	209261.i	−0.168991	+	0.0813818i	−0.516467	−	0.856307i	$-0.672753\pi$
$137$	−434536.	+	209261.i	−0.168991	+	0.0813818i	0.347476	+	0.937689i	$0.387039\pi$
$138$	121825.	−	97152.3i	0.0463553	−	0.0369671i
$139$	1.29739e6	−	2.69405e6i	0.483087	−	1.00314i	−0.506903	−	0.862003i	$-0.669210\pi$
$139$	1.29739e6	−	2.69405e6i	0.483087	−	1.00314i	0.989990	−	0.141137i	$-0.0450759\pi$
$140$	775216.	−	41322.6i	0.282513	−	0.0150593i
$141$	887753.	−	427519.i	0.316690	−	0.152510i
$142$	−1.18560e6	−	570955.i	−0.414069	−	0.199405i
$143$	−847068.	+	193338.i	−0.289674	+	0.0661163i
$144$	622204.	+	299638.i	0.208375	+	0.100348i
$145$	193746.	+	154508.i	0.0635520	+	0.0506810i
$146$			782472.i			0.251426i
$147$	−397573.	−	3.71866e6i	−0.125160	−	1.17067i
$148$	−2.70899e6			−0.835646
$149$	−2.58540e6	+	3.24200e6i	−0.781573	+	0.980062i	0.218418	+	0.975855i	$0.429910\pi$
$149$	−2.58540e6	+	3.24200e6i	−0.781573	+	0.980062i	−0.999991	+	0.00420667i	$0.998661\pi$
$150$	575712.	−	1.19548e6i	0.170581	−	0.354216i
$151$	1.30344e6	+	5.71073e6i	0.378581	+	1.65867i	0.701819	+	0.712355i	$0.252371\pi$
$151$	1.30344e6	+	5.71073e6i	0.378581	+	1.65867i	−0.323238	+	0.946318i	$0.604771\pi$
$152$	1.63282e6	−	3.39058e6i	0.464950	−	0.965479i
$153$	244457.	+	507620.i	0.0682540	+	0.141731i
$154$	−564653.	−	1.02856e6i	−0.154603	−	0.281624i
$155$	−1.22565e6	−	590241.i	−0.329132	−	0.158502i
$156$	−829814.	−	1.04055e6i	−0.218578	−	0.274088i
$157$	−188542.	−	391512.i	−0.0487202	−	0.101169i	0.875188	−	0.483784i	$-0.160738\pi$
$157$	−188542.	−	391512.i	−0.0487202	−	0.101169i	−0.923908	+	0.382615i	$0.875024\pi$
$158$	195001.	−	244523.i	0.0494385	−	0.0619939i
$159$	6.81282e6	+	1.55498e6i	1.69487	+	0.386842i
$160$	970255.	+	773752.i	0.236879	+	0.188904i
$161$	270075.	+	491965.i	0.0647152	+	0.117884i
$162$	−1.22796e6	−	1.53981e6i	−0.288827	−	0.362178i
$163$	4.50899e6	−	2.17142e6i	1.04116	−	0.501395i	0.166452	−	0.986050i	$-0.446769\pi$
$163$	4.50899e6	−	2.17142e6i	1.04116	−	0.501395i	0.874706	+	0.484654i	$0.161055\pi$
$164$	−6.69752e6	−	1.52866e6i	−1.51839	−	0.346562i
$165$	−1.49304e6			−0.332368
$166$		−	604814.i		−	0.132220i
$167$	−4.65251e6	−	1.06190e6i	−0.998936	−	0.228001i	−0.308367	−	0.951267i	$-0.599783\pi$
$167$	−4.65251e6	−	1.06190e6i	−0.998936	−	0.228001i	−0.690569	+	0.723267i	$0.742640\pi$
$168$	2.25883e6	−	3.16441e6i	0.476383	−	0.667367i
$169$	−945235.	−	4.14134e6i	−0.195830	−	0.857988i
$170$	54883.0	+	240458.i	0.0111710	+	0.0489433i
$171$	−2.32266e6	+	1.85226e6i	−0.464512	+	0.370436i
$172$	−2.20655e6	−	2.76692e6i	−0.433638	−	0.543765i
$173$	4.49404e6	−	1.02573e6i	0.867957	−	0.198106i	0.234720	−	0.972063i	$-0.424583\pi$
$173$	4.49404e6	−	1.02573e6i	0.867957	−	0.198106i	0.633238	+	0.773957i	$0.281726\pi$
$174$	559360.	−	127670.i	0.106180	−	0.0242349i
$175$	3.88973e6	+	2.77658e6i	0.725780	+	0.518080i
$176$	−623377.	+	2.73119e6i	−0.114344	+	0.500973i
$177$	5.78749e6			1.04369
$178$			2.09500e6i			0.371470i
$179$	−944880.	+	4.13979e6i	−0.164747	+	0.721804i	0.823294	+	0.567615i	$0.192134\pi$
$179$	−944880.	+	4.13979e6i	−0.164747	+	0.721804i	−0.988041	+	0.154189i	$0.950724\pi$
$180$	−276428.	−	574009.i	−0.0473985	−	0.0984240i
$181$	3.79593e6	−	3.02716e6i	0.640152	−	0.510504i	−0.248770	−	0.968563i	$-0.580026\pi$
$181$	3.79593e6	−	3.02716e6i	0.640152	−	0.510504i	0.888922	+	0.458059i	$0.151455\pi$
$182$	−685388.	+	376258.i	−0.113690	+	0.0624125i
$183$	−1.00331e6	+	1.25811e6i	−0.163713	+	0.205290i
$184$	−129827.	+	568811.i	−0.0208407	+	0.0913092i
$185$	1.58323e6	+	1.26259e6i	0.250052	+	0.199410i
$186$	−2.83768e6	+	1.36656e6i	−0.440986	+	0.212368i
$187$	−1.78689e6	+	1.42500e6i	−0.273259	+	0.217917i
$188$	−740031.	+	1.53669e6i	−0.111372	+	0.231266i
$189$	4.27723e6	−	2.34807e6i	0.633544	−	0.347798i
$190$	−1.17171e6	+	564266.i	−0.170828	+	0.0822665i
$191$	−4.98672e6	−	2.40148e6i	−0.715673	−	0.344650i	0.0403585	−	0.999185i	$-0.487150\pi$
$191$	−4.98672e6	−	2.40148e6i	−0.715673	−	0.344650i	−0.756031	+	0.654535i	$0.772864\pi$
$192$	−2.06487e6	+	471293.i	−0.291736	+	0.0665867i
$193$	9.63487e6	+	4.63991e6i	1.34021	+	0.645413i	0.960134	−	0.279541i	$-0.0901823\pi$
$193$	9.63487e6	+	4.63991e6i	1.34021	+	0.645413i	0.380080	+	0.924954i	$0.375897\pi$
$194$	−2.76095e6	−	2.20179e6i	−0.378141	−	0.301557i
$195$			994893.i			0.134175i
$196$	4.55143e6	+	4.60353e6i	0.604476	+	0.611396i
$197$	−9.12979e6			−1.19416			−0.597080	−	0.802182i	$-0.703672\pi$
$197$	−9.12979e6			−1.19416			−0.597080	+	0.802182i	$0.703672\pi$
$198$	−600387.	+	752861.i	−0.0773456	+	0.0969883i
$199$	1.17414e6	−	2.43812e6i	0.148991	−	0.309383i	−0.813094	−	0.582132i	$-0.802219\pi$
$199$	1.17414e6	−	2.43812e6i	0.148991	−	0.309383i	0.962085	+	0.272749i	$0.0879329\pi$
$200$	1.10554e6	+	4.84369e6i	0.138193	+	0.605461i
$201$	−1.17564e6	+	2.44125e6i	−0.144773	+	0.300624i
$202$	2.06633e6	+	4.29078e6i	0.250695	+	0.520573i
$203$	109996.	+	2.06354e6i	0.0131489	+	0.246675i
$204$	−3.15429e6	−	1.51902e6i	−0.371544	−	0.178926i
$205$	3.20181e6	+	4.01494e6i	0.371650	+	0.466034i
$206$	1.04682e6	+	2.17373e6i	0.119748	+	0.248659i
$207$	287166.	−	360095.i	0.0323759	−	0.0405981i
$208$	1.81994e6	+	415390.i	0.202240	+	0.0461600i
$209$	−9.42197e6	−	7.51377e6i	−1.03206	−	0.823037i
$210$	−1.29212e6	+	368274.i	−0.139523	+	0.0397661i
$211$	1.13509e6	+	1.42336e6i	0.120833	+	0.151519i	0.838569	−	0.544796i	$-0.183393\pi$
$211$	1.13509e6	+	1.42336e6i	0.120833	+	0.151519i	−0.717736	+	0.696315i	$0.754821\pi$
$212$	−1.08983e7	+	5.24834e6i	−1.14380	+	0.550826i
$213$	−1.36129e7	−	3.10705e6i	−1.40868	−	0.321521i
$214$	−4.29236e6			−0.437981
$215$			2.64550e6i			0.266191i
$216$	4.94534e6	+	1.12874e6i	0.490721	+	0.112004i
$217$	−3.10938e6	−	1.09095e7i	−0.304295	−	1.06764i
$218$	728054.	+	3.18981e6i	0.0702739	+	0.307890i
$219$	1.84752e6	+	8.09450e6i	0.175896	+	0.770651i
$220$	2.02059e6	−	1.61137e6i	0.189763	−	0.151331i
$221$	949554.	+	1.19070e6i	0.0879717	+	0.110313i
$222$	4.57092e6	−	1.04328e6i	0.417777	−	0.0953548i
$223$	−3.89221e6	+	888373.i	−0.350980	+	0.0801089i	−0.394376	−	0.918949i	$-0.629039\pi$
$223$	−3.89221e6	+	888373.i	−0.350980	+	0.0801089i	0.0433964	+	0.999058i	$0.486182\pi$
$224$	550847.	+	1.03339e7i	0.0490102	+	0.919436i
$225$	872736.	−	3.82371e6i	0.0766188	−	0.335689i
$226$	−1.13514e6			−0.0983390
$227$			1.93920e7i			1.65785i	0.559359	+	0.828925i	$0.311047\pi$
$227$			1.93920e7i			1.65785i	−0.559359	+	0.828925i	$0.688953\pi$
$228$	4.10776e6	−	1.79973e7i	0.346578	−	1.51846i
$229$	6.13496e6	+	1.27394e7i	0.510864	+	1.06082i	0.983725	+	0.179683i	$0.0575071\pi$
$229$	6.13496e6	+	1.27394e7i	0.510864	+	1.06082i	−0.472861	+	0.881137i	$0.656779\pi$
$230$	157636.	−	125711.i	0.0129560	−	0.0103321i
$231$	−8.26978e6	−	9.30706e6i	−0.670901	−	0.755052i
$232$	−1.33943e6	+	1.67959e6i	−0.107265	+	0.134505i
$233$	5.47687e6	−	2.39958e7i	0.432977	−	1.89700i	−0.00897793	−	0.999960i	$-0.502858\pi$
$233$	5.47687e6	−	2.39958e7i	0.432977	−	1.89700i	0.441955	−	0.897037i	$-0.354285\pi$
$234$	501671.	+	400070.i	0.0391536	+	0.0312240i
$235$	1.14871e6	−	553190.i	0.0885130	−	0.0426256i
$236$	−7.83244e6	+	6.24616e6i	−0.595883	+	0.475201i
$237$	1.43989e6	−	2.98996e6i	0.108164	−	0.224606i
$238$	−1.19494e6	+	1.67399e6i	−0.0886368	+	0.124172i
$239$	1.26316e7	−	6.08308e6i	0.925265	−	0.445584i	0.0903171	−	0.995913i	$-0.471212\pi$
$239$	1.26316e7	−	6.08308e6i	0.925265	−	0.445584i	0.834948	+	0.550329i	$0.185498\pi$
$240$	2.89015e6	+	1.39182e6i	0.209068	+	0.100682i
$241$	2.38111e7	−	5.43474e6i	1.70110	−	0.388264i	0.741791	−	0.670631i	$-0.233977\pi$
$241$	2.38111e7	−	5.43474e6i	1.70110	−	0.388264i	0.959306	+	0.282367i	$0.0911196\pi$
$242$	1.26231e6	+	607898.i	0.0890678	+	0.0428928i
$243$	−8.23073e6	−	6.56379e6i	−0.573614	−	0.457442i
$244$		−	2.78549e6i		−	0.191748i
$245$	−514442.	−	4.81177e6i	−0.0349814	−	0.327195i
$246$	1.18895e7			0.798655
$247$	−5.00683e6	+	6.27837e6i	−0.332255	+	0.416635i
$248$	5.11682e6	−	1.06252e7i	0.335463	−	0.696596i
$249$	−1.42804e6	−	6.25667e6i	−0.0925003	−	0.405270i
$250$	1.58035e6	−	3.28162e6i	0.101142	−	0.210024i
