LMFDB - Embedded newform 62.7.f.a.15.14

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [62,7,Mod(15,62)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(62, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("62.15"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 62 = 2 \cdot 31 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	62.f (of order $10$, degree $4$, 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:	$14.2633531844$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$16$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			15.14
Character	$\chi$	$=$	62.15
Dual form			62.7.f.a.29.14

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.57649 - 3.32502i) q^{2} +(15.4410 - 21.2527i) q^{3} +(9.88854 - 30.4338i) q^{4} +6.26454 q^{5} -148.604i q^{6} +(109.443 - 336.831i) q^{7} +(-55.9381 - 172.160i) q^{8} +(12.0203 + 36.9947i) q^{9} +(28.6696 - 20.8297i) q^{10} +(-988.558 - 321.202i) q^{11} +(-494.112 - 680.086i) q^{12} +(1598.75 - 2200.48i) q^{13} +(-619.103 - 1905.40i) q^{14} +(96.7308 - 133.138i) q^{15} +(-828.433 - 601.892i) q^{16} +(576.948 - 187.462i) q^{17} +(178.019 + 129.338i) q^{18} +(-9178.28 + 6668.41i) q^{19} +(61.9472 - 190.654i) q^{20} +(-5468.66 - 7526.96i) q^{21} +(-5592.13 + 1816.99i) q^{22} +(12987.6 - 4219.91i) q^{23} +(-4522.60 - 1469.48i) q^{24} -15585.8 q^{25} -15386.3i q^{26} +(19185.2 + 6233.65i) q^{27} +(-9168.81 - 6661.53i) q^{28} +(-3018.28 - 4154.30i) q^{29} -930.938i q^{30} +(9749.41 - 28150.5i) q^{31} -5792.62 q^{32} +(-22090.7 + 16049.8i) q^{33} +(2017.08 - 2776.28i) q^{34} +(685.610 - 2110.09i) q^{35} +1244.75 q^{36} -20798.0i q^{37} +(-19831.8 + 61035.9i) q^{38} +(-22080.0 - 67955.3i) q^{39} +(-350.426 - 1078.50i) q^{40} +(21655.4 - 15733.6i) q^{41} +(-50054.5 - 16263.7i) q^{42} +(78114.4 + 107515. i) q^{43} +(-19550.8 + 26909.4i) q^{44} +(75.3017 + 231.755i) q^{45} +(45406.2 - 62496.2i) q^{46} +(69915.4 + 50796.5i) q^{47} +(-25583.7 + 8312.64i) q^{48} +(-6297.21 - 4575.19i) q^{49} +(-71328.1 + 51822.9i) q^{50} +(4924.58 - 15156.3i) q^{51} +(-51159.8 - 70415.5i) q^{52} +(165534. - 53785.2i) q^{53} +(108528. - 35262.9i) q^{54} +(-6192.86 - 2012.18i) q^{55} -64110.7 q^{56} +298030. i q^{57} +(-27626.3 - 8976.31i) q^{58} +(213614. + 155200. i) q^{59} +(-3095.38 - 4260.43i) q^{60} +240009. i q^{61} +(-48982.9 - 161248. i) q^{62} +13776.5 q^{63} +(-26509.9 + 19260.5i) q^{64} +(10015.4 - 13785.0i) q^{65} +(-47732.0 + 146904. i) q^{66} +135109. q^{67} -19412.4i q^{68} +(110856. - 341180. i) q^{69} +(-3878.40 - 11936.5i) q^{70} +(24551.9 + 75563.1i) q^{71} +(5696.60 - 4138.82i) q^{72} +(87800.2 + 28528.0i) q^{73} +(-69153.8 - 95182.0i) q^{74} +(-240660. + 331239. i) q^{75} +(112185. + 345271. i) q^{76} +(-216381. + 297823. i) q^{77} +(-327001. - 237580. i) q^{78} +(206942. - 67239.7i) q^{79} +(-5189.76 - 3770.58i) q^{80} +(405779. - 294816. i) q^{81} +(46791.4 - 144009. i) q^{82} +(23542.5 + 32403.4i) q^{83} +(-283151. + 92001.4i) q^{84} +(3614.31 - 1174.36i) q^{85} +(714980. + 232311. i) q^{86} -134895. q^{87} +188157. i q^{88} +(-1.25555e6 - 407954. i) q^{89} +(1115.21 + 810.245i) q^{90} +(-566219. - 779334. i) q^{91} -436989. i q^{92} +(-447734. - 641874. i) q^{93} +488867. q^{94} +(-57497.8 + 41774.6i) q^{95} +(-89443.8 + 123109. i) q^{96} +(-21348.5 + 65703.9i) q^{97} -44031.7 q^{98} -40432.3i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9} + 1344 q^{10} + 3200 q^{11} - 3600 q^{13} + 4560 q^{14} + 9520 q^{15} - 16384 q^{16} - 1400 q^{17} - 11200 q^{18} + 2912 q^{19} - 9216 q^{20} + 4860 q^{21}+ \cdots + 13577088 q^{98}+O(q^{100}) $ 64 * q - 512 * q^4 - 288 * q^5 - 692 * q^7 + 3248 * q^9 + 1344 * q^10 + 3200 * q^11 - 3600 * q^13 + 4560 * q^14 + 9520 * q^15 - 16384 * q^16 - 1400 * q^17 - 11200 * q^18 + 2912 * q^19 - 9216 * q^20 + 4860 * q^21 + 6720 * q^22 - 26240 * q^23 + 241592 * q^25 - 206100 * q^27 + 16896 * q^28 - 48160 * q^29 + 142924 * q^31 + 291360 * q^33 + 123840 * q^34 + 16728 * q^35 - 518144 * q^36 - 89856 * q^38 - 169400 * q^39 - 64512 * q^40 - 291056 * q^41 + 220320 * q^42 + 145600 * q^43 - 44412 * q^45 - 213120 * q^46 + 596760 * q^47 - 163840 * q^48 + 481596 * q^49 - 295744 * q^50 + 1117652 * q^51 + 115200 * q^52 - 1276880 * q^53 + 290880 * q^55 - 97280 * q^56 - 367200 * q^58 + 469780 * q^59 - 304640 * q^60 - 963152 * q^62 - 1359328 * q^63 - 524288 * q^64 + 934760 * q^65 - 789792 * q^66 + 1470992 * q^67 - 933024 * q^69 + 515232 * q^70 - 906672 * q^71 - 358400 * q^72 + 1236840 * q^73 - 126400 * q^74 - 2881620 * q^75 - 139776 * q^76 + 3063520 * q^77 + 2374288 * q^78 + 4375280 * q^79 + 442368 * q^80 - 3676208 * q^81 + 1386144 * q^82 + 4922820 * q^83 - 601600 * q^84 - 1012320 * q^85 - 2054800 * q^86 - 5911600 * q^87 - 1219900 * q^89 - 2696992 * q^90 + 163640 * q^91 - 248320 * q^93 + 290592 * q^94 + 2034328 * q^95 - 1078884 * q^97 + 13577088 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/62\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	4.57649	−	3.32502i	0.572061	−	0.415627i
$2$	4.57649	−	3.32502i	0.572061	−	0.415627i
$3$	15.4410	−	21.2527i	0.571889	−	0.787137i	−0.420888	−	0.907112i	$-0.638282\pi$
$3$	15.4410	−	21.2527i	0.571889	−	0.787137i	0.992777	+	0.119975i	$0.0382816\pi$
$4$	9.88854	−	30.4338i	0.154508	−	0.475528i
$5$	6.26454			0.0501163			0.0250582	−	0.999686i	$-0.492023\pi$
$5$	6.26454			0.0501163			0.0250582	+	0.999686i	$0.492023\pi$
$6$		−	148.604i		−	0.687983i
$7$	109.443	−	336.831i	0.319076	−	0.982014i	−0.654968	−	0.755656i	$-0.727318\pi$
$7$	109.443	−	336.831i	0.319076	−	0.982014i	0.974044	−	0.226358i	$-0.0726819\pi$
$8$	−55.9381	−	172.160i	−0.109254	−	0.336249i
$9$	12.0203	+	36.9947i	0.0164888	+	0.0507472i
$10$	28.6696	−	20.8297i	0.0286696	−	0.0208297i
$11$	−988.558	−	321.202i	−0.742718	−	0.241324i	−0.0868731	−	0.996219i	$-0.527687\pi$
$11$	−988.558	−	321.202i	−0.742718	−	0.241324i	−0.655845	+	0.754896i	$0.727687\pi$
$12$	−494.112	−	680.086i	−0.285944	−	0.393569i
$13$	1598.75	−	2200.48i	0.727695	−	1.00159i	−0.271538	−	0.962428i	$-0.587532\pi$
$13$	1598.75	−	2200.48i	0.727695	−	1.00159i	0.999233	−	0.0391581i	$-0.0124676\pi$
$14$	−619.103	−	1905.40i	−0.225621	−	0.694389i
$15$	96.7308	−	133.138i	0.0286610	−	0.0394484i
$16$	−828.433	−	601.892i	−0.202254	−	0.146946i
$17$	576.948	−	187.462i	0.117433	−	0.0381562i	−0.249711	−	0.968320i	$-0.580336\pi$
$17$	576.948	−	187.462i	0.117433	−	0.0381562i	0.367144	+	0.930164i	$0.380336\pi$
$18$	178.019	+	129.338i	0.0305245	+	0.0221773i
$19$	−9178.28	+	6668.41i	−1.33814	+	0.972214i	−0.338627	+	0.940921i	$0.609962\pi$
$19$	−9178.28	+	6668.41i	−1.33814	+	0.972214i	−0.999510	+	0.0312929i	$0.990038\pi$
$20$	61.9472	−	190.654i	0.00774340	−	0.0238317i
$21$	−5468.66	−	7526.96i	−0.590504	−	0.812759i
$22$	−5592.13	+	1816.99i	−0.525181	+	0.170642i
$23$	12987.6	−	4219.91i	1.06744	−	0.346833i	0.277950	−	0.960595i	$-0.410345\pi$
$23$	12987.6	−	4219.91i	1.06744	−	0.346833i	0.789490	+	0.613763i	$0.210345\pi$
$24$	−4522.60	−	1469.48i	−0.327155	−	0.106299i
$25$	−15585.8			−0.997488
$26$		−	15386.3i		−	0.875418i
$27$	19185.2	+	6233.65i	0.974710	+	0.316702i
$28$	−9168.81	−	6661.53i	−0.417676	−	0.303459i
$29$	−3018.28	−	4154.30i	−0.123756	−	0.170335i	0.742644	−	0.669687i	$-0.233572\pi$
$29$	−3018.28	−	4154.30i	−0.123756	−	0.170335i	−0.866399	+	0.499352i	$0.833572\pi$
$30$		−	930.938i		−	0.0344792i
$31$	9749.41	−	28150.5i	0.327260	−	0.944934i
$31$	9749.41	−	28150.5i	0.327260	−	0.944934i
$32$	−5792.62			−0.176777
$33$	−22090.7	+	16049.8i	−0.614707	+	0.446611i
$34$	2017.08	−	2776.28i	0.0513200	−	0.0706360i
$35$	685.610	−	2110.09i	0.0159909	−	0.0492150i
$36$	1244.75			0.0266794
$37$		−	20798.0i		−	0.410598i	−0.978699	−	0.205299i	$-0.934183\pi$
$37$		−	20798.0i		−	0.410598i	0.978699	−	0.205299i	$-0.0658167\pi$
$38$	−19831.8	+	61035.9i	−0.361419	+	1.11233i
$39$	−22080.0	−	67955.3i	−0.372225	−	1.14559i
$40$	−350.426	−	1078.50i	−0.00547541	−	0.0168516i
$41$	21655.4	−	15733.6i	0.314206	−	0.228284i	−0.419493	−	0.907759i	$-0.637792\pi$
$41$	21655.4	−	15733.6i	0.314206	−	0.228284i	0.733699	+	0.679474i	$0.237792\pi$
$42$	−50054.5	−	16263.7i	−0.675609	−	0.219519i
$43$	78114.4	+	107515.i	0.982484	+	1.35227i	0.935480	+	0.353379i	$0.114967\pi$
$43$	78114.4	+	107515.i	0.982484	+	1.35227i	0.0470043	+	0.998895i	$0.485033\pi$
$44$	−19550.8	+	26909.4i	−0.229512	+	0.315897i
$45$	75.3017	+	231.755i	0.000826357	+	0.00254326i
$46$	45406.2	−	62496.2i	0.466489	−	0.642067i
$47$	69915.4	+	50796.5i	0.673410	+	0.489261i	0.871165	−	0.490990i	$-0.163365\pi$
$47$	69915.4	+	50796.5i	0.673410	+	0.489261i	−0.197755	+	0.980251i	$0.563365\pi$
$48$	−25583.7	+	8312.64i	−0.231334	+	0.0751649i
$49$	−6297.21	−	4575.19i	−0.0535254	−	0.0388885i
$50$	−71328.1	+	51822.9i	−0.570625	+	0.414583i
$51$	4924.58	−	15156.3i	0.0371243	−	0.114257i
$52$	−51159.8	−	70415.5i	−0.363847	−	0.500793i
$53$	165534.	−	53785.2i	1.11188	−	0.361273i	0.305219	−	0.952282i	$-0.401270\pi$
$53$	165534.	−	53785.2i	1.11188	−	0.361273i	0.806665	+	0.591009i	$0.201270\pi$
$54$	108528.	−	35262.9i	0.689224	−	0.223942i
$55$	−6192.86	−	2012.18i	−0.0372223	−	0.0120943i
$56$	−64110.7			−0.365062
$57$			298030.i			1.60930i
$58$	−27626.3	−	8976.31i	−0.141592	−	0.0460060i
$59$	213614.	+	155200.i	1.04010	+	0.755674i	0.970304	−	0.241887i	$-0.0777665\pi$
$59$	213614.	+	155200.i	1.04010	+	0.755674i	0.0697919	+	0.997562i	$0.477766\pi$
$60$	−3095.38	−	4260.43i	−0.0143305	−	0.0197242i
$61$			240009.i			1.05740i	0.848809	+	0.528699i	$0.177320\pi$
$61$			240009.i			1.05740i	−0.848809	+	0.528699i	$0.822680\pi$
$62$	−48982.9	−	161248.i	−0.205527	−	0.676579i
$63$	13776.5			0.0550956
