LMFDB - Embedded newform 19.5.f.a.3.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,5,Mod(2,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("19.2");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	19.f (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.96402929859$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$6$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.1
Character	$\chi$	$=$	19.3
Dual form			19.5.f.a.13.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.01717 + 5.97923i) q^{2} +(4.42557 + 12.1592i) q^{3} +(-7.80084 - 44.2408i) q^{4} +(-1.37942 + 7.82309i) q^{5} +(-94.9062 - 34.5430i) q^{6} +(-2.12885 - 3.68728i) q^{7} +(195.510 + 112.878i) q^{8} +(-66.2097 + 55.5565i) q^{9} +O(q^{10})$	\(q+(-5.01717 + 5.97923i) q^{2} +(4.42557 + 12.1592i) q^{3} +(-7.80084 - 44.2408i) q^{4} +(-1.37942 + 7.82309i) q^{5} +(-94.9062 - 34.5430i) q^{6} +(-2.12885 - 3.68728i) q^{7} +(195.510 + 112.878i) q^{8} +(-66.2097 + 55.5565i) q^{9} +(-39.8553 - 47.4977i) q^{10} +(-34.8687 + 60.3943i) q^{11} +(503.407 - 290.642i) q^{12} +(-46.7545 + 128.457i) q^{13} +(32.7279 + 5.77082i) q^{14} +(-101.227 + 17.8490i) q^{15} +(-980.405 + 356.838i) q^{16} +(152.200 + 127.711i) q^{17} -674.620i q^{18} +(240.172 - 269.515i) q^{19} +356.860 q^{20} +(35.4128 - 42.2033i) q^{21} +(-186.170 - 511.497i) q^{22} +(-57.8431 - 328.044i) q^{23} +(-507.255 + 2876.78i) q^{24} +(528.010 + 192.180i) q^{25} +(-533.499 - 924.047i) q^{26} +(-60.8549 - 35.1346i) q^{27} +(-146.521 + 122.946i) q^{28} +(624.599 + 744.368i) q^{29} +(401.149 - 694.811i) q^{30} +(43.5728 - 25.1568i) q^{31} +(1549.84 - 4258.14i) q^{32} +(-888.657 - 156.694i) q^{33} +(-1527.22 + 269.291i) q^{34} +(31.7825 - 11.5679i) q^{35} +(2974.35 + 2495.78i) q^{36} +51.5297i q^{37} +(406.507 + 2788.25i) q^{38} -1768.84 q^{39} +(-1152.74 + 1373.79i) q^{40} +(-338.953 - 931.265i) q^{41} +(74.6715 + 423.483i) q^{42} +(285.991 - 1621.94i) q^{43} +(2943.90 + 1071.49i) q^{44} +(-343.293 - 594.600i) q^{45} +(2251.66 + 1300.00i) q^{46} +(-2681.81 + 2250.31i) q^{47} +(-8677.70 - 10341.7i) q^{48} +(1191.44 - 2063.63i) q^{49} +(-3798.21 + 2192.89i) q^{50} +(-879.283 + 2415.81i) q^{51} +(6047.76 + 1066.38i) q^{52} +(2857.21 - 503.803i) q^{53} +(515.397 - 187.589i) q^{54} +(-424.372 - 356.090i) q^{55} -961.200i q^{56} +(4339.97 + 1727.53i) q^{57} -7584.47 q^{58} +(776.686 - 925.618i) q^{59} +(1579.31 + 4339.12i) q^{60} +(-888.240 - 5037.46i) q^{61} +(-68.1941 + 386.748i) q^{62} +(345.803 + 125.862i) q^{63} +(9338.00 + 16173.9i) q^{64} +(-940.437 - 542.961i) q^{65} +(5395.46 - 4527.33i) q^{66} +(2047.05 + 2439.58i) q^{67} +(4462.73 - 7729.67i) q^{68} +(3732.75 - 2155.11i) q^{69} +(-90.2912 + 248.073i) q^{70} +(-6515.81 - 1148.91i) q^{71} +(-19215.8 + 3388.26i) q^{72} +(3998.62 - 1455.38i) q^{73} +(-308.108 - 258.533i) q^{74} +7270.66i q^{75} +(-13797.1 - 8522.96i) q^{76} +296.921 q^{77} +(8874.59 - 10576.3i) q^{78} +(-1522.69 - 4183.56i) q^{79} +(-1439.19 - 8162.03i) q^{80} +(-1057.80 + 5999.08i) q^{81} +(7268.84 + 2645.64i) q^{82} +(-444.741 - 770.313i) q^{83} +(-2143.36 - 1237.47i) q^{84} +(-1209.04 + 1014.50i) q^{85} +(8263.07 + 9847.54i) q^{86} +(-6286.67 + 10888.8i) q^{87} +(-13634.4 + 7871.80i) q^{88} +(-1978.44 + 5435.72i) q^{89} +(5277.61 + 930.585i) q^{90} +(573.191 - 101.069i) q^{91} +(-14061.7 + 5118.04i) q^{92} +(498.720 + 418.476i) q^{93} -27325.4i q^{94} +(1777.14 + 2250.66i) q^{95} +58634.2 q^{96} +(-3129.82 + 3729.97i) q^{97} +(6361.27 + 17477.4i) q^{98} +(-1046.65 - 5935.87i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{2} - 18 q^{3} - 48 q^{4} - 6 q^{5} - 48 q^{7} - 9 q^{8} + 246 q^{9}+O(q^{10}) $ 36 * q - 6 * q^2 - 18 * q^3 - 48 * q^4 - 6 * q^5 - 48 * q^7 - 9 * q^8 + 246 * q^9	\( 36 q - 6 q^{2} - 18 q^{3} - 48 q^{4} - 6 q^{5} - 48 q^{7} - 9 q^{8} + 246 q^{9} - 153 q^{10} - 48 q^{11} + 855 q^{12} + 555 q^{13} - 399 q^{14} - 1647 q^{15} - 2112 q^{16} + 39 q^{17} - 12 q^{19} + 2886 q^{20} + 912 q^{21} + 1386 q^{22} + 1074 q^{23} + 168 q^{24} + 2448 q^{25} - 3675 q^{26} + 1215 q^{27} + 2316 q^{28} - 1743 q^{29} + 2580 q^{30} - 2817 q^{31} - 6039 q^{32} - 7368 q^{33} - 8460 q^{34} - 1326 q^{35} - 4581 q^{36} + 2892 q^{38} + 7164 q^{39} + 4482 q^{40} + 6150 q^{41} + 22299 q^{42} + 2091 q^{43} + 34053 q^{44} + 3165 q^{45} + 7326 q^{46} + 4539 q^{47} - 44943 q^{48} + 102 q^{49} - 51876 q^{50} - 25836 q^{51} - 3279 q^{52} - 11607 q^{53} + 6069 q^{54} - 7044 q^{55} + 2532 q^{57} + 13644 q^{58} - 681 q^{59} + 63654 q^{60} + 44346 q^{61} + 14796 q^{62} + 53388 q^{63} + 939 q^{64} + 3636 q^{65} + 11148 q^{66} - 52089 q^{67} + 5262 q^{68} - 54954 q^{69} - 69999 q^{70} - 24504 q^{71} - 101118 q^{72} - 6666 q^{73} - 9675 q^{74} - 6462 q^{76} + 48918 q^{77} + 56871 q^{78} + 41043 q^{79} + 65649 q^{80} + 2919 q^{81} + 114711 q^{82} - 17598 q^{83} + 11115 q^{84} + 52344 q^{85} - 55716 q^{86} + 2121 q^{87} - 69057 q^{88} - 11706 q^{89} - 41394 q^{90} - 84249 q^{91} - 88668 q^{92} - 60321 q^{93} + 93405 q^{95} + 167166 q^{96} + 4401 q^{97} + 69381 q^{98} + 58386 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 - 18 * q^3 - 48 * q^4 - 6 * q^5 - 48 * q^7 - 9 * q^8 + 246 * q^9 - 153 * q^10 - 48 * q^11 + 855 * q^12 + 555 * q^13 - 399 * q^14 - 1647 * q^15 - 2112 * q^16 + 39 * q^17 - 12 * q^19 + 2886 * q^20 + 912 * q^21 + 1386 * q^22 + 1074 * q^23 + 168 * q^24 + 2448 * q^25 - 3675 * q^26 + 1215 * q^27 + 2316 * q^28 - 1743 * q^29 + 2580 * q^30 - 2817 * q^31 - 6039 * q^32 - 7368 * q^33 - 8460 * q^34 - 1326 * q^35 - 4581 * q^36 + 2892 * q^38 + 7164 * q^39 + 4482 * q^40 + 6150 * q^41 + 22299 * q^42 + 2091 * q^43 + 34053 * q^44 + 3165 * q^45 + 7326 * q^46 + 4539 * q^47 - 44943 * q^48 + 102 * q^49 - 51876 * q^50 - 25836 * q^51 - 3279 * q^52 - 11607 * q^53 + 6069 * q^54 - 7044 * q^55 + 2532 * q^57 + 13644 * q^58 - 681 * q^59 + 63654 * q^60 + 44346 * q^61 + 14796 * q^62 + 53388 * q^63 + 939 * q^64 + 3636 * q^65 + 11148 * q^66 - 52089 * q^67 + 5262 * q^68 - 54954 * q^69 - 69999 * q^70 - 24504 * q^71 - 101118 * q^72 - 6666 * q^73 - 9675 * q^74 - 6462 * q^76 + 48918 * q^77 + 56871 * q^78 + 41043 * q^79 + 65649 * q^80 + 2919 * q^81 + 114711 * q^82 - 17598 * q^83 + 11115 * q^84 + 52344 * q^85 - 55716 * q^86 + 2121 * q^87 - 69057 * q^88 - 11706 * q^89 - 41394 * q^90 - 84249 * q^91 - 88668 * q^92 - 60321 * q^93 + 93405 * q^95 + 167166 * q^96 + 4401 * q^97 + 69381 * q^98 + 58386 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−5.01717	+	5.97923i	−1.25429	+	1.49481i	−0.459185	+	0.888341i	$0.651858\pi$
$2$	−5.01717	+	5.97923i	−1.25429	+	1.49481i	−0.795108	+	0.606467i	$0.792586\pi$
$3$	4.42557	+	12.1592i	0.491730	+	1.35102i	0.899096	+	0.437752i	$0.144225\pi$
$3$	4.42557	+	12.1592i	0.491730	+	1.35102i	−0.407366	+	0.913265i	$0.633553\pi$
$4$	−7.80084	−	44.2408i	−0.487552	−	2.76505i
$5$	−1.37942	+	7.82309i	−0.0551769	+	0.312924i	−0.999888	−	0.0149808i	$-0.995231\pi$
$5$	−1.37942	+	7.82309i	−0.0551769	+	0.312924i	0.944711	+	0.327904i	$0.106342\pi$
$6$	−94.9062	−	34.5430i	−2.63628	−	0.959529i
$7$	−2.12885	−	3.68728i	−0.0434460	−	0.0752506i	0.843485	−	0.537153i	$-0.180500\pi$
$7$	−2.12885	−	3.68728i	−0.0434460	−	0.0752506i	−0.886931	+	0.461903i	$0.847167\pi$
$8$	195.510	+	112.878i	3.05484	+	1.76372i
$9$	−66.2097	+	55.5565i	−0.817403	+	0.685883i
$10$	−39.8553	−	47.4977i	−0.398553	−	0.474977i
$11$	−34.8687	+	60.3943i	−0.288171	+	0.499127i	−0.973373	−	0.229226i	$-0.926380\pi$