$251$	1.24896e6	+	2.59350e6i	0.0789820	+	0.164008i	0.936720	−	0.350079i	$-0.113845\pi$
$251$	1.24896e6	+	2.59350e6i	0.0789820	+	0.164008i	−0.857738	+	0.514087i	$0.828131\pi$
$252$	2.04705e6	−	4.90252e6i	0.127917	−	0.306350i
$253$	1.68334e6	+	810651.i	0.103946	+	0.0500579i
$254$	−4.57329e6	−	5.73472e6i	−0.279079	−	0.349954i
$255$	1.13551e6	+	2.35790e6i	0.0684808	+	0.142202i
$256$	−1.32091e6	+	1.65636e6i	−0.0787321	+	0.0987270i
$257$	−1.10544e7	−	2.52309e6i	−0.651230	−	0.148639i	−0.115872	−	0.993264i	$-0.536966\pi$
$257$	−1.10544e7	−	2.52309e6i	−0.651230	−	0.148639i	−0.535358	+	0.844625i	$0.679823\pi$
$258$	4.78873e6	+	3.81888e6i	0.278844	+	0.222371i
$259$	898857.	+	1.68626e7i	0.0517358	+	0.970568i
$260$	−1.07374e6	−	1.34643e6i	−0.0610913	−	0.0766061i
$261$	1.52795e6	−	735822.i	0.0859384	−	0.0413858i
$262$	3.08862e6	+	704958.i	0.171736	+	0.0391976i
$263$	−2.09116e7			−1.14953			−0.574765	−	0.818318i	$-0.694907\pi$
$263$	−2.09116e7			−1.14953			−0.574765	+	0.818318i	$0.694907\pi$
$264$		−	1.29432e7i		−	0.703445i
$265$	8.81547e6	+	2.01207e6i	0.473705	+	0.108120i
$266$	−1.00074e7	−	4.17860e6i	−0.531711	−	0.222017i
$267$	4.94656e6	+	2.16723e7i	0.259878	+	1.13860i
$268$	−1.04368e6	−	4.57266e6i	−0.0542204	−	0.237555i
$269$	2.24180e7	−	1.78778e7i	1.15170	−	0.918453i	0.154128	−	0.988051i	$-0.450743\pi$
$269$	2.24180e7	−	1.78778e7i	1.15170	−	0.918453i	0.997575	+	0.0695981i	$0.0221717\pi$
$270$	−1.09295e6	−	1.37051e6i	−0.0555276	−	0.0696294i
$271$	−2.03359e7	+	4.64155e6i	−1.02178	+	0.233214i	−0.700410	−	0.713740i	$-0.747000\pi$
$271$	−2.03359e7	+	4.64155e6i	−1.02178	+	0.233214i	−0.321368	+	0.946954i	$0.604143\pi$
$272$	4.78737e6	−	1.09269e6i	0.237898	−	0.0542986i
$273$	−6.20179e6	+	5.51060e6i	−0.304810	+	0.270839i
$274$	−321517.	+	1.40866e6i	−0.0156298	+	0.0684784i
$275$	1.59100e7			0.765017
$276$			2.86198e6i			0.136125i
$277$	8.35819e6	−	3.66196e7i	0.393254	−	1.72296i	−0.259816	−	0.965658i	$-0.583662\pi$
$277$	8.35819e6	−	3.66196e7i	0.393254	−	1.72296i	0.653069	−	0.757298i	$-0.273481\pi$
$278$	−3.88675e6	−	8.07093e6i	−0.180906	−	0.375655i
$279$	−7.27860e6	+	5.80449e6i	−0.335147	+	0.267271i
$280$	2.92283e6	−	4.09460e6i	0.133146	−	0.186525i
$281$	1.44242e7	−	1.80874e7i	0.650089	−	0.815186i	−0.342135	−	0.939651i	$-0.611150\pi$
$281$	1.44242e7	−	1.80874e7i	0.650089	−	0.815186i	0.992224	+	0.124465i	$0.0397214\pi$
$282$	656856.	−	2.87788e6i	0.0292903	−	0.128329i
$283$	−3.70696e6	−	2.95620e6i	−0.163553	−	0.130429i	0.538293	−	0.842757i	$-0.319069\pi$
$283$	−3.70696e6	−	2.95620e6i	−0.163553	−	0.130429i	−0.701846	+	0.712328i	$0.747641\pi$
$284$	2.17761e7	−	1.04868e7i	0.950661	−	0.457814i
$285$	−1.07888e7	+	8.60376e6i	−0.466056	+	0.371667i
$286$	−1.12937e6	+	2.34516e6i	−0.0482768	+	0.100248i
$287$	−7.29320e6	+	4.21972e7i	−0.308512	+	1.78500i
$288$	7.65176e6	−	3.68489e6i	0.320320	−	0.154258i
$289$	−1.81378e7	−	8.73468e6i	−0.751433	−	0.361871i
$290$	723786.	−	165199.i	0.0296767	−	0.00677352i
$291$	−3.37602e7	−	1.62580e7i	−1.37002	−	0.659765i
$292$	−1.12363e7	−	8.96068e6i	−0.451311	−	0.359909i
$293$			1.00356e7i			0.398969i	0.979901	+	0.199485i	$0.0639268\pi$
$293$			1.00356e7i			0.398969i	−0.979901	+	0.199485i	$0.936073\pi$
$294$	−9.45259e6	−	6.01476e6i	−0.371971	−	0.236688i
$295$	7.48874e6			0.291704
$296$	−1.09454e7	+	1.37251e7i	−0.422043	+	0.529225i
$297$	7.04794e6	−	1.46352e7i	0.269025	−	0.558637i
$298$	2.76431e6	+	1.21113e7i	0.104457	+	0.457657i
$299$	540180.	−	1.12170e6i	0.0202081	−	0.0419625i
$300$	1.05742e7	+	2.19576e7i	0.391637	+	0.813243i
$301$	−1.64911e7	+	1.46532e7i	−0.604714	+	0.537318i
$302$	1.58105e7	+	7.61394e6i	0.574018	+	0.276432i
$303$	3.15068e7	+	3.95083e7i	1.13260	+	1.42024i
$304$	1.12342e7	+	2.33280e7i	0.399871	+	0.830342i
$305$	−1.29824e6	+	1.62794e6i	−0.0457568	+	0.0573772i
$306$	1.64558e6	+	375593.i	0.0574321	+	0.0131085i
$307$	−1.20201e7	−	9.58573e6i	−0.415426	−	0.331291i	0.393370	−	0.919380i	$-0.371309\pi$
$307$	−1.20201e7	−	9.58573e6i	−0.415426	−	0.331291i	−0.808796	+	0.588089i	$0.799881\pi$
$308$	2.12365e7	+	3.67043e6i	0.726827	+	0.125622i
$309$	1.59615e7	+	2.00151e7i	0.541003	+	0.678396i
$310$	−3.67183e6	+	1.76826e6i	−0.123253	+	0.0593556i
$311$	−4.32431e7	−	9.86996e6i	−1.43759	−	0.328121i	−0.568465	−	0.822708i	$-0.692462\pi$
$311$	−4.32431e7	−	9.86996e6i	−1.43759	−	0.328121i	−0.869128	+	0.494586i	$0.835320\pi$
$312$	−8.62476e6			−0.283977
$313$		−	2.35607e7i		−	0.768344i	−0.923262	−	0.384172i	$-0.874487\pi$
$313$		−	2.35607e7i		−	0.768344i	0.923262	−	0.384172i	$-0.125513\pi$
$314$	−1.26918e6	−	289683.i	−0.0409955	−	0.00935695i
$315$	−3.48131e6	+	1.91114e6i	−0.111381	+	0.0611449i
$316$	1.27826e6	+	5.60044e6i	0.0405098	+	0.177485i
$317$	2.00525e6	+	8.78556e6i	0.0629492	+	0.275798i	0.996601	−	0.0823846i	$-0.0262536\pi$
$317$	2.00525e6	+	8.78556e6i	0.0629492	+	0.275798i	−0.933651	+	0.358183i	$0.883396\pi$
$318$	1.63676e7	−	1.30527e7i	0.508983	−	0.405901i
$319$	4.28929e6	+	5.37860e6i	0.132134	+	0.165690i
$320$	−2.67185e6	+	609832.i	−0.0815383	+	0.0186106i
$321$	−4.44036e7	+	1.01348e7i	−1.34246	+	0.306409i
$322$	1.65676e6	+	286348.i	0.0496241	+	0.00857683i
$323$	−4.70050e6	+	2.05942e7i	−0.139488	+	0.611137i
$324$	3.61740e7			1.06356
$325$		−	1.06017e7i		−	0.308833i
$326$	3.33624e6	−	1.46170e7i	0.0962953	−	0.421897i
$327$	1.50631e7	+	3.12789e7i	0.430796	+	0.894557i
$328$	−3.48057e7	+	2.77566e7i	−0.986344	+	0.786583i
$329$	9.81096e6	+	4.09658e6i	0.275502	+	0.115036i
$330$	−2.78881e6	+	3.49705e6i	−0.0776026	+	0.0973106i
$331$	1.03234e7	−	4.52299e7i	0.284669	−	1.24722i	−0.607063	−	0.794654i	$-0.707653\pi$
$331$	1.03234e7	−	4.52299e7i	0.284669	−	1.24722i	0.891732	−	0.452563i	$-0.149490\pi$
$332$	8.68516e6	+	6.92618e6i	0.237336	+	0.189269i
$333$	1.24859e7	−	6.01291e6i	0.338133	−	0.162836i
$334$	−1.11775e7	+	8.91377e6i	−0.299989	+	0.239233i
$335$	−1.52123e6	+	3.15886e6i	−0.0404632	+	0.0840226i
$336$	7.33211e6	+	2.57253e7i	0.193291	+	0.678176i
$337$	−6.09932e7	+	2.93728e7i	−1.59365	+	0.767460i	−0.999324	−	0.0367673i	$-0.988294\pi$
$337$	−6.09932e7	+	2.93728e7i	−1.59365	+	0.767460i	−0.594322	+	0.804227i	$0.702580\pi$
$338$	−1.14656e7	−	5.52153e6i	−0.296924	−	0.142991i
$339$	−1.17428e7	+	2.68022e6i	−0.301421	+	0.0687973i
$340$	−4.08150e6	−	1.96555e6i	−0.103844	−	0.0500088i
$341$	−2.95260e7	−	2.35462e7i	−0.744632	−	0.593824i
$342$			8.89998e6i			0.222490i
$343$	2.71454e7	−	2.98587e7i	0.672688	−	0.739927i
$344$	−2.29340e7			−0.563383
$345$	1.33389e6	−	1.67265e6i	0.0324835	−	0.0407331i
$346$	5.99177e6	−	1.24420e7i	0.144653	−	0.300374i
$347$	7.28733e6	+	3.19279e7i	0.174413	+	0.764155i	0.984147	+	0.177357i	$0.0567547\pi$
$347$	7.28733e6	+	3.19279e7i	0.174413	+	0.764155i	−0.809733	+	0.586798i	$0.800388\pi$
$348$	−4.57230e6	+	9.49448e6i	−0.108492	+	0.225286i
$349$	−2.11118e7	−	4.38390e7i	−0.496647	−	1.03130i	−0.987141	−	0.159854i	$-0.948898\pi$
$349$	−2.11118e7	−	4.38390e7i	−0.496647	−	1.03130i	0.490494	−	0.871445i	$-0.336817\pi$
$350$	1.37689e7	−	3.92436e6i	0.321141	−	0.0915302i
$351$	−9.75222e6	−	4.69642e6i	−0.225518	−	0.108604i
$352$	2.14802e7	+	2.69353e7i	0.492504	+	0.617580i
$353$	−6.66082e6	−	1.38313e7i	−0.151427	−	0.314442i	0.811432	−	0.584447i	$-0.198689\pi$
$353$	−6.66082e6	−	1.38313e7i	−0.151427	−	0.314442i	−0.962859	+	0.270006i	$0.912974\pi$
$354$	1.08103e7	−	1.35557e7i	0.243684	−	0.305570i
$355$	−1.76144e7	−	4.02038e6i	−0.393716	−	0.0898632i
$356$	−3.00843e7	−	2.39914e7i	−0.666791	−	0.531748i
$357$	−8.40885e6	+	2.01385e7i	−0.184813	+	0.442611i
$358$	7.93144e6	+	9.94572e6i	0.172863	+	0.216764i
$359$	4.54547e7	−	2.18898e7i	0.982416	−	0.473106i	0.127480	−	0.991841i	$-0.459311\pi$
$359$	4.54547e7	−	2.18898e7i	0.982416	−	0.473106i	0.854935	+	0.518735i	$0.173597\pi$
$360$	−4.02510e6	−	918703.i	−0.0862718	−	0.0196910i
$361$	−6.43365e7			−1.36753
$362$		−	1.45453e7i		−	0.306618i
$363$	1.44937e7	+	3.30809e6i	0.303011	+	0.0691603i
$364$	2.44581e6	−	1.41510e7i	0.0507128	−	0.293416i
$365$	2.39060e6	+	1.04739e7i	0.0491619	+	0.215392i
$366$	1.07274e6	+	4.69999e6i	0.0218802	+	0.0958635i