$64$	−26509.9	+	19260.5i	−0.101127	+	0.0734732i
$65$	10015.4	−	13785.0i	0.0364694	−	0.0501958i
$66$	−47732.0	+	146904.i	−0.166027	+	0.510977i
$67$	135109.			0.449220			0.224610	−	0.974449i	$-0.427889\pi$
$67$	135109.			0.449220			0.224610	+	0.974449i	$0.427889\pi$
$68$		−	19412.4i		−	0.0617381i
$69$	110856.	−	341180.i	0.337452	−	1.03857i
$70$	−3878.40	−	11936.5i	−0.0113073	−	0.0348002i
$71$	24551.9	+	75563.1i	0.0685979	+	0.211123i	0.979479	−	0.201546i	$-0.0645967\pi$
$71$	24551.9	+	75563.1i	0.0685979	+	0.211123i	−0.910881	+	0.412669i	$0.864597\pi$
$72$	5696.60	−	4138.82i	0.0152622	−	0.0110887i
$73$	87800.2	+	28528.0i	0.225697	+	0.0733336i	0.419683	−	0.907671i	$-0.362141\pi$
$73$	87800.2	+	28528.0i	0.225697	+	0.0733336i	−0.193985	+	0.981004i	$0.562141\pi$
$74$	−69153.8	−	95182.0i	−0.170656	−	0.234887i
$75$	−240660.	+	331239.i	−0.570452	+	0.785160i
$76$	112185.	+	345271.i	0.255561	+	0.786537i
$77$	−216381.	+	297823.i	−0.473967	+	0.652359i
$78$	−327001.	−	237580.i	−0.689074	−	0.500642i
$79$	206942.	−	67239.7i	0.419728	−	0.136378i	−0.0915355	−	0.995802i	$-0.529178\pi$
$79$	206942.	−	67239.7i	0.419728	−	0.136378i	0.511264	+	0.859424i	$0.329178\pi$
$80$	−5189.76	−	3770.58i	−0.0101362	−	0.00736441i
$81$	405779.	−	294816.i	0.763545	−	0.554748i
$82$	46791.4	−	144009.i	0.0848642	−	0.261185i
$83$	23542.5	+	32403.4i	0.0411735	+	0.0566704i	0.829107	−	0.559089i	$-0.188849\pi$
$83$	23542.5	+	32403.4i	0.0411735	+	0.0566704i	−0.787934	+	0.615760i	$0.788849\pi$
$84$	−283151.	+	92001.4i	−0.477728	+	0.155223i
$85$	3614.31	−	1174.36i	0.00588531	−	0.00191225i
$86$	714980.	+	232311.i	1.12408	+	0.365237i
$87$	−134895.			−0.204852
$88$			188157.i			0.276104i
$89$	−1.25555e6	−	407954.i	−1.78101	−	0.578684i	−0.782002	−	0.623276i	$-0.785801\pi$
$89$	−1.25555e6	−	407954.i	−1.78101	−	0.578684i	−0.999005	+	0.0445922i	$0.985801\pi$
$90$	1115.21	+	810.245i	0.00152978	+	0.00111145i
$91$	−566219.	−	779334.i	−0.751382	−	1.03419i
$92$		−	436989.i		−	0.561187i
$93$	−447734.	−	641874.i	−0.556636	−	0.797996i
$94$	488867.			0.588582
$95$	−57497.8	+	41774.6i	−0.0670625	+	0.0487238i
$96$	−89443.8	+	123109.i	−0.101097	+	0.139147i
$97$	−21348.5	+	65703.9i	−0.0233912	+	0.0719907i	−0.962071	−	0.272800i	$-0.912050\pi$
$97$	−21348.5	+	65703.9i	−0.0233912	+	0.0719907i	0.938680	+	0.344791i	$0.112050\pi$
$98$	−44031.7			−0.0467829
$99$		−	40432.3i		−	0.0416700i
$100$	−154120.	+	474334.i	−0.154120	+	0.474334i
$101$	−362158.	−	1.11461e6i	−0.351507	−	1.08183i	−0.958007	−	0.286743i	$-0.907427\pi$
$101$	−362158.	−	1.11461e6i	−0.351507	−	1.08183i	0.606501	−	0.795083i	$-0.292573\pi$
$102$	−27857.6	−	85736.9i	−0.0262508	−	0.0807918i
$103$	473233.	−	343824.i	0.433075	−	0.314647i	−0.349802	−	0.936824i	$-0.613751\pi$
$103$	473233.	−	343824.i	0.433075	−	0.314647i	0.782877	+	0.622176i	$0.213751\pi$
$104$	−468265.	−	152149.i	−0.416286	−	0.135260i
$105$	−34258.6	−	47153.0i	−0.0295939	−	0.0407325i
$106$	578728.	−	796551.i	0.485911	−	0.668799i
$107$	−158399.	−	487503.i	−0.129301	−	0.397948i	0.865359	−	0.501152i	$-0.167090\pi$
$107$	−158399.	−	487503.i	−0.129301	−	0.397948i	−0.994660	+	0.103205i	$0.967090\pi$
$108$	379428.	−	522237.i	0.301202	−	0.414569i
$109$	−605771.	−	440118.i	−0.467766	−	0.339852i	0.328804	−	0.944398i	$-0.393354\pi$
$109$	−605771.	−	440118.i	−0.467766	−	0.339852i	−0.796570	+	0.604546i	$0.793354\pi$
$110$	−35032.1	+	11382.6i	−0.0263201	+	0.00855193i
$111$	−442014.	−	321142.i	−0.323197	−	0.234816i
$112$	−293402.	+	213169.i	−0.208838	+	0.151730i
$113$	−61359.8	+	188846.i	−0.0425254	+	0.130880i	−0.970065	−	0.242845i	$-0.921919\pi$
$113$	−61359.8	+	188846.i	−0.0425254	+	0.130880i	0.927540	+	0.373724i	$0.121919\pi$
$114$	990955.	+	1.36393e6i	0.668866	+	0.920616i
$115$	81361.1	−	26435.8i	0.0534962	−	0.0173820i
$116$	−156278.	+	50777.7i	−0.100121	+	0.0325311i
$117$	100624.	+	32694.6i	0.0628265	+	0.0204136i
$118$	1.49364e6			0.909077
$119$		−	214850.i		−	0.127495i
$120$	−28332.0	−	9205.62i	−0.0163958	−	0.00532733i
$121$	−559148.	−	406244.i	−0.315624	−	0.229314i
$122$	798035.	+	1.09840e6i	0.439483	+	0.604897i
$123$		−	703178.i		−	0.377877i
$124$	−760320.	−	575080.i	−0.398778	−	0.301622i
$125$	−195521.			−0.100107
$126$	63048.0	−	45807.1i	0.0315181	−	0.0228992i
$127$	−1.84382e6	+	2.53780e6i	−0.900135	+	1.23893i	0.0702901	+	0.997527i	$0.477607\pi$
$127$	−1.84382e6	+	2.53780e6i	−0.900135	+	1.23893i	−0.970425	+	0.241403i	$0.922393\pi$
$128$	−57280.6	+	176291.i	−0.0273135	+	0.0840623i
$129$	3.49115e6			1.62630
$130$		−	96388.4i		−	0.0438728i
$131$	−1.34441e6	+	4.13767e6i	−0.598023	+	1.84053i	−0.0589594	+	0.998260i	$0.518778\pi$
$131$	−1.34441e6	+	4.13767e6i	−0.598023	+	1.84053i	−0.539064	+	0.842265i	$0.681222\pi$
$132$	270013.	+	831014.i	0.117399	+	0.361316i
$133$	1.24163e6	+	3.82134e6i	0.527760	+	1.62428i
$134$	618324.	−	449239.i	0.256981	−	0.186708i
$135$	120187.	+	39051.0i	0.0488489	+	0.0158720i
$136$	−64546.6	−	88840.8i	−0.0256600	−	0.0353180i
$137$	1.03409e6	−	1.42330e6i	0.402158	−	0.553523i	−0.559126	−	0.829083i	$-0.688863\pi$
$137$	1.03409e6	−	1.42330e6i	0.402158	−	0.553523i	0.961284	+	0.275560i	$0.0888632\pi$
$138$	−627097.	−	1.93001e6i	−0.238615	−	0.734381i
$139$	−2.69709e6	+	3.71223e6i	−1.00427	+	1.38226i	−0.0816039	+	0.996665i	$0.526004\pi$
$139$	−2.69709e6	+	3.71223e6i	−1.00427	+	1.38226i	−0.922668	+	0.385596i	$0.873996\pi$
$140$	−57438.4	−	41731.5i	−0.0209324	−	0.0152083i
$141$	2.15913e6	−	701543.i	0.770231	−	0.250263i
$142$	363610.	+	264178.i	0.126990	+	0.0922639i
$143$	−2.28725e6	+	1.66179e6i	−0.782178	+	0.568286i
$144$	12308.8	−	37882.6i	0.00412219	−	0.0126868i
$145$	−18908.1	−	26024.8i	−0.00620219	−	0.00853658i
$146$	496673.	−	161379.i	0.159592	−	0.0518547i
$147$	−194470.	+	63187.2i	−0.0612211	+	0.0198919i
$148$	−632963.	−	205662.i	−0.195251	−	0.0634409i
$149$	2.05914e6			0.622484			0.311242	−	0.950331i	$-0.399255\pi$
$149$	2.05914e6			0.622484			0.311242	+	0.950331i	$0.399255\pi$
$150$			2.31611e6i			0.686255i
$151$	2.62771e6	+	853795.i	0.763215	+	0.247984i	0.664658	−	0.747148i	$-0.268577\pi$
$151$	2.62771e6	+	853795.i	0.763215	+	0.247984i	0.0985570	+	0.995131i	$0.468577\pi$
$152$	1.66145e6	+	1.20711e6i	0.473103	+	0.343729i
$153$	13870.2	+	19090.7i	0.00387265	+	0.00533024i
$154$			2.08246e6i			0.570183i
$155$	61075.6	−	176350.i	0.0164011	−	0.0473566i
$156$	−2.28648e6			−0.602273
$157$	2.03205e6	−	1.47637e6i	0.525091	−	0.381501i	−0.293427	−	0.955981i	$-0.594796\pi$
$157$	2.03205e6	−	1.47637e6i	0.525091	−	0.381501i	0.818518	+	0.574480i	$0.194796\pi$
$158$	723497.	−	995808.i	0.183428	−	0.252467i
$159$	1.41293e6	−	4.34854e6i	0.351502	−	1.08181i
$160$	−36288.1			−0.00885940
$161$		−	4.83645e6i		−	1.15891i
$162$	876778.	−	2.69845e6i	0.206227	−	0.634700i
$163$	−1.01988e6	−	3.13888e6i	−0.235498	−	0.724788i	−0.997055	−	0.0766904i	$-0.975565\pi$
$163$	−1.01988e6	−	3.13888e6i	−0.235498	−	0.724788i	0.761557	−	0.648098i	$-0.224435\pi$
$164$	−264692.	−	814639.i	−0.0600081	−	0.184686i
$165$	−138388.	+	100545.i	−0.0308069	+	0.0223825i
$166$	215484.	+	70014.9i	0.0471075	+	0.0153062i
$167$	−1.68494e6	−	2.31911e6i	−0.361771	−	0.497935i	0.588870	−	0.808228i	$-0.299573\pi$
$167$	−1.68494e6	−	2.31911e6i	−0.361771	−	0.497935i	−0.950641	+	0.310293i	$0.899573\pi$
$168$	−989933.	+	1.36253e6i	−0.208775	+	0.287354i
$169$	−794577.	−	2.44546e6i	−0.164617	−	0.506641i
$170$	12636.1	−	17392.1i	0.00257197	−	0.00354002i
$171$	−357022.	−	259392.i	−0.0714014	−	0.0518761i
$172$	4.04454e6	−	1.31415e6i	0.794847	−	0.258261i
$173$	−357880.	−	260015.i	−0.0691192	−	0.0502180i	0.552689	−	0.833388i	$-0.313602\pi$
$173$	−357880.	−	260015.i	−0.0691192	−	0.0502180i	−0.621808	+	0.783169i	$0.713602\pi$
$174$	−617348.	+	448529.i	−0.117188	+	0.0851419i
$175$	−1.70575e6	+	5.24976e6i	−0.318274	+	0.979548i
$176$	625625.	+	861099.i	0.114756	+	0.157948i
$177$	6.59682e6	−	2.14344e6i	1.18964	−	0.386537i
$178$	−7.10249e6	+	2.30774e6i	−1.25936	+	0.409192i
$179$	−2.73323e6	−	888081.i	−0.476560	−	0.154844i	0.0608813	−	0.998145i	$-0.480609\pi$
$179$	−2.73323e6	−	888081.i	−0.476560	−	0.154844i	−0.537441	+	0.843301i	$0.680609\pi$
$180$	7797.81			0.00133707
$181$		−	791395.i		−	0.133462i	−0.997771	−	0.0667310i	$-0.978743\pi$
$181$		−	791395.i		−	0.133462i	0.997771	−	0.0667310i	$-0.0212569\pi$
$182$	−5.18260e6	−	1.68393e6i	−0.859673	−	0.279325i
$183$	5.10085e6	+	3.70598e6i	0.832318	+	0.604714i
$184$	−1.45300e6	−	1.99988e6i	−0.233244	−	0.321033i
$185$		−	130290.i		−	0.0205777i
$186$	−4.18329e6	−	1.44880e6i	−0.650099	−	0.225150i
$187$	−630559.			−0.0964275
$188$	2.23729e6	−	1.62549e6i	0.336705	−	0.244630i
$189$	4.19937e6	−	5.77994e6i	0.622012	−	0.856127i
$190$	−124237.	+	382362.i	−0.0181130	+	0.0557460i
$191$	−9.56901e6			−1.37331			−0.686653	−	0.726986i	$-0.740921\pi$
$191$	−9.56901e6			−1.37331			−0.686653	+	0.726986i	$0.740921\pi$
$192$			860808.i			0.121619i
$193$	−3.30078e6	+	1.01588e7i	−0.459139	+	1.41309i	0.407067	+	0.913398i	$0.366552\pi$
$193$	−3.30078e6	+	1.01588e7i	−0.459139	+	1.41309i	−0.866206	+	0.499687i	$0.833448\pi$
$194$	120765.	+	371678.i	0.0165401	+	0.0509051i
$195$	−138321.	−	425709.i	−0.0186546	−	0.0574128i
$196$	−201511.	+	146406.i	−0.0267627	+	0.0194442i
$197$	3.22409e6	+	1.04757e6i	0.421704	+	0.137020i	0.512179	−	0.858879i	$-0.328838\pi$
$197$	3.22409e6	+	1.04757e6i	0.421704	+	0.137020i	−0.0904746	+	0.995899i	$0.528838\pi$
$198$	−134438.	−	185038.i	−0.0173192	−	0.0238378i
$199$	−5.88687e6	+	8.10258e6i	−0.747008	+	1.02817i	0.251177	+	0.967941i	$0.419182\pi$
$199$	−5.88687e6	+	8.10258e6i	−0.747008	+	1.02817i	−0.998185	+	0.0602269i	$0.980818\pi$
$200$	871837.	+	2.68324e6i	0.108980	+	0.335405i
$201$	2.08621e6	−	2.87143e6i	0.256904	−	0.353598i