$11$	−34.8687	+	60.3943i	−0.288171	+	0.499127i	0.685202	+	0.728353i	$0.259714\pi$
$12$	503.407	−	290.642i	3.49588	−	2.01835i
$13$	−46.7545	+	128.457i	−0.276654	+	0.760101i	0.721082	+	0.692850i	$0.243645\pi$
$13$	−46.7545	+	128.457i	−0.276654	+	0.760101i	−0.997736	+	0.0672511i	$0.978577\pi$
$14$	32.7279	+	5.77082i	0.166979	+	0.0294429i
$15$	−101.227	+	17.8490i	−0.449897	+	0.0793290i
$16$	−980.405	+	356.838i	−3.82971	+	1.39390i
$17$	152.200	+	127.711i	0.526642	+	0.441905i	0.866940	−	0.498413i	$-0.166083\pi$
$17$	152.200	+	127.711i	0.526642	+	0.441905i	−0.340298	+	0.940318i	$0.610528\pi$
$18$		−	674.620i		−	2.08216i
$19$	240.172	−	269.515i	0.665297	−	0.746579i
$19$	240.172	−	269.515i	0.665297	−	0.746579i
$20$	356.860			0.892150
$21$	35.4128	−	42.2033i	0.0803012	−	0.0956992i
$22$	−186.170	−	511.497i	−0.384648	−	1.05681i
$23$	−57.8431	−	328.044i	−0.109344	−	0.620122i	−0.989396	−	0.145244i	$-0.953603\pi$
$23$	−57.8431	−	328.044i	−0.109344	−	0.620122i	0.880052	−	0.474878i	$-0.157508\pi$
$24$	−507.255	+	2876.78i	−0.880650	+	4.99442i
$25$	528.010	+	192.180i	0.844816	+	0.307488i
$26$	−533.499	−	924.047i	−0.789200	−	1.36693i
$27$	−60.8549	−	35.1346i	−0.0834772	−	0.0481956i
$28$	−146.521	+	122.946i	−0.186889	+	0.156819i
$29$	624.599	+	744.368i	0.742686	+	0.885098i	0.996622	−	0.0821227i	$-0.0261699\pi$
$29$	624.599	+	744.368i	0.742686	+	0.885098i	−0.253937	+	0.967221i	$0.581725\pi$
$30$	401.149	−	694.811i	0.445721	−	0.772012i
$31$	43.5728	−	25.1568i	0.0453411	−	0.0261777i	−0.477158	−	0.878817i	$-0.658333\pi$
$31$	43.5728	−	25.1568i	0.0453411	−	0.0261777i	0.522499	+	0.852640i	$0.325000\pi$
$32$	1549.84	−	4258.14i	1.51351	−	4.15834i
$33$	−888.657	−	156.694i	−0.816031	−	0.143888i
$34$	−1527.22	+	269.291i	−1.32113	+	0.232950i
$35$	31.7825	−	11.5679i	0.0259449	−	0.00944317i
$36$	2974.35	+	2495.78i	2.29503	+	1.92576i
$37$			51.5297i			0.0376404i	0.999823	+	0.0188202i	$0.00599100\pi$
$37$			51.5297i			0.0376404i	−0.999823	+	0.0188202i	$0.994009\pi$
$38$	406.507	+	2788.25i	0.281515	+	1.93092i
$39$	−1768.84			−1.16295
$40$	−1152.74	+	1373.79i	−0.720465	+	0.858617i
$41$	−338.953	−	931.265i	−0.201638	−	0.553995i	0.797120	−	0.603821i	$-0.206356\pi$
$41$	−338.953	−	931.265i	−0.201638	−	0.553995i	−0.998758	+	0.0498257i	$0.984133\pi$
$42$	74.6715	+	423.483i	0.0423308	+	0.240070i
$43$	285.991	−	1621.94i	0.154673	−	0.877196i	−0.804410	−	0.594074i	$-0.797519\pi$
$43$	285.991	−	1621.94i	0.154673	−	0.877196i	0.959084	−	0.283122i	$-0.0913703\pi$
$44$	2943.90	+	1071.49i	1.52061	+	0.553456i
$45$	−343.293	−	594.600i	−0.169527	−	0.293630i
$46$	2251.66	+	1300.00i	1.06411	+	0.614366i
$47$	−2681.81	+	2250.31i	−1.21404	+	1.01870i	−0.214924	+	0.976631i	$0.568950\pi$
$47$	−2681.81	+	2250.31i	−1.21404	+	1.01870i	−0.999115	+	0.0420687i	$0.986605\pi$
$48$	−8677.70	−	10341.7i	−3.76636	−	4.48858i
$49$	1191.44	−	2063.63i	0.496225	−	0.859487i
$50$	−3798.21	+	2192.89i	−1.51928	+	0.877158i
$51$	−879.283	+	2415.81i	−0.338056	+	0.928800i
$52$	6047.76	+	1066.38i	2.23660	+	0.394373i
$53$	2857.21	−	503.803i	1.01716	−	0.179353i	0.359880	−	0.932998i	$-0.382818\pi$
$53$	2857.21	−	503.803i	1.01716	−	0.179353i	0.657281	+	0.753645i	$0.271706\pi$
$54$	515.397	−	187.589i	0.176748	−	0.0643310i
$55$	−424.372	−	356.090i	−0.140288	−	0.117716i
$56$		−	961.200i		−	0.306505i
$57$	4339.97	+	1727.53i	1.33579	+	0.531712i
$58$	−7584.47			−2.25460
$59$	776.686	−	925.618i	0.223121	−	0.265906i	−0.642858	−	0.765985i	$-0.722251\pi$
$59$	776.686	−	925.618i	0.223121	−	0.265906i	0.865979	+	0.500080i	$0.166696\pi$
$60$	1579.31	+	4339.12i	0.438697	+	1.20531i
$61$	−888.240	−	5037.46i	−0.238710	−	1.35379i	−0.834658	−	0.550769i	$-0.814335\pi$
$61$	−888.240	−	5037.46i	−0.238710	−	1.35379i	0.595948	−	0.803023i	$-0.296777\pi$
$62$	−68.1941	+	386.748i	−0.0177404	+	0.100611i
$63$	345.803	+	125.862i	0.0871260	+	0.0317113i
$64$	9338.00	+	16173.9i	2.27979	+	3.94871i
$65$	−940.437	−	542.961i	−0.222589	−	0.128512i
$66$	5395.46	−	4527.33i	1.23863	−	1.03933i
$67$	2047.05	+	2439.58i	0.456015	+	0.543457i	0.944239	−	0.329261i	$-0.106800\pi$
$67$	2047.05	+	2439.58i	0.456015	+	0.543457i	−0.488224	+	0.872718i	$0.662355\pi$
$68$	4462.73	−	7729.67i	0.965123	−	1.67164i
$69$	3732.75	−	2155.11i	0.784027	−	0.452658i
$70$	−90.2912	+	248.073i	−0.0184268	+	0.0506272i
$71$	−6515.81	−	1148.91i	−1.29256	−	0.227914i	−0.515257	−	0.857036i	$-0.672303\pi$
$71$	−6515.81	−	1148.91i	−1.29256	−	0.227914i	−0.777307	+	0.629122i	$0.783415\pi$
$72$	−19215.8	+	3388.26i	−3.70674	+	0.653599i
$73$	3998.62	−	1455.38i	0.750351	−	0.273105i	0.0615975	−	0.998101i	$-0.480380\pi$
$73$	3998.62	−	1455.38i	0.750351	−	0.273105i	0.688753	+	0.724996i	$0.258158\pi$
$74$	−308.108	−	258.533i	−0.0562651	−	0.0472120i
$75$			7270.66i			1.29256i
$76$	−13797.1	−	8522.96i	−2.38869	−	1.47558i
$77$	296.921			0.0500794
$78$	8874.59	−	10576.3i	1.45868	−	1.73838i
$79$	−1522.69	−	4183.56i	−0.243982	−	0.670336i	−0.999878	−	0.0156433i	$-0.995020\pi$
$79$	−1522.69	−	4183.56i	−0.243982	−	0.670336i	0.755895	−	0.654692i	$-0.227202\pi$
$80$	−1439.19	−	8162.03i	−0.224873	−	1.27532i
$81$	−1057.80	+	5999.08i	−0.161225	+	0.914355i
$82$	7268.84	+	2645.64i	1.08103	+	0.393462i
$83$	−444.741	−	770.313i	−0.0645581	−	0.111818i	0.831940	−	0.554866i	$-0.187230\pi$
$83$	−444.741	−	770.313i	−0.0645581	−	0.111818i	−0.896498	+	0.443048i	$0.853897\pi$
$84$	−2143.36	−	1237.47i	−0.303764	−	0.175378i
$85$	−1209.04	+	1014.50i	−0.167341	+	0.140416i
$86$	8263.07	+	9847.54i	1.11723	+	1.33147i
$87$	−6286.67	+	10888.8i	−0.830582	+	1.43861i
$88$	−13634.4	+	7871.80i	−1.76063	+	1.01650i
$89$	−1978.44	+	5435.72i	−0.249772	+	0.686242i	0.749923	+	0.661525i	$0.230091\pi$
$89$	−1978.44	+	5435.72i	−0.249772	+	0.686242i	−0.999694	+	0.0247166i	$0.992132\pi$
$90$	5277.61	+	930.585i	0.651557	+	0.114887i
$91$	573.191	−	101.069i	0.0692175	−	0.0122049i
$92$	−14061.7	+	5118.04i	−1.66135	+	0.604684i
$93$	498.720	+	418.476i	0.0576621	+	0.0483843i
$94$		−	27325.4i		−	3.09250i
$95$	1777.14	+	2250.66i	0.196913	+	0.249381i
$96$	58634.2			6.36222
$97$	−3129.82	+	3729.97i	−0.332641	+	0.396426i	−0.906277	−	0.422684i	$-0.861088\pi$
$97$	−3129.82	+	3729.97i	−0.332641	+	0.396426i	0.573636	+	0.819110i	$0.305532\pi$
$98$	6361.27	+	17477.4i	0.662356	+	1.81981i
$99$	−1046.65	−	5935.87i	−0.106791	−	0.605639i
$100$	4383.26	−	24858.7i	0.438326	−	2.48587i
$101$	−3947.43	−	1436.75i	−0.386965	−	0.140844i	0.141209	−	0.989980i	$-0.454901\pi$
$101$	−3947.43	−	1436.75i	−0.386965	−	0.140844i	−0.528174	+	0.849136i	$0.677123\pi$
$102$	−10033.2	−	17378.0i	−0.964357	−	1.67032i
$103$	−15636.3	−	9027.60i	−1.47387	−	0.850938i	−0.474300	−	0.880363i	$-0.657299\pi$
$103$	−15636.3	−	9027.60i	−1.47387	−	0.850938i	−0.999567	+	0.0294254i	$0.990632\pi$
$104$	−23640.9	+	19837.1i	−2.18574	+	1.83405i
$105$	281.311	+	335.254i	0.0255158	+	0.0304085i
$106$	−11322.7	+	19611.6i	−1.00772	+	1.74542i
$107$	15088.6	−	8711.39i	1.31789	−	0.760887i	0.334505	−	0.942394i	$-0.391431\pi$
$107$	15088.6	−	8711.39i	1.31789	−	0.760887i	0.983390	+	0.181507i	$0.0580975\pi$
$108$	−1079.66	+	2966.35i	−0.0925636	+	0.254316i
$109$	17653.1	+	3112.72i	1.48583	+	0.261992i	0.856905	−	0.515475i	$-0.172384\pi$
$109$	17653.1	+	3112.72i	1.48583	+	0.261992i	0.628924	+	0.777467i	$0.283496\pi$
$110$	4258.29	−	750.852i	0.351925	−	0.0620539i
$111$	−626.557	+	228.048i	−0.0508528	+	0.0185089i