$367$	4.01878e7	−	3.20487e7i	0.813010	−	0.648354i	−0.126082	−	0.992020i	$-0.540240\pi$
$367$	4.01878e7	−	3.20487e7i	0.813010	−	0.648354i	0.939092	+	0.343666i	$0.111669\pi$
$368$	−2.50282e6	−	3.13843e6i	−0.0502210	−	0.0629752i
$369$	3.42624e7	−	7.82016e6i	0.681928	−	0.155646i
$370$	5.91455e6	−	1.34996e6i	0.116766	−	0.0266511i
$371$	3.62854e7	+	6.60970e7i	0.710575	+	1.29438i
$372$	1.28727e7	−	5.63988e7i	0.250057	−	1.09557i
$373$	9.30865e7			1.79374			0.896872	−	0.442291i	$-0.145834\pi$
$373$	9.30865e7			1.79374			0.896872	+	0.442291i	$0.145834\pi$
$374$			6.84704e6i			0.130884i
$375$	8.60000e6	−	3.76791e7i	0.163082	−	0.714507i
$376$	4.79562e6	+	9.95821e6i	0.0902156	+	0.187335i
$377$	3.58405e6	−	2.85818e6i	0.0668882	−	0.0533416i
$378$	2.48956e6	−	1.44042e7i	0.0460943	−	0.266694i
$379$	−1.22025e7	+	1.53014e7i	−0.224146	+	0.281070i	−0.881170	−	0.472799i	$-0.843244\pi$
$379$	−1.22025e7	+	1.53014e7i	−0.224146	+	0.281070i	0.657024	+	0.753870i	$0.271815\pi$
$380$	5.31525e6	−	2.32876e7i	0.0968664	−	0.424399i
$381$	−6.08501e7	−	4.85263e7i	−1.10024	−	0.877410i
$382$	−1.49394e7	+	7.19442e6i	−0.268004	+	0.129064i
$383$	7.11460e7	−	5.67371e7i	1.26635	−	1.00988i	0.267425	−	0.963579i	$-0.413827\pi$
$383$	7.11460e7	−	5.67371e7i	1.26635	−	1.00988i	0.998927	−	0.0463032i	$-0.0147440\pi$
$384$	−2.93852e7	+	6.10191e7i	−0.518962	+	1.07764i
$385$	−1.07007e7	−	1.20429e7i	−0.187513	−	0.211032i
$386$	2.88644e7	−	1.39004e7i	0.501882	−	0.241693i
$387$	1.63116e7	+	7.85526e6i	0.281426	+	0.135528i
$388$	6.32355e7	−	1.44331e7i	1.08259	−	0.247095i
$389$	1.03636e8	+	4.99085e7i	1.76061	+	0.847864i	0.972699	+	0.232072i	$0.0745505\pi$
$389$	1.03636e8	+	4.99085e7i	1.76061	+	0.847864i	0.787909	+	0.615792i	$0.211164\pi$
$390$	2.33027e6	+	1.85833e6i	0.0392837	+	0.0313277i
$391$		−	3.27496e6i		−	0.0547867i
$392$	4.17134e7	−	4.45971e6i	0.692496	−	0.0740369i
$393$	3.36156e7			0.553814
$394$	−1.70533e7	+	2.13841e7i	−0.278817	+	0.349625i
$395$	1.86315e6	−	3.86887e6i	0.0302313	−	0.0627760i
$396$	−3.93564e6	−	1.72432e7i	−0.0633767	−	0.277672i
$397$	1.08453e6	−	2.25206e6i	0.0173329	−	0.0359921i	−0.892123	−	0.451793i	$-0.850784\pi$
$397$	1.08453e6	−	2.25206e6i	0.0173329	−	0.0359921i	0.909456	+	0.415801i	$0.136499\pi$
$398$	−3.51752e6	−	7.30420e6i	−0.0557940	−	0.115857i
$399$	−1.13391e8	−	1.95980e7i	−1.78508	−	0.308526i
$400$	−3.07977e7	−	1.48314e7i	−0.481213	−	0.231740i
$401$	−3.70679e7	−	4.64817e7i	−0.574864	−	0.720857i	0.406363	−	0.913712i	$-0.366797\pi$
$401$	−3.70679e7	−	4.64817e7i	−0.574864	−	0.720857i	−0.981227	+	0.192855i	$0.938225\pi$
$402$	3.52203e6	+	7.31356e6i	0.0542144	+	0.112577i
$403$	−1.56901e7	+	1.96748e7i	−0.239723	+	0.300604i
$404$	−8.52789e7	−	1.94643e7i	−1.29329	−	0.295186i
$405$	−2.11415e7	−	1.68597e7i	−0.318251	−	0.253797i
$406$	5.03876e6	+	3.59679e6i	0.0752914	+	0.0537449i
$407$	3.50507e7	+	4.39522e7i	0.519893	+	0.651925i
$408$	−2.04407e7	+	9.84374e6i	−0.300965	+	0.144937i
$409$	−1.14593e8	−	2.61551e7i	−1.67490	−	0.382284i	−0.723517	−	0.690307i	$-0.757476\pi$
$409$	−1.14593e8	−	2.61551e7i	−1.67490	−	0.382284i	−0.951379	+	0.308022i	$0.900333\pi$
$410$	1.53845e7			0.223219
$411$			1.53314e7i			0.220829i
$412$	−4.32028e7	−	9.86076e6i	−0.617761	−	0.141000i
$413$	4.14793e7	+	4.66820e7i	0.588818	+	0.662673i
$414$	−307038.	−	1.34522e6i	−0.00432704	−	0.0189580i
$415$	−1.84782e6	−	8.09584e6i	−0.0258533	−	0.113271i
$416$	1.79484e7	−	1.43134e7i	0.249314	−	0.198821i
$417$	−5.92641e7	−	7.43149e7i	−0.817304	−	1.02487i
$418$	−3.51980e7	+	8.03372e6i	−0.481936	+	0.109999i
$419$	6.18893e7	−	1.41258e7i	0.841344	−	0.192031i	0.219932	−	0.975515i	$-0.429416\pi$
$419$	6.18893e7	−	1.41258e7i	0.841344	−	0.192031i	0.621412	+	0.783484i	$0.286559\pi$
$420$	9.50860e6	−	2.27723e7i	0.128342	−	0.307368i
$421$	−1.52638e7	+	6.68752e7i	−0.204558	+	0.896229i	0.763560	+	0.645737i	$0.223450\pi$
$421$	−1.52638e7	+	6.68752e7i	−0.204558	+	0.896229i	−0.968119	+	0.250492i	$0.919408\pi$
$422$	5.45406e6			0.0725742
$423$		−	8.72529e6i		−	0.115281i
$424$	−1.74427e7	+	7.64216e7i	−0.228832	+	1.00258i
$425$	−1.21000e7	−	2.51260e7i	−0.157623	−	0.327308i
$426$	−3.27045e7	+	2.60810e7i	−0.423037	+	0.337361i
$427$	−1.73388e7	+	924238.i	−0.222708	+	0.0118714i
$428$	4.91551e7	−	6.16386e7i	0.626956	−	0.786179i
$429$	−6.14586e6	+	2.69268e7i	−0.0778414	+	0.341046i
$430$	6.19639e6	+	4.94146e6i	0.0779352	+	0.0621512i
$431$	−5.78850e6	+	2.78760e6i	−0.0722994	+	0.0348175i	−0.469684	−	0.882835i	$-0.655632\pi$
$431$	−5.78850e6	+	2.78760e6i	−0.0722994	+	0.0348175i	0.397385	+	0.917652i	$0.369918\pi$
$432$	−2.72861e7	+	2.17599e7i	−0.338446	+	0.269902i
$433$	3.75854e7	−	7.80468e7i	0.462972	−	0.961372i	−0.530541	−	0.847659i	$-0.678011\pi$
$433$	3.75854e7	−	7.80468e7i	0.462972	−	0.961372i	0.993514	−	0.113713i	$-0.0362744\pi$
$434$	−3.13606e7	−	1.30946e7i	−0.383632	−	0.160186i
$435$	7.09735e6	−	3.41790e6i	0.0862240	−	0.0415233i
$436$	−5.41434e7	−	2.60741e7i	−0.653260	−	0.314593i
$437$	1.68353e7	−	3.84255e6i	0.201733	−	0.0460442i
$438$	2.24101e7	+	1.07922e7i	0.266700	+	0.128436i
$439$	4.59450e7	+	3.66399e7i	0.543056	+	0.433073i	0.856209	−	0.516630i	$-0.172814\pi$
$439$	4.59450e7	+	3.66399e7i	0.543056	+	0.433073i	−0.313153	+	0.949703i	$0.601385\pi$
$440$		−	1.67479e7i		−	0.196609i
$441$	−3.11959e7	−	1.11156e7i	−0.363732	−	0.129604i
$442$	4.56255e6			0.0528373
$443$	−2.35662e7	+	2.95511e7i	−0.271069	+	0.339909i	−0.898670	−	0.438626i	$-0.855465\pi$
$443$	−2.35662e7	+	2.95511e7i	−0.271069	+	0.339909i	0.627601	+	0.778535i	$0.284037\pi$
$444$	−3.73634e7	+	7.75860e7i	−0.426872	+	0.886409i
$445$	6.40063e6	+	2.80430e7i	0.0726344	+	0.318232i
$446$	−5.18937e6	+	1.07758e7i	−0.0584939	+	0.121464i
$447$	5.71925e7	+	1.18761e8i	0.640348	+	1.32970i
$448$	−1.86005e7	−	1.32775e7i	−0.206867	−	0.147667i
$449$	6.47608e7	+	3.11872e7i	0.715440	+	0.344538i	0.755939	−	0.654642i	$-0.227181\pi$
$449$	6.47608e7	+	3.11872e7i	0.715440	+	0.344538i	−0.0404992	+	0.999180i	$0.512895\pi$
$450$	−7.32586e6	−	9.18634e6i	−0.0803935	−	0.100810i
$451$	6.18550e7	+	1.28443e8i	0.674288	+	1.40017i
$452$	1.29994e7	−	1.63007e7i	0.140769	−	0.176519i
$453$	1.81534e8	+	4.14339e7i	1.95282	+	0.445719i
$454$	4.54207e7	+	3.62218e7i	0.485384	+	0.387081i
$455$	−8.02483e6	+	7.13046e6i	−0.0851926	+	0.0756978i
$456$	−7.45863e7	−	9.35283e7i	−0.786619	−	0.986389i
$457$	−1.04001e8	+	5.00842e7i	−1.08965	+	0.524750i	−0.890391	−	0.455196i	$-0.849569\pi$
$457$	−1.04001e8	+	5.00842e7i	−1.08965	+	0.524750i	−0.199263	+	0.979946i	$0.563855\pi$
$458$	4.12979e7	+	9.42598e6i	0.429865	+	0.0981138i
$459$	−2.84730e7			−0.294439
$460$			3.70327e6i			0.0380462i
$461$	9.79649e7	+	2.23599e7i	0.999926	+	0.228227i	0.690996	−	0.722858i	$-0.257172\pi$
$461$	9.79649e7	+	2.23599e7i	0.999926	+	0.228227i	0.308930	+	0.951085i	$0.400029\pi$
$462$	−3.72462e7	+	1.98540e6i	−0.377708	+	0.0201336i
$463$	1.54690e7	+	6.77741e7i	0.155854	+	0.682843i	0.991117	+	0.132992i	$0.0424584\pi$
$463$	1.54690e7	+	6.77741e7i	0.155854	+	0.682843i	−0.835263	+	0.549851i	$0.814684\pi$
$464$	−3.28901e6	−	1.44101e7i	−0.0329239	−	0.144249i
$465$	−3.38092e7	+	2.69619e7i	−0.336261	+	0.268159i
$466$	−4.59736e7	−	5.76491e7i	−0.454308	−	0.569685i
$467$	−1.93044e7	+	4.40611e6i	−0.189542	+	0.0432618i	−0.316238	−	0.948680i	$-0.602420\pi$
$467$	−1.93044e7	+	4.40611e6i	−0.189542	+	0.0432618i	0.126696	+	0.991942i	$0.459563\pi$
$468$	−1.14900e7	+	2.62253e6i	−0.112094	+	0.0255848i
$469$	−2.81171e7	+	8.01381e6i	−0.272553	+	0.0776820i
$470$	849942.	−	3.72384e6i	0.00818645	−	0.0358672i
$471$	−1.38134e7			−0.132202
$472$			6.49201e7i			0.617381i
$473$	−1.63424e7	+	7.16006e7i	−0.154430	+	0.676602i
$474$	−4.31367e6	−	8.95742e6i	−0.0405053	−	0.0841101i
$475$	1.14966e8	−	9.16824e7i	1.07273	−	0.855471i
$476$	−1.03545e7	−	3.63295e7i	−0.0960080	−	0.336852i
$477$	3.85817e7	−	4.83799e7i	0.355489	−	0.445769i
$478$	9.34627e6	−	4.09487e7i	0.0855765	−	0.374935i
$479$	4.94249e7	+	3.94151e7i	0.449717	+	0.358637i	0.822005	−	0.569480i	$-0.192855\pi$