$202$	−5.36350e6	−	3.89681e6i	−0.650720	−	0.472775i
$203$	−1.72963e6	+	561990.i	−0.206759	+	0.0671801i
$204$	−412567.	−	299747.i	−0.0485963	−	0.0353073i
$205$	135661.	−	98563.7i	0.0157469	−	0.0114408i
$206$	1.02253e6	−	3.14701e6i	0.116970	−	0.359995i
$207$	312229.	+	429746.i	0.0352016	+	0.0484508i
$208$	−2.64891e6	+	860682.i	−0.294359	+	0.0956429i
$209$	1.12152e7	−	3.64403e6i	1.22848	−	0.399156i
$210$	−313569.	−	101885.i	−0.0338591	−	0.0110015i
$211$	−882678.			−0.0939626			−0.0469813	−	0.998896i	$-0.514960\pi$
$211$	−882678.			−0.0939626			−0.0469813	+	0.998896i	$0.514960\pi$
$212$		−	5.56969e6i		−	0.584552i
$213$	1.98503e6	+	644974.i	0.205413	+	0.0667426i
$214$	−2.34587e6	−	1.70437e6i	−0.239366	−	0.173910i
$215$	489351.	+	673534.i	0.0492385	+	0.0677710i
$216$		−	3.65162e6i		−	0.362346i
$217$	−8.41496e6	−	6.36478e6i	−0.823518	−	0.622880i
$218$	−4.23570e6			−0.408843
$219$	1.96202e6	−	1.42549e6i	0.186797	−	0.135716i
$220$	−122477.	+	168575.i	−0.0115023	+	0.0158316i
$221$	509886.	−	1.56927e6i	0.0472385	−	0.145385i
$222$	−3.09068e6			−0.282485
$223$			1.70298e7i			1.53566i	0.640656	+	0.767828i	$0.278663\pi$
$223$			1.70298e7i			1.53566i	−0.640656	+	0.767828i	$0.721337\pi$
$224$	−633961.	+	1.95113e6i	−0.0564052	+	0.173597i
$225$	−187346.	−	576590.i	−0.0164474	−	0.0506197i
$226$	347103.	+	1.06827e6i	0.0300700	+	0.0925459i
$227$	1.70260e7	−	1.23701e7i	1.45557	−	1.05754i	0.471083	−	0.882089i	$-0.343863\pi$
$227$	1.70260e7	−	1.23701e7i	1.45557	−	1.05754i	0.984489	−	0.175447i	$-0.0561369\pi$
$228$	9.07019e6	+	2.94708e6i	0.765265	+	0.248650i
$229$	−1.10877e7	−	1.52610e7i	−0.923286	−	1.27079i	−0.962421	−	0.271561i	$-0.912460\pi$
$229$	−1.10877e7	−	1.52610e7i	−0.923286	−	1.27079i	0.0391348	−	0.999234i	$-0.487540\pi$
$230$	284449.	−	391510.i	0.0233787	−	0.0321780i
$231$	2.98841e6	+	9.19738e6i	0.242440	+	0.746153i
$232$	−546367.	+	752009.i	−0.0437543	+	0.0602226i
$233$	−1.14034e6	−	828503.i	−0.0901499	−	0.0654977i	0.541797	−	0.840509i	$-0.317744\pi$
$233$	−1.14034e6	−	828503.i	−0.0901499	−	0.0654977i	−0.631947	+	0.775011i	$0.717744\pi$
$234$	569213.	−	184949.i	0.0444250	−	0.0144346i
$235$	437988.	+	318217.i	0.0337488	+	0.0245200i
$236$	6.83565e6	−	4.96639e6i	0.520048	−	0.377837i
$237$	1.76637e6	−	5.43633e6i	0.132690	−	0.408377i
$238$	−714380.	−	983260.i	−0.0529905	−	0.0729352i
$239$	8.07698e6	−	2.62437e6i	0.591637	−	0.192235i	0.00212998	−	0.999998i	$-0.499322\pi$
$239$	8.07698e6	−	2.62437e6i	0.591637	−	0.192235i	0.589507	+	0.807763i	$0.299322\pi$
$240$	−160270.	+	52074.9i	−0.0115936	+	0.00376699i
$241$	−2.41756e6	−	785513.i	−0.172713	−	0.0561180i	0.221384	−	0.975187i	$-0.428943\pi$
$241$	−2.41756e6	−	785513.i	−0.172713	−	0.0561180i	−0.394097	+	0.919069i	$0.628943\pi$
$242$	−3.90970e6			−0.275866
$243$			1.52961e6i			0.106601i
$244$	7.30440e6	+	2.37334e6i	0.502823	+	0.163377i
$245$	−39449.1	−	28661.5i	−0.00268250	−	0.00194895i
$246$	−2.33808e6	−	3.21809e6i	−0.157056	−	0.216169i
$247$			3.08578e7i			2.04773i
$248$	−5.39175e6	−	103769.i	−0.353488	−	0.00680320i
$249$	1.05218e6			0.0681540
$250$	−894801.	+	650111.i	−0.0572672	+	0.0416071i
$251$	1.66371e7	−	2.28990e7i	1.05210	−	1.44809i	0.165126	−	0.986272i	$-0.447197\pi$
$251$	1.66371e7	−	2.28990e7i	1.05210	−	1.44809i	0.886974	−	0.461819i	$-0.152803\pi$
$252$	136229.	−	419271.i	0.00851274	−	0.0261995i
$253$	−1.41944e7			−0.876506
$254$			1.77450e7i			1.08286i
$255$	30850.2	−	94947.2i	0.00186053	−	0.00572614i
$256$	324028.	+	997255.i	0.0193136	+	0.0594410i
$257$	3.92374e6	+	1.20760e7i	0.231154	+	0.711418i	0.997608	+	0.0691196i	$0.0220190\pi$
$257$	3.92374e6	+	1.20760e7i	0.231154	+	0.711418i	−0.766455	+	0.642298i	$0.777981\pi$
$258$	1.59772e7	−	1.16081e7i	0.930341	−	0.675933i
$259$	−7.00542e6	−	2.27620e6i	−0.403213	−	0.131012i
$260$	−320493.	−	441121.i	−0.0182347	−	0.0250979i
$261$	117407.	−	161596.i	0.00660345	−	0.00908887i
$262$	7.60513e6	+	2.34062e7i	0.422866	+	1.30145i
$263$	440394.	−	606151.i	0.0242089	−	0.0333206i	−0.796741	−	0.604321i	$-0.793444\pi$
$263$	440394.	−	606151.i	0.0242089	−	0.0333206i	0.820950	+	0.571000i	$0.193444\pi$
$264$	3.99885e6	+	2.90533e6i	0.217332	+	0.157901i
$265$	1.03699e6	−	336940.i	0.0557236	−	0.0181057i
$266$	1.83883e7	+	1.33599e7i	0.977006	+	0.709836i
$267$	−2.80571e7	+	2.03847e7i	−1.47404	+	1.07095i
$268$	1.33603e6	−	4.11187e6i	0.0694083	−	0.213617i
$269$	1.25749e7	+	1.73079e7i	0.646024	+	0.889176i	0.998919	−	0.0464867i	$-0.0148025\pi$
$269$	1.25749e7	+	1.73079e7i	0.646024	+	0.889176i	−0.352894	+	0.935663i	$0.614803\pi$
$270$	679878.	−	220906.i	0.0345414	−	0.0112232i
$271$	−2.85813e7	+	9.28663e6i	−1.43607	+	0.466606i	−0.920669	−	0.390345i	$-0.872356\pi$
$271$	−2.85813e7	+	9.28663e6i	−1.43607	+	0.466606i	−0.515397	+	0.856951i	$0.672356\pi$
$272$	−590794.	−	191961.i	−0.0293582	−	0.00953906i
$273$	−2.53059e7			−1.24375
$274$		−	9.95210e6i		−	0.483797i
$275$	1.54074e7	+	5.00617e6i	0.740852	+	0.240718i
$276$	−9.28721e6	−	6.74755e6i	−0.441731	−	0.320936i
$277$	1.32419e7	+	1.82260e7i	0.623035	+	0.857534i	0.997569	−	0.0696791i	$-0.0221975\pi$
$277$	1.32419e7	+	1.82260e7i	0.623035	+	0.857534i	−0.374535	+	0.927213i	$0.622198\pi$
$278$			2.59568e7i			1.20814i
$279$	1.15861e6	+	22298.6i	0.0533489	+	0.00102675i
$280$	−401624.			−0.0182956
$281$	2.93637e7	−	2.13340e7i	1.32340	−	0.961507i	0.323518	−	0.946222i	$-0.395134\pi$
$281$	2.93637e7	−	2.13340e7i	1.32340	−	0.961507i	0.999883	−	0.0152849i	$-0.00486553\pi$
$282$	7.54859e6	−	1.03897e7i	0.336603	−	0.463295i
$283$	3.05347e6	−	9.39761e6i	0.134721	−	0.414627i	−0.860826	−	0.508900i	$-0.830052\pi$
$283$	3.05347e6	−	9.39761e6i	0.134721	−	0.414627i	0.995546	+	0.0942722i	$0.0300524\pi$
$284$	2.54245e6			0.110994
$285$			1.86702e6i			0.0806520i
$286$	−4.94212e6	+	1.52103e7i	−0.211259	+	0.650189i
$287$	−2.92952e6	−	9.01614e6i	−0.123923	−	0.381395i
$288$	−69629.1	−	214296.i	−0.00291483	−	0.00897092i
$289$	−1.92300e7	+	1.39714e7i	−0.796682	+	0.578824i
$290$	−173066.	−	56232.5i	−0.00709606	−	0.00230565i
$291$	1.06674e6	+	1.46825e6i	0.0432894	+	0.0595827i
$292$	1.73643e6	−	2.38999e6i	0.0697444	−	0.0959949i
$293$	−1.50704e7	−	4.63820e7i	−0.599132	−	1.84394i	−0.532980	−	0.846128i	$-0.678928\pi$
$293$	−1.50704e7	−	4.63820e7i	−0.599132	−	1.84394i	−0.0661517	−	0.997810i	$-0.521072\pi$
$294$	−679893.	+	935792.i	−0.0267546	+	0.0368246i
$295$	1.33819e6	+	972255.i	0.0521258	+	0.0378716i
$296$	−3.58058e6	+	1.16340e6i	−0.138063	+	0.0448595i
$297$	−1.69634e7	−	1.23247e7i	−0.647507	−	0.470441i
$298$	9.42366e6	−	6.84669e6i	0.356099	−	0.258721i
$299$	1.14779e7	−	3.53255e7i	0.429388	−	1.32152i
$300$	7.70110e6	+	1.05997e7i	0.285226	+	0.392580i
$301$	4.47635e7	−	1.45445e7i	1.64144	−	0.533336i
$302$	1.48646e7	−	4.82980e6i	0.539674	−	0.175351i
$303$	−2.92805e7	−	9.51380e6i	−1.05257	−	0.342000i
$304$	1.16173e7			0.413507
$305$			1.50355e6i			0.0529930i
$306$	126953.	+	41249.7i	0.00443078	+	0.00143965i
$307$	3.03442e7	+	2.20464e7i	1.04872	+	0.761942i	0.971969	−	0.235108i	$-0.0755445\pi$
$307$	3.03442e7	+	2.20464e7i	1.04872	+	0.761942i	0.0767535	+	0.997050i	$0.475545\pi$
$308$	6.92420e6	+	9.53035e6i	0.236983	+	0.326179i
$309$		−	1.53665e7i		−	0.520833i
$310$	−306855.	−	1.01014e6i	−0.0103003	−	0.0339076i
$311$	−5.92155e7			−1.96859			−0.984293	−	0.176545i	$-0.943508\pi$
$311$	−5.92155e7			−1.96859			−0.984293	+	0.176545i	$0.943508\pi$
$312$	−1.04640e7	+	7.60257e6i	−0.344537	+	0.250321i
$313$	−5.18842e6	+	7.14125e6i	−0.169201	+	0.232885i	−0.885194	−	0.465223i	$-0.845974\pi$
$313$	−5.18842e6	+	7.14125e6i	−0.169201	+	0.232885i	0.715993	+	0.698108i	$0.245974\pi$
$314$	4.39070e6	−	1.35132e7i	0.141822	−	0.436484i
$315$	86303.5			0.00276119
$316$		−	6.96295e6i		−	0.220664i
$317$	−8.63019e6	+	2.65610e7i	−0.270921	+	0.833809i	0.719349	+	0.694649i	$0.244440\pi$
$317$	−8.63019e6	+	2.65610e7i	−0.270921	+	0.833809i	−0.990270	+	0.139160i	$0.955560\pi$
$318$	−7.99272e6	−	2.45991e7i	−0.248550	−	0.764957i
$319$	1.64937e6	+	5.07625e6i	0.0508097	+	0.156376i
$320$	−166072.	+	120659.i	−0.00506812	+	0.00368221i
$321$	−1.28066e7	−	4.16112e6i	−0.387185	−	0.125804i
$322$	−1.60813e7	−	2.21340e7i	−0.481673	−	0.662966i
$323$	−4.04532e6	+	5.56790e6i	−0.120045	+	0.165228i
$324$	−4.95981e6	−	1.52647e7i	−0.145824	−	0.448801i
$325$	−2.49176e7	+	3.42962e7i	−0.725867	+	0.999070i
$326$	−1.51043e7	−	1.09739e7i	−0.435961	−	0.316744i
$327$	−1.87074e7	+	6.07840e6i	−0.535020	+	0.173839i
$328$	−3.92005e6	−	2.84808e6i	−0.111089	−	0.0807107i
$329$	2.47616e7	−	1.79904e7i	0.695330	−	0.505187i
$330$	−299019.	+	920286.i	−0.00832065	+	0.0256083i
$331$	−2.21209e7	−	3.04469e7i	−0.609986	−	0.839573i	0.386591	−	0.922251i	$-0.373653\pi$
$331$	−2.21209e7	−	3.04469e7i	−0.609986	−	0.839573i	−0.996576	+	0.0826780i	$0.973653\pi$
$332$	1.21896e6	−	396064.i	0.0333100	−	0.0108231i
$333$	769417.	−	249999.i	0.0208367	−	0.00677026i
$334$	−1.54222e7	−	5.01097e6i	−0.413910	−	0.134488i
$335$	846395.			0.0225133
$336$			9.52713e6i			0.251156i
$337$	177764.	+	57759.1i	0.00464467	+	0.00150914i	0.311338	−	0.950299i	$-0.399223\pi$
$337$	177764.	+	57759.1i	0.00464467	+	0.00150914i	−0.306694	+	0.951808i	$0.599223\pi$
$338$	−1.17676e7	−	8.54963e6i	−0.304745	−	0.221410i
$339$	3.06603e6	+	4.22003e6i	0.0787005	+	0.108322i
$340$		−	121610.i		−	0.00309409i
$341$	−1.86799e7	+	2.46969e7i	−0.471097	+	0.622844i
$342$	−2.49639e6			−0.0624071
$343$	3.14792e7	−	2.28710e7i	0.780083	−	0.566764i
$344$	1.41402e7	−	1.94623e7i	0.347361	−	0.478101i
$345$	694463.	−	2.13734e6i	0.0169119	−	0.0520494i
$346$	−2.50239e6			−0.0604124
$347$		−	4.32261e6i		−	0.103456i	−0.998661	−	0.0517282i	$-0.983527\pi$
$347$		−	4.32261e6i		−	0.103456i	0.998661	−	0.0517282i	$-0.0164730\pi$