$112$	3402.90	+	2855.37i	0.271277	+	0.227629i
$113$			8735.60i			0.684126i	0.939677	+	0.342063i	$0.111126\pi$
$113$			8735.60i			0.684126i	−0.939677	+	0.342063i	$0.888874\pi$
$114$	−32103.7	+	17282.4i	−2.47028	+	1.32982i
$115$	2646.11			0.200084
$116$	28059.0	−	33439.4i	2.08524	−	2.48509i
$117$	−4041.02	−	11102.6i	−0.295202	−	0.811061i
$118$	1637.72	+	9287.97i	0.117618	+	0.667048i
$119$	146.894	−	833.079i	0.0103732	−	0.0588291i
$120$	−21805.6	−	7936.60i	−1.51428	−	0.551153i
$121$	4888.85	+	8467.74i	0.333915	+	0.578358i
$122$	34576.6	+	19962.8i	2.32307	+	1.34123i
$123$	9823.34	−	8242.76i	0.649305	−	0.544832i
$124$	−1452.86	−	1731.45i	−0.0944888	−	0.112607i
$125$	−4714.22	+	8165.27i	−0.301710	+	0.522577i
$126$	−2487.51	+	1436.17i	−0.156684	+	0.0904614i
$127$	4300.13	−	11814.5i	0.266608	−	0.732501i	−0.732076	−	0.681223i	$-0.761448\pi$
$127$	4300.13	−	11814.5i	0.266608	−	0.732501i	0.998684	−	0.0512777i	$-0.0163294\pi$
$128$	−72156.7	−	12723.2i	−4.40409	−	0.776561i
$129$	20987.0	−	3700.58i	1.26116	−	0.222377i
$130$	7964.83	−	2898.96i	0.471291	−	0.171536i
$131$	−14470.0	−	12141.8i	−0.843192	−	0.707522i	0.115088	−	0.993355i	$-0.463285\pi$
$131$	−14470.0	−	12141.8i	−0.843192	−	0.707522i	−0.958279	+	0.285834i	$0.907730\pi$
$132$			40537.2i			2.32652i
$133$	−1505.07	−	311.825i	−0.0850850	−	0.0176282i
$134$	−24857.2			−1.38434
$135$	358.806	−	427.608i	0.0196876	−	0.0234627i
$136$	15340.9	+	42148.6i	0.829415	+	2.27880i
$137$	−4517.48	−	25619.9i	−0.240689	−	1.36501i	−0.830296	−	0.557323i	$-0.811829\pi$
$137$	−4517.48	−	25619.9i	−0.240689	−	1.36501i	0.589607	−	0.807690i	$-0.299283\pi$
$138$	−5841.98	+	33131.5i	−0.306762	+	1.73974i
$139$	8171.00	+	2974.00i	0.422908	+	0.153926i	0.544702	−	0.838629i	$-0.316643\pi$
$139$	8171.00	+	2974.00i	0.422908	+	0.153926i	−0.121794	+	0.992555i	$0.538865\pi$
$140$	−759.702	−	1315.84i	−0.0387603	−	0.0671349i
$141$	−39230.4	−	22649.7i	−1.97326	−	1.13926i
$142$	39560.6	−	33195.3i	1.96194	−	1.64626i
$143$	−6127.81	−	7302.83i	−0.299663	−	0.357124i
$144$	45087.6	−	78094.1i	2.17436	−	3.76611i
$145$	−6684.84	+	3859.49i	−0.317947	+	0.183567i
$146$	−11359.7	+	31210.6i	−0.532920	+	1.46418i
$147$	30364.7	+	5354.12i	1.40519	+	0.247773i
$148$	2279.71	−	401.975i	0.104077	−	0.0183517i
$149$	−8888.72	+	3235.23i	−0.400375	+	0.145725i	−0.534356	−	0.845259i	$-0.679446\pi$
$149$	−8888.72	+	3235.23i	−0.400375	+	0.145725i	0.133982	+	0.990984i	$0.457224\pi$
$150$	−43473.0	−	36478.1i	−1.93213	−	1.62125i
$151$			15195.2i			0.666427i	0.942851	+	0.333214i	$0.108133\pi$
$151$			15195.2i			0.666427i	−0.942851	+	0.333214i	$0.891867\pi$
$152$	77378.3	−	25582.8i	3.34913	−	1.10729i
$153$	−17172.2			−0.733574
$154$	−1489.70	+	1775.36i	−0.0628143	+	0.0748592i
$155$	136.699	+	375.576i	0.00568984	+	0.0156327i
$156$	13798.5	+	78255.0i	0.566998	+	3.21561i
$157$	−3084.41	+	17492.6i	−0.125133	+	0.709666i	0.856095	+	0.516818i	$0.172884\pi$
$157$	−3084.41	+	17492.6i	−0.125133	+	0.709666i	−0.981229	+	0.192848i	$0.938227\pi$
$158$	32654.1	+	11885.1i	1.30805	+	0.476091i
$159$	18770.6	+	32511.6i	0.742478	+	1.28601i
$160$	31173.9	+	17998.3i	1.21773	+	0.703058i
$161$	−1086.45	+	911.642i	−0.0419140	+	0.0351700i
$162$	−30562.8	−	36423.3i	−1.16456	−	1.38787i
$163$	−17936.2	+	31066.5i	−0.675082	+	1.16928i	0.301364	+	0.953509i	$0.402558\pi$
$163$	−17936.2	+	31066.5i	−0.675082	+	1.16928i	−0.976445	+	0.215766i	$0.930775\pi$
$164$	−38555.8	+	22260.2i	−1.43351	+	0.827639i
$165$	2451.67	−	6735.90i	0.0900520	−	0.247416i
$166$	6837.22	+	1205.59i	0.248121	+	0.0437504i
$167$	5444.37	−	959.990i	0.195216	−	0.0344218i	−0.0751852	−	0.997170i	$-0.523955\pi$
$167$	5444.37	−	959.990i	0.195216	−	0.0344218i	0.270401	+	0.962748i	$0.412844\pi$
$168$	11687.4	−	4253.86i	0.414094	−	0.150718i
$169$	7563.77	+	6346.76i	0.264829	+	0.222218i
$170$		−	12319.1i		−	0.426265i
$171$	−928.414	+	31187.6i	−0.0317504	+	1.06657i
$172$	−73986.7			−2.50090
$173$	−3060.41	+	3647.26i	−0.102256	+	0.121864i	−0.814745	−	0.579819i	$-0.803123\pi$
$173$	−3060.41	+	3647.26i	−0.102256	+	0.121864i	0.712489	+	0.701683i	$0.247568\pi$
$174$	−33565.6	−	92220.7i	−1.10865	−	3.04600i
$175$	−415.434	−	2356.04i	−0.0135652	−	0.0769320i
$176$	12634.4	−	71653.4i	0.407878	−	2.31319i
$177$	14692.0	+	5347.45i	0.468959	+	0.170687i
$178$	−22575.3	−	39101.5i	−0.712513	−	1.23411i
$179$	−23687.3	−	13675.9i	−0.739281	−	0.426824i	0.0825266	−	0.996589i	$-0.473701\pi$
$179$	−23687.3	−	13675.9i	−0.739281	−	0.426824i	−0.821808	+	0.569765i	$0.807034\pi$
$180$	−23627.6	+	19825.9i	−0.729247	+	0.611911i
$181$	−11843.8	−	14114.9i	−0.361521	−	0.430843i	0.554371	−	0.832270i	$-0.312959\pi$
$181$	−11843.8	−	14114.9i	−0.361521	−	0.430843i	−0.915891	+	0.401426i	$0.868515\pi$
$182$	−2271.48	+	3934.32i	−0.0685751	+	0.118776i
$183$	57320.3	−	33093.9i	1.71162	−	0.988201i
$184$	25720.0	−	70665.2i	0.759689	−	2.08723i
$185$	−403.121	−	71.0812i	−0.0117786	−	0.00207688i
$186$	−5004.33	+	882.398i	−0.144650	+	0.0255058i
$187$	−13020.0	+	4738.89i	−0.372329	+	0.135517i
$188$	120476.	+	101091.i	3.40866	+	2.86021i
$189$			299.185i			0.00837562i
$190$	−22373.5	−	666.028i	−0.619764	−	0.0184495i
$191$	−14359.5			−0.393616			−0.196808	−	0.980442i	$-0.563058\pi$
$191$	−14359.5			−0.393616			−0.196808	+	0.980442i	$0.563058\pi$
$192$	−155335.	+	185121.i	−4.21373	+	5.02173i
$193$	15939.0	+	43792.0i	0.427903	+	1.17565i	0.947083	+	0.320989i	$0.104015\pi$
$193$	15939.0	+	43792.0i	0.427903	+	1.17565i	−0.519180	+	0.854665i	$0.673762\pi$
$194$	−6599.54	−	37427.8i	−0.175352	−	0.994469i
$195$	2439.98	−	13837.8i	0.0641678	−	0.363914i
$196$	−100591.	−	36612.0i	−2.61846	−	0.953040i
$197$	−24405.6	−	42271.7i	−0.628864	−	1.08922i	−0.987780	−	0.155854i	$-0.950187\pi$
$197$	−24405.6	−	42271.7i	−0.628864	−	1.08922i	0.358916	−	0.933370i	$-0.383146\pi$
$198$	40743.2	+	23523.1i	1.03926	+	0.600018i
$199$	6559.24	−	5503.86i	0.165633	−	0.138983i	−0.556204	−	0.831046i	$-0.687743\pi$
$199$	6559.24	−	5503.86i	0.165633	−	0.138983i	0.721837	+	0.692063i	$0.243298\pi$
$200$	81538.4	+	97173.7i	2.03846	+	2.42934i
$201$	−20603.9	+	35686.9i	−0.509984	+	0.883318i
$202$	28395.6	−	16394.2i	0.695902	−	0.401779i
$203$	1415.01	−	3887.72i	0.0343375	−	0.0943415i
$204$	113736.	+	20054.8i	2.73300	+	0.481901i
$205$	7752.93	−	1367.05i	0.184484	−	0.0325295i
$206$	132428.	−	48199.8i	3.12065	−	1.13582i
$207$	22054.8	+	18506.2i	0.514709	+	0.431892i
$208$		−	142624.i		−	3.29659i
$209$	7902.68	+	23902.7i	0.180918	+	0.547210i
$210$	−3415.95			−0.0774592
$211$	16574.3	−	19752.5i	0.372281	−	0.443667i	−0.547081	−	0.837080i	$-0.684261\pi$
$211$	16574.3	−	19752.5i	0.372281	−	0.443667i	0.919362	+	0.393412i	$0.128706\pi$
$212$	−44577.2	−	122475.i	−0.991839	−	2.72506i
$213$	−14866.4	−	84311.3i	−0.327677	−	1.85835i
$214$	−23614.5	+	133925.i	−0.515646	+	2.92438i
$215$	12294.1	+	4474.67i	0.265961	+	0.0968019i
$216$	−7931.83	−	13738.3i	−0.170007	−	0.294460i
$217$	−185.520	−	107.110i	−0.00393978	−	0.00227463i
$218$	−107181.	+	89935.1i	−2.25529	+	1.89242i
$219$	35392.3	+	42178.9i	0.737940	+	0.879443i
$220$	−12443.2	+	21552.3i	−0.257092	+	0.445296i
$221$	−23521.3	+	13580.1i	−0.481590	+	0.278046i
$222$	1779.99	−	4890.49i	0.0361170	−	0.0992307i
$223$	10586.9	+	1866.76i	0.212892	+	0.0375386i	0.279077	−	0.960269i	$-0.409972\pi$
$223$	10586.9	+	1866.76i	0.212892	+	0.0375386i	−0.0661848	+	0.997807i	$0.521083\pi$
$224$	−19000.3	+	3350.27i	−0.378673	+	0.0667703i
$225$	−45636.2	+	16610.2i	−0.901456	+	0.328103i