$479$	4.94249e7	+	3.94151e7i	0.449717	+	0.358637i	−0.372288	+	0.928117i	$0.621427\pi$
$480$	3.55425e7	−	1.71164e7i	0.321384	−	0.154771i
$481$	2.92877e7	−	2.33562e7i	0.263179	−	0.209878i
$482$	3.17467e7	−	6.59227e7i	0.283503	−	0.588700i
$483$	1.78149e7	−	949619.i	0.158104	−	0.00842768i
$484$	−2.31851e7	+	1.11654e7i	−0.204491	+	0.0984776i
$485$	−4.36841e7	−	2.10371e7i	−0.382911	−	0.184400i
$486$	−3.07479e7	+	7.01800e6i	−0.267859	+	0.0611371i
$487$	2.10161e7	+	1.01208e7i	0.181955	+	0.0876251i	0.522644	−	0.852551i	$-0.324946\pi$
$487$	2.10161e7	+	1.01208e7i	0.181955	+	0.0876251i	−0.340688	+	0.940176i	$0.610660\pi$
$488$	−1.41127e7	−	1.12545e7i	−0.121437	−	0.0968425i
$489$		−	1.59087e8i		−	1.36053i
$490$	−1.22312e7	−	7.78282e6i	−0.103964	−	0.0661529i
$491$	−1.33457e8			−1.12745			−0.563726	−	0.825962i	$-0.690633\pi$
$491$	−1.33457e8			−1.12745			−0.563726	+	0.825962i	$0.690633\pi$
$492$	−1.36156e8	+	1.70734e8i	−1.14325	+	1.43359i
$493$	5.23207e6	−	1.08645e7i	0.0436650	−	0.0906712i
$494$	5.35330e6	+	2.34543e7i	0.0444059	+	0.194555i
$495$	−5.73644e6	+	1.19118e7i	−0.0472963	+	0.0982117i
$496$	3.52050e7	+	7.31039e7i	0.288509	+	0.599094i
$497$	−7.25028e7	−	1.32070e8i	−0.590589	−	1.07581i
$498$	−1.73220e7	−	8.34183e6i	−0.140252	−	0.0675419i
$499$	−6.26806e7	−	7.85990e7i	−0.504466	−	0.632580i	0.462764	−	0.886481i	$-0.346858\pi$
$499$	−6.26806e7	−	7.85990e7i	−0.504466	−	0.632580i	−0.967230	+	0.253901i	$0.918286\pi$
$500$	2.90265e7	+	6.02742e7i	0.232212	+	0.482194i
$501$	−9.45824e7	+	1.18603e8i	−0.752137	+	0.943150i
$502$	8.40748e6	+	1.91895e6i	0.0664591	+	0.0151689i
$503$	−3.24507e7	−	2.58786e7i	−0.254988	−	0.203346i	0.487650	−	0.873039i	$-0.337854\pi$
$503$	−3.24507e7	−	2.58786e7i	−0.254988	−	0.203346i	−0.742638	+	0.669693i	$0.766426\pi$
$504$	−1.65677e7	−	3.01796e7i	−0.129411	−	0.235734i
$505$	4.07684e7	+	5.11219e7i	0.316555	+	0.396947i
$506$	5.04299e6	−	2.42857e6i	0.0389257	−	0.0187456i
$507$	−1.31646e8	−	3.00473e7i	−1.01014	−	0.230559i
$508$	1.34723e8			1.02766
$509$			1.80349e8i			1.36760i	0.729668	+	0.683801i	$0.239674\pi$
$509$			1.80349e8i			1.36760i	−0.729668	+	0.683801i	$0.760326\pi$
$510$	7.64374e6	+	1.74463e6i	0.0576229	+	0.0131521i
$511$	−5.20492e7	+	7.29160e7i	−0.390078	+	0.546462i
$512$	−2.89294e7	−	1.26748e8i	−0.215541	−	0.944347i
$513$	−3.34078e7	−	1.46369e8i	−0.247454	−	1.08417i
$514$	−2.65578e7	+	2.11791e7i	−0.195570	+	0.155962i
$515$	2.06535e7	+	2.58987e7i	0.151207	+	0.189608i
$516$	−1.09679e8	+	2.50334e7i	−0.798313	+	0.182210i
$517$	3.45072e7	−	7.87604e6i	0.249711	−	0.0569949i
$518$	4.11752e7	+	2.93919e7i	0.296242	+	0.211465i
$519$	3.26063e7	−	1.42857e8i	0.233238	−	1.02188i
$520$	−1.11600e7			−0.0793698
$521$		−	1.31758e8i		−	0.931674i	−0.884871	−	0.465837i	$-0.845753\pi$
$521$		−	1.31758e8i		−	0.931674i	0.884871	−	0.465837i	$-0.154247\pi$
$522$	1.13054e6	−	4.95323e6i	0.00794833	−	0.0348239i
$523$	6.49949e6	+	1.34963e7i	0.0454333	+	0.0943431i	0.922450	−	0.386117i	$-0.126184\pi$
$523$	6.49949e6	+	1.34963e7i	0.0454333	+	0.0943431i	−0.877017	+	0.480460i	$0.840470\pi$
$524$	−4.54934e7	+	3.62798e7i	−0.316195	+	0.252157i
$525$	1.33171e8	−	7.31068e7i	0.920302	−	0.505220i
$526$	−3.90602e7	+	4.89799e7i	−0.268397	+	0.336559i
$527$	−1.47301e7	+	6.45370e7i	−0.100641	+	0.440937i
$528$	6.96241e7	+	5.55233e7i	0.472996	+	0.377202i
$529$	1.30964e8	−	6.30688e7i	0.884675	−	0.426037i
$530$	2.11789e7	−	1.68896e7i	0.142258	−	0.113447i
$531$	2.22362e7	−	4.61740e7i	0.148517	−	0.308400i
$532$	1.74607e8	−	9.58543e7i	1.15965	−	0.636615i
$533$	8.55886e7	−	4.12173e7i	0.565242	−	0.272206i
$534$	6.00012e7	+	2.88950e7i	0.394036	+	0.189758i
$535$	−5.74562e7	+	1.31140e7i	−0.375211	+	0.0856394i
$536$	−2.73843e7	−	1.31876e7i	−0.177831	−	0.0856388i
$537$	1.05532e8	+	8.41591e7i	0.681494	+	0.543473i
$538$		−	8.59017e7i		−	0.551639i
$539$	1.58009e7	−	1.33409e8i	0.100906	−	0.851957i
$540$	3.21968e7			0.204471
$541$	−2.18240e7	+	2.73664e7i	−0.137830	+	0.172833i	−0.845956	−	0.533253i	$-0.820969\pi$
$541$	−2.18240e7	+	2.73664e7i	−0.137830	+	0.172833i	0.708126	+	0.706086i	$0.249541\pi$
$542$	−2.71133e7	+	5.63014e7i	−0.170288	+	0.353607i
$543$	−3.43433e7	−	1.50468e8i	−0.214508	−	0.939820i
$544$	2.62015e7	−	5.44080e7i	0.162753	−	0.337961i
$545$	1.94910e7	+	4.04734e7i	0.120405	+	0.250023i
$546$	1.32298e6	+	2.48191e7i	0.00812782	+	0.152479i
$547$	−1.82200e8	−	8.77428e7i	−1.11323	−	0.536104i	−0.215437	−	0.976518i	$-0.569118\pi$
$547$	−1.82200e8	−	8.77428e7i	−1.11323	−	0.536104i	−0.897795	+	0.440413i	$0.854832\pi$
$548$	−1.65465e7	−	2.07486e7i	−0.100546	−	0.126080i
$549$	6.18270e6	+	1.28385e7i	0.0373647	+	0.0775885i
$550$	2.97177e7	−	3.72648e7i	0.178619	−	0.223981i
$551$	6.19892e7	+	1.41486e7i	0.370562	+	0.0845784i
$552$	1.45002e7	+	1.15635e7i	0.0862100	+	0.0687502i
$553$	3.44369e7	−	9.81506e6i	0.203633	−	0.0580387i
$554$	−7.01597e7	−	8.79775e7i	−0.412628	−	0.517419i
$555$	5.79973e7	−	2.79300e7i	0.339257	−	0.163378i
$556$	1.60409e8	+	3.66123e7i	0.933264	+	0.213011i
$557$	1.36568e8			0.790287			0.395143	−	0.918619i	$-0.370695\pi$
$557$	1.36568e8			0.790287			0.395143	+	0.918619i	$0.370695\pi$
$558$			2.78902e7i			0.160527i
$559$	4.77113e7	+	1.08898e7i	0.273140	+	0.0623425i
$560$	9.48741e6	+	3.32873e7i	0.0540236	+	0.189546i
$561$	1.61668e7	+	7.08312e7i	0.0915660	+	0.401177i
$562$	−1.54224e7	−	6.75697e7i	−0.0868844	−	0.380665i
$563$	−1.63517e7	+	1.30400e7i	−0.0916299	+	0.0730724i	−0.668233	−	0.743952i	$-0.732949\pi$
$563$	−1.63517e7	+	1.30400e7i	−0.0916299	+	0.0730724i	0.576603	+	0.817024i	$0.304378\pi$
$564$	3.38043e7	+	4.23892e7i	0.188423	+	0.236275i
$565$	−1.51947e7	+	3.46808e6i	−0.0842453	+	0.0192284i
$566$	−1.38482e7	+	3.16077e6i	−0.0763738	+	0.0174318i
$567$	−1.20027e7	−	2.25172e8i	−0.0658462	−	1.23528i
$568$	3.48528e7	−	1.52700e8i	0.190192	−	0.833286i
$569$	−975067.			−0.00529295			−0.00264647	−	0.999996i	$-0.500842\pi$
$569$	−975067.			−0.00529295			−0.00264647	+	0.999996i	$0.500842\pi$
$570$			4.13406e7i			0.223230i
$571$	−5.43816e7	+	2.38261e8i	−0.292108	+	1.27981i	0.589477	+	0.807785i	$0.299334\pi$
$571$	−5.43816e7	+	2.38261e8i	−0.292108	+	1.27981i	−0.881585	+	0.472025i	$0.843523\pi$
$572$	−2.07434e7	−	4.30740e7i	−0.110839	−	0.230159i
$573$	−1.37557e8	+	1.09698e8i	−0.731173	+	0.583091i
$574$	8.52130e7	+	9.59012e7i	0.450578	+	0.507094i
$575$	−1.42141e7	+	1.78239e7i	−0.0747678	+	0.0937558i
$576$	−4.17339e6	+	1.82848e7i	−0.0218384	+	0.0956805i
$577$	−1.34073e8	−	1.06920e8i	−0.697935	−	0.556585i	0.208969	−	0.977922i	$-0.432989\pi$
$577$	−1.34073e8	−	1.06920e8i	−0.697935	−	0.556585i	−0.906904	+	0.421338i	$0.861561\pi$
$578$	−5.43376e7	+	2.61676e7i	−0.281396	+	0.135513i
$579$	2.65776e8	−	2.11949e8i	1.36924	−	1.09193i
$580$	−5.91635e6	+	1.22854e7i	−0.0303228	+	0.0629660i
$581$	4.02316e7	−	5.63606e7i	0.205134	−	0.287374i
$582$	−1.01140e8	+	4.87063e7i	−0.513042	+	0.247068i
$583$	2.26161e8	+	1.08914e8i	1.14133	+	0.549638i
$584$	−9.07987e7	+	2.07242e7i	−0.455870	+	0.104049i
$585$	7.93750e6	+	3.82250e6i	0.0396475	+	0.0190932i
$586$	2.35057e7	+	1.87452e7i	0.116810	+	0.0931529i
$587$			2.73339e6i			0.0135141i	0.999977	+	0.00675705i	$0.00215085\pi$
$587$			2.73339e6i			0.0135141i	−0.999977	+	0.00675705i	$0.997849\pi$
$588$	1.94621e8	−	6.68600e7i	0.957321	−	0.328878i
$589$	−3.49043e8			−1.70818
$590$	1.39880e7	−	1.75404e7i	0.0681082	−	0.0854050i
$591$	−1.25922e8	+	2.61479e8i	−0.610011	+	1.26670i
$592$	−2.68768e7	−	1.17755e8i	−0.129543	−	0.567563i
$593$	−1.40630e8	+	2.92022e8i	−0.674396	+	1.40040i	0.229783	+	0.973242i	$0.426198\pi$
$593$	−1.40630e8	+	2.92022e8i	−0.674396	+	1.40040i	−0.904178	+	0.427155i	$0.859516\pi$
$594$	−2.11144e7	−	4.38446e7i	−0.100744	−	0.209198i
$595$	−1.08807e7	+	2.60583e7i	−0.0516541	+	0.123707i
$596$	−2.05574e8	−	9.89994e7i	−0.971025	−	0.467621i
$597$	−5.36341e7	−	6.72551e7i	−0.252068	−	0.316084i
$598$	−1.61829e6	−	3.36041e6i	−0.00756750	−	0.0157141i
$599$	−2.16953e8	+	2.72050e8i	−1.00945	+	1.26581i	−0.0457124	+	0.998955i	$0.514556\pi$
$599$	−2.16953e8	+	2.72050e8i	−1.00945	+	1.26581i	−0.963737	+	0.266855i	$0.914016\pi$