$348$	−1.33392e6	+	4.10538e6i	−0.0316513	+	0.0974127i
$349$	7.84988e6	+	2.41595e7i	0.184666	+	0.568344i	0.999942	−	0.0107284i	$-0.00341502\pi$
$349$	7.84988e6	+	2.41595e7i	0.184666	+	0.568344i	−0.815276	+	0.579072i	$0.803415\pi$
$350$	9.64919e6	+	2.96971e7i	0.225054	+	0.692645i
$351$	4.43893e7	−	3.22507e7i	1.02650	−	0.745793i
$352$	5.72634e6	+	1.86060e6i	0.131295	+	0.0426604i
$353$	−3.20799e7	−	4.41542e7i	−0.729305	−	1.00380i	−0.999163	−	0.0409017i	$-0.986977\pi$
$353$	−3.20799e7	−	4.41542e7i	−0.729305	−	1.00380i	0.269859	−	0.962900i	$-0.413023\pi$
$354$	2.30633e7	−	3.17440e7i	0.519891	−	0.715569i
$355$	153807.	+	473368.i	0.00343787	+	0.0105807i
$356$	−2.48312e7	+	3.41772e7i	−0.550361	+	0.757507i
$357$	−4.56614e6	−	3.31750e6i	−0.100356	−	0.0729132i
$358$	−1.54615e7	+	5.02374e6i	−0.336979	+	0.109491i
$359$	4.25900e7	+	3.09434e7i	0.920501	+	0.668783i	0.943649	−	0.330949i	$-0.107369\pi$
$359$	4.25900e7	+	3.09434e7i	0.920501	+	0.668783i	−0.0231480	+	0.999732i	$0.507369\pi$
$360$	35686.6	−	25927.8i	0.000764888	−	0.000555724i
$361$	2.52352e7	−	7.76659e7i	0.536395	−	1.65085i
$362$	−2.63140e6	−	3.62181e6i	−0.0554704	−	0.0763484i
$363$	−1.72676e7	+	5.61058e6i	−0.361004	+	0.117297i
$364$	−2.93172e7	+	9.52573e6i	−0.607880	+	0.197512i
$365$	550028.	+	178715.i	0.0113111	+	0.00367521i
$366$	3.56664e7			0.727472
$367$			3.52991e7i			0.714111i	0.934083	+	0.357056i	$0.116219\pi$
$367$			3.52991e7i			0.714111i	−0.934083	+	0.357056i	$0.883781\pi$
$368$	−1.32993e7	−	4.32119e6i	−0.266860	−	0.0867081i
$369$	842364.	+	612013.i	0.0167657	+	0.0121810i
$370$	−433217.	−	596272.i	−0.00855264	−	0.0117717i
$371$		−	6.16433e7i		−	1.20716i
$372$	−2.39621e7	+	7.27907e6i	−0.465475	+	0.141399i
$373$	6.10315e7			1.17606			0.588028	−	0.808841i	$-0.299905\pi$
$373$	6.10315e7			1.17606			0.588028	+	0.808841i	$0.299905\pi$
$374$	−2.88575e6	+	2.09662e6i	−0.0551624	+	0.0400779i
$375$	−3.01904e6	+	4.15535e6i	−0.0572499	+	0.0787978i
$376$	4.83418e6	−	1.48781e7i	0.0909409	−	0.279887i
$377$	−1.39669e7			−0.260662
$378$		−	4.04148e7i		−	0.748282i
$379$	−1.82306e7	+	5.61081e7i	−0.334876	+	1.03064i	0.631907	+	0.775044i	$0.282272\pi$
$379$	−1.82306e7	+	5.61081e7i	−0.334876	+	1.03064i	−0.966783	+	0.255598i	$0.917728\pi$
$380$	702790.	+	2.16297e6i	0.0128078	+	0.0394184i
$381$	2.54647e7	+	7.83723e7i	0.460430	+	1.41706i
$382$	−4.37925e7	+	3.18171e7i	−0.785615	+	0.570783i
$383$	1.39293e7	+	4.52592e6i	0.247933	+	0.0805583i	0.430347	−	0.902663i	$-0.358391\pi$
$383$	1.39293e7	+	4.52592e6i	0.247933	+	0.0805583i	−0.182414	+	0.983222i	$0.558391\pi$
$384$	2.86220e6	+	3.93948e6i	0.0505483	+	0.0695737i
$385$	−1.35553e6	+	1.86573e6i	−0.0237535	+	0.0326938i
$386$	1.86720e7	+	5.74666e7i	0.324661	+	0.999202i
$387$	−3.03854e6	+	4.18219e6i	−0.0524242	+	0.0721557i
$388$	1.78852e6	+	1.29943e6i	0.0306195	+	0.0222463i
$389$	−6.21268e7	+	2.01862e7i	−1.05543	+	0.342930i	−0.784798	−	0.619752i	$-0.787233\pi$
$389$	−6.21268e7	+	2.01862e7i	−1.05543	+	0.342930i	−0.270634	+	0.962682i	$0.587233\pi$
$390$	−2.04851e6	−	1.48833e6i	−0.0345339	−	0.0250903i
$391$	6.70207e6	−	4.86934e6i	0.112119	−	0.0814591i
$392$	−435409.	+	1.34005e6i	−0.00722836	+	0.0222466i
$393$	6.71776e7	+	9.24620e7i	1.10674	+	1.52330i
$394$	1.82382e7	−	5.92595e6i	0.298190	−	0.0968878i
$395$	1.29640e6	−	421226.i	0.0210352	−	0.00683477i
$396$	−1.23051e6	−	399817.i	−0.0198153	−	0.00643837i
$397$	2.36574e7			0.378090			0.189045	−	0.981968i	$-0.439461\pi$
$397$	2.36574e7			0.378090			0.189045	+	0.981968i	$0.439461\pi$
$398$			5.66553e7i			0.898652i
$399$	1.00386e8	+	3.26173e7i	1.58035	+	0.513487i
$400$	1.29118e7	+	9.38094e6i	0.201746	+	0.146577i
$401$	−1.81406e7	−	2.49684e7i	−0.281331	−	0.387219i	0.644843	−	0.764315i	$-0.276923\pi$
$401$	−1.81406e7	−	2.49684e7i	−0.281331	−	0.387219i	−0.926174	+	0.377096i	$0.876923\pi$
$402$		−	2.00778e7i		−	0.309056i
$403$	−4.63580e7	−	6.64590e7i	−0.708287	−	1.01540i
$404$	−3.75029e7			−0.568750
$405$	2.54202e6	−	1.84689e6i	0.0382661	−	0.0278020i
$406$	−6.04700e6	+	8.32298e6i	−0.0903570	+	0.124366i
$407$	−6.68037e6	+	2.05601e7i	−0.0990871	+	0.304959i
$408$	−2.88477e6			−0.0424748
$409$			4.95623e7i			0.724406i	0.932099	+	0.362203i	$0.117975\pi$
$409$			4.95623e7i			0.724406i	−0.932099	+	0.362203i	$0.882025\pi$
$410$	293127.	−	902152.i	0.00425309	−	0.0130897i
$411$	−1.42817e7	−	4.39544e7i	−0.205709	−	0.633107i
$412$	−5.78428e6	−	1.78022e7i	−0.0827100	−	0.254555i
$413$	7.56546e7	−	5.49662e7i	1.07395	−	0.780272i
$414$	2.85782e6	+	928564.i	0.0402749	+	0.0130861i
$415$	147483.	+	202993.i	0.00206346	+	0.00284011i
$416$	−9.26092e6	+	1.27466e7i	−0.128639	+	0.177057i
$417$	3.72491e7	+	1.14641e8i	0.513698	+	1.58100i
$418$	3.92097e7	−	5.39675e7i	0.536864	−	0.738930i
$419$	7.11602e7	+	5.17009e7i	0.967376	+	0.702840i	0.954852	−	0.297082i	$-0.0960134\pi$
$419$	7.11602e7	+	5.17009e7i	0.967376	+	0.702840i	0.0125239	+	0.999922i	$0.496013\pi$
$420$	−1.77381e6	+	576347.i	−0.0239420	+	0.00777922i
$421$	−1.59652e7	−	1.15994e7i	−0.213957	−	0.155449i	0.475645	−	0.879637i	$-0.342215\pi$
$421$	−1.59652e7	−	1.15994e7i	−0.213957	−	0.155449i	−0.689602	+	0.724188i	$0.742215\pi$
$422$	−4.03957e6	+	2.93492e6i	−0.0537524	+	0.0390534i
$423$	−1.03880e6	+	3.19709e6i	−0.0137249	+	0.0422410i
$424$	−1.85193e7	−	2.54896e7i	−0.242956	−	0.334400i
$425$	−8.99216e6	+	2.92173e6i	−0.117138	+	0.0380604i
$426$	1.12290e7	−	3.64852e6i	0.145249	−	0.0471942i
$427$	8.08426e7	+	2.62673e7i	1.03838	+	0.337390i
$428$	−1.64029e7			−0.209214
$429$			7.42699e7i			0.940678i
$430$	4.47902e6	+	1.45532e6i	0.0563349	+	0.0183043i
$431$	−4.46391e7	−	3.24322e7i	−0.557550	−	0.405083i	0.273012	−	0.962011i	$-0.411980\pi$
$431$	−4.46391e7	−	3.24322e7i	−0.557550	−	0.405083i	−0.830561	+	0.556927i	$0.811980\pi$
$432$	−1.21417e7	−	1.67116e7i	−0.150601	−	0.207284i
$433$		−	4.17540e7i		−	0.514321i	−0.966369	−	0.257161i	$-0.917213\pi$
$433$		−	4.17540e7i		−	0.514321i	0.966369	−	0.257161i	$-0.0827869\pi$
$434$	−5.96740e7	−	1.14848e6i	−0.729988	−	0.0140493i
$435$	−845058.			−0.0102664
$436$	−1.93847e7	+	1.40838e7i	−0.233883	+	0.169926i
$437$	−9.10633e7	+	1.25338e8i	−1.09119	+	1.50189i
$438$	4.23938e6	−	1.30475e7i	0.0504522	−	0.155276i
$439$	−1.94430e6			−0.0229811			−0.0114905	−	0.999934i	$-0.503658\pi$
$439$	−1.94430e6			−0.0229811			−0.0114905	+	0.999934i	$0.503658\pi$
$440$			1.17872e6i			0.0138373i
$441$	93563.4	−	287959.i	0.00109091	−	0.00335749i
$442$	−2.88435e6	−	8.87712e6i	−0.0334027	−	0.102803i
$443$	−2.81522e7	−	8.66435e7i	−0.323818	−	0.996609i	−0.971971	−	0.235099i	$-0.924459\pi$
$443$	−2.81522e7	−	8.66435e7i	−0.323818	−	0.996609i	0.648154	−	0.761510i	$-0.275541\pi$
$444$	−1.41445e7	+	1.02766e7i	−0.161599	+	0.117408i
$445$	−7.86548e6	−	2.55565e6i	−0.0892576	−	0.0290015i
$446$	5.66242e7	+	7.79366e7i	0.638260	+	0.878490i
$447$	3.17952e7	−	4.37624e7i	0.355991	−	0.489980i
$448$	3.58623e6	+	1.10373e7i	0.0398845	+	0.122752i
$449$	−1.21239e7	+	1.66871e7i	−0.133938	+	0.184349i	−0.870718	−	0.491783i	$-0.836345\pi$
$449$	−1.21239e7	+	1.66871e7i	−0.133938	+	0.184349i	0.736780	+	0.676132i	$0.236345\pi$
$450$	−2.77456e6	−	2.01583e6i	−0.0304478	−	0.0221216i
$451$	−2.64613e7	+	8.59779e6i	−0.288457	+	0.0937254i
$452$	5.14054e6	+	3.73482e6i	0.0556665	+	0.0404440i
$453$	5.87199e7	−	4.26625e7i	0.631671	−	0.458936i
$454$	3.67884e7	−	1.13223e8i	0.393137	−	1.20995i
$455$	−3.54711e6	−	4.88217e6i	−0.0376565	−	0.0518297i
$456$	5.13088e7	−	1.66712e7i	0.541124	−	0.175822i
$457$	−1.07330e8	+	3.48738e7i	−1.12454	+	0.365385i	−0.811498	−	0.584355i	$-0.801348\pi$
$457$	−1.07330e8	+	3.48738e7i	−1.12454	+	0.365385i	−0.313041	+	0.949740i	$0.601348\pi$
$458$	−1.01486e8	−	3.29748e7i	−1.05635	−	0.343230i
$459$	1.22374e7			0.126547
$460$		−	2.73754e6i		−	0.0281246i
$461$	5.70840e6	+	1.85477e6i	0.0582655	+	0.0189316i	0.338005	−	0.941144i	$-0.390248\pi$
$461$	5.70840e6	+	1.85477e6i	0.0582655	+	0.0189316i	−0.279739	+	0.960076i	$0.590248\pi$
$462$	4.42578e7	+	3.21552e7i	0.448812	+	0.326081i
$463$	−8.08475e7	−	1.11277e8i	−0.814561	−	1.12115i	−0.990604	−	0.136764i	$-0.956330\pi$
$463$	−8.08475e7	−	1.11277e8i	−0.814561	−	1.12115i	0.176043	−	0.984383i	$-0.443670\pi$
$464$			5.25824e6i			0.0526365i
$465$	−2.80485e6	−	4.02104e6i	−0.0278966	−	0.0399926i
$466$	−7.97352e6			−0.0787939
$467$	−2.37257e7	+	1.72377e7i	−0.232953	+	0.169250i	−0.698138	−	0.715963i	$-0.745988\pi$
$467$	−2.37257e7	+	1.72377e7i	−0.232953	+	0.169250i	0.465185	+	0.885214i	$0.345988\pi$
$468$	1.99004e6	−	2.73906e6i	0.0194144	−	0.0267217i
$469$	1.47867e7	−	4.55088e7i	0.143335	−	0.441140i
$470$	3.06253e6			0.0294976
$471$		−	6.59831e7i		−	0.631495i
$472$	1.47700e7	−	4.54573e7i	0.140460	−	0.432292i
$473$	−4.26865e7	−	1.31375e8i	−0.403373	−	1.24145i
$474$	−9.99211e6	−	3.07525e7i	−0.0938257	−	0.288766i
$475$	1.43050e8	−	1.03932e8i	1.33478	−	0.969772i
$476$	−6.53871e6	−	2.12455e6i	−0.0606277	−	0.0196991i
$477$	3.97954e6	+	5.47736e6i	0.0366672	+	0.0504680i
$478$	2.82382e7	−	3.88665e7i	0.258555	−	0.355870i
$479$	−8.31136e6	−	2.55797e7i	−0.0756250	−	0.232750i	0.906097	−	0.423070i	$-0.139047\pi$
$479$	−8.31136e6	−	2.55797e7i	−0.0756250	−	0.232750i	−0.981722	+	0.190320i	$0.939047\pi$
$480$	−560324.	+	771220.i	−0.00506659	+	0.00697356i
$481$	−4.57657e7	−	3.32508e7i	−0.411249	−	0.298790i
$482$	−1.36758e7	+	4.44353e6i	−0.122127	+	0.0396814i
$483$	−1.02788e8	−	7.46795e7i	−0.912219	−	0.662766i
$484$	−1.78927e7	+	1.29998e7i	−0.157812	+	0.114657i
$485$	−133739.	+	411605.i	−0.00117228	+	0.00360791i
$486$	5.08599e6	+	7.00027e6i	0.0443065	+	0.0609826i
$487$	1.14559e8	−	3.72224e7i	0.991839	−	0.322268i	0.232239	−	0.972659i	$-0.425395\pi$