$226$	−52232.2	−	43828.0i	−1.02264	−	0.858094i
$227$		−	50150.1i		−	0.973240i	−0.873614	−	0.486620i	$-0.838230\pi$
$227$		−	50150.1i		−	0.973240i	0.873614	−	0.486620i	$-0.161770\pi$
$228$	42572.0	−	205480.i	0.818943	−	3.95275i
$229$	−3983.41			−0.0759598			−0.0379799	−	0.999279i	$-0.512092\pi$
$229$	−3983.41			−0.0759598			−0.0379799	+	0.999279i	$0.512092\pi$
$230$	−13276.0	+	15821.7i	−0.250964	+	0.299087i
$231$	1314.04	+	3610.31i	0.0246256	+	0.0676582i
$232$	38092.7	+	216035.i	0.707728	+	4.01372i
$233$	321.724	−	1824.59i	0.00592614	−	0.0336088i	−0.981701	−	0.190427i	$-0.939013\pi$
$233$	321.724	−	1824.59i	0.00592614	−	0.0336088i	0.987627	+	0.156818i	$0.0501238\pi$
$234$	86659.6	+	31541.5i	1.58265	+	0.576038i
$235$	−13905.0	−	24084.2i	−0.251788	−	0.436110i
$236$	−47008.8	−	27140.6i	−0.844026	−	0.487298i
$237$	44129.8	−	37029.3i	0.785661	−	0.659248i
$238$	4244.18	+	5058.02i	0.0749273	+	0.0892948i
$239$	50736.9	−	87878.9i	0.888236	−	1.53847i	0.0462761	−	0.998929i	$-0.485265\pi$
$239$	50736.9	−	87878.9i	0.888236	−	1.53847i	0.841960	−	0.539541i	$-0.181402\pi$
$240$	92874.1	−	53620.9i	1.61240	−	0.930919i
$241$	−30989.8	+	85143.9i	−0.533562	+	1.46595i	0.321241	+	0.946998i	$0.395900\pi$
$241$	−30989.8	+	85143.9i	−0.533562	+	1.46595i	−0.854803	+	0.518953i	$0.826322\pi$
$242$	−75158.8	−	13252.5i	−1.28336	−	0.226291i
$243$	−83230.5	+	14675.8i	−1.40952	+	0.248536i
$244$	−215932.	+	78592.8i	−3.62692	+	1.32009i
$245$	14500.5	+	12167.3i	0.241574	+	0.202704i
$246$			100091.i			1.65396i
$247$	23391.9	+	43452.9i	0.383418	+	0.712237i
$248$	11358.6			0.184680
$249$	7398.13	−	8816.74i	0.119323	−	0.142203i
$250$	−25170.0	−	69154.0i	−0.402720	−	1.10646i
$251$	−8087.69	−	45867.6i	−0.128374	−	0.728045i	−0.979246	−	0.202673i	$-0.935037\pi$
$251$	−8087.69	−	45867.6i	−0.128374	−	0.728045i	0.850872	−	0.525372i	$-0.176074\pi$
$252$	2870.68	−	16280.4i	0.0452047	−	0.256368i
$253$	21828.9	+	7945.08i	0.341029	+	0.124124i
$254$	49067.2	+	84986.9i	0.760543	+	1.31730i
$255$	−17686.2	−	10211.1i	−0.271991	−	0.157034i
$256$	209191.	−	175532.i	3.19200	−	2.67841i
$257$	59844.5	+	71319.9i	0.906063	+	1.07980i	0.996474	+	0.0838990i	$0.0267373\pi$
$257$	59844.5	+	71319.9i	0.906063	+	1.07980i	−0.0904115	+	0.995904i	$0.528818\pi$
$258$	−83169.0	+	144053.i	−1.24946	+	2.16413i
$259$	190.004	−	109.699i	0.00283246	−	0.00163532i
$260$	−16684.8	+	45841.2i	−0.246817	+	0.678124i
$261$	−82708.9	−	14583.8i	−1.21415	−	0.214087i
$262$	145197.	−	25602.2i	2.11522	−	0.372970i
$263$	4520.53	−	1645.34i	0.0653549	−	0.0237872i	−0.309136	−	0.951018i	$-0.600040\pi$
$263$	4520.53	−	1645.34i	0.0653549	−	0.0237872i	0.374491	+	0.927231i	$0.377818\pi$
$264$	−156054.	−	130945.i	−2.23907	−	1.87880i
$265$			23047.1i			0.328190i
$266$	9415.66	−	7434.67i	0.133072	−	0.105075i
$267$	−74849.5			−1.04994
$268$	91960.2	−	109594.i	1.28035	−	1.52587i
$269$	2702.20	+	7424.22i	0.0373433	+	0.102600i	0.956963	−	0.290210i	$-0.0937252\pi$
$269$	2702.20	+	7424.22i	0.0373433	+	0.102600i	−0.919620	+	0.392810i	$0.871503\pi$
$270$	756.578	+	4290.77i	0.0103783	+	0.0588582i
$271$	1912.53	−	10846.5i	0.0260418	−	0.147690i	−0.969014	−	0.247004i	$-0.920554\pi$
$271$	1912.53	−	10846.5i	0.0260418	−	0.147690i	0.995056	+	0.0993142i	$0.0316649\pi$
$272$	−194789.	−	70897.5i	−2.63286	−	0.958282i
$273$	3765.61	+	6522.22i	0.0505254	+	0.0875125i
$274$	175852.	+	101528.i	2.34233	+	1.35234i
$275$	−30017.6	+	25187.7i	−0.396927	+	0.333061i
$276$	−124462.	−	148328.i	−1.63388	−	1.94718i
$277$	59590.8	−	103214.i	0.776640	−	1.34518i	−0.157229	−	0.987562i	$-0.550256\pi$
$277$	59590.8	−	103214.i	0.776640	−	1.34518i	0.933868	−	0.357617i	$-0.116411\pi$
$278$	−58777.6	+	33935.3i	−0.760540	+	0.439098i
$279$	−1487.32	+	4086.38i	−0.0191072	+	0.0524965i
$280$	7519.56	+	1325.90i	0.0959127	+	0.0169120i
$281$	709.722	−	125.143i	0.00898826	−	0.00158487i	−0.169152	−	0.985590i	$-0.554103\pi$
$281$	709.722	−	125.143i	0.00898826	−	0.00158487i	0.178140	+	0.984005i	$0.442992\pi$
$282$	332253.	−	120930.i	4.17802	−	1.52068i
$283$	−39254.1	−	32938.1i	−0.490130	−	0.411268i	0.363943	−	0.931421i	$-0.381430\pi$
$283$	−39254.1	−	32938.1i	−0.490130	−	0.411268i	−0.854073	+	0.520153i	$0.825875\pi$
$284$			297227.i			3.68512i
$285$	−19501.3	+	31569.0i	−0.240090	+	0.388661i
$286$	74409.6			0.909697
$287$	−2712.26	+	3232.34i	−0.0329281	+	0.0392422i
$288$	133953.	+	368033.i	1.61498	+	4.43713i
$289$	−7648.56	−	43377.1i	−0.0915765	−	0.519356i
$290$	10462.2	−	59334.0i	0.124402	−	0.705517i
$291$	−59204.6	−	21548.7i	−0.699148	−	0.254469i
$292$	−95579.6	−	165549.i	−1.12098	−	1.94160i
$293$	13128.7	+	7579.87i	0.152928	+	0.0882930i	0.574511	−	0.818497i	$-0.305192\pi$
$293$	13128.7	+	7579.87i	0.152928	+	0.0882930i	−0.421583	+	0.906790i	$0.638525\pi$
$294$	−184359.	+	154695.i	−2.13289	+	1.78971i
$295$	6169.82	+	7352.90i	0.0708971	+	0.0844918i
$296$	−5816.55	+	10074.6i	−0.0663869	+	0.114985i
$297$	4243.86	−	2450.19i	0.0481114	−	0.0277771i
$298$	25252.1	−	69379.4i	0.284357	−	0.781265i
$299$	44844.0	+	7907.21i	0.501606	+	0.0884466i
$300$	321659.	−	56717.2i	3.57399	−	0.630191i
$301$	−6589.37	+	2398.33i	−0.0727295	+	0.0264714i
$302$	−90855.7	−	76237.0i	−0.996181	−	0.835895i
$303$		−	54355.8i		−	0.592053i
$304$	−139293.	+	349937.i	−1.50724	+	3.78654i
$305$	40633.8			0.436805
$306$	86156.1	−	102677.i	0.920117	−	1.09655i
$307$	48768.0	+	133989.i	0.517438	+	1.42165i	0.873333	+	0.487124i	$0.161954\pi$
$307$	48768.0	+	133989.i	0.517438	+	1.42165i	−0.355895	+	0.934526i	$0.615824\pi$
$308$	−2316.23	−	13136.0i	−0.0244164	−	0.138472i
$309$	40568.6	−	230076.i	0.424886	−	2.40965i
$310$	−2931.50	−	1066.98i	−0.0305046	−	0.0111028i
$311$	22506.4	+	38982.3i	0.232694	+	0.403038i	0.958600	−	0.284756i	$-0.0919125\pi$
$311$	22506.4	+	38982.3i	0.232694	+	0.403038i	−0.725906	+	0.687794i	$0.758579\pi$
$312$	−345827.	−	199663.i	−3.55262	−	2.05111i
$313$	119802.	−	100526.i	1.22286	−	1.02610i	0.224190	−	0.974545i	$-0.428026\pi$
$313$	119802.	−	100526.i	1.22286	−	1.02610i	0.998670	−	0.0515563i	$-0.0164182\pi$
$314$	−89117.1	−	106206.i	−0.903861	−	1.07718i
$315$	−1461.64	+	2531.63i	−0.0147305	+	0.0255141i
$316$	−173206.	+	100000.i	−1.73456	+	1.00145i
$317$	−21238.2	+	58351.4i	−0.211348	+	0.580674i	−0.999389	−	0.0349486i	$-0.988873\pi$
$317$	−21238.2	+	58351.4i	−0.211348	+	0.580674i	0.788041	+	0.615623i	$0.211095\pi$
$318$	−288570.	−	50882.6i	−2.85362	−	0.503170i
$319$	−66734.5	+	11767.1i	−0.655796	+	0.115635i
$320$	−139411.	+	50741.4i	−1.36143	+	0.495522i
$321$	172699.	+	144911.i	1.67602	+	1.40635i
$322$		−	11070.0i		−	0.106767i
$323$	70974.0	−	10347.5i	0.680290	−	0.0991816i
$324$	273656.			2.60684
$325$	−49373.7	+	58841.3i	−0.467443	+	0.557077i
$326$	−95764.5	−	263111.i	−0.901093	−	2.47573i
$327$	40277.1	+	228423.i	0.376671	+	2.13621i
$328$	38850.5	−	220332.i	0.361118	−	2.04800i
$329$	14006.7	+	5098.02i	0.129403	+	0.0470988i
$330$	27975.1	+	48454.3i	0.256888	+	0.444943i
$331$	−35314.0	−	20388.5i	−0.322322	−	0.186093i	0.330105	−	0.943944i	$-0.392916\pi$
$331$	−35314.0	−	20388.5i	−0.322322	−	0.186093i	−0.652427	+	0.757851i	$0.726249\pi$
$332$	−30609.9	+	25684.8i	−0.277706	+	0.233023i
$333$	−2862.81	−	3411.76i	−0.0258169	−	0.0307674i
$334$	−21575.4	+	37369.6i	−0.193404	+	0.334985i
$335$	−21908.8	+	12649.1i	−0.195222	+	0.112712i
$336$	−19659.1	+	54013.0i	−0.174135	+	0.478432i
$337$	12944.4	+	2282.45i	0.113978	+	0.0200975i	0.230346	−	0.973109i	$-0.426014\pi$