$600$	1.53972e8	+	3.51432e7i	0.712834	+	0.162700i
$601$	−2.66922e8	−	2.12863e8i	−1.22959	−	0.980565i	−0.999973	−	0.00728361i	$-0.997682\pi$
$601$	−2.66922e8	−	2.12863e8i	−1.22959	−	0.980565i	−0.229616	−	0.973281i	$-0.573747\pi$
$602$	3.51790e6	+	6.59962e7i	0.0161248	+	0.302503i
$603$	1.49599e7	+	1.87591e7i	0.0682303	+	0.0855581i
$604$	−2.90395e8	+	1.39847e8i	−1.31789	+	0.634661i
$605$	1.87541e7	+	4.28051e6i	0.0846898	+	0.0193299i
$606$	1.51388e8			0.680259
$607$		−	3.60146e8i		−	1.61032i	−0.593055	−	0.805162i	$-0.702078\pi$
$607$		−	3.60146e8i		−	1.61032i	0.593055	−	0.805162i	$-0.297922\pi$
$608$	3.10433e8	+	7.08544e7i	1.38120	+	0.315251i
$609$	6.06174e7	+	2.53109e7i	0.268377	+	0.112061i
$610$	1.38808e6	+	6.08157e6i	0.00611539	+	0.0267933i
$611$	−5.24822e6	−	2.29940e7i	−0.0230085	−	0.100807i
$612$	−2.42383e7	+	1.93294e7i	−0.105742	+	0.0843265i
$613$	1.33431e8	+	1.67318e8i	0.579264	+	0.726374i	0.981987	−	0.188948i	$-0.0605077\pi$
$613$	1.33431e8	+	1.67318e8i	0.579264	+	0.726374i	−0.402723	+	0.915322i	$0.631936\pi$
$614$	−4.49041e7	+	1.02491e7i	−0.193991	+	0.0442771i
$615$	1.59149e8	−	3.63248e7i	0.684194	−	0.156163i
$616$	1.04400e8	−	9.27648e7i	0.446642	−	0.396864i
$617$	−7.58076e7	+	3.32135e8i	−0.322743	+	1.41403i	0.509906	+	0.860230i	$0.329680\pi$
$617$	−7.58076e7	+	3.32135e8i	−0.322743	+	1.41403i	−0.832649	+	0.553801i	$0.813177\pi$
$618$	7.66942e7			0.324936
$619$		−	5.31701e7i		−	0.224179i	−0.993698	−	0.112090i	$-0.964246\pi$
$619$		−	5.31701e7i		−	0.224179i	0.993698	−	0.112090i	$-0.0357544\pi$
$620$	1.66566e7	−	7.29774e7i	0.0698895	−	0.306206i
$621$	1.00991e7	+	2.09710e7i	0.0421703	+	0.0875676i
$622$	−1.03890e8	+	8.28498e7i	−0.431722	+	0.344287i
$623$	−1.39357e8	+	1.95226e8i	−0.576322	+	0.807372i
$624$	3.69982e7	−	4.63942e7i	0.152274	−	0.190946i
$625$	−3.73159e7	+	1.63492e8i	−0.152846	+	0.669662i
$626$	−5.51847e7	−	4.40083e7i	−0.224955	−	0.179396i
$627$	−3.45147e8	+	1.66214e8i	−1.40024	+	0.674319i
$628$	1.86943e7	−	1.49082e7i	0.0754795	−	0.0601929i
$629$	4.27549e7	−	8.87814e7i	0.171804	−	0.356755i
$630$	−2.02629e6	+	1.17238e7i	−0.00810365	+	0.0468864i
$631$	1.73347e7	−	8.34793e6i	0.0689965	−	0.0332270i	−0.399067	−	0.916922i	$-0.630666\pi$
$631$	1.73347e7	−	8.34793e6i	0.0689965	−	0.0332270i	0.468064	+	0.883695i	$0.344952\pi$
$632$	3.35394e7	+	1.61517e7i	0.132863	+	0.0639834i
$633$	5.64210e7	−	1.28777e7i	0.222449	−	0.0507725i
$634$	2.43234e7	+	1.17135e7i	0.0954456	+	0.0459642i
$635$	−7.87372e7	−	6.27908e7i	−0.307510	−	0.245231i
$636$			3.84516e8i			1.49466i
$637$	−8.88973e7	−	1.05290e7i	−0.343930	−	0.0407351i
$638$	2.06098e7			0.0793617
$639$	−7.70911e7	+	9.66692e7i	−0.295462	+	0.370498i
$640$	−3.80231e7	+	7.89559e7i	−0.145047	+	0.301193i
$641$	6.57129e7	+	2.87907e8i	0.249503	+	1.09315i	0.932057	+	0.362311i	$0.118012\pi$
$641$	6.57129e7	+	2.87907e8i	0.249503	+	1.09315i	−0.682554	+	0.730835i	$0.739131\pi$
$642$	−5.92020e7	+	1.22934e8i	−0.223733	+	0.464587i
$643$	3.67975e7	+	7.64108e7i	0.138416	+	0.287423i	0.958641	−	0.284617i	$-0.0918664\pi$
$643$	3.67975e7	+	7.64108e7i	0.138416	+	0.287423i	−0.820226	+	0.572040i	$0.806152\pi$
$644$	−2.30848e7	+	2.05120e7i	−0.0864308	+	0.0767980i
$645$	7.57678e7	+	3.64878e7i	0.282361	+	0.135978i
$646$	3.94566e7	+	4.94770e7i	0.146360	+	0.183530i
$647$	−2.04754e8	−	4.25176e8i	−0.755996	−	1.56984i	−0.820315	−	0.571912i	$-0.806202\pi$
$647$	−2.04754e8	−	4.25176e8i	−0.755996	−	1.56984i	0.0643190	−	0.997929i	$-0.479512\pi$
$648$	1.46158e8	−	1.83276e8i	0.537151	−	0.673566i
$649$	2.02683e8	+	4.62610e7i	0.741452	+	0.169232i
$650$	−2.48316e7	−	1.98025e7i	−0.0904199	−	0.0721074i
$651$	−3.55336e8	−	6.14149e7i	−1.28794	−	0.222603i
$652$	1.71696e8	+	2.15299e8i	0.619464	+	0.776784i
$653$	−3.76455e7	+	1.81291e7i	−0.135199	+	0.0651084i	−0.500260	−	0.865875i	$-0.666762\pi$
$653$	−3.76455e7	+	1.81291e7i	−0.135199	+	0.0651084i	0.365061	+	0.930983i	$0.381048\pi$
$654$	1.01398e8	+	2.31435e7i	0.362492	+	0.0827364i
$655$	4.34971e7			0.154788
$656$		−	3.06296e8i		−	1.08500i
$657$	7.16783e7	+	1.63601e7i	0.252750	+	0.0576886i
$658$	2.79208e7	−	1.53277e7i	0.0980053	−	0.0538021i
$659$	−7.17563e7	−	3.14385e8i	−0.250729	−	1.09851i	−0.930846	−	0.365411i	$-0.880928\pi$
$659$	−7.17563e7	−	3.14385e8i	−0.250729	−	1.09851i	0.680118	−	0.733103i	$-0.261929\pi$
$660$	−1.82811e7	−	8.00948e7i	−0.0635873	−	0.278594i
$661$	−7.54068e7	+	6.01349e7i	−0.261100	+	0.208220i	−0.745286	−	0.666745i	$-0.767687\pi$
$661$	−7.54068e7	+	6.01349e7i	−0.261100	+	0.208220i	0.484186	+	0.874965i	$0.339116\pi$
$662$	−8.66563e7	−	1.08664e8i	−0.298694	−	0.374550i
$663$	4.71986e7	−	1.07728e7i	0.161953	−	0.0369647i
$664$	7.01831e7	−	1.60188e7i	0.239733	−	0.0547175i
$665$	−1.46722e8	−	2.53589e7i	−0.498920	−	0.0862313i
$666$	9.23845e6	−	4.04763e7i	0.0312735	−	0.137018i
$667$	−9.85770e6			−0.0332199
$668$		−	2.62588e8i		−	0.880938i
$669$	−2.82398e7	+	1.23727e8i	−0.0943155	+	0.413223i
$670$	4.55734e6	+	9.46341e6i	0.0151526	+	0.0314647i
$671$	−4.51934e7	+	3.60405e7i	−0.149592	+	0.119295i
$672$	3.03563e8	+	1.26753e8i	1.00033	+	0.417687i
$673$	2.50644e8	−	3.14297e8i	0.822265	−	1.03109i	−0.176639	−	0.984276i	$-0.556522\pi$
$673$	2.50644e8	−	3.14297e8i	0.822265	−	1.03109i	0.998904	−	0.0468120i	$-0.0149062\pi$
$674$	−4.51294e7	+	1.97725e8i	−0.147394	+	0.645776i
$675$	1.54964e8	+	1.23579e8i	0.503870	+	0.401823i
$676$	2.10590e8	−	1.01415e8i	0.681708	−	0.328293i
$677$	−4.80096e7	+	3.82864e7i	−0.154726	+	0.123390i	−0.697793	−	0.716300i	$-0.745834\pi$
$677$	−4.80096e7	+	3.82864e7i	−0.154726	+	0.123390i	0.543067	+	0.839689i	$0.317263\pi$
$678$	−1.56563e7	+	3.25107e7i	−0.0502344	+	0.104313i
$679$	−1.10823e8	−	3.88833e8i	−0.354016	−	1.24209i
$680$	−2.64494e7	+	1.27373e7i	−0.0841179	+	0.0405091i
$681$	5.55391e8	+	2.67462e8i	1.75856	+	0.846879i
$682$	−1.10301e8	+	2.51756e7i	−0.347719	+	0.0793645i
$683$	−3.59965e8	−	1.73350e8i	−1.12979	−	0.544078i	−0.226887	−	0.973921i	$-0.572855\pi$
$683$	−3.59965e8	−	1.73350e8i	−1.12979	−	0.544078i	−0.902904	+	0.429843i	$0.858569\pi$
$684$	−1.27804e8	−	1.01920e8i	−0.399371	−	0.318488i
$685$			1.98381e7i			0.0617204i
$686$	−1.92321e7	−	1.19353e8i	−0.0595736	−	0.369710i
$687$	4.49474e8			1.38623
$688$	9.83813e7	−	1.23366e8i	0.302098	−	0.378818i
$689$	7.25750e7	−	1.50703e8i	0.221886	−	0.460750i
$690$	−1.42620e6	−	6.24858e6i	−0.00434142	−	0.0190210i
$691$	−3.02227e7	+	6.27582e7i	−0.0916009	+	0.190211i	−0.941736	−	0.336354i	$-0.890806\pi$
$691$	−3.02227e7	+	6.27582e7i	−0.0916009	+	0.190211i	0.850135	+	0.526565i	$0.176520\pi$
$692$	1.10052e8	+	2.28525e8i	0.332108	+	0.689629i
$693$	−1.06028e8	+	3.02195e7i	−0.318580	+	0.0908004i
$694$	8.83943e7	+	4.25685e7i	0.264451	+	0.127353i
$695$	−7.66850e7	−	9.61600e7i	−0.228432	−	0.286444i
$696$	2.96299e7	+	6.15271e7i	0.0878825	+	0.182490i
$697$	1.55803e8	−	1.95371e8i	0.460127	−	0.576981i
$698$	−1.42115e8	−	3.24369e7i	−0.417902	−	0.0953834i
$699$	−6.11704e8	−	4.87817e8i	−1.79106	−	1.42832i
$700$	−1.01324e8	+	2.42663e8i	−0.295406	+	0.707473i
$701$	1.80809e8	+	2.26727e8i	0.524886	+	0.658187i	0.971639	−	0.236471i	$-0.0759908\pi$
$701$	1.80809e8	+	2.26727e8i	0.524886	+	0.658187i	−0.446752	+	0.894658i	$0.647419\pi$
$702$	−2.92160e7	+	1.40697e7i	−0.0844519	+	0.0406699i
$703$	5.06557e8	+	1.15618e8i	1.45801	+	0.332782i
$704$	−7.60808e7			−0.218050
$705$		−	4.05291e7i		−	0.115664i
$706$	−4.48378e7	−	1.02339e7i	−0.127418	−	0.0290823i
$707$	−9.28636e7	+	5.37293e8i	−0.262777	+	1.52038i
$708$	7.08632e7	+	3.10472e8i	0.199674	+	0.874828i
$709$	−1.49666e8	−	6.55732e8i	−0.419939	−	1.83987i	−0.532774	−	0.846257i	$-0.678851\pi$
$709$	−1.49666e8	−	6.55732e8i	−0.419939	−	1.83987i	0.112836	−	0.993614i	$-0.464007\pi$
$710$	−4.23181e7	+	3.37476e7i	−0.118236	+	0.0942904i
$711$	−1.83224e7	−	2.29756e7i	−0.0509770	−	0.0639231i
$712$	−2.43105e8	+	5.54872e7i	−0.673526	+	0.153728i
$713$	5.27574e7	−	1.20415e7i	0.145551	−	0.0332211i
$714$	3.14624e7	+	5.73116e7i	0.0864366	+	0.157452i
$715$	−7.95246e6	+	3.48420e7i	−0.0217562	+	0.0953202i
$716$	−2.33650e8			−0.636541