$487$	1.14559e8	−	3.72224e7i	0.991839	−	0.322268i	0.759600	+	0.650391i	$0.225395\pi$
$488$	4.13199e7	−	1.34257e7i	0.355550	−	0.115525i
$489$	−8.24576e7	−	2.67921e7i	−0.705186	−	0.229129i
$490$	−275838.			−0.00234459
$491$			1.97602e8i			1.66935i	0.550744	+	0.834674i	$0.314344\pi$
$491$			1.97602e8i			1.66935i	−0.550744	+	0.834674i	$0.685656\pi$
$492$	−2.14004e7	−	6.95341e6i	−0.179691	−	0.0583852i
$493$	−2.52016e6	−	1.83100e6i	−0.0210323	−	0.0152809i
$494$	1.02603e8	+	1.41220e8i	0.851093	+	1.17143i
$495$		−	253290.i		−	0.00208835i
$496$	−2.50203e7	+	1.74527e7i	−0.205044	+	0.143027i
$497$	2.81390e7			0.229213
$498$	4.81529e6	−	3.49851e6i	0.0389883	−	0.0283266i
$499$	−1.24648e8	+	1.71563e8i	−1.00319	+	1.38077i	−0.0798409	+	0.996808i	$0.525441\pi$
$499$	−1.24648e8	+	1.71563e8i	−1.00319	+	1.38077i	−0.923348	+	0.383964i	$0.874559\pi$
$500$	−1.93342e6	+	5.95045e6i	−0.0154674	+	0.0476036i
$501$	−7.53045e7			−0.598836
$502$		−	1.60116e8i		−	1.26568i
$503$	5.98242e7	−	1.84120e8i	0.470081	−	1.44676i	−0.382397	−	0.923998i	$-0.624901\pi$
$503$	5.98242e7	−	1.84120e8i	0.470081	−	1.44676i	0.852478	−	0.522763i	$-0.175099\pi$
$504$	−770630.	−	2.37176e6i	−0.00601942	−	0.0185259i
$505$	−2.26875e6	−	6.98250e6i	−0.0176162	−	0.0542172i
$506$	−6.49605e7	+	4.71966e7i	−0.501415	+	0.364300i
$507$	−6.42416e7	−	2.08734e7i	−0.492938	−	0.160165i
$508$	5.90023e7	+	8.12097e7i	0.450067	+	0.619465i
$509$	−4.29893e7	+	5.91697e7i	−0.325992	+	0.448690i	−0.940285	−	0.340389i	$-0.889441\pi$
$509$	−4.29893e7	+	5.91697e7i	−0.325992	+	0.448690i	0.614293	+	0.789078i	$0.289441\pi$
$510$	−174515.	−	537103.i	−0.00131560	−	0.00404899i
$511$	1.92182e7	−	2.64516e7i	0.144029	−	0.198239i
$512$	4.79880e6	+	3.48653e6i	0.0357538	+	0.0259767i
$513$	−2.17656e8	+	7.07207e7i	−1.61220	+	0.523835i
$514$	5.81099e7	+	4.22193e7i	0.427919	+	0.310901i
$515$	2.96459e6	−	2.15390e6i	0.0217041	−	0.0157690i
$516$	3.45224e7	−	1.06249e8i	0.251277	−	0.773350i
$517$	−5.27995e7	−	7.26723e7i	−0.382083	−	0.525893i
$518$	−3.96286e7	+	1.28761e7i	−0.285115	+	0.0926394i
$519$	−1.10520e7	+	3.59102e6i	−0.0790570	+	0.0256872i
$520$	−2.93347e6	−	953141.i	−0.0208627	−	0.00677871i
$521$	−2.58662e8			−1.82902			−0.914510	−	0.404562i	$-0.867424\pi$
$521$	−2.58662e8			−1.82902			−0.914510	+	0.404562i	$0.867424\pi$
$522$		−	1.12992e6i		−	0.00794397i
$523$	1.39387e8	+	4.52895e7i	0.974353	+	0.316586i	0.752572	−	0.658510i	$-0.228813\pi$
$523$	1.39387e8	+	4.52895e7i	0.974353	+	0.316586i	0.221781	+	0.975096i	$0.428813\pi$
$524$	1.12631e8	+	8.18310e7i	0.782822	+	0.568754i
$525$	8.52331e7	+	1.17313e8i	0.589021	+	0.810718i
$526$		−	4.23836e6i		−	0.0291233i
$527$	347755.	−	1.80690e7i	0.00237597	−	0.123453i
$528$	2.79610e7			0.189955
$529$	3.11053e7	−	2.25993e7i	0.210120	−	0.152661i
$530$	3.62547e6	−	4.99003e6i	0.0243521	−	0.0335178i
$531$	−3.17386e6	+	9.76813e6i	−0.0211984	+	0.0652421i
$532$	1.28576e8			0.853934
$533$		−	7.28064e7i		−	0.480826i
$534$	−6.06238e7	+	1.86581e8i	−0.398125	+	1.22530i
$535$	−992300.	−	3.05398e6i	−0.00648010	−	0.0199437i
$536$	−7.55772e6	−	2.32603e7i	−0.0490791	−	0.151050i
$537$	−6.10779e7	+	4.43757e7i	−0.394422	+	0.286564i
$538$	1.15098e8	+	3.73977e7i	0.739131	+	0.240158i
$539$	4.75559e6	+	6.54551e6i	0.0303696	+	0.0418001i
$540$	2.37694e6	−	3.27158e6i	0.0150951	−	0.0207767i
$541$	8.12656e7	+	2.50110e8i	0.513233	+	1.57957i	0.786473	+	0.617624i	$0.211905\pi$
$541$	8.12656e7	+	2.50110e8i	0.513233	+	1.57957i	−0.273240	+	0.961946i	$0.588095\pi$
$542$	−9.99240e7	+	1.37534e8i	−0.627584	+	0.863795i
$543$	−1.68193e7	−	1.22199e7i	−0.105053	−	0.0763254i
$544$	−3.34204e6	+	1.08589e6i	−0.0207594	+	0.00674514i
$545$	−3.79488e6	−	2.75714e6i	−0.0234427	−	0.0170321i
$546$	−1.15812e8	+	8.41427e7i	−0.711504	+	0.516938i
$547$	8.24126e7	−	2.53640e8i	0.503538	−	1.54973i	−0.299678	−	0.954040i	$-0.596879\pi$
$547$	8.24126e7	−	2.53640e8i	0.503538	−	1.54973i	0.803215	−	0.595689i	$-0.203121\pi$
$548$	−3.30909e7	−	4.55457e7i	−0.201079	−	0.276761i
$549$	−8.87908e6	+	2.88499e6i	−0.0536600	+	0.0174352i
$550$	8.71575e7	−	2.83192e7i	0.523862	−	0.170213i
$551$	5.54052e7	+	1.80023e7i	0.331204	+	0.107615i
$552$	−6.49385e7			−0.386087
$553$		−	7.70635e7i		−	0.455694i
$554$	1.21203e8	+	3.93813e7i	0.712828	+	0.231612i
$555$	−2.76902e6	−	2.01181e6i	−0.0161975	−	0.0117681i
$556$	8.63069e7	+	1.18791e8i	0.502136	+	0.691131i
$557$		−	1.85682e8i		−	1.07449i	−0.843425	−	0.537247i	$-0.819464\pi$
$557$		−	1.85682e8i		−	1.07449i	0.843425	−	0.537247i	$-0.180536\pi$
$558$	5.37652e6	−	3.75035e6i	0.0309456	−	0.0215859i
$559$	3.61471e8			2.06937
$560$	−1.83803e6	+	1.33541e6i	−0.0104662	+	0.00760413i
$561$	−9.73645e6	+	1.34011e7i	−0.0551458	+	0.0759016i
$562$	6.34469e7	−	1.95269e8i	0.357438	−	1.10008i
$563$	−1.04279e8			−0.584348			−0.292174	−	0.956365i	$-0.594379\pi$
$563$	−1.04279e8			−0.584348			−0.292174	+	0.956365i	$0.594379\pi$
$564$		−	7.26477e7i		−	0.404934i
$565$	−384391.	+	1.18303e6i	−0.00213122	+	0.00655921i
$566$	−1.72730e7	−	5.31609e7i	−0.0952619	−	0.293186i
$567$	−5.48934e7	−	1.68945e8i	−0.301142	−	0.926819i
$568$	1.16355e7	−	8.45370e6i	0.0634952	−	0.0461320i
$569$	1.11367e8	+	3.61855e7i	0.604535	+	0.196425i	0.595262	−	0.803532i	$-0.297048\pi$
$569$	1.11367e8	+	3.61855e7i	0.604535	+	0.196425i	0.00927278	+	0.999957i	$0.497048\pi$
$570$	6.20788e6	+	8.54441e6i	0.0335211	+	0.0461379i
$571$	−6.51079e7	+	8.96133e7i	−0.349724	+	0.481353i	−0.947250	−	0.320496i	$-0.896150\pi$
$571$	−6.51079e7	+	8.96133e7i	−0.349724	+	0.481353i	0.597526	+	0.801849i	$0.296150\pi$
$572$	2.79569e7	+	8.60424e7i	0.149383	+	0.459753i
$573$	−1.47755e8	+	2.03367e8i	−0.785377	+	1.08098i
$574$	−4.33858e7	−	3.15216e7i	−0.229410	−	0.166676i
$575$	−2.02421e8	+	6.57705e7i	−1.06476	+	0.345961i
$576$	−1.03120e6	−	749207.i	−0.00539602	−	0.00392044i
$577$	5.79376e7	−	4.20941e7i	0.301601	−	0.219126i	−0.426683	−	0.904401i	$-0.640318\pi$
$577$	5.79376e7	−	4.20941e7i	0.301601	−	0.219126i	0.728284	+	0.685275i	$0.240318\pi$
$578$	−4.15507e7	+	1.27880e8i	−0.215177	+	0.662245i
$579$	1.64934e8	+	2.27012e8i	0.849715	+	1.16953i
$580$	−979008.	+	318099.i	−0.00501767	+	0.00163034i
$581$	1.34910e7	−	4.38350e6i	0.0687886	−	0.0223508i
$582$	9.76389e6	+	3.17248e6i	0.0495284	+	0.0160927i
$583$	−1.80916e8			−0.913000
$584$		−	1.67114e7i		−	0.0839026i
$585$	630361.	+	204817.i	0.00314863	+	0.00102305i
$586$	−2.23190e8	−	1.62157e8i	−1.10913	−	0.805830i
$587$	1.58240e8	+	2.17799e8i	0.782353	+	1.07682i	0.995018	+	0.0996913i	$0.0317855\pi$
$587$	1.58240e8	+	2.17799e8i	0.782353	+	1.07682i	−0.212666	+	0.977125i	$0.568214\pi$
$588$			6.54330e6i			0.0321858i
$589$	9.82365e7	+	3.23387e8i	0.480759	+	1.58262i
$590$	9.35699e6			0.0455596
$591$	7.20468e7	−	5.23451e7i	0.349022	−	0.253579i
$592$	−1.25182e7	+	1.72298e7i	−0.0603359	+	0.0830452i
$593$	1.24008e8	−	3.81657e8i	0.594683	−	1.83024i	0.0383830	−	0.999263i	$-0.487779\pi$
$593$	1.24008e8	−	3.81657e8i	0.594683	−	1.83024i	0.556300	−	0.830982i	$-0.312221\pi$
$594$	−1.18613e8			−0.565942
$595$		−	1.34594e6i		−	0.00638961i
$596$	2.03619e7	−	6.26676e7i	0.0961790	−	0.296009i
$597$	8.13026e7	+	2.50224e8i	0.382104	+	1.17600i
$598$	−6.49290e7	−	1.99831e8i	−0.303623	−	0.934457i
$599$	9.94286e7	−	7.22391e7i	0.462627	−	0.336118i	−0.331934	−	0.943303i	$-0.607701\pi$
$599$	9.94286e7	−	7.22391e7i	0.462627	−	0.336118i	0.794561	+	0.607185i	$0.207701\pi$
$600$	7.04881e7	+	2.29030e7i	0.326334	+	0.106032i
$601$	−1.08361e8	−	1.49145e8i	−0.499169	−	0.687047i	0.482877	−	0.875688i	$-0.339592\pi$
$601$	−1.08361e8	−	1.49145e8i	−0.499169	−	0.687047i	−0.982046	+	0.188641i	$0.939592\pi$
$602$	1.56499e8	−	2.15402e8i	0.717335	−	0.987327i
$603$	1.62405e6	+	4.99831e6i	0.00740708	+	0.0227967i
$604$	5.19685e7	−	7.15285e7i	0.235846	−	0.324615i
$605$	−3.50280e6	−	2.54494e6i	−0.0158179	−	0.0114924i
$606$	−1.65635e8	+	5.38182e7i	−0.744278	+	0.241831i
$607$	2.06271e8	+	1.49865e8i	0.922299	+	0.670089i	0.944095	−	0.329673i	$-0.106938\pi$
$607$	2.06271e8	+	1.49865e8i	0.922299	+	0.670089i	−0.0217962	+	0.999762i	$0.506938\pi$
$608$	5.31663e7	−	3.86276e7i	0.236551	−	0.171865i
$609$	−1.47634e7	+	4.54369e7i	−0.0653632	+	0.201167i
$610$	4.99933e6	+	6.88098e6i	0.0220253	+	0.0303152i
$611$	2.23554e8	−	7.26371e7i	0.980074	−	0.318445i
$612$	718157.	−	233343.i	0.00313304	−	0.00101799i
$613$	−1.70671e8	−	5.54543e7i	−0.740931	−	0.240743i	−0.0858568	−	0.996307i	$-0.527363\pi$
$613$	−1.70671e8	−	5.54543e7i	−0.740931	−	0.240743i	−0.655074	+	0.755564i	$0.727363\pi$
$614$	2.12174e8			0.916617
$615$		−	4.40509e6i		−	0.0189378i
$616$	6.33771e7	+	2.05925e7i	0.271138	+	0.0880981i
$617$	2.05705e7	+	1.49453e7i	0.0875767	+	0.0636282i	0.630712	−	0.776017i	$-0.282763\pi$
$617$	2.05705e7	+	1.49453e7i	0.0875767	+	0.0636282i	−0.543135	+	0.839645i	$0.682763\pi$
$618$	−5.10937e7	−	7.03244e7i	−0.216472	−	0.297948i
$619$		−	6.26056e6i		−	0.0263962i	−0.999913	−	0.0131981i	$-0.995799\pi$
$619$		−	6.26056e6i		−	0.0263962i	0.999913	−	0.0131981i	$-0.00420120\pi$
$620$	−4.76306e6	−	3.60261e6i	−0.0199853	−	0.0151162i
$621$	2.75474e8			1.15029
$622$	−2.70999e8	+	1.96892e8i	−1.12615	+	0.818197i
$623$	−2.74823e8	+	3.78262e8i	−1.13655	+	1.56433i
$624$	−2.26099e7	+	6.95862e7i	−0.0930563	+	0.286398i
$625$	2.42303e8			0.992471
$626$			4.99335e7i			0.203549i
$627$	9.57278e7	−	2.94620e8i	0.388361	−	1.19525i
$628$	−2.48375e7	−	7.64421e7i	−0.100284	−	0.308641i
$629$	−3.89883e6	−	1.19994e7i	−0.0156669	−	0.0482177i
$630$	394967.	−	286960.i	0.00157957	−	0.00114763i
$631$	−2.68870e8	−	8.73612e7i	−1.07017	−	0.347721i	−0.279619	−	0.960111i	$-0.590208\pi$
$631$	−2.68870e8	−	8.73612e7i	−1.07017	−	0.347721i	−0.790555	+	0.612390i	$0.790208\pi$
$632$	−2.31519e7	−	3.18659e7i	−0.0917140	−	0.126233i