$337$	12944.4	+	2282.45i	0.113978	+	0.0200975i	−0.116368	+	0.993206i	$0.537125\pi$
$338$	−75897.5	+	13382.8i	−0.664346	+	0.117142i
$339$	−106217.	+	38660.0i	−0.924265	+	0.336405i
$340$	54313.9	+	45574.8i	0.469844	+	0.394246i
$341$			3508.74i			0.0301746i
$342$	−181820.	−	162025.i	−1.55450	−	1.38525i
$343$	−20368.3			−0.173128
$344$	238995.	−	284823.i	2.01963	−	2.40690i
$345$	11710.5	+	32174.5i	0.0983873	+	0.270317i
$346$	−6453.19	−	36597.9i	−0.0539042	−	0.305706i
$347$	−21987.1	+	124695.i	−0.182603	+	1.03559i	0.746393	+	0.665505i	$0.231784\pi$
$347$	−21987.1	+	124695.i	−0.182603	+	1.03559i	−0.928996	+	0.370089i	$0.879327\pi$
$348$	530772.	+	193185.i	4.38278	+	1.59520i
$349$	−56618.7	−	98066.5i	−0.464846	−	0.805137i	0.534348	−	0.845264i	$-0.320557\pi$
$349$	−56618.7	−	98066.5i	−0.464846	−	0.805137i	−0.999195	+	0.0401271i	$0.987224\pi$
$350$	16171.6	+	9336.70i	0.132013	+	0.0762179i
$351$	7358.53	−	6174.54i	0.0597278	−	0.0501176i
$352$	203127.	+	242077.i	1.63939	+	1.95375i
$353$	−28952.8	+	50147.7i	−0.232349	+	0.402441i	−0.958499	−	0.285096i	$-0.907975\pi$
$353$	−28952.8	+	50147.7i	−0.232349	+	0.402441i	0.726150	+	0.687537i	$0.241308\pi$
$354$	−105686.	+	61017.8i	−0.843356	+	0.486912i
$355$	17976.1	−	49389.0i	0.142639	−	0.391898i
$356$	255914.	+	45124.5i	2.01927	+	0.356051i
$357$	10779.6	−	1900.74i	0.0845799	−	0.0149137i
$358$	200615.	−	73017.7i	1.56530	−	0.569721i
$359$	−177148.	−	148645.i	−1.37451	−	1.15335i	−0.971195	−	0.238285i	$-0.923415\pi$
$359$	−177148.	−	148645.i	−1.37451	−	1.15335i	−0.403311	−	0.915063i	$-0.632141\pi$
$360$		−	155000.i		−	1.19599i
$361$	−14955.6	−	129460.i	−0.114760	−	0.993393i
$362$	143818.			1.09748
$363$	−81324.6	+	96918.8i	−0.617175	+	0.735521i
$364$	−8942.73	−	24570.0i	−0.0674944	−	0.185439i
$365$	5869.78	+	33289.1i	0.0440591	+	0.249872i
$366$	−89709.7	+	508769.i	−0.669695	+	3.79803i
$367$	−175005.	−	63696.5i	−1.29932	−	0.472915i	−0.402548	−	0.915399i	$-0.631875\pi$
$367$	−175005.	−	63696.5i	−1.29932	−	0.472915i	−0.896777	+	0.442483i	$0.854098\pi$
$368$	173769.	+	300976.i	1.28314	+	2.22247i
$369$	74179.8	+	42827.7i	0.544795	+	0.314537i
$370$	2447.54	−	2053.73i	0.0178783	−	0.0150017i
$371$	−7940.23	−	9462.80i	−0.0576880	−	0.0687499i
$372$	14623.2	−	25328.2i	0.105671	−	0.183028i
$373$	−83889.0	+	48433.4i	−0.602959	+	0.348118i	−0.770205	−	0.637797i	$-0.779846\pi$
$373$	−83889.0	+	48433.4i	−0.602959	+	0.348118i	0.167246	+	0.985915i	$0.446513\pi$
$374$	36988.6	−	101625.i	0.264439	−	0.726539i
$375$	−120146.	−	21184.9i	−0.854370	−	0.150649i
$376$	−778331.	+	137241.i	−5.50540	+	0.970750i
$377$	−124822.	+	45431.5i	−0.878231	+	0.319650i
$378$	−1788.90	−	1501.06i	−0.0125199	−	0.0105055i
$379$		−	205731.i		−	1.43226i	−0.697967	−	0.716130i	$-0.745912\pi$
$379$		−	205731.i		−	1.43226i	0.697967	−	0.716130i	$-0.254088\pi$
$380$	85707.9	−	96179.1i	0.593545	−	0.666060i
$381$	162685.			1.12072
$382$	72044.0	−	85858.7i	0.493709	−	0.588380i
$383$	92926.8	+	255314.i	0.633496	+	1.74052i	0.671253	+	0.741228i	$0.265756\pi$
$383$	92926.8	+	255314.i	0.633496	+	1.74052i	−0.0377575	+	0.999287i	$0.512021\pi$
$384$	−164631.	−	933671.i	−1.11648	−	6.33186i
$385$	−409.579	+	2322.84i	−0.00276323	+	0.0156710i
$386$	−341811.	−	124409.i	−2.29409	−	0.834982i
$387$	71173.7	+	123277.i	0.475223	+	0.823111i
$388$	189432.	+	109369.i	1.25832	+	0.726490i
$389$	131353.	−	110218.i	0.868043	−	0.728375i	−0.0956421	−	0.995416i	$-0.530490\pi$
$389$	131353.	−	110218.i	0.868043	−	0.728375i	0.963685	+	0.267041i	$0.0860460\pi$
$390$	70497.8	+	84016.0i	0.463496	+	0.552373i
$391$	33091.1	−	57315.4i	0.216450	−	0.374902i
$392$	465875.	−	268973.i	3.03178	−	1.75040i
$393$	83595.7	−	229677.i	0.541251	−	1.48708i
$394$	375199.	+	66157.8i	2.41696	+	0.426175i
$395$	34828.8	−	6141.27i	0.223226	−	0.0393608i
$396$	−254443.	+	92609.5i	−1.62256	+	0.590562i
$397$	78451.6	+	65828.7i	0.497761	+	0.417671i	0.856798	−	0.515652i	$-0.172450\pi$
$397$	78451.6	+	65828.7i	0.497761	+	0.417671i	−0.359037	+	0.933323i	$0.616895\pi$
$398$			66833.0i			0.421915i
$399$	−2869.26	−	19680.4i	−0.0180229	−	0.123620i
$400$	−586241.			−3.66401
$401$	−168425.	+	200721.i	−1.04741	+	1.24826i	−0.0795388	+	0.996832i	$0.525345\pi$
$401$	−168425.	+	200721.i	−1.04741	+	1.24826i	−0.967876	+	0.251428i	$0.919100\pi$
$402$	−110007.	−	302243.i	−0.680722	−	1.87027i
$403$	1194.34	+	6773.43i	0.00735389	+	0.0417060i
$404$	−32769.5	+	185845.i	−0.200774	+	1.13865i
$405$	−45472.2	−	16550.5i	−0.277227	−	0.100903i
$406$	16146.2	+	27966.0i	0.0979531	+	0.169660i
$407$	−3112.10	−	1796.77i	−0.0187873	−	0.0108469i
$408$	−444600.	+	373063.i	−2.67085	+	2.24111i
$409$	−70246.1	−	83716.0i	−0.419928	−	0.500451i	0.514060	−	0.857754i	$-0.328141\pi$
$409$	−70246.1	−	83716.0i	−0.419928	−	0.500451i	−0.933989	+	0.357303i	$0.883696\pi$
$410$	−30723.9	+	53215.3i	−0.182771	+	0.316569i
$411$	291524.	−	168312.i	1.72580	−	0.996392i
$412$	−277412.	+	762183.i	−1.63430	+	4.49019i
$413$	−5066.46	−	893.354i	−0.0297033	−	0.00523749i
$414$	−221305.	+	39022.1i	−1.29119	+	0.227672i
$415$	6639.72	−	2416.66i	0.0385526	−	0.0140320i
$416$	474526.	+	398175.i	2.74204	+	2.30084i
$417$			112514.i			0.647046i
$418$	−182569.	−	72671.8i	−1.04490	−	0.415923i
$419$	239429.			1.36379			0.681897	−	0.731448i	$-0.261155\pi$
$419$	239429.			1.36379			0.681897	+	0.731448i	$0.261155\pi$
$420$	12637.4	−	15060.7i	0.0716407	−	0.0853781i
$421$	−77493.6	−	212912.i	−0.437222	−	1.20126i	−0.941292	−	0.337594i	$-0.890387\pi$
$421$	−77493.6	−	212912.i	−0.437222	−	1.20126i	0.504070	−	0.863663i	$-0.331835\pi$
$422$	34948.6	+	198203.i	0.196248	+	1.11298i
$423$	52542.7	−	297984.i	0.293651	−	1.66538i
$424$	615481.	+	224017.i	3.42360	+	1.24609i
$425$	55819.5	+	96682.1i	0.309035	+	0.535264i
$426$	578704.	+	334115.i	3.18887	+	1.84110i
$427$	−16683.6	+	13999.2i	−0.0915027	+	0.0767799i
$428$	−503102.	−	599574.i	−2.74643	−	3.27307i
$429$	61677.2	−	106828.i	0.335128	−	0.580458i
$430$	−88436.5	+	51058.8i	−0.478293	+	0.276143i
$431$	86129.1	−	236638.i	0.463656	−	1.27388i	−0.459061	−	0.888405i	$-0.651814\pi$
$431$	86129.1	−	236638.i	0.463656	−	1.27388i	0.922717	−	0.385479i	$-0.125964\pi$
$432$	72199.8	+	12730.8i	0.386873	+	0.0682162i
$433$	196032.	−	34565.8i	1.04557	−	0.184362i	0.375623	−	0.926773i	$-0.377429\pi$
$433$	196032.	−	34565.8i	1.04557	−	0.184362i	0.669945	+	0.742411i	$0.266318\pi$
$434$	1571.22	−	571.879i	0.00834178	−	0.00303616i
$435$	−76512.4	−	64201.5i	−0.404346	−	0.339287i
$436$		−	805270.i		−	4.23612i
$437$	−102305.	−	63197.6i	−0.535716	−	0.330931i
$438$	−429767.			−2.24019
$439$	−89250.7	+	106365.i	−0.463108	+	0.551911i	−0.946168	−	0.323677i	$-0.895081\pi$
$439$	−89250.7	+	106365.i	−0.463108	+	0.551911i	0.483060	+	0.875588i	$0.339525\pi$
$440$	−42774.3	−	117521.i	−0.220941	−	0.607032i
$441$	35763.4	+	202824.i	0.183891	+	1.04290i
$442$	36812.3	−	208773.i	0.188429	−	1.06864i
$443$	−86308.2	−	31413.6i	−0.439789	−	0.160070i	0.112629	−	0.993637i	$-0.464073\pi$
$443$	−86308.2	−	31413.6i	−0.439789	−	0.160070i	−0.552418	+	0.833567i	$0.686295\pi$
$444$	14976.7	+	25940.4i	0.0759713	+	0.131586i
$445$	−39795.0	−	22975.7i	−0.200960	−	0.116024i
$446$	−64278.1	+	53935.7i	−0.323142	+	0.271148i
$447$	−78675.3	−	93761.6i	−0.393753	−	0.469256i
$448$	39758.5	−	68863.7i	0.198095	−	0.343111i
$449$	−188202.	+	108658.i	−0.933537	+	0.538978i	−0.887928	−	0.459982i	$-0.847856\pi$