$717$		−	4.45673e8i		−	1.20909i
$718$	3.36323e7	−	1.47353e8i	0.0908623	−	0.398094i
$719$	8.34303e7	+	1.73245e8i	0.224459	+	0.466094i	0.982536	−	0.186071i	$-0.0595754\pi$
$719$	8.34303e7	+	1.73245e8i	0.224459	+	0.466094i	−0.758077	+	0.652165i	$0.773861\pi$
$720$	2.22086e7	−	1.77108e7i	0.0595009	−	0.0474504i
$721$	−4.70453e7	+	2.72196e8i	−0.125519	+	0.726233i
$722$	−1.20172e8	+	1.50691e8i	−0.319295	+	0.400383i
$723$	1.72761e8	−	7.56914e8i	0.457120	−	2.00277i
$724$	2.08871e8	+	1.66569e8i	0.550380	+	0.438914i
$725$	−7.56299e7	+	3.64214e7i	−0.198463	+	0.0955747i
$726$	3.48206e7	−	2.77685e7i	0.0909969	−	0.0725676i
$727$	1.63480e8	−	3.39469e8i	0.425461	−	0.883480i	−0.572515	−	0.819894i	$-0.694032\pi$
$727$	1.63480e8	−	3.39469e8i	0.425461	−	0.883480i	0.997976	−	0.0635854i	$-0.0202535\pi$
$728$	−6.18142e7	−	6.95675e7i	−0.160212	−	0.180307i
$729$	1.30282e8	−	6.27404e7i	0.336280	−	0.161944i
$730$	2.89977e7	+	1.39646e7i	0.0745410	+	0.0358970i
$731$	1.25505e8	−	2.86457e7i	0.321299	−	0.0733344i
$732$	−7.97768e7	−	3.84185e7i	−0.203397	−	0.0979506i
$733$	−1.88565e8	−	1.50376e8i	−0.478796	−	0.381827i	0.354144	−	0.935191i	$-0.384772\pi$
$733$	−1.88565e8	−	1.50376e8i	−0.478796	−	0.381827i	−0.832939	+	0.553364i	$0.813344\pi$
$734$		−	1.53992e8i		−	0.389413i
$735$	−1.44905e8	−	5.16321e7i	−0.364941	−	0.130034i
$736$	−4.93660e7			−0.123821
$737$	−6.06856e7	+	7.60974e7i	−0.151594	+	0.190093i
$738$	4.56810e7	−	9.48576e7i	0.113649	−	0.235995i
$739$	−4.64809e7	−	2.03646e8i	−0.115170	−	0.504594i	−0.999302	−	0.0373565i	$-0.988106\pi$
$739$	−4.64809e7	−	2.03646e8i	−0.115170	−	0.504594i	0.884132	−	0.467238i	$-0.154751\pi$
$740$	−4.83466e7	+	1.00393e8i	−0.119308	+	0.247746i
$741$	1.10757e8	+	2.29990e8i	0.272219	+	0.565268i
$742$	2.22591e8	+	3.84718e7i	0.544874	+	0.0941739i
$743$	4.88852e8	+	2.35419e8i	1.19182	+	0.573950i	0.921333	−	0.388774i	$-0.127101\pi$
$743$	4.88852e8	+	2.35419e8i	1.19182	+	0.573950i	0.270487	+	0.962724i	$0.412815\pi$
$744$	−2.33734e8	−	2.93093e8i	−0.567549	−	0.711683i
$745$	7.40044e7	+	1.53672e8i	0.178973	+	0.371642i
$746$	1.73873e8	−	2.18030e8i	0.418810	−	0.525171i
$747$	−5.54039e7	−	1.26456e7i	−0.132916	−	0.0303373i
$748$	−9.83239e7	−	7.84107e7i	−0.234938	−	0.187357i
$749$	−3.99991e8	−	2.85524e8i	−0.951930	−	0.679511i
$750$	−7.21896e7	−	9.05228e7i	−0.171116	−	0.214573i
$751$	3.90298e8	−	1.87958e8i	0.921460	−	0.443752i	0.0878680	−	0.996132i	$-0.471995\pi$
$751$	3.90298e8	−	1.87958e8i	0.921460	−	0.443752i	0.833592	+	0.552380i	$0.186280\pi$
$752$	−7.41393e7	−	1.69218e7i	−0.174339	−	0.0397918i
$753$	9.15044e7			0.214317
$754$		−	1.37334e7i		−	0.0320379i
$755$	2.34896e8	+	5.36136e7i	0.545803	+	0.124576i
$756$	1.78335e8	+	2.00703e8i	0.412734	+	0.464503i
$757$	9.88433e7	+	4.33061e8i	0.227856	+	0.998300i	0.951384	+	0.308006i	$0.0996617\pi$
$757$	9.88433e7	+	4.33061e8i	0.227856	+	0.998300i	−0.723529	+	0.690294i	$0.757481\pi$
$758$	1.30469e7	+	5.71622e7i	0.0299571	+	0.131251i
$759$	4.64344e7	−	3.70302e7i	0.106198	−	0.0846898i
$760$	−9.65112e7	−	1.21021e8i	−0.219855	−	0.275690i
$761$	−5.88577e8	+	1.34339e8i	−1.33552	+	0.304823i	−0.829889	−	0.557928i	$-0.811596\pi$
$761$	−5.88577e8	+	1.34339e8i	−1.33552	+	0.304823i	−0.505628	+	0.862751i	$0.668739\pi$
$762$	−2.27320e8	+	5.18843e7i	−0.513775	+	0.117266i
$763$	−1.44338e8	+	3.45677e8i	−0.324943	+	0.778211i
$764$	6.77697e7	−	2.96919e8i	0.151969	−	0.665821i
$765$	2.31747e7			0.0517642
$766$		−	2.72618e8i		−	0.606553i
$767$	3.08262e7	−	1.35058e8i	0.0683178	−	0.299320i
$768$	2.92201e7	+	6.06762e7i	0.0645057	+	0.133948i
$769$	−5.78369e8	+	4.61234e8i	−1.27182	+	1.01424i	−0.273188	+	0.961961i	$0.588078\pi$
$769$	−5.78369e8	+	4.61234e8i	−1.27182	+	1.01424i	−0.998632	+	0.0522824i	$0.983350\pi$
$770$	−4.81949e7	+	2.56901e6i	−0.105567	+	0.00562722i
$771$	−2.24728e8	+	2.81800e8i	−0.490336	+	0.614861i
$772$	−1.30938e8	+	5.73679e8i	−0.284587	+	1.24686i
$773$	9.79546e6	+	7.81162e6i	0.0212074	+	0.0169123i	0.634036	−	0.773303i	$-0.281397\pi$
$773$	9.79546e6	+	7.81162e6i	0.0212074	+	0.0169123i	−0.612829	+	0.790216i	$0.709968\pi$
$774$	4.88669e7	−	2.35330e7i	0.105388	−	0.0507522i
$775$	3.60274e8	−	2.87309e8i	0.773976	−	0.617225i
$776$	1.82372e8	−	3.78699e8i	0.390276	−	0.810417i
$777$	4.95346e8	+	2.06833e8i	1.05596	+	0.440916i
$778$	3.10476e8	−	1.49518e8i	0.659310	−	0.317507i
$779$	1.18713e9	+	5.71693e8i	2.51123	+	1.20935i
$780$	−5.33714e7	+	1.21817e7i	−0.112467	+	0.0256699i
$781$	−4.51899e8	−	2.17623e8i	−0.948611	−	0.456827i
$782$	−7.67071e6	−	6.11719e6i	−0.0160404	−	0.0127918i
$783$			8.57045e7i			0.178533i
$784$	−1.54951e8	+	2.43516e8i	−0.321548	+	0.505334i
$785$	−1.78739e7			−0.0369497
$786$	6.27896e7	−	7.87357e7i	0.129307	−	0.162145i
$787$	−1.94919e8	+	4.04754e8i	−0.399881	+	0.830362i	0.599666	+	0.800251i	$0.295300\pi$
$787$	−1.94919e8	+	4.04754e8i	−0.399881	+	0.830362i	−0.999547	+	0.0301108i	$0.990414\pi$
$788$	−1.11787e8	−	4.89771e8i	−0.228462	−	1.00096i
$789$	−2.88421e8	+	5.98913e8i	−0.587214	+	1.21936i
$790$	−5.58169e6	−	1.15905e7i	−0.0113210	−	0.0235083i
$791$	−1.05780e8	−	7.55086e7i	−0.213735	−	0.152569i
$792$	−1.03264e8	−	4.97294e7i	−0.207861	−	0.100101i
$793$	2.40157e7	+	3.01147e7i	0.0481588	+	0.0603893i
$794$	−3.24908e6	−	6.74678e6i	−0.00649080	−	0.0134783i
$795$	1.79213e8	−	2.24726e8i	0.356671	−	0.447251i
$796$	1.45170e8	+	3.31342e7i	0.287832	+	0.0656958i
$797$	−2.07360e8	−	1.65364e8i	−0.409591	−	0.326638i	0.396924	−	0.917851i	$-0.370078\pi$
$797$	−2.07360e8	−	1.65364e8i	−0.409591	−	0.326638i	−0.806515	+	0.591214i	$0.798649\pi$
$798$	−2.57702e8	+	2.28981e8i	−0.507118	+	0.450599i
$799$	−3.86822e7	−	4.85059e7i	−0.0758351	−	0.0950942i
$800$	−3.78744e8	+	1.82394e8i	−0.739735	+	0.356237i
$801$	1.91912e8	+	4.38027e7i	0.373427	+	0.0852322i
$802$	−1.78109e8			−0.345273
$803$			2.98244e8i			0.576004i
$804$	−1.45357e8	−	3.31767e7i	−0.279683	−	0.0638359i
$805$	2.30517e7	−	1.22876e6i	0.0441891	−	0.00235549i
$806$	1.67758e7	+	7.34998e7i	0.0320390	+	0.140372i
$807$	−2.02825e8	−	8.88634e8i	−0.385923	−	1.69084i
$808$	−4.43177e8	+	3.53422e8i	−0.840124	+	0.669977i
$809$	4.36568e8	+	5.47438e8i	0.824529	+	1.03393i	0.998788	+	0.0492268i	$0.0156757\pi$
$809$	4.36568e8	+	5.47438e8i	0.824529	+	1.03393i	−0.174259	+	0.984700i	$0.555753\pi$
$810$	−7.89790e7	+	1.80264e7i	−0.148613	+	0.0339199i
$811$	−1.02640e8	+	2.34268e7i	−0.192421	+	0.0439188i	−0.317645	−	0.948210i	$-0.602892\pi$
$811$	−1.02640e8	+	2.34268e7i	−0.192421	+	0.0439188i	0.125224	+	0.992128i	$0.460035\pi$
$812$	−1.09353e8	+	3.11673e7i	−0.204250	+	0.0582144i
$813$	−1.47547e8	+	6.46444e8i	−0.274573	+	1.20298i
$814$	1.68417e8			0.312257
$815$		−	2.05852e8i		−	0.380261i
$816$	3.47346e7	−	1.52182e8i	0.0639280	−	0.280087i
$817$	2.94514e8	+	6.11564e8i	0.540056	+	1.12144i
$818$	−2.75306e8	+	2.19549e8i	−0.502986	+	0.401118i
$819$	2.01369e7	+	7.06518e7i	0.0366556	+	0.128609i
$820$	−1.76180e8	+	2.20922e8i	−0.319532	+	0.400680i
$821$	−1.87927e8	+	8.23364e8i	−0.339594	+	1.48786i	0.460324	+	0.887751i	$0.347733\pi$
$821$	−1.87927e8	+	8.23364e8i	−0.339594	+	1.48786i	−0.799918	+	0.600109i	$0.795124\pi$
$822$	3.59097e7	+	2.86371e7i	0.0646542	+	0.0515600i
$823$	−1.48929e8	+	7.17206e7i	−0.267166	+	0.128660i	−0.562671	−	0.826681i	$-0.690226\pi$
$823$	−1.48929e8	+	7.17206e7i	−0.267166	+	0.128660i	0.295505	+	0.955341i	$0.404512\pi$
$824$	−2.24516e8	+	1.79046e8i	−0.401297	+	0.320024i
$825$	2.19436e8	−	4.55664e8i	0.390793	−	0.811490i
$826$	1.86818e8	−	9.95828e6i	0.331497	−	0.0176703i
$827$	2.40277e8	−	1.15711e8i	0.424811	−	0.204578i	−0.209248	−	0.977863i	$-0.567102\pi$
$827$	2.40277e8	−	1.15711e8i	0.424811	−	0.204578i	0.634059	+	0.773284i	$0.281387\pi$
$828$	2.28336e7	+	1.09961e7i	0.0402238	+	0.0193707i
$829$	6.02677e8	−	1.37557e8i	1.05784	−	0.241446i	0.341994	−	0.939702i	$-0.388898\pi$
$829$	6.02677e8	−	1.37557e8i	1.05784	−	0.241446i	0.715848	+	0.698256i	$0.246040\pi$
$830$	−2.24138e7	−	1.07939e7i	−0.0391996	−	0.0188776i
$831$	−9.33513e8	−	7.44452e8i	−1.62674	−	1.29728i
$832$			5.06967e7i			0.0880257i
$833$	−2.22704e8	+	7.65078e7i	−0.385295	+	0.132364i