$633$	−1.36294e7	+	1.87593e7i	−0.0537361	+	0.0739614i
$634$	4.88197e7	+	1.50252e8i	0.191570	+	0.589592i
$635$	−1.15507e7	+	1.58982e7i	−0.0451115	+	0.0620906i
$636$	−1.18371e8	−	8.60015e7i	−0.460122	−	0.334299i
$637$	−2.01353e7	+	6.54234e6i	−0.0779003	+	0.0253113i
$638$	2.44269e7	+	1.77472e7i	0.0940604	+	0.0683389i
$639$	−2.50031e6	+	1.81658e6i	−0.00958278	+	0.00696230i
$640$	−358837.	+	1.10439e6i	−0.00136885	+	0.00421290i
$641$	2.12974e8	+	2.93133e8i	0.808634	+	1.11299i	0.991533	+	0.129857i	$0.0414518\pi$
$641$	2.12974e8	+	2.93133e8i	0.808634	+	1.11299i	−0.182899	+	0.983132i	$0.558548\pi$
$642$	−7.24451e7	+	2.35388e7i	−0.273781	+	0.0889569i
$643$	−1.81979e8	+	5.91285e7i	−0.684523	+	0.222415i	−0.630575	−	0.776129i	$-0.717181\pi$
$643$	−1.81979e8	+	5.91285e7i	−0.684523	+	0.222415i	−0.0539487	+	0.998544i	$0.517181\pi$
$644$	−1.47192e8	−	4.78254e7i	−0.551093	−	0.179061i
$645$	2.18705e7			0.0815040
$646$			3.89322e7i			0.144415i
$647$	6.28574e7	+	2.04236e7i	0.232083	+	0.0754084i	0.422750	−	0.906246i	$-0.361065\pi$
$647$	6.28574e7	+	2.04236e7i	0.232083	+	0.0754084i	−0.190667	+	0.981655i	$0.561065\pi$
$648$	−7.34539e7	−	5.33674e7i	−0.269954	−	0.196133i
$649$	−1.61319e8	−	2.22037e8i	−0.590136	−	0.812253i
$650$			2.39808e8i			0.873219i
$651$	−2.65204e8	+	8.05622e7i	−0.961252	+	0.292004i
$652$	−1.05613e8			−0.381044
$653$	−3.27100e7	+	2.37652e7i	−0.117474	+	0.0853496i	−0.644971	−	0.764207i	$-0.723131\pi$
$653$	−3.27100e7	+	2.37652e7i	−0.117474	+	0.0853496i	0.527497	+	0.849557i	$0.323131\pi$
$654$	−6.54035e7	+	9.00201e7i	−0.233812	+	0.321815i
$655$	−8.42211e6	+	2.59206e7i	−0.0299707	+	0.0922404i
$656$	−2.74100e7			−0.0970951
$657$			3.59106e6i			0.0126627i
$658$	5.35030e7	−	1.64665e8i	0.187802	−	0.577996i
$659$	1.59121e8	+	4.89724e8i	0.555996	+	1.71118i	0.693299	+	0.720650i	$0.256156\pi$
$659$	1.59121e8	+	4.89724e8i	0.555996	+	1.71118i	−0.137304	+	0.990529i	$0.543844\pi$
$660$	1.69151e6	+	5.20592e6i	0.00588359	+	0.0181078i
$661$	2.24779e8	−	1.63311e8i	0.778307	−	0.565473i	−0.126164	−	0.992009i	$-0.540266\pi$
$661$	2.24779e8	−	1.63311e8i	0.778307	−	0.565473i	0.904470	+	0.426536i	$0.140266\pi$
$662$	−2.02473e8	−	6.57873e7i	−0.697899	−	0.226761i
$663$	−2.54780e7	−	3.50675e7i	−0.0874229	−	0.120327i
$664$	4.26164e6	−	5.86564e6i	0.0145570	−	0.0200360i
$665$	7.77824e6	+	2.39389e7i	0.0264494	+	0.0814029i
$666$	2.68998e6	−	3.70244e6i	0.00910598	−	0.0125333i
$667$	−5.67309e7	−	4.12174e7i	−0.191180	−	0.138900i
$668$	−8.72410e7	+	2.83463e7i	−0.292679	+	0.0950971i
$669$	3.61928e8	+	2.62956e8i	1.20877	+	0.878224i
$670$	3.87352e6	−	2.81428e6i	0.0128790	−	0.00935712i
$671$	7.70915e7	−	2.37263e8i	0.255175	−	0.785349i
$672$	3.16778e7	+	4.36008e7i	0.104387	+	0.143677i
$673$	−2.61337e8	+	8.49134e7i	−0.857344	+	0.278568i	−0.704519	−	0.709685i	$-0.748837\pi$
$673$	−2.61337e8	+	8.49134e7i	−0.857344	+	0.278568i	−0.152825	+	0.988253i	$0.548837\pi$
$674$	1.00559e6	−	326735.i	0.00328428	−	0.00106713i
$675$	−2.99016e8	−	9.71562e7i	−0.972262	−	0.315907i
$676$	−8.22818e7			−0.266357
$677$		−	2.91443e8i		−	0.939263i	−0.882862	−	0.469632i	$-0.844387\pi$
$677$		−	2.91443e8i		−	0.939263i	0.882862	−	0.469632i	$-0.155613\pi$
$678$	2.80633e7	+	9.11832e6i	0.0900430	+	0.0292567i
$679$	1.97947e7	+	1.43817e7i	0.0632323	+	0.0459410i
$680$	−404355.	−	556547.i	−0.00128599	−	0.00177001i
$681$		−	5.52854e8i		−	1.75053i
$682$	−3.37065e6	+	1.75136e8i	−0.0106258	+	0.552106i
$683$	1.34558e8			0.422325			0.211163	−	0.977451i	$-0.432275\pi$
$683$	1.34558e8			0.422325			0.211163	+	0.977451i	$0.432275\pi$
$684$	−1.14247e7	+	8.30053e6i	−0.0357007	+	0.0259381i
$685$	6.47810e6	−	8.91634e6i	0.0201547	−	0.0277405i
$686$	6.80179e7	−	2.09338e8i	0.210693	−	0.648447i
$687$	−4.95542e8			−1.52831
$688$		−	1.36086e8i		−	0.417876i
$689$	1.46293e8	−	4.50244e8i	0.447266	−	1.37654i
$690$	−3.92848e6	−	1.20906e7i	−0.0119585	−	0.0368045i
$691$	−1.68776e8	−	5.19440e8i	−0.511537	−	1.57435i	−0.789495	−	0.613757i	$-0.789658\pi$
$691$	−1.68776e8	−	5.19440e8i	−0.511537	−	1.57435i	0.277958	−	0.960593i	$-0.410342\pi$
$692$	−1.14522e7	+	8.32047e6i	−0.0345596	+	0.0251090i
$693$	−1.36189e7	−	4.42504e6i	−0.0409205	−	0.0132959i
$694$	−1.43727e7	−	1.97824e7i	−0.0429993	−	0.0591834i
$695$	−1.68960e7	+	2.32554e7i	−0.0503304	+	0.0692739i
$696$	7.54579e6	+	2.32235e7i	0.0223809	+	0.0688812i
$697$	9.54460e6	−	1.31370e7i	0.0281877	−	0.0387970i
$698$	1.16256e8	+	8.44646e7i	0.341859	+	0.248375i
$699$	−3.52158e7	+	1.14423e7i	−0.103111	+	0.0335029i
$700$	1.42903e8	+	1.03825e8i	0.416626	+	0.302697i
$701$	−1.07961e8	+	7.84380e7i	−0.313409	+	0.227705i	−0.733358	−	0.679843i	$-0.762048\pi$
$701$	−1.07961e8	+	7.84380e7i	−0.313409	+	0.227705i	0.419949	+	0.907548i	$0.362048\pi$
$702$	9.59132e7	−	2.95190e8i	0.277247	−	0.853279i
$703$	1.38690e8	+	1.90890e8i	0.399189	+	0.549437i
$704$	3.23931e7	−	1.05251e7i	0.0928397	−	0.0301655i
$705$	1.35259e7	−	4.39485e6i	0.0386012	−	0.0125423i
$706$	−2.93627e8	−	9.54051e7i	−0.834414	−	0.271118i
$707$	−4.15070e8			−1.17453
$708$		−	2.21962e8i		−	0.625430i
$709$	6.49174e8	+	2.10930e8i	1.82147	+	0.591832i	0.999759	+	0.0219309i	$0.00698137\pi$
$709$	6.49174e8	+	2.10930e8i	1.82147	+	0.591832i	0.821713	+	0.569901i	$0.193019\pi$
$710$	2.27785e6	+	1.65496e6i	0.00636429	+	0.00462393i
$711$	4.97502e6	+	6.84753e6i	0.0138416	+	0.0190513i
$712$			2.38976e8i			0.662086i
$713$	7.82824e6	−	4.06748e8i	0.0215971	−	1.12217i
$714$	−3.19277e7			−0.0877147
$715$	−1.43286e7	+	1.04103e7i	−0.0391999	+	0.0284804i
$716$	−5.40554e7	+	7.44008e7i	−0.147265	+	0.202693i
$717$	6.89416e7	−	2.12181e8i	0.187036	−	0.575636i
$718$	2.97800e8			0.804547
$719$		−	5.43051e8i		−	1.46101i	−0.682906	−	0.730506i	$-0.739284\pi$
$719$		−	5.43051e8i		−	1.46101i	0.682906	−	0.730506i	$-0.260716\pi$
$720$	77109.0	−	237317.i	0.000206589	−	0.000635816i
$721$	−6.40184e7	−	1.97028e8i	−0.170804	−	0.525682i
$722$	−1.42752e8	−	4.39345e8i	−0.379289	−	1.16733i
$723$	−5.40238e7	+	3.92506e7i	−0.142945	+	0.103856i
$724$	−2.40852e7	−	7.82574e6i	−0.0634649	−	0.0206210i
$725$	4.70422e7	+	6.47480e7i	0.123445	+	0.169907i
$726$	−6.03697e7	+	8.30917e7i	−0.157764	+	0.217144i
$727$	−7.31991e7	−	2.25284e8i	−0.190503	−	0.586309i	0.809496	−	0.587125i	$-0.199740\pi$
$727$	−7.31991e7	−	2.25284e8i	−0.190503	−	0.586309i	−1.00000		0.000815931i	$0.999740\pi$
$728$	−1.02497e8	+	1.41075e8i	−0.265654	+	0.365641i
$729$	3.28322e8	+	2.38540e8i	0.847455	+	0.615712i
$730$	3.11143e6	−	1.01096e6i	0.00799818	−	0.00259877i
$731$	6.52229e7	+	4.73872e7i	0.166974	+	0.121313i
$732$	1.63227e8	−	1.18591e8i	0.416159	−	0.302357i
$733$	1.99090e7	−	6.12737e7i	0.0505520	−	0.155583i	−0.922594	−	0.385773i	$-0.873935\pi$
$733$	1.99090e7	−	6.12737e7i	0.0505520	−	0.155583i	0.973146	+	0.230190i	$0.0739348\pi$
$734$	1.17370e8	+	1.61546e8i	0.296804	+	0.408515i
$735$	−1.21827e6	+	395839.i	−0.00306818	+	0.000996911i
$736$	−7.52319e7	+	2.44443e7i	−0.188699	+	0.0613119i
$737$	−1.33563e8	−	4.33972e7i	−0.333644	−	0.108407i
$738$	5.89003e6			0.0146537
$739$			4.61963e8i			1.14465i	0.820026	+	0.572327i	$0.193959\pi$
$739$			4.61963e8i			1.14465i	−0.820026	+	0.572327i	$0.806041\pi$
$740$	−3.96523e6	−	1.28838e6i	−0.00978527	−	0.00317943i
$741$	6.55811e8	+	4.76474e8i	1.61185	+	1.17108i
$742$	−2.04965e8	−	2.82110e8i	−0.501728	−	0.690569i
$743$			2.93405e8i			0.715320i	0.933852	+	0.357660i	$0.116425\pi$
$743$			2.93405e8i			0.715320i	−0.933852	+	0.357660i	$0.883575\pi$
$744$	−8.54593e7	+	1.12987e8i	−0.207511	+	0.274353i
$745$	1.28996e7			0.0311966
$746$	2.79310e8	−	2.02931e8i	0.672776	−	0.488800i
$747$	−915767.	+	1.26045e6i	−0.00219697	+	0.00302386i
$748$	−6.23531e6	+	1.91903e7i	−0.0148989	+	0.0458540i
$749$	−1.81542e8			−0.432047
$750$			2.90553e7i			0.0688718i
$751$	−2.23930e8	+	6.89187e8i	−0.528680	+	1.62711i	0.228241	+	0.973605i	$0.426703\pi$
$751$	−2.23930e8	+	6.89187e8i	−0.528680	+	1.62711i	−0.756921	+	0.653506i	$0.773297\pi$
$752$	−2.73463e7	−	8.41631e7i	−0.0643049	−	0.197910i
$753$	−2.29773e8	−	7.07168e8i	−0.538163	−	1.65629i
$754$	−6.39196e7	+	4.64403e7i	−0.149114	+	0.108338i
$755$	1.64614e7	+	5.34864e6i	0.0382495	+	0.0124280i
$756$	−1.34380e8	−	1.84958e8i	−0.311006	−	0.428063i
$757$	−2.55932e8	+	3.52260e8i	−0.589980	+	0.812038i	−0.994745	−	0.102383i	$-0.967353\pi$
$757$	−2.55932e8	+	3.52260e8i	−0.589980	+	0.812038i	0.404765	+	0.914421i	$0.367353\pi$
$758$	1.03128e8	+	3.17395e8i	0.236793	+	0.728774i
$759$	−2.19175e8	+	3.01669e8i	−0.501264	+	0.689931i
$760$	1.04082e7	+	7.56200e6i	0.0237102	+	0.0172265i
$761$	−3.03823e8	+	9.87182e7i	−0.689394	+	0.223998i	−0.632703	−	0.774394i	$-0.718055\pi$
$761$	−3.03823e8	+	9.87182e7i	−0.689394	+	0.223998i	−0.0566903	+	0.998392i	$0.518055\pi$
$762$	3.77128e8	+	2.74000e8i	0.852362	+	0.619277i
$763$	−2.14543e8	+	1.55874e8i	−0.482992	+	0.350914i
$764$	−9.46236e7	+	2.91222e8i	−0.212187	+	0.653045i
$765$	86890.3	+	119594.i	0.000194083	+	0.000267132i
$766$	7.87963e7	−	2.56025e7i	0.175315	−	0.0569633i
$767$	6.83028e8	−	2.21929e8i	1.51374	−	0.491846i
$768$	2.61977e7	+	8.51214e6i	0.0578334	+	0.0187912i
$769$	−3.68523e8			−0.810374			−0.405187	−	0.914234i	$-0.632794\pi$
$769$	−3.68523e8			−0.810374			−0.405187	+	0.914234i	$0.632794\pi$
$770$			1.30456e7i			0.0285755i
$771$	3.17235e8	+	1.03076e8i	0.692178	+	0.224902i
$772$	2.76530e8	+	2.00911e8i	0.601021	+	0.436667i
$773$	−8.39558e7	−	1.15555e8i	−0.181766	−	0.250179i	0.708405	−	0.705806i	$-0.249415\pi$
$773$	−8.39558e7	−	1.15555e8i	−0.181766	−	0.250179i	−0.890171	+	0.455627i	$0.849415\pi$
$774$			2.92429e7i			0.0630664i
$775$	−1.51952e8	+	4.38747e8i	−0.326438	+	0.942561i
$776$	1.25058e7			0.0267624
$777$	−1.56546e8	+	1.13737e8i	−0.333717	+	0.242460i