$449$	−188202.	+	108658.i	−0.933537	+	0.538978i	−0.0456084	+	0.998959i	$0.514523\pi$
$450$	129648.	−	356206.i	0.640239	−	1.75904i
$451$	68062.0	+	12001.2i	0.334620	+	0.0590025i
$452$	386470.	−	68145.0i	1.89164	−	0.333547i
$453$	−184761.	+	67247.4i	−0.900354	+	0.327702i
$454$	299859.	+	251612.i	1.45481	+	1.22073i
$455$			4623.54i			0.0223332i
$456$	653508.	+	827636.i	3.14283	+	3.98025i
$457$	94989.6			0.454824			0.227412	−	0.973799i	$-0.426974\pi$
$457$	94989.6			0.454824			0.227412	+	0.973799i	$0.426974\pi$
$458$	19985.4	−	23817.7i	0.0952758	−	0.113545i
$459$	−4775.03	−	13119.3i	−0.0226647	−	0.0622708i
$460$	−20641.9	−	117066.i	−0.0975515	−	0.553242i
$461$	−39511.2	+	224079.i	−0.185917	+	1.05439i	0.738855	+	0.673864i	$0.235367\pi$
$461$	−39511.2	+	224079.i	−0.185917	+	1.05439i	−0.924772	+	0.380522i	$0.875744\pi$
$462$	−28179.7	−	10256.6i	−0.132024	−	0.0480527i
$463$	93072.0	+	161206.i	0.434167	+	0.752000i	0.997227	−	0.0744161i	$-0.0237093\pi$
$463$	93072.0	+	161206.i	0.434167	+	0.752000i	−0.563060	+	0.826416i	$0.690376\pi$
$464$	−877979.	−	506901.i	−4.07801	−	2.35444i
$465$	−3961.72	+	3324.28i	−0.0183222	+	0.0153742i
$466$	9295.50	+	11077.9i	0.0428056	+	0.0510138i
$467$	32476.0	−	56250.0i	0.148912	−	0.257922i	−0.781914	−	0.623386i	$-0.785756\pi$
$467$	32476.0	−	56250.0i	0.148912	−	0.257922i	0.930825	+	0.365464i	$0.119090\pi$
$468$	−459665.	+	265388.i	−2.09870	+	1.21168i
$469$	4637.55	−	12741.6i	0.0210835	−	0.0579264i
$470$	213769.	+	37693.2i	0.967717	+	0.170635i
$471$	−226345.	+	39910.7i	−1.02030	+	0.179907i
$472$	256332.	−	93297.1i	1.15058	−	0.418778i
$473$	87983.6	+	73827.0i	0.393260	+	0.329984i
$474$			449645.i			2.00130i
$475$	178609.	−	96150.3i	0.791617	−	0.426151i
$476$	−38002.0			−0.167723
$477$	−161185.	+	192093.i	−0.708416	+	0.844257i
$478$	270893.	+	744271.i	1.18561	+	3.25743i
$479$	36725.2	+	208279.i	0.160064	+	0.907766i	0.954009	+	0.299777i	$0.0969124\pi$
$479$	36725.2	+	208279.i	0.160064	+	0.907766i	−0.793946	+	0.607989i	$0.791976\pi$
$480$	−80881.4	+	458701.i	−0.351048	+	1.99089i
$481$	−6619.35	−	2409.25i	−0.0286105	−	0.0104134i
$482$	−353614.	−	612477.i	−1.52207	−	2.63630i
$483$	−15893.0	−	9175.80i	−0.0681256	−	0.0393323i
$484$	336482.	−	282342.i	1.43639	−	1.20527i
$485$	−24862.6	−	29630.1i	−0.105697	−	0.125965i
$486$	329832.	−	571285.i	1.39643	−	2.41869i
$487$	−246263.	+	142180.i	−1.03834	+	0.599488i	−0.919364	−	0.393409i	$-0.871296\pi$
$487$	−246263.	+	142180.i	−1.03834	+	0.599488i	−0.118980	+	0.992897i	$0.537962\pi$
$488$	394958.	−	1.08514e6i	1.65848	−	4.55664i
$489$	−457120.	−	80602.6i	−1.91167	−	0.337079i
$490$	−145503.	+	25656.0i	−0.606008	+	0.106856i
$491$	357832.	−	130240.i	1.48428	−	0.540234i	0.532345	−	0.846528i	$-0.321311\pi$
$491$	357832.	−	130240.i	1.48428	−	0.540234i	0.951937	+	0.306293i	$0.0990888\pi$
$492$	−441296.	−	370291.i	−1.82306	−	1.52973i
$493$			193060.i			0.794326i
$494$	−377176.	−	78144.5i	−1.54558	−	0.320217i
$495$	47880.6			0.195411
$496$	−33742.1	+	40212.3i	−0.137154	+	0.163454i
$497$	9634.83	+	26471.5i	0.0390060	+	0.107168i
$498$	15599.7	+	88470.2i	0.0629010	+	0.356729i
$499$	−20305.7	+	115160.i	−0.0815488	+	0.462486i	0.916499	+	0.400036i	$0.131002\pi$
$499$	−20305.7	+	115160.i	−0.0815488	+	0.462486i	−0.998048	+	0.0624499i	$0.980109\pi$
$500$	398012.	+	144865.i	1.59205	+	0.579459i
$501$	35767.1	+	61950.5i	0.142498	+	0.246814i
$502$	314830.	+	181767.i	1.24931	+	0.721288i
$503$	−38432.2	+	32248.5i	−0.151901	+	0.127460i	−0.715571	−	0.698540i	$-0.753833\pi$
$503$	−38432.2	+	32248.5i	−0.151901	+	0.127460i	0.563670	+	0.826000i	$0.309389\pi$
$504$	53400.9	+	63640.8i	0.210227	+	0.250538i
$505$	16685.0	−	28899.2i	0.0654249	−	0.113319i
$506$	−157025.	+	90658.4i	−0.613293	+	0.354085i
$507$	−43697.2	+	120057.i	−0.169996	+	0.467059i
$508$	−556227.	−	98077.9i	−2.15538	−	0.380052i
$509$	−69791.6	+	12306.1i	−0.269382	+	0.0474992i	−0.306707	−	0.951804i	$-0.599227\pi$
$509$	−69791.6	+	12306.1i	−0.269382	+	0.0474992i	0.0373256	+	0.999303i	$0.488116\pi$
$510$	149789.	−	54518.9i	0.575892	−	0.209607i
$511$	−13878.9	−	11645.7i	−0.0531511	−	0.0445990i
$512$			959158.i			3.65890i
$513$	−24085.0	+	7962.95i	−0.0915190	+	0.0302579i
$514$	−726689.			−2.75057
$515$	92192.7	−	109871.i	0.347602	−	0.414256i
$516$	−327433.	−	899615.i	−1.22977	−	3.37876i
$517$	−42394.5	−	240431.i	−0.158609	−	0.899519i
$518$	−297.368	+	1686.46i	−0.00110824	+	0.00628516i
$519$	−57891.7	−	21070.8i	−0.214922	−	0.0782253i
$520$	−122577.	−	212309.i	−0.453316	−	0.785166i
$521$	−129905.	−	75000.6i	−0.478575	−	0.276305i	0.241247	−	0.970464i	$-0.422443\pi$
$521$	−129905.	−	75000.6i	−0.478575	−	0.276305i	−0.719822	+	0.694158i	$0.755777\pi$
$522$	502165.	−	421366.i	1.84292	−	1.54639i
$523$	195955.	+	233530.i	0.716394	+	0.853765i	0.994275	−	0.106850i	$-0.0340766\pi$
$523$	195955.	+	233530.i	0.716394	+	0.853765i	−0.277881	+	0.960615i	$0.589632\pi$
$524$	−424283.	+	734880.i	−1.54523	+	2.67642i
$525$	26809.0	−	15478.2i	0.0972660	−	0.0561566i
$526$	−12842.4	+	35284.3i	−0.0464168	+	0.127529i
$527$	9844.55	+	1735.86i	0.0354466	+	0.00625019i
$528$	927159.	−	163483.i	3.32573	−	0.586415i
$529$	158697.	−	57761.1i	0.567098	−	0.206407i
$530$	−137804.	−	115631.i	−0.490581	−	0.411646i
$531$			104435.i			0.370388i
$532$	−2054.57	+	69017.8i	−0.00725935	+	0.243859i
$533$	135475.			0.476876
$534$	375533.	−	447542.i	1.31694	−	1.56947i
$535$	47336.5	+	130056.i	0.165382	+	0.454384i
$536$	124845.	+	708029.i	0.434550	+	2.46446i
$537$	61457.2	−	348541.i	0.213120	−	1.20866i
$538$	−57948.5	−	21091.5i	−0.200206	−	0.0728692i
$539$	83087.6	+	143912.i	0.285995	+	0.495358i
$540$	−21716.7	−	12538.1i	−0.0744742	−	0.0429977i
$541$	−148522.	+	124625.i	−0.507453	+	0.425804i	−0.860232	−	0.509903i	$-0.829681\pi$
$541$	−148522.	+	124625.i	−0.507453	+	0.425804i	0.352779	+	0.935707i	$0.385237\pi$
$542$	55258.4	+	65854.4i	0.188105	+	0.224174i
$543$	119209.	−	206477.i	0.404306	−	0.700279i
$544$	779694.	−	450156.i	2.63467	−	1.52113i
$545$	−48702.2	+	133808.i	−0.163967	+	0.450495i
$546$	−57890.6	−	10207.7i	−0.194188	−	0.0342406i
$547$	−299408.	+	52793.7i	−1.00066	+	0.176444i	−0.649900	−	0.760020i	$-0.725189\pi$
$547$	−299408.	+	52793.7i	−1.00066	+	0.176444i	−0.350764	+	0.936464i	$0.614078\pi$
$548$	−1.09820e6	+	399714.i	−3.65698	+	1.33103i
$549$	338674.	+	284181.i	1.12367	+	0.942867i
$550$		−	305853.i		−	1.01109i
$551$	350629.	+	10437.8i	1.15490	+	0.0343799i
$552$	973054.			3.19344
$553$	−12184.4	+	14520.8i	−0.0398431	+	0.0474832i
$554$	318165.	+	874151.i	1.03665	+	2.84818i
$555$	−919.754	−	5216.19i	−0.00298597	−	0.0169343i
$556$	67831.4	−	384691.i	0.219423	−	1.24441i
$557$	16821.9	+	6122.67i	0.0542206	+	0.0197347i	0.368988	−	0.929434i	$-0.379704\pi$
$557$	16821.9	+	6122.67i	0.0542206	+	0.0197347i	−0.314767	+	0.949169i	$0.601927\pi$
$558$	−16971.3	−	29395.1i	−0.0545062	−	0.0944075i
$559$	194978.	+	112570.i	0.623967	+	0.360247i
$560$	−27031.9	+	22682.4i	−0.0861986	+	0.0723292i
$561$	−115242.	−	137340.i	−0.366171	−	0.436386i
$562$	−2812.54	+	4871.46i	−0.00890483	+	0.0154236i
$563$	323677.	−	186875.i	1.02116	−	0.589568i	0.106721	−	0.994289i	$-0.465965\pi$
$563$	323677.	−	186875.i	1.02116	−	0.589568i	0.914440	+	0.404721i	$0.132631\pi$
$564$	−696008.	+	1.91227e6i	−2.18805	+	6.01160i
$565$	−68339.4	−	12050.1i	−0.214079	−	0.0377479i
$566$	393889.	−	69453.2i	1.22953	−	0.216800i
$567$	24372.2	−	8870.76i	0.0758104	−	0.0275927i
$568$	−1.14422e6	−	960114.i	−3.54660	−	2.97595i