$834$	−2.84760e8			−0.490887
$835$	−1.22385e8	+	1.53466e8i	−0.210218	+	0.263605i
$836$	2.87715e8	−	5.97446e8i	0.492429	−	1.02254i
$837$	−1.04691e8	−	4.58682e8i	−0.178539	−	0.782232i
$838$	8.25152e7	−	1.71345e8i	0.140217	−	0.291164i
$839$	4.43147e8	+	9.20204e8i	0.750346	+	1.55811i	0.827741	+	0.561110i	$0.189625\pi$
$839$	4.43147e8	+	9.20204e8i	0.750346	+	1.55811i	−0.0773950	+	0.997001i	$0.524660\pi$
$840$	−7.69573e7	−	1.40185e8i	−0.129841	−	0.236517i
$841$	5.03215e8	+	2.42335e8i	0.845990	+	0.407408i
$842$	1.28127e8	+	1.60666e8i	0.214636	+	0.269145i
$843$	−3.19082e8	−	6.62580e8i	−0.532622	−	1.10600i
$844$	−6.24585e7	+	7.83205e7i	−0.103888	+	0.130271i
$845$	−1.70344e8	−	3.88798e7i	−0.282329	−	0.0644398i
$846$	−2.04367e7	−	1.62977e7i	−0.0337520	−	0.0269163i
$847$	7.71940e7	+	1.40616e8i	0.127038	+	0.231411i
$848$	−3.36262e8	−	4.21659e8i	−0.551429	−	0.691470i
$849$	−1.35794e8	+	6.53949e7i	−0.221900	+	0.106861i
$850$	−8.14523e7	−	1.85910e7i	−0.132631	−	0.0302723i
$851$	−8.05541e7			−0.130707
$852$		−	7.68311e8i		−	1.24228i
$853$	−8.40825e8	−	1.91913e8i	−1.35475	−	0.309212i	−0.517335	−	0.855783i	$-0.673076\pi$
$853$	−8.40825e8	−	1.91913e8i	−1.35475	−	0.309212i	−0.837413	+	0.546571i	$0.815933\pi$
$854$	−3.02218e7	+	4.23379e7i	−0.0485229	+	0.0679760i
$855$	2.71912e7	+	1.19132e8i	0.0435040	+	0.190604i
$856$	−1.13686e8	−	4.98089e8i	−0.181253	−	0.794120i
$857$	−4.60633e8	+	3.67343e8i	−0.731834	+	0.583618i	−0.916904	−	0.399107i	$-0.869320\pi$
$857$	−4.60633e8	+	3.67343e8i	−0.731834	+	0.583618i	0.185070	+	0.982725i	$0.440749\pi$
$858$	5.15892e7	+	6.46908e7i	0.0816764	+	0.102419i
$859$	7.14170e8	−	1.63005e8i	1.12674	−	0.257170i	0.381760	−	0.924262i	$-0.375318\pi$
$859$	7.14170e8	−	1.63005e8i	1.12674	−	0.257170i	0.744976	+	0.667092i	$0.232461\pi$
$860$	−1.41919e8	+	3.23921e7i	−0.223124	+	0.0509265i
$861$	1.10795e9	+	7.90879e8i	1.73584	+	1.23908i
$862$	−4.28297e6	+	1.87649e7i	−0.00668687	+	0.0292971i
$863$	1.17847e9			1.83352			0.916759	−	0.399440i	$-0.130795\pi$
$863$	1.17847e9			1.83352			0.916759	+	0.399440i	$0.130795\pi$
$864$			4.29196e8i			0.665449i
$865$	4.21910e7	−	1.84851e8i	0.0651886	−	0.285610i
$866$	−1.12599e8	−	2.33815e8i	−0.173373	−	0.360013i
$867$	−5.00326e8	+	3.98997e8i	−0.767707	+	0.612226i
$868$	5.47173e8	−	3.00382e8i	0.836692	−	0.459320i
$869$	7.43258e7	−	9.32017e7i	0.113261	−	0.142025i
$870$	5.25139e6	−	2.30079e7i	0.00797474	−	0.0349396i
$871$	5.07077e7	+	4.04381e7i	0.0767397	+	0.0611978i
$872$	−3.50866e8	+	1.68968e8i	−0.529165	+	0.254832i
$873$	−2.59421e8	+	2.06882e8i	−0.389909	+	0.310942i
$874$	2.24460e7	−	4.66096e7i	0.0336205	−	0.0698138i
$875$	3.65557e8	−	2.00681e8i	0.545672	−	0.299558i
$876$	−4.11612e8	+	1.98222e8i	−0.612315	+	0.294876i
$877$	7.89077e8	+	3.79999e8i	1.16982	+	0.563357i	0.914930	−	0.403612i	$-0.132245\pi$
$877$	7.89077e8	+	3.79999e8i	1.16982	+	0.563357i	0.254893	+	0.966969i	$0.417960\pi$
$878$	1.71639e8	−	3.91754e7i	0.253589	−	0.0578801i
$879$	2.87421e8	+	1.38415e8i	0.423206	+	0.203805i
$880$	9.00903e7	+	7.18446e7i	0.132200	+	0.105426i
$881$			2.71702e7i			0.0397343i	0.999803	+	0.0198672i	$0.00632433\pi$
$881$			2.71702e7i			0.0397343i	−0.999803	+	0.0198672i	$0.993676\pi$
$882$	−8.43052e7	+	5.23056e7i	−0.122871	+	0.0762329i
$883$	−4.31694e8			−0.627038			−0.313519	−	0.949582i	$-0.601508\pi$
$883$	−4.31694e8			−0.627038			−0.313519	+	0.949582i	$0.601508\pi$
$884$	−5.22492e7	+	6.55184e7i	−0.0756350	+	0.0948433i
$885$	1.03288e8	−	2.14479e8i	0.149011	−	0.309425i
$886$	2.51970e7	+	1.10395e8i	0.0362283	+	0.158727i
$887$	4.41295e8	−	9.16359e8i	0.632351	−	1.31309i	−0.300828	−	0.953678i	$-0.597263\pi$
$887$	4.41295e8	−	9.16359e8i	0.632351	−	1.31309i	0.933179	−	0.359412i	$-0.117023\pi$
$888$	2.42126e8	+	5.02781e8i	0.345783	+	0.718025i
$889$	−4.47018e7	−	8.38610e8i	−0.0636238	−	1.19359i
$890$	7.76388e7	+	3.73889e7i	0.110131	+	0.0530362i
$891$	−4.68044e8	−	5.86909e8i	−0.661688	−	0.829731i
$892$	−9.53142e7	−	1.97922e8i	−0.134296	−	0.278869i
$893$	2.03964e8	−	2.55763e8i	0.286417	−	0.359156i
$894$	3.84995e8	+	8.78726e7i	0.538819	+	0.122982i
$895$	1.36554e8	+	1.08898e8i	0.190474	+	0.151898i
$896$	−7.02787e8	+	2.00306e8i	−0.977012	+	0.278464i
$897$	−2.46752e7	−	3.09417e7i	−0.0341888	−	0.0428714i
$898$	1.94012e8	−	9.34315e7i	0.267917	−	0.129022i
$899$	1.94258e8	+	4.43381e7i	0.267362	+	0.0610236i
$900$	2.15810e8			0.296036
$901$		−	4.40001e8i		−	0.601560i
$902$	4.16382e8	+	9.50364e7i	0.567377	+	0.129500i
$903$	1.92218e8	+	6.74410e8i	0.261054	+	0.915927i
$904$	−3.00649e7	−	1.31723e8i	−0.0406963	−	0.178302i
$905$	−4.44387e7	−	1.94699e8i	−0.0599536	−	0.262674i
$906$	4.36130e8	−	3.47802e8i	0.586450	−	0.467678i
$907$	−3.97892e8	−	4.98941e8i	−0.533265	−	0.668693i	0.440101	−	0.897948i	$-0.354943\pi$
$907$	−3.97892e8	−	4.98941e8i	−0.533265	−	0.668693i	−0.973366	+	0.229255i	$0.926371\pi$
$908$	−1.04029e9	+	2.37440e8i	−1.38963	+	0.317173i
$909$	4.36260e8	−	9.95735e7i	0.580836	−	0.132572i
$910$	1.71187e6	+	3.21148e7i	0.00227168	+	0.0426168i
$911$	2.87081e8	−	1.25778e9i	0.379707	−	1.66361i	−0.318662	−	0.947868i	$-0.603233\pi$
$911$	2.87081e8	−	1.25778e9i	0.379707	−	1.66361i	0.698369	−	0.715738i	$-0.253909\pi$
$912$	8.23065e8			1.08505
$913$		−	2.30529e8i		−	0.302909i
$914$	−7.69513e7	+	3.37146e8i	−0.100781	+	0.441549i
$915$	2.87187e7	+	5.96351e7i	0.0374888	+	0.0778464i
$916$	−6.08291e8	+	4.85096e8i	−0.791453	+	0.631163i
$917$	2.40925e8	+	2.71145e8i	0.312446	+	0.351636i
$918$	−5.31839e7	+	6.66905e7i	−0.0687467	+	0.0862057i
$919$	5.00765e7	−	2.19400e8i	0.0645190	−	0.282676i	−0.932369	−	0.361508i	$-0.882262\pi$
$919$	5.00765e7	−	2.19400e8i	0.0645190	−	0.282676i	0.996888	+	0.0788320i	$0.0251191\pi$
$920$	1.87626e7	+	1.49627e7i	0.0240952	+	0.0192153i
$921$	−4.40323e8	+	2.12049e8i	−0.563629	+	0.271429i
$922$	2.35358e8	−	1.87692e8i	0.300286	−	0.239470i
$923$	−1.45014e8	+	3.01124e8i	−0.184419	+	0.382949i
$924$	3.98024e8	−	5.57594e8i	0.504537	−	0.706809i
$925$	−6.18024e8	+	2.97625e8i	−0.780873	+	0.376048i
$926$	1.87637e8	+	9.03612e7i	0.236312	+	0.113802i
$927$	2.21012e8	−	5.04445e7i	0.277445	−	0.0633249i
$928$	−1.63769e8	−	7.88672e7i	−0.204922	−	0.0986853i
$929$	−5.06376e8	−	4.03821e8i	−0.631576	−	0.503665i	0.254580	−	0.967052i	$-0.418063\pi$
$929$	−5.06376e8	−	4.03821e8i	−0.631576	−	0.503665i	−0.886156	+	0.463387i	$0.846634\pi$
$930$			1.29551e8i			0.161061i
$931$	−6.54599e8	−	1.05507e9i	−0.811197	−	1.30747i
$932$	1.35432e9			1.67292
$933$	−8.79104e8	+	1.10236e9i	−1.08242	+	1.35731i
$934$	−2.57380e7	+	5.34455e7i	−0.0315889	+	0.0655949i
$935$	2.09190e7	+	9.16522e7i	0.0255921	+	0.112127i
$936$	−3.31374e7	+	6.88104e7i	−0.0404101	+	0.0839125i
$937$	−1.77503e7	−	3.68589e7i	−0.0215768	−	0.0448047i	0.889902	−	0.456152i	$-0.150773\pi$
$937$	−1.77503e7	−	3.68589e7i	−0.0215768	−	0.0448047i	−0.911479	+	0.411347i	$0.865058\pi$
$938$	−3.37488e7	+	8.08256e7i	−0.0408931	+	0.0979355i
$939$	−6.74783e8	−	3.24959e8i	−0.815019	−	0.392492i
$940$	4.37412e7	+	5.48497e7i	0.0526632	+	0.0660375i
$941$	−5.38900e8	−	1.11904e9i	−0.646755	−	1.34300i	−0.924071	−	0.382221i	$-0.875159\pi$
$941$	−5.38900e8	−	1.11904e9i	−0.646755	−	1.34300i	0.277316	−	0.960779i	$-0.410555\pi$
$942$	−2.58017e7	+	3.23543e7i	−0.0308670	+	0.0387060i
$943$	−1.99156e8	−	4.54561e7i	−0.237497	−	0.0542072i
$944$	−3.49218e8	−	2.78492e8i	−0.415127	−	0.331053i
$945$	−1.06831e7	−	2.00415e8i	−0.0126590	−	0.237485i
$946$	1.37180e8	+	1.72018e8i	0.162038	+	0.203189i
$947$	−1.26396e9	+	6.08689e8i	−1.48827	+	0.716714i	−0.988749	−	0.149587i	$-0.952206\pi$
$947$	−1.26396e9	+	6.08689e8i	−1.48827	+	0.716714i	−0.499523	+	0.866301i	$0.666491\pi$
$948$	1.78028e8	+	4.06338e7i	0.208960	+	0.0476938i
$949$	1.98736e8			0.232530
$950$		−	4.40528e8i		−	0.513810i
$951$	2.79277e8	+	6.37432e7i	0.324709	+	0.0741126i
$952$	−2.25900e8	−	9.43248e7i	−0.261821	−	0.109324i
$953$	−2.07258e8	−	9.08056e8i	−0.239460	−	1.04914i	−0.941502	−	0.337006i	$-0.890586\pi$
$953$	−2.07258e8	−	9.08056e8i	−0.239460	−	1.04914i	0.702043	−	0.712135i	$-0.252272\pi$