$778$	−2.17203e8	+	2.98955e8i	−0.461240	+	0.634843i
$779$	−9.38415e7	+	2.88815e8i	−0.198510	+	0.610951i
$780$	−1.43237e7			−0.0301837
$781$		−	8.25846e7i		−	0.173359i
$782$	1.44813e7	−	4.45689e7i	0.0302823	−	0.0931992i
$783$	−3.20098e7	−	9.85161e7i	−0.0666804	−	0.205221i
$784$	2.46305e6	+	7.58048e6i	0.00511122	+	0.0157307i
$785$	1.27298e7	−	9.24878e6i	0.0263157	−	0.0191194i
$786$	6.14875e8	+	1.99785e8i	1.26625	+	0.411430i
$787$	1.88288e8	+	2.59156e8i	0.386277	+	0.531665i	0.957234	−	0.289315i	$-0.0934276\pi$
$787$	1.88288e8	+	2.59156e8i	0.386277	+	0.531665i	−0.570957	+	0.820980i	$0.693428\pi$
$788$	6.37631e7	−	8.77623e7i	0.130314	−	0.179362i
$789$	−6.08222e6	−	1.87191e7i	−0.0123831	−	0.0381114i
$790$	4.53238e6	−	6.23828e6i	0.00919274	−	0.0126527i
$791$	5.68937e7	+	4.13357e7i	0.114957	+	0.0835211i
$792$	−6.96082e6	+	2.26171e6i	−0.0140115	+	0.00455261i
$793$	5.28137e8	+	3.83714e8i	1.05908	+	0.769463i
$794$	1.08268e8	−	7.86611e7i	0.216291	−	0.157144i
$795$	8.85134e6	−	2.72416e7i	0.0176160	−	0.0542165i
$796$	1.88380e8	+	2.59283e8i	0.373504	+	0.514084i
$797$	6.41920e8	−	2.08572e8i	1.26796	−	0.411985i	0.403636	−	0.914920i	$-0.367746\pi$
$797$	6.41920e8	−	2.08572e8i	1.26796	−	0.411985i	0.864325	+	0.502934i	$0.167746\pi$
$798$	5.67868e8	−	1.84511e8i	1.11748	−	0.363090i
$799$	4.98600e7	+	1.62005e7i	0.0977488	+	0.0317605i
$800$	9.02823e7			0.176333
$801$		−	5.13526e7i		−	0.0999229i
$802$	−1.66040e8	−	5.39498e7i	−0.321877	−	0.104584i
$803$	−7.76323e7	−	5.64031e7i	−0.149932	−	0.108932i
$804$	−6.67588e7	−	9.18857e7i	−0.128452	−	0.176799i
$805$		−	3.02981e7i		−	0.0580802i
$806$	−4.33134e8	−	1.50008e8i	−0.827212	−	0.286490i
$807$	5.62009e8			1.06936
$808$	−1.71632e8	+	1.24698e8i	−0.325360	+	0.236388i
$809$	−5.22976e8	+	7.19814e8i	−0.987724	+	1.35949i	−0.0551620	+	0.998477i	$0.517568\pi$
$809$	−5.22976e8	+	7.19814e8i	−0.987724	+	1.35949i	−0.932562	+	0.361009i	$0.882432\pi$
$810$	5.49261e6	−	1.69045e7i	0.0103353	−	0.0318088i
$811$	−6.32571e8			−1.18590			−0.592948	−	0.805241i	$-0.702036\pi$
$811$	−6.32571e8			−1.18590			−0.592948	+	0.805241i	$0.702036\pi$
$812$			5.81964e7i			0.108700i
$813$	−2.43958e8	+	7.50825e8i	−0.453987	+	1.39723i
$814$	3.77899e7	+	1.16305e8i	0.0700651	+	0.215638i
$815$	−6.38910e6	−	1.96636e7i	−0.0118023	−	0.0363237i
$816$	−1.32021e7	+	9.59191e6i	−0.0242982	+	0.0176537i
$817$	−1.43391e9	−	4.65906e8i	−2.62940	−	0.854343i
$818$	1.64796e8	+	2.26822e8i	0.301082	+	0.414404i
$819$	2.20251e7	−	3.03150e7i	0.0400928	−	0.0551830i
$820$	−1.65818e6	−	5.10334e6i	−0.00300739	−	0.00925578i
$821$	−8.30312e7	+	1.14283e8i	−0.150042	+	0.206515i	−0.877421	−	0.479721i	$-0.840738\pi$
$821$	−8.30312e7	+	1.14283e8i	−0.150042	+	0.206515i	0.727380	+	0.686235i	$0.240738\pi$
$822$	−2.11509e8	−	1.53670e8i	−0.380814	−	0.276678i
$823$	1.20451e8	−	3.91369e7i	0.216078	−	0.0702081i	−0.198977	−	0.980004i	$-0.563762\pi$
$823$	1.20451e8	−	3.91369e7i	0.216078	−	0.0702081i	0.415056	+	0.909796i	$0.363762\pi$
$824$	−8.56643e7	−	6.22387e7i	−0.153115	−	0.111245i
$825$	3.44300e8	−	2.50149e8i	0.613163	−	0.445489i
$826$	1.63469e8	−	5.03105e8i	0.290065	−	0.892727i
$827$	2.68378e8	+	3.69390e8i	0.474493	+	0.653084i	0.977435	−	0.211236i	$-0.0677490\pi$
$827$	2.68378e8	+	3.69390e8i	0.474493	+	0.653084i	−0.502942	+	0.864320i	$0.667749\pi$
$828$	1.61663e7	−	5.25275e6i	0.0284787	−	0.00925328i
$829$	9.26903e8	−	3.01169e8i	1.62694	−	0.528624i	0.653373	−	0.757036i	$-0.273353\pi$
$829$	9.26903e8	−	3.01169e8i	1.62694	−	0.528624i	0.973565	+	0.228412i	$0.0733534\pi$
$830$	1.34991e6	+	438611.i	0.00236086	+	0.000767089i
$831$	5.91820e8			1.03130
$832$			8.91272e7i			0.154754i
$833$	−4.49083e6	−	1.45916e6i	−0.00776948	−	0.00252446i
$834$	5.51653e8	+	4.00799e8i	0.950972	+	0.690922i
$835$	−1.05553e7	−	1.45282e7i	−0.0181306	−	0.0249547i
$836$		−	3.77354e8i		−	0.645848i
$837$	3.62525e8	−	4.79300e8i	0.618247	−	0.817393i
$838$	4.97571e8			0.845518
$839$	−8.56647e8	+	6.22390e8i	−1.45049	+	1.05385i	−0.464778	+	0.885427i	$0.653866\pi$
$839$	−8.56647e8	+	6.22390e8i	−1.45049	+	1.05385i	−0.985716	+	0.168418i	$0.946134\pi$
$840$	−6.20148e6	+	8.53560e6i	−0.0104630	+	0.0144011i
$841$	1.75662e8	−	5.40633e8i	0.295318	−	0.908897i
$842$	−1.11633e8			−0.187006
$843$		−	9.53475e8i		−	1.59157i
$844$	−8.72840e6	+	2.68633e7i	−0.0145180	+	0.0446819i
$845$	−4.97766e6	−	1.53197e7i	−0.00825003	−	0.0253910i
$846$	5.87633e6	+	1.80855e7i	0.00970499	+	0.0298689i
$847$	−1.98030e8	+	1.43878e8i	−0.325898	+	0.236779i
$848$	−1.69507e8	−	5.50761e7i	−0.277971	−	0.0903182i
$849$	−1.52576e8	−	2.10003e8i	−0.249323	−	0.343164i
$850$	−3.14378e7	+	4.32704e7i	−0.0511911	+	0.0704586i
$851$	−8.77659e7	−	2.70116e8i	−0.142409	−	0.438289i
$852$	3.92580e7	−	5.40340e7i	0.0634760	−	0.0873672i
$853$	−8.30445e8	−	6.03354e8i	−1.33802	−	0.972131i	−0.999514	−	0.0311687i	$-0.990077\pi$
$853$	−8.30445e8	−	6.03354e8i	−1.33802	−	0.972131i	−0.338510	−	0.940963i	$-0.609923\pi$
$854$	4.57315e8	−	1.48591e8i	0.734246	−	0.238571i
$855$	−2.23658e6	−	1.62497e6i	−0.00357837	−	0.00259984i
$856$	−7.50678e7	+	5.45399e7i	−0.119683	+	0.0869548i
$857$	2.03496e8	−	6.26295e8i	0.323305	−	0.995031i	−0.648895	−	0.760878i	$-0.724768\pi$
$857$	2.03496e8	−	6.26295e8i	0.323305	−	0.995031i	0.972200	−	0.234153i	$-0.0752315\pi$
$858$	2.46948e8	+	3.39895e8i	0.390971	+	0.538125i
$859$	4.73102e8	−	1.53720e8i	0.746406	−	0.242522i	0.0889718	−	0.996034i	$-0.471642\pi$
$859$	4.73102e8	−	1.53720e8i	0.746406	−	0.242522i	0.657434	+	0.753512i	$0.271642\pi$
$860$	2.53372e7	−	8.23255e6i	0.0398348	−	0.0129431i
$861$	−2.36852e8	−	7.69579e7i	−0.371080	−	0.120571i
$862$	−3.12128e8			−0.487316
$863$		−	4.13182e8i		−	0.642849i	−0.946935	−	0.321425i	$-0.895838\pi$
$863$		−	4.13182e8i		−	0.642849i	0.946935	−	0.321425i	$-0.104162\pi$
$864$	−1.11133e8	−	3.61092e7i	−0.172306	−	0.0559856i
$865$	−2.24195e6	−	1.62887e6i	−0.00346400	−	0.00251674i
$866$	−1.38833e8	−	1.91087e8i	−0.213766	−	0.294223i
$867$			6.24421e8i			0.958121i
$868$	−2.76916e8	+	1.93161e8i	−0.423437	+	0.295366i
$869$	−2.26172e8			−0.344651
$870$	−3.86740e6	+	2.80983e6i	−0.00587302	+	0.00426700i
$871$	2.16005e8	−	2.97305e8i	0.326895	−	0.449932i
$872$	−4.18849e7	+	1.28909e8i	−0.0631697	+	0.194416i
$873$	−2.68731e6			−0.00403902
$874$			8.76395e8i			1.31270i
$875$	−2.13984e7	+	6.58575e7i	−0.0319417	+	0.0983063i
$876$	−2.39816e7	−	7.38077e7i	−0.0356751	−	0.109797i
$877$	−1.60026e7	−	4.92510e7i	−0.0237242	−	0.0730157i	0.938493	−	0.345297i	$-0.112222\pi$
$877$	−1.60026e7	−	4.92510e7i	−0.0237242	−	0.0730157i	−0.962218	+	0.272281i	$0.912222\pi$
$878$	−8.89809e6	+	6.46484e6i	−0.0131466	+	0.00955156i
$879$	−1.21844e9	−	3.95896e8i	−1.79407	−	0.582928i
$880$	3.91926e6	+	5.39439e6i	0.00575116	+	0.00791580i
$881$	3.96965e8	−	5.46375e8i	0.580530	−	0.799030i	−0.413224	−	0.910630i	$-0.635597\pi$
$881$	3.96965e8	−	5.46375e8i	0.580530	−	0.799030i	0.993753	+	0.111599i	$0.0355972\pi$
$882$	−529275.	−	1.62894e6i	−0.000771392	−	0.00237410i
$883$	−6.70105e8	+	9.22321e8i	−0.973332	+	1.33968i	−0.0329860	+	0.999456i	$0.510502\pi$
$883$	−6.70105e8	+	9.22321e8i	−0.973332	+	1.33968i	−0.940346	+	0.340220i	$0.889498\pi$
$884$	−4.27167e7	−	3.10355e7i	−0.0618360	−	0.0449265i
$885$	4.13261e7	−	1.34277e7i	0.0596203	−	0.0193718i
$886$	−4.16929e8	−	3.02917e8i	−0.599461	−	0.435534i
$887$	1.91999e8	−	1.39496e8i	0.275124	−	0.199889i	−0.441664	−	0.897181i	$-0.645612\pi$
$887$	1.91999e8	−	1.39496e8i	0.275124	−	0.199889i	0.716788	+	0.697291i	$0.245612\pi$
$888$	−3.05623e7	+	9.40611e7i	−0.0436463	+	0.134329i
$889$	6.53017e8	+	8.98800e8i	0.929435	+	1.27926i
$890$	−4.44939e7	+	1.44569e7i	−0.0631146	+	0.0205072i
$891$	−4.95832e8	+	1.61105e8i	−0.700973	+	0.227760i
$892$	5.18281e8	+	1.68400e8i	0.730248	+	0.237272i
$893$	−9.80436e8			−1.37678
$894$		−	3.05998e8i		−	0.428258i
$895$	−1.71224e7	−	5.56342e6i	−0.0238834	−	0.00776020i
$896$	5.31114e7	+	3.85877e7i	0.0738353	+	0.0536445i
$897$	−5.73531e8	−	7.89397e8i	−0.794656	−	1.09375i
$898$			1.16680e8i			0.161127i
$899$	−1.46372e8	+	4.44641e7i	−0.201456	+	0.0611971i
$900$	−1.94004e7			−0.0266124
$901$	8.54217e7	−	6.20625e7i	0.116787	−	0.0848506i
$902$	−9.25120e7	+	1.27332e8i	−0.126060	+	0.173507i
$903$	3.82082e8	−	1.17593e9i	0.518912	−	1.59705i
$904$	3.59440e7			0.0486543
$905$		−	4.95773e6i		−	0.00668863i
$906$	1.26878e8	−	3.90489e8i	0.170608	−	0.525079i
$907$	−2.84630e8	−	8.76002e8i	−0.381469	−	1.17404i	−0.939010	−	0.343891i	$-0.888255\pi$
$907$	−2.84630e8	−	8.76002e8i	−0.381469	−	1.17404i	0.557541	−	0.830150i	$-0.311745\pi$
$908$	−2.08107e8	−	6.40487e8i	−0.277990	−	0.855564i
$909$	3.68813e7	−	2.67958e7i	0.0491037	−	0.0356760i
$910$	−3.24666e7	−	1.05490e7i	−0.0430837	−	0.0139987i
$911$	−1.10181e8	−	1.51652e8i	−0.145731	−	0.200582i	0.729911	−	0.683542i	$-0.239562\pi$
$911$	−1.10181e8	−	1.51652e8i	−0.145731	−	0.200582i	−0.875642	+	0.482960i	$0.839562\pi$
$912$	1.79382e8	−	2.46898e8i	0.236480	−	0.325487i
$913$	−1.28650e7	−	3.95945e7i	−0.0169044	−	0.0520263i
$914$	−3.75241e8	+	5.16475e8i	−0.491441	+	0.676411i
$915$	3.19545e7	+	2.32163e7i	0.0417127	+	0.0303061i
$916$	−5.74091e8	+	1.86533e8i	−0.746954	+	0.242700i
$917$	1.24656e9	+	9.05678e8i	1.61661	+	1.17453i
$918$	5.60045e7	−	4.06897e7i	0.0723927	−	0.0525964i
$919$	−1.57496e8	+	4.84723e8i	−0.202919	+	0.624521i	0.796873	+	0.604146i	$0.206486\pi$
$919$	−1.57496e8	+	4.84723e8i	−0.202919	+	0.624521i	−0.999792	+	0.0203744i	$0.993514\pi$
$920$	−9.10236e6	−	1.25283e7i	−0.0116894	−	0.0160890i
$921$	9.37089e8	−	3.04479e8i	1.19950	−	0.389743i
$922$	3.22916e7	−	1.04922e7i	0.0412000	−	0.0133867i
$923$	2.05528e8	+	6.67800e7i	0.261376	+	0.0849261i
$924$	3.09462e8			0.392276