$569$		−	400661.i		−	1.23752i	−0.785580	−	0.618760i	$-0.787635\pi$
$569$		−	400661.i		−	1.23752i	0.785580	−	0.618760i	$-0.212365\pi$
$570$	−90917.0	−	274990.i	−0.279831	−	0.846383i
$571$	254514.			0.780620			0.390310	−	0.920684i	$-0.372368\pi$
$571$	254514.			0.780620			0.390310	+	0.920684i	$0.372368\pi$
$572$	−275281.	+	328067.i	−0.841364	+	1.00270i
$573$	−63548.9	−	174599.i	−0.193553	−	0.531781i
$574$	−5719.06	−	32434.4i	−0.0173581	−	0.0984424i
$575$	32501.8	−	184327.i	0.0983042	−	0.557511i
$576$	−1.51683e6	−	552082.i	−4.57185	−	1.66402i
$577$	−246876.	−	427602.i	−0.741528	−	1.28436i	−0.951799	−	0.306721i	$-0.900768\pi$
$577$	−246876.	−	427602.i	−0.741528	−	1.28436i	0.210272	−	0.977643i	$-0.432565\pi$
$578$	297736.	+	171898.i	0.891202	+	0.514535i
$579$	−461934.	+	387609.i	−1.37792	+	1.15621i
$580$	222894.	+	265635.i	0.662587	+	0.789641i
$581$	−1893.57	+	3279.77i	−0.00560958	+	0.00971607i
$582$	425884.	−	245884.i	1.25732	−	0.725913i
$583$	−69200.2	+	190126.i	−0.203596	+	0.559377i
$584$	946050.	+	166814.i	2.77389	+	0.489111i
$585$	92431.1	−	16298.1i	0.270089	−	0.0476239i
$586$	−111191.	+	40470.2i	−0.323798	+	0.117853i
$587$	−204484.	−	171582.i	−0.593448	−	0.497962i	0.295884	−	0.955224i	$-0.404386\pi$
$587$	−204484.	−	171582.i	−0.593448	−	0.497962i	−0.889332	+	0.457262i	$0.848830\pi$
$588$		−	1.38513e6i		−	4.00622i
$589$	3684.85	−	17785.5i	0.0106216	−	0.0512667i
$590$	−74919.8			−0.215225
$591$	405979.	−	483827.i	1.16233	−	1.38521i
$592$	−18387.8	−	50520.0i	−0.0524669	−	0.144152i
$593$	−98642.5	−	559430.i	−0.280514	−	1.59087i	−0.720882	−	0.693058i	$-0.756263\pi$
$593$	−98642.5	−	559430.i	−0.280514	−	1.59087i	0.440368	−	0.897817i	$-0.354848\pi$
$594$	−6641.90	+	37668.1i	−0.0188243	+	0.106758i
$595$	6314.63	+	2298.34i	0.0178367	+	0.00649202i
$596$	212469.	+	368006.i	0.598139	+	1.03601i
$597$	95950.6	+	55397.1i	0.269215	+	0.155431i
$598$	−272269.	+	228461.i	−0.761371	+	0.638866i
$599$	−72111.2	−	85938.8i	−0.200978	−	0.239517i	0.656136	−	0.754642i	$-0.272190\pi$
$599$	−72111.2	−	85938.8i	−0.200978	−	0.239517i	−0.857115	+	0.515126i	$0.827745\pi$
$600$	−820696.	+	1.42149e6i	−2.27971	+	3.94857i
$601$	−398665.	+	230169.i	−1.10372	+	0.637233i	−0.937196	−	0.348804i	$-0.886588\pi$
$601$	−398665.	+	230169.i	−1.10372	+	0.637233i	−0.166524	+	0.986037i	$0.553254\pi$
$602$	18719.8	−	51432.2i	0.0516545	−	0.141920i
$603$	−271069.	−	47796.8i	−0.745496	−	0.131451i
$604$	672247.	−	118535.i	1.84270	−	0.324918i
$605$	−72987.7	+	26565.3i	−0.199406	+	0.0725779i
$606$	325006.	+	272713.i	0.885006	+	0.742608i
$607$			428202.i			1.16218i	0.813841	+	0.581088i	$0.197373\pi$
$607$			428202.i			1.16218i	−0.813841	+	0.581088i	$0.802627\pi$
$608$	−775404.	−	1.44039e6i	−2.09759	−	3.89649i
$609$	53533.6			0.144342
$610$	−203867.	+	242959.i	−0.547881	+	0.652940i
$611$	−163681.	−	449710.i	−0.438445	−	1.20462i
$612$	133958.	+	759713.i	0.357656	+	2.02837i
$613$	−43047.2	+	244133.i	−0.114558	+	0.649689i	0.872411	+	0.488774i	$0.162556\pi$
$613$	−43047.2	+	244133.i	−0.114558	+	0.649689i	−0.986968	+	0.160915i	$0.948556\pi$
$614$	−1.04583e6	−	380651.i	−2.77411	−	1.00969i
$615$	50933.3	+	88219.1i	0.134664	+	0.233245i
$616$	58051.0	+	33515.8i	0.152985	+	0.0883259i
$617$	−196898.	+	165217.i	−0.517216	+	0.433995i	−0.863660	−	0.504075i	$-0.831833\pi$
$617$	−196898.	+	165217.i	−0.517216	+	0.433995i	0.346444	+	0.938071i	$0.387389\pi$
$618$	1.17214e6	+	1.39690e6i	3.06903	+	3.65753i
$619$	44579.7	−	77214.3i	0.116347	−	0.201519i	−0.801970	−	0.597364i	$-0.796215\pi$
$619$	44579.7	−	77214.3i	0.116347	−	0.201519i	0.918317	+	0.395845i	$0.129548\pi$
$620$	15549.4	−	8977.45i	0.0404511	−	0.0233545i
$621$	−8005.67	+	21995.4i	−0.0207594	+	0.0570360i
$622$	−346003.	−	61009.6i	−0.894332	−	0.157695i
$623$	24254.8	−	4276.78i	0.0624917	−	0.0110190i
$624$	1.73418e6	−	631191.i	4.45375	−	1.62103i
$625$	211649.	+	177594.i	0.541821	+	0.454642i
$626$			1.22068e6i			3.11497i
$627$	−255662.	+	201873.i	−0.650327	+	0.513503i
$628$	797945.			2.02327
$629$	−6580.88	+	7842.79i	−0.0166335	+	0.0198230i
$630$	−7803.93	−	21441.1i	−0.0196622	−	0.0540214i
$631$	−30915.8	−	175332.i	−0.0776465	−	0.440355i	−0.998702	−	0.0509251i	$-0.983783\pi$
$631$	−30915.8	−	175332.i	−0.0776465	−	0.440355i	0.921056	−	0.389430i	$-0.127328\pi$
$632$	174530.	−	989807.i	0.436953	−	2.47809i
$633$	313525.	+	114114.i	0.782464	+	0.284793i
$634$	−242341.	−	419747.i	−0.602904	−	1.04426i
$635$	86494.2	+	49937.5i	0.214506	+	0.123845i
$636$	1.29191e6	−	1.08404e6i	3.19388	−	2.67998i
$637$	209382.	+	249532.i	0.516014	+	0.614961i
$638$	264460.	−	458059.i	0.649709	−	1.12533i
$639$	495239.	−	285927.i	1.21287	−	0.700250i
$640$	199069.	−	546938.i	0.486008	−	1.33530i
$641$	−14073.2	−	2481.49i	−0.0342514	−	0.00603944i	0.156496	−	0.987679i	$-0.449980\pi$
$641$	−14073.2	−	2481.49i	−0.0342514	−	0.00603944i	−0.190748	+	0.981639i	$0.561091\pi$
$642$	−1.73292e6	+	305560.i	−4.20444	+	0.741356i
$643$	−687644.	+	250282.i	−1.66319	+	0.605351i	−0.990859	−	0.134901i	$-0.956929\pi$
$643$	−687644.	+	250282.i	−1.66319	+	0.605351i	−0.672330	+	0.740252i	$0.734706\pi$
$644$	48807.0	+	40953.9i	0.117682	+	0.0987469i
$645$			169288.i			0.406918i
$646$	−294219.	+	476285.i	−0.705026	+	1.14131i
$647$	−556479.			−1.32935			−0.664677	−	0.747131i	$-0.731431\pi$
$647$	−556479.			−1.32935			−0.664677	+	0.747131i	$0.731431\pi$
$648$	−883974.	+	1.05348e6i	−2.10518	+	2.50886i
$649$	28820.1	+	79182.5i	0.0684236	+	0.187992i
$650$	−104109.	−	590434.i	−0.246413	−	1.39748i
$651$	481.336	−	2729.79i	0.00113576	−	0.00644121i
$652$	1.51432e6	+	551168.i	3.56224	+	1.29655i
$653$	93474.8	+	161903.i	0.219214	+	0.379690i	0.954568	−	0.297994i	$-0.0963174\pi$
$653$	93474.8	+	161903.i	0.219214	+	0.379690i	−0.735354	+	0.677683i	$0.762984\pi$
$654$	−1.56787e6	−	905210.i	−3.66568	−	2.11638i
$655$	114947.	−	96451.6i	0.267925	−	0.224816i
$656$	664622.	+	792066.i	1.54443	+	1.84058i
$657$	−183892.	+	318510.i	−0.426021	+	0.737890i
$658$	−100756.	+	58171.6i	−0.232713	+	0.134357i
$659$	−53750.1	+	147677.i	−0.123768	+	0.340050i	−0.986067	−	0.166350i	$-0.946802\pi$
$659$	−53750.1	+	147677.i	−0.123768	+	0.340050i	0.862299	+	0.506400i	$0.169024\pi$
$660$	−317126.	−	55917.9i	−0.728022	−	0.128370i
$661$	652968.	−	115136.i	1.49448	−	0.263516i	0.634129	−	0.773227i	$-0.281359\pi$
$661$	652968.	−	115136.i	1.49448	−	0.263516i	0.860346	+	0.509711i	$0.170248\pi$
$662$	299084.	−	108858.i	0.682460	−	0.248395i
$663$	−269217.	−	225900.i	−0.612457	−	0.513913i
$664$		−	200805.i		−	0.455448i
$665$	4515.56	−	11344.1i	0.0102110	−	0.0256524i
$666$	34762.9			0.0783732
$667$	208057.	−	247953.i	0.467660	−	0.557336i
$668$	−84941.4	−	233374.i	−0.190356	−	0.522999i
$669$	24154.9	+	136989.i	0.0539701	+	0.306079i
$670$	34288.6	−	194460.i	0.0763836	−	0.433193i
$671$	335206.	+	122005.i	0.744503	+	0.270977i
$672$	−124824.	−	216201.i	−0.276413	−	0.478761i
$673$	−442626.	−	255550.i	−0.977252	−	0.564217i	−0.0758125	−	0.997122i	$-0.524155\pi$
$673$	−442626.	−	255550.i	−0.977252	−	0.564217i	−0.901439	+	0.432905i	$0.857488\pi$
$674$	−78591.6	+	65946.2i	−0.173004	+	0.145168i
$675$	−25379.8	−	30246.5i	−0.0557033	−	0.0663846i
$676$	221782.	−	384137.i	0.485325	−	0.840607i
$677$	−505379.	+	291780.i	−1.10265	+	0.636618i	−0.936917	−	0.349552i	$-0.886334\pi$
$677$	−505379.	+	291780.i	−1.10265	+	0.636618i	−0.165737	+	0.986170i	$0.553000\pi$
$678$	301754.	−	829063.i	0.656438	−	1.80355i