$954$	−4.12515e7	−	1.80735e8i	−0.0475111	−	0.208160i
$955$	−1.77993e8	+	1.41945e8i	−0.204359	+	0.162971i
$956$	4.80994e8	+	6.03147e8i	0.550511	+	0.690319i
$957$	2.13204e8	−	4.86623e7i	0.243253	−	0.0555210i
$958$	1.84639e8	−	4.21426e7i	0.210003	−	0.0479319i
$959$	−1.23663e8	+	1.09881e8i	−0.140212	+	0.124585i
$960$	−1.93855e7	+	8.49333e7i	−0.0219110	+	0.0959985i
$961$	−2.06306e8			−0.232457
$962$		−	1.12225e8i		−	0.126056i
$963$	−8.97458e7	+	3.93202e8i	−0.100493	+	0.440288i
$964$	5.83098e8	+	1.21081e9i	0.650894	+	1.35159i
$965$	3.43902e8	−	2.74252e8i	0.382694	−	0.305189i
$966$	3.10518e7	−	4.35005e7i	0.0344473	−	0.0482573i
$967$	−9.97697e7	+	1.25107e8i	−0.110336	+	0.138358i	−0.833933	−	0.551866i	$-0.813916\pi$
$967$	−9.97697e7	+	1.25107e8i	−0.110336	+	0.138358i	0.723597	+	0.690223i	$0.242488\pi$
$968$	−3.71079e7	+	1.62580e8i	−0.0409110	+	0.179243i
$969$	5.24992e8	+	4.18667e8i	0.577007	+	0.460148i
$970$	−1.30870e8	+	6.30237e7i	−0.143392	+	0.0690540i
$971$	3.20611e8	−	2.55679e8i	0.350204	−	0.279278i	−0.432550	−	0.901610i	$-0.642386\pi$
$971$	3.20611e8	−	2.55679e8i	0.350204	−	0.279278i	0.782754	+	0.622332i	$0.213815\pi$
$972$	2.51338e8	−	5.21909e8i	0.273691	−	0.568324i
$973$	1.74676e8	−	1.01065e9i	0.189625	−	1.09714i
$974$	6.29606e7	−	3.03202e7i	0.0681384	−	0.0328137i
$975$	−3.03633e8	−	1.46222e8i	−0.327594	−	0.157761i
$976$	1.21080e8	−	2.76358e7i	0.130234	−	0.0297250i
$977$	1.14475e9	+	5.51283e8i	1.22752	+	0.591140i	0.931395	−	0.364010i	$-0.118593\pi$
$977$	1.14475e9	+	5.51283e8i	1.22752	+	0.591140i	0.296121	+	0.955151i	$0.404307\pi$
$978$	−3.72620e8	−	2.97155e8i	−0.398336	−	0.317662i
$979$			7.98523e8i			0.851019i
$980$	2.51831e8	−	8.65138e7i	0.267566	−	0.0919194i
$981$	3.07425e8			0.325636
$982$	−2.49281e8	+	3.12589e8i	−0.263242	+	0.330095i
$983$	3.14735e8	−	6.53555e8i	0.331349	−	0.688052i	−0.667027	−	0.745034i	$-0.732433\pi$
$983$	3.14735e8	−	6.53555e8i	0.331349	−	0.688052i	0.998375	+	0.0569814i	$0.0181476\pi$
$984$	3.14901e8	+	1.37967e9i	0.330513	+	1.44807i
$985$	−1.62937e8	+	3.38342e8i	−0.170495	+	0.354036i
$986$	−1.56744e7	−	3.25482e7i	−0.0163516	−	0.0339545i
$987$	2.52644e8	−	2.24486e8i	0.262758	−	0.233474i
$988$	−3.98110e8	−	1.91720e8i	−0.412793	−	0.198791i
$989$	−6.56135e7	−	8.22767e7i	−0.0678273	−	0.0850527i
$990$	1.71854e7	+	3.56859e7i	0.0177115	+	0.0367782i
$991$	1.90079e7	−	2.38352e7i	0.0195305	−	0.0244905i	−0.771970	−	0.635659i	$-0.780729\pi$
$991$	1.90079e7	−	2.38352e7i	0.0195305	−	0.0244905i	0.791501	+	0.611168i	$0.209300\pi$
$992$	9.72817e8	+	2.22039e8i	0.996543	+	0.227454i
$993$	−1.15301e9	−	9.19494e8i	−1.17757	−	0.939077i
$994$	−4.44765e8	−	7.68714e7i	−0.452868	−	0.0782719i
$995$	−6.94001e7	−	8.70250e7i	−0.0704516	−	0.0883435i
$996$	3.18156e8	−	1.53216e8i	0.322005	−	0.155069i
$997$	−8.66912e8	−	1.97867e8i	−0.874761	−	0.199659i	−0.238510	−	0.971140i	$-0.576659\pi$
$997$	−8.66912e8	−	1.97867e8i	−0.874761	−	0.199659i	−0.636252	+	0.771482i	$0.719516\pi$
$998$	−3.01177e8			−0.302991
$999$			7.00351e8i			0.702456i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	49.7.f.a.6.17	✓	162
49.41	odd	14	inner	49.7.f.a.41.17	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
49.7.f.a.6.17	✓	162	1.1	even	1	trivial
49.7.f.a.41.17	yes	162	49.41	odd	14	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 49 = 7^{2} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	49.f (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.86787 - 2.34223i) q^{2} +(13.7924 - 28.6402i) q^{3} +(12.2442 + 53.6454i) q^{4} +(17.8467 - 37.0591i) q^{5} +(-41.3197 - 85.8012i) q^{6} +(329.864 - 94.0163i) q^{7} +(321.266 + 154.714i) q^{8} +(-175.506 - 220.078i) q^{9} +(-53.4657 - 111.023i) q^{10} +(711.951 - 892.758i) q^{11} +(1705.29 + 389.222i) q^{12} +(-594.892 - 474.411i) q^{13} +(395.934 - 948.228i) q^{14} +(-815.230 - 1022.27i) q^{15} +(-2210.39 + 1064.47i) q^{16} +(-1951.36 - 445.385i) q^{17} -843.298 q^{18} -10553.8i q^{19} +(2206.57 + 503.635i) q^{20} +(1856.96 - 10744.1i) q^{21} +(-761.217 - 3335.11i) q^{22} +(364.092 + 1595.19i) q^{23} +(8862.06 - 7067.26i) q^{24} +(8687.16 + 10893.4i) q^{25} +(-2222.36 + 507.240i) q^{26} +(13868.9 - 3165.48i) q^{27} +(9082.46 + 16544.5i) q^{28} +(-1340.62 + 5873.65i) q^{29} -3917.13 q^{30} -33072.8i q^{31} +(-6713.65 + 29414.4i) q^{32} +(-15749.3 - 32703.7i) q^{33} +(-4688.09 + 3738.62i) q^{34} +(2402.82 - 13902.3i) q^{35} +(9657.24 - 12109.8i) q^{36} +(-10955.1 + 47997.6i) q^{37} +(-24719.4 - 19713.1i) q^{38} +(-21792.2 + 10494.6i) q^{39} +(11467.1 - 9144.70i) q^{40} +(-54169.5 + 112484. i) q^{41} +(-21696.6 - 24418.0i) q^{42} +(-57947.3 + 27906.0i) q^{43} +(56609.6 + 27261.8i) q^{44} +(-11288.1 + 2576.44i) q^{45} +(4416.39 + 2126.82i) q^{46} +(24234.2 + 19326.2i) q^{47} +77987.6i q^{48} +(99970.9 - 62025.1i) q^{49} +41741.3 q^{50} +(-39669.9 + 49744.4i) q^{51} +(18166.0 - 37722.0i) q^{52} +(48916.9 + 214319. i) q^{53} +(18490.9 - 38396.8i) q^{54} +(-20378.8 - 42317.0i) q^{55} +(120520. + 20830.1i) q^{56} +(-302262. - 145562. i) q^{57} +(11253.4 + 14111.3i) q^{58} +(78994.6 + 164034. i) q^{59} +(44858.1 - 56250.2i) q^{60} +(-49353.0 - 11264.5i) q^{61} +(-77464.3 - 61775.7i) q^{62} +(-78584.1 - 56095.3i) q^{63} +(-41541.7 - 52091.6i) q^{64} +(-28198.1 + 13579.5i) q^{65} +(-106017. - 24197.7i) q^{66} -85238.5 q^{67} -110135. i q^{68} +(50708.3 + 11573.8i) q^{69} +(-28074.3 - 31595.7i) q^{70} +(-97742.1 - 428236. i) q^{71} +(-22335.2 - 97857.0i) q^{72} +(-204204. + 162847. i) q^{73} +(91958.9 + 115313. i) q^{74} +(431804. - 98556.5i) q^{75} +(566162. - 129223. i) q^{76} +(150913. - 361423. i) q^{77} +(-16124.2 + 70644.9i) q^{78} +104397. q^{79} +100912. i q^{80} +(146288. - 640928. i) q^{81} +(162283. + 336983. i) q^{82} +(157840. - 125873. i) q^{83} +(599107. - 31935.2i) q^{84} +(-51331.0 + 64367.0i) q^{85} +(-42875.8 + 187851. i) q^{86} +(149732. + 119407. i) q^{87} +(366848. - 176665. i) q^{88} +(-546739. + 436010. i) q^{89} +(-15050.1 + 31251.8i) q^{90} +(-240836. - 100561. i) q^{91} +(-81116.7 + 39063.7i) q^{92} +(-947211. - 456153. i) q^{93} +(90532.8 - 20663.5i) q^{94} +(-391114. - 188350. i) q^{95} +(749837. + 597975. i) q^{96} -1.17877e6i q^{97} +(41455.3 - 350010. i) q^{98} -321428. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q - 5 q^{2} - 7 q^{3} - 837 q^{4} - 7 q^{5} - 791 q^{6} + 70 q^{7} - 843 q^{8} + 2990 q^{9} - 7 q^{10} + 1171 q^{11} - 13482 q^{12} - 7 q^{13} + 22533 q^{14} + 6181 q^{15} - 17901 q^{16} - 3143 q^{17}+ \cdots + 4449580 q^{99}+O(q^{100}) \) 162 * q - 5 * q^2 - 7 * q^3 - 837 * q^4 - 7 * q^5 - 791 * q^6 + 70 * q^7 - 843 * q^8 + 2990 * q^9 - 7 * q^10 + 1171 * q^11 - 13482 * q^12 - 7 * q^13 + 22533 * q^14 + 6181 * q^15 - 17901 * q^16 - 3143 * q^17 - 22692 * q^18 + 50169 * q^20 + 28553 * q^21 - 33057 * q^22 - 49677 * q^23 - 119077 * q^24 + 30038 * q^25 + 59577 * q^26 + 11753 * q^27 + 42994 * q^28 + 80383 * q^29 + 27328 * q^30 + 253875 * q^32 - 7 * q^33 + 54677 * q^34 - 74067 * q^35 - 193099 * q^36 + 118463 * q^37 - 121079 * q^38 - 304143 * q^39 - 702079 * q^40 - 58023 * q^41 - 1137479 * q^42 + 93963 * q^43 + 352505 * q^44 + 1333577 * q^45 + 782877 * q^46 + 408261 * q^47 - 149338 * q^49 + 1164004 * q^50 - 911743 * q^51 + 721273 * q^52 - 992325 * q^53 - 576646 * q^54 - 1502935 * q^55 + 1368514 * q^56 + 116032 * q^57 + 2610717 * q^58 + 24493 * q^59 - 1027131 * q^60 + 563101 * q^61 - 262199 * q^62 - 966154 * q^63 - 2839067 * q^64 - 140287 * q^65 - 1523319 * q^66 - 1313660 * q^67 + 2216753 * q^69 + 1806959 * q^70 + 1031011 * q^71 - 3123354 * q^72 - 846727 * q^73 + 1270357 * q^74 + 873173 * q^75 + 5463990 * q^76 + 1565235 * q^77 + 1006005 * q^78 + 82420 * q^79 + 2259538 * q^81 - 7672672 * q^82 - 3860031 * q^83 - 9104942 * q^84 + 1596833 * q^85 + 224039 * q^86 + 2590525 * q^87 + 4179421 * q^88 + 5417433 * q^89 + 6759578 * q^90 - 6163507 * q^91 - 7060306 * q^92 + 1903160 * q^93 + 4029998 * q^94 + 2115400 * q^95 + 957950 * q^96 - 1546783 * q^98 + 4449580 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more