$925$			3.24153e8i			0.409567i
$926$	−7.39996e8	−	2.40439e8i	−0.931958	−	0.302811i
$927$	1.84081e7	+	1.33742e7i	0.0231083	+	0.0167892i
$928$	1.74837e7	+	2.40643e7i	0.0218771	+	0.0301113i
$929$		−	1.19101e7i		−	0.0148548i	−0.999972	−	0.00742740i	$-0.997636\pi$
$929$		−	1.19101e7i		−	0.0148548i	0.999972	−	0.00742740i	$-0.00236424\pi$
$930$	−2.62064e7	−	9.07610e6i	−0.0325806	−	0.0112837i
$931$	8.83068e7			0.109432
$932$	−3.64908e7	+	2.65121e7i	−0.0450749	+	0.0327489i
$933$	−9.14346e8	+	1.25849e9i	−1.12581	+	1.54955i
$934$	−5.12648e7	+	1.57777e8i	−0.0629185	+	0.193643i
$935$	−3.95016e6			−0.00483259
$936$		−	1.91522e7i		−	0.0233556i
$937$	1.44335e8	−	4.44216e8i	0.175449	−	0.539977i	−0.824204	−	0.566292i	$-0.808377\pi$
$937$	1.44335e8	−	4.44216e8i	0.175449	−	0.539977i	0.999654	+	0.0263151i	$0.00837731\pi$
$938$	−8.36462e7	−	2.57437e8i	−0.101353	−	0.311933i
$939$	7.16565e7	+	2.20536e8i	0.0865483	+	0.266368i
$940$	1.40156e7	−	1.01829e7i	0.0168744	−	0.0122600i
$941$	4.90776e8	+	1.59463e8i	0.588998	+	0.191377i	0.588328	−	0.808623i	$-0.299787\pi$
$941$	4.90776e8	+	1.59463e8i	0.588998	+	0.191377i	0.000670626		1.00000i	$0.499787\pi$
$942$	−2.19395e8	−	3.01971e8i	−0.262466	−	0.361254i
$943$	2.14857e8	−	2.95725e8i	0.256220	−	0.352657i
$944$	−8.35515e7	−	2.57145e8i	−0.0993203	−	0.305677i
$945$	2.63072e7	−	3.62087e7i	0.0311730	−	0.0429059i
$946$	−6.32180e8	−	4.59306e8i	−0.746736	−	0.542536i
$947$	1.02564e9	−	3.33251e8i	1.20766	−	0.392394i	0.365088	−	0.930973i	$-0.381039\pi$
$947$	1.02564e9	−	3.33251e8i	1.20766	−	0.392394i	0.842575	+	0.538579i	$0.181039\pi$
$948$	−1.47981e8	−	1.07515e8i	−0.173693	−	0.126195i
$949$	2.03145e8	−	1.47594e8i	0.237689	−	0.172691i
$950$	3.09093e8	−	9.51290e8i	0.360511	−	1.10954i
$951$	4.31234e8	+	5.93543e8i	0.501385	+	0.690098i
$952$	−3.69885e7	+	1.20183e7i	−0.0428702	+	0.0139294i
$953$	−1.15679e9	+	3.75864e8i	−1.33652	+	0.434262i	−0.888137	−	0.459579i	$-0.848000\pi$
$953$	−1.15679e9	+	3.75864e8i	−1.33652	+	0.434262i	−0.448385	+	0.893841i	$0.648000\pi$
$954$	3.64246e7	+	1.18351e7i	0.0419518	+	0.0136310i
$955$	−5.99455e7			−0.0688250
$956$		−	2.71765e8i		−	0.311042i
$957$	1.33352e8	+	4.33286e7i	0.152147	+	0.0494355i
$958$	−1.23090e8	−	8.94300e7i	−0.139999	−	0.101715i
$959$	−3.66238e8	−	5.04084e8i	−0.415248	−	0.571540i
$960$			5.39257e6i			0.00609512i
$961$	−6.97402e8	−	5.48902e8i	−0.785801	−	0.618479i
$962$	−3.20006e8			−0.359445
$963$	1.61310e7	−	1.17199e7i	0.0180627	−	0.0131233i
$964$	−4.78123e7	+	6.58080e7i	−0.0533714	+	0.0734594i
$965$	−2.06779e7	+	6.36399e7i	−0.0230104	+	0.0708187i
$966$	−7.18717e8			−0.797309
$967$			6.81085e8i			0.753220i	0.926372	+	0.376610i	$0.122910\pi$
$967$			6.81085e8i			0.753220i	−0.926372	+	0.376610i	$0.877090\pi$
$968$	−3.86613e7	+	1.18987e8i	−0.0426236	+	0.131182i
$969$	5.58692e7	+	1.71948e8i	0.0614047	+	0.188984i
$970$	756540.	+	2.32839e6i	0.000828928	+	0.00255118i
$971$	8.49860e8	−	6.17460e8i	0.928303	−	0.674452i	−0.0172737	−	0.999851i	$-0.505499\pi$
$971$	8.49860e8	−	6.17460e8i	0.928303	−	0.674452i	0.945577	+	0.325399i	$0.105499\pi$
$972$	4.65520e7	+	1.51257e7i	0.0506920	+	0.0164708i
$973$	9.55215e8	+	1.31474e9i	1.03696	+	1.42725i
$974$	4.00512e8	−	5.51257e8i	0.433449	−	0.596592i
$975$	3.44134e8	+	1.05913e9i	0.371290	+	1.14271i
$976$	1.44460e8	−	1.98832e8i	0.155381	−	0.213863i
$977$	−1.22070e9	−	8.86893e8i	−1.30896	−	0.951016i	−0.308961	−	0.951075i	$-0.599981\pi$
$977$	−1.22070e9	−	8.86893e8i	−1.30896	−	0.951016i	−1.00000		5.92014e-5i	$0.999981\pi$
$978$	−4.66450e8	+	1.51559e8i	−0.498642	+	0.162019i
$979$	1.11015e9	+	8.06573e8i	1.18314	+	0.859598i
$980$	−1.26237e6	+	917167.i	−0.00134125	+	0.000974474i
$981$	9.00049e6	−	2.77007e7i	0.00953365	−	0.0293416i
$982$	6.57030e8	+	9.04324e8i	0.693826	+	0.954970i
$983$	9.52039e8	−	3.09336e8i	1.00229	−	0.325664i	0.238511	−	0.971140i	$-0.423341\pi$
$983$	9.52039e8	−	3.09336e8i	1.00229	−	0.325664i	0.763781	+	0.645475i	$0.223341\pi$
$984$	−1.21059e8	+	3.93344e7i	−0.127061	+	0.0412845i
$985$	2.01974e7	+	6.56254e6i	0.0211343	+	0.00686695i
$986$	−1.76216e7			−0.0183829
$987$		−	8.04040e8i		−	0.836231i
$988$	9.39119e8	+	3.05138e8i	0.973755	+	0.316392i
$989$	1.46822e9	+	1.06672e9i	1.51776	+	1.10271i
$990$	−842194.	−	1.15918e6i	−0.000867973	−	0.00119466i
$991$		−	5.54183e8i		−	0.569419i	−0.958614	−	0.284710i	$-0.908103\pi$
$991$		−	5.54183e8i		−	0.569419i	0.958614	−	0.284710i	$-0.0918972\pi$
$992$	−5.64746e7	+	1.63065e8i	−0.0578520	+	0.167042i
$993$	−9.88648e8			−1.00970
$994$	1.28778e8	−	9.35626e7i	0.131124	−	0.0952672i
$995$	−3.68785e7	+	5.07590e7i	−0.0374373	+	0.0515280i
$996$	1.04045e7	−	3.20218e7i	0.0105304	−	0.0324092i
$997$	−9.29473e8			−0.937889			−0.468944	−	0.883228i	$-0.655366\pi$
$997$	−9.29473e8			−0.937889			−0.468944	+	0.883228i	$0.655366\pi$
$998$			1.19961e9i			1.20684i
$999$	1.29648e8	−	3.99015e8i	0.130037	−	0.400214i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	62.7.f.a.15.14	✓	64
31.29	odd	10	inner	62.7.f.a.29.14	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
62.7.f.a.15.14	✓	64	1.1	even	1	trivial
62.7.f.a.29.14	yes	64	31.29	odd	10	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:	\( N \)	\(=\)	\( 62 = 2 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	62.f (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(4.57649 - 3.32502i) q^{2} +(15.4410 - 21.2527i) q^{3} +(9.88854 - 30.4338i) q^{4} +6.26454 q^{5} -148.604i q^{6} +(109.443 - 336.831i) q^{7} +(-55.9381 - 172.160i) q^{8} +(12.0203 + 36.9947i) q^{9} +(28.6696 - 20.8297i) q^{10} +(-988.558 - 321.202i) q^{11} +(-494.112 - 680.086i) q^{12} +(1598.75 - 2200.48i) q^{13} +(-619.103 - 1905.40i) q^{14} +(96.7308 - 133.138i) q^{15} +(-828.433 - 601.892i) q^{16} +(576.948 - 187.462i) q^{17} +(178.019 + 129.338i) q^{18} +(-9178.28 + 6668.41i) q^{19} +(61.9472 - 190.654i) q^{20} +(-5468.66 - 7526.96i) q^{21} +(-5592.13 + 1816.99i) q^{22} +(12987.6 - 4219.91i) q^{23} +(-4522.60 - 1469.48i) q^{24} -15585.8 q^{25} -15386.3i q^{26} +(19185.2 + 6233.65i) q^{27} +(-9168.81 - 6661.53i) q^{28} +(-3018.28 - 4154.30i) q^{29} -930.938i q^{30} +(9749.41 - 28150.5i) q^{31} -5792.62 q^{32} +(-22090.7 + 16049.8i) q^{33} +(2017.08 - 2776.28i) q^{34} +(685.610 - 2110.09i) q^{35} +1244.75 q^{36} -20798.0i q^{37} +(-19831.8 + 61035.9i) q^{38} +(-22080.0 - 67955.3i) q^{39} +(-350.426 - 1078.50i) q^{40} +(21655.4 - 15733.6i) q^{41} +(-50054.5 - 16263.7i) q^{42} +(78114.4 + 107515. i) q^{43} +(-19550.8 + 26909.4i) q^{44} +(75.3017 + 231.755i) q^{45} +(45406.2 - 62496.2i) q^{46} +(69915.4 + 50796.5i) q^{47} +(-25583.7 + 8312.64i) q^{48} +(-6297.21 - 4575.19i) q^{49} +(-71328.1 + 51822.9i) q^{50} +(4924.58 - 15156.3i) q^{51} +(-51159.8 - 70415.5i) q^{52} +(165534. - 53785.2i) q^{53} +(108528. - 35262.9i) q^{54} +(-6192.86 - 2012.18i) q^{55} -64110.7 q^{56} +298030. i q^{57} +(-27626.3 - 8976.31i) q^{58} +(213614. + 155200. i) q^{59} +(-3095.38 - 4260.43i) q^{60} +240009. i q^{61} +(-48982.9 - 161248. i) q^{62} +13776.5 q^{63} +(-26509.9 + 19260.5i) q^{64} +(10015.4 - 13785.0i) q^{65} +(-47732.0 + 146904. i) q^{66} +135109. q^{67} -19412.4i q^{68} +(110856. - 341180. i) q^{69} +(-3878.40 - 11936.5i) q^{70} +(24551.9 + 75563.1i) q^{71} +(5696.60 - 4138.82i) q^{72} +(87800.2 + 28528.0i) q^{73} +(-69153.8 - 95182.0i) q^{74} +(-240660. + 331239. i) q^{75} +(112185. + 345271. i) q^{76} +(-216381. + 297823. i) q^{77} +(-327001. - 237580. i) q^{78} +(206942. - 67239.7i) q^{79} +(-5189.76 - 3770.58i) q^{80} +(405779. - 294816. i) q^{81} +(46791.4 - 144009. i) q^{82} +(23542.5 + 32403.4i) q^{83} +(-283151. + 92001.4i) q^{84} +(3614.31 - 1174.36i) q^{85} +(714980. + 232311. i) q^{86} -134895. q^{87} +188157. i q^{88} +(-1.25555e6 - 407954. i) q^{89} +(1115.21 + 810.245i) q^{90} +(-566219. - 779334. i) q^{91} -436989. i q^{92} +(-447734. - 641874. i) q^{93} +488867. q^{94} +(-57497.8 + 41774.6i) q^{95} +(-89443.8 + 123109. i) q^{96} +(-21348.5 + 65703.9i) q^{97} -44031.7 q^{98} -40432.3i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 512 q^{4} - 288 q^{5} - 692 q^{7} + 3248 q^{9} + 1344 q^{10} + 3200 q^{11} - 3600 q^{13} + 4560 q^{14} + 9520 q^{15} - 16384 q^{16} - 1400 q^{17} - 11200 q^{18} + 2912 q^{19} - 9216 q^{20} + 4860 q^{21}+ \cdots + 13577088 q^{98}+O(q^{100}) \) 64 * q - 512 * q^4 - 288 * q^5 - 692 * q^7 + 3248 * q^9 + 1344 * q^10 + 3200 * q^11 - 3600 * q^13 + 4560 * q^14 + 9520 * q^15 - 16384 * q^16 - 1400 * q^17 - 11200 * q^18 + 2912 * q^19 - 9216 * q^20 + 4860 * q^21 + 6720 * q^22 - 26240 * q^23 + 241592 * q^25 - 206100 * q^27 + 16896 * q^28 - 48160 * q^29 + 142924 * q^31 + 291360 * q^33 + 123840 * q^34 + 16728 * q^35 - 518144 * q^36 - 89856 * q^38 - 169400 * q^39 - 64512 * q^40 - 291056 * q^41 + 220320 * q^42 + 145600 * q^43 - 44412 * q^45 - 213120 * q^46 + 596760 * q^47 - 163840 * q^48 + 481596 * q^49 - 295744 * q^50 + 1117652 * q^51 + 115200 * q^52 - 1276880 * q^53 + 290880 * q^55 - 97280 * q^56 - 367200 * q^58 + 469780 * q^59 - 304640 * q^60 - 963152 * q^62 - 1359328 * q^63 - 524288 * q^64 + 934760 * q^65 - 789792 * q^66 + 1470992 * q^67 - 933024 * q^69 + 515232 * q^70 - 906672 * q^71 - 358400 * q^72 + 1236840 * q^73 - 126400 * q^74 - 2881620 * q^75 - 139776 * q^76 + 3063520 * q^77 + 2374288 * q^78 + 4375280 * q^79 + 442368 * q^80 - 3676208 * q^81 + 1386144 * q^82 + 4922820 * q^83 - 601600 * q^84 - 1012320 * q^85 - 2054800 * q^86 - 5911600 * q^87 - 1219900 * q^89 - 2696992 * q^90 + 163640 * q^91 - 248320 * q^93 + 290592 * q^94 + 2034328 * q^95 - 1078884 * q^97 + 13577088 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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