$679$	20416.4	+	3599.96i	0.0442832	+	0.00780833i
$680$	−350894.	+	61872.1i	−0.758854	+	0.133806i
$681$	609782.	−	221943.i	1.31486	−	0.478571i
$682$	−20979.5	−	17603.9i	−0.0451053	−	0.0378478i
$683$		−	470626.i		−	1.00887i	−0.863450	−	0.504434i	$-0.831701\pi$
$683$		−	470626.i		−	1.00887i	0.863450	−	0.504434i	$-0.168299\pi$
$684$	1.38701e6	−	202216.i	2.96460	−	0.432218i
$685$	206659.			0.440425
$686$	102191.	−	121787.i	0.217153	−	0.258793i
$687$	−17628.8	−	48434.8i	−0.0373517	−	0.102623i
$688$	298382.	+	1.69221e6i	0.630370	+	3.57501i
$689$	−68870.4	+	390583.i	−0.145075	+	0.822764i
$690$	−251132.	−	91404.7i	−0.527478	−	0.191986i
$691$	−49650.9	−	85997.9i	−0.103985	−	0.180107i	0.809338	−	0.587343i	$-0.199826\pi$
$691$	−49650.9	−	85997.9i	−0.103985	−	0.180107i	−0.913323	+	0.407236i	$0.866493\pi$
$692$	185231.	+	106943.i	0.386814	+	0.223327i
$693$	−19659.0	+	16495.9i	−0.0409351	+	0.0343486i
$694$	−635266.	−	757081.i	−1.31898	−	1.57189i
$695$	−34537.2	+	59820.1i	−0.0715018	+	0.123845i
$696$	−2.45822e6	+	1.41925e6i	−5.07460	+	2.92982i
$697$	67344.0	−	185026.i	0.138622	−	0.380862i
$698$	870429.	+	153480.i	1.78658	+	0.315022i
$699$	23609.3	−	4162.95i	0.0483201	−	0.00852014i
$700$	−100992.	+	36758.2i	−0.206107	+	0.0750168i
$701$	−437756.	−	367321.i	−0.890833	−	0.747497i	0.0775444	−	0.996989i	$-0.475292\pi$
$701$	−437756.	−	367321.i	−0.890833	−	0.747497i	−0.968377	+	0.249492i	$0.919736\pi$
$702$			74977.1i			0.152144i
$703$	13888.0	+	12376.0i	0.0281015	+	0.0250420i
$704$	−1.30242e6			−2.62787
$705$	231306.	−	275659.i	0.465380	−	0.554619i
$706$	−154584.	−	424715.i	−0.310138	−	0.852096i
$707$	3105.81	+	17613.9i	0.00621349	+	0.0352385i
$708$	121965.	−	691700.i	0.243316	−	1.37991i
$709$	220905.	+	80402.8i	0.439453	+	0.159948i	0.552265	−	0.833668i	$-0.313764\pi$
$709$	220905.	+	80402.8i	0.439453	+	0.159948i	−0.112812	+	0.993616i	$0.535986\pi$
$710$	205119.	+	355276.i	0.406901	+	0.704773i
$711$	333241.	+	192397.i	0.659204	+	0.380591i
$712$	−1.00038e6	+	839416.i	−1.97335	+	1.65584i
$713$	−10772.9	−	12838.7i	−0.0211912	−	0.0252546i
$714$	−42718.3	+	73990.2i	−0.0837949	+	0.145137i
$715$	65583.6	−	37864.7i	0.128287	−	0.0740666i
$716$	−420250.	+	1.15463e6i	−0.819751	+	2.25225i
$717$	1.29307e6	+	228004.i	2.51527	+	0.443510i
$718$	1.77756e6	−	313432.i	3.44807	−	0.607987i
$719$	402082.	−	146346.i	0.777780	−	0.283089i	0.0775335	−	0.996990i	$-0.475296\pi$
$719$	402082.	−	146346.i	0.777780	−	0.283089i	0.700247	+	0.713901i	$0.253073\pi$
$720$	548742.	+	460449.i	1.05853	+	0.888212i
$721$			76873.7i			0.147879i
$722$	849106.	+	560100.i	1.62887	+	1.07446i
$723$	−1.17242e6			−2.24289
$724$	−532061.	+	634085.i	−1.01504	+	1.20968i
$725$	186742.	+	513069.i	0.355276	+	0.976112i
$726$	−171481.	−	972517.i	−0.325344	−	1.84512i
$727$	−121695.	+	690166.i	−0.230252	+	1.30582i	0.622134	+	0.782911i	$0.286266\pi$
$727$	−121695.	+	690166.i	−0.230252	+	1.30582i	−0.852386	+	0.522913i	$0.824845\pi$
$728$	123473.	+	44940.5i	0.232975	+	0.0847959i
$729$	−300076.	−	519747.i	−0.564646	−	0.977996i
$730$	−228493.	−	131921.i	−0.428773	−	0.247552i
$731$	250666.	−	210334.i	0.469095	−	0.393618i
$732$	−1.91124e6	−	2.27773e6i	−3.56693	−	4.25090i
$733$	−152862.	+	264765.i	−0.284506	+	0.492779i	−0.972489	−	0.232948i	$-0.925163\pi$
$733$	−152862.	+	264765.i	−0.284506	+	0.492779i	0.687983	+	0.725727i	$0.258496\pi$
$734$	1.25889e6	−	726818.i	2.33665	−	1.34907i
$735$	−83771.6	+	230161.i	−0.155068	+	0.426046i
$736$	−1.48651e6	−	262111.i	−2.74417	−	0.483871i
$737$	−218715.	+	38565.3i	−0.402664	+	0.0710006i
$738$	−628250.	+	228664.i	−1.15351	+	0.419842i
$739$	85874.1	+	72056.9i	0.157244	+	0.131943i	0.718015	−	0.696028i	$-0.245051\pi$
$739$	85874.1	+	72056.9i	0.157244	+	0.131943i	−0.560771	+	0.827971i	$0.689495\pi$
$740$			18388.9i			0.0335809i
$741$	−424827.	+	476730.i	−0.773706	+	0.868232i
$742$	96417.8			0.175125
$743$	−124878.	+	148824.i	−0.226208	+	0.269585i	−0.867196	−	0.497966i	$-0.834080\pi$
$743$	−124878.	+	148824.i	−0.226208	+	0.269585i	0.640988	+	0.767551i	$0.278525\pi$
$744$	50268.1	+	138111.i	0.0908128	+	0.249506i
$745$	−13048.2	−	74000.0i	−0.0235092	−	0.133327i
$746$	131291.	−	744591.i	0.235917	−	1.33795i
$747$	72242.1	+	26294.0i	0.129464	+	0.0471210i
$748$	311219.	+	539047.i	0.556241	+	0.963437i
$749$	−64242.7	−	37090.5i	−0.114514	−	0.0661149i
$750$	729462.	−	612091.i	1.29682	−	1.08816i
$751$	−419814.	−	500315.i	−0.744351	−	0.887082i	0.252401	−	0.967623i	$-0.418780\pi$
$751$	−419814.	−	500315.i	−0.744351	−	0.887082i	−0.996751	+	0.0805404i	$0.974335\pi$
$752$	1.82627e6	−	3.16319e6i	3.22945	−	5.59357i
$753$	521918.	−	301330.i	0.920476	−	0.531437i
$754$	354608.	−	974278.i	0.623743	−	1.71372i
$755$	−118874.	−	20960.6i	−0.208541	−	0.0367714i
$756$	13236.2	−	2333.90i	0.0231590	−	0.00408355i
$757$	184536.	−	67165.5i	0.322024	−	0.117207i	−0.175950	−	0.984399i	$-0.556300\pi$
$757$	184536.	−	67165.5i	0.322024	−	0.117207i	0.497974	+	0.867192i	$0.334077\pi$
$758$	1.23011e6	+	1.03219e6i	2.14095	+	1.79647i
$759$			300583.i			0.521772i
$760$	93399.0	+	640627.i	0.161702	+	1.10912i
$761$	−385758.			−0.666110			−0.333055	−	0.942907i	$-0.608079\pi$
$761$	−385758.			−0.666110			−0.333055	+	0.942907i	$0.608079\pi$
$762$	−816218.	+	972730.i	−1.40571	+	1.67526i
$763$	−26103.4	−	71718.6i	−0.0448382	−	0.123192i
$764$	112016.	+	635275.i	0.191908	+	1.08837i
$765$	23687.8	−	134340.i	0.0404763	−	0.229553i
$766$	−1.99281e6	−	725325.i	−3.39633	−	1.23616i
$767$	82588.6	+	143048.i	0.140388	+	0.243159i
$768$	3.06011e6	+	1.76675e6i	5.18817	+	2.99539i
$769$	729520.	−	612140.i	1.23363	−	1.03514i	0.235634	−	0.971842i	$-0.424284\pi$
$769$	729520.	−	612140.i	1.23363	−	1.03514i	0.997995	−	0.0632951i	$-0.0201609\pi$
$770$	−11833.9	−	14103.1i	−0.0199593	−	0.0237866i
$771$	−602344.	+	1.04329e6i	−1.01329	+	1.75508i
$772$	1.81305e6	−	1.04677e6i	3.04211	−	1.75637i
$773$	118815.	−	326441.i	0.198844	−	0.546318i	−0.799692	−	0.600410i	$-0.795004\pi$
$773$	118815.	−	326441.i	0.198844	−	0.546318i	0.998536	+	0.0540916i	$0.0172263\pi$
$774$	−1.09419e6	−	192935.i	−1.82646	−	0.322055i
$775$	27841.5	−	4909.21i	0.0463542	−	0.00817350i
$776$	−1.03294e6	+	375960.i	−1.71535	+	0.624336i
$777$	2174.72	+	1824.81i	0.00360215	+	0.00302256i
$778$			1.33838e6i			2.21115i
$779$	−332397.	−	132311.i	−0.547750	−	0.218033i
$780$	−631230.			−1.03752
$781$	296586.	−	353457.i	0.486237	−	0.579475i
$782$	176679.	+	485420.i	0.288915	+	0.793788i
$783$	−11856.8	−	67243.4i	−0.0193395	−	0.109680i
$784$	−431709.	+	2.44834e6i	−0.702358	+	3.98327i
$785$	−132591.	−	48259.3i	−0.215167	−	0.0783143i
$786$	953880.	+	1.65217e6i	1.54401	+	2.67430i
$787$	311708.	+	179965.i	0.503267	+	0.290561i	0.730062	−	0.683381i	$-0.239491\pi$
$787$	311708.	+	179965.i	0.503267	+	0.290561i	−0.226795	+	0.973943i	$0.572825\pi$
$788$	−1.67975e6	+	1.40948e6i	−2.70515	+	2.26989i
$789$	40011.9	+	47684.3i	0.0642739	+	0.0765987i
$790$	−138022.	+	239062.i	−0.221154	+	0.383050i
$791$	32210.6	−	18596.8i	0.0514809	−	0.0297225i
$792$	465396.	−	1.27867e6i	0.741947	−	2.03848i
$793$	688627.	+	121423.i	1.09506	+	0.193088i
$794$	−787211.	+	138806.i	−1.24868	+	0.220175i
$795$	−280234.	+	101997.i	−0.443390	+	0.161381i
$796$	−294662.	−	247251.i	−0.465049	−	0.390222i
$797$		−	81093.2i		−	0.127664i	−0.997961	−	0.0638319i	$-0.979668\pi$
$797$		−	81093.2i		−	0.127664i	0.997961	−	0.0638319i	$-0.0203321\pi$
$798$	132069.	+	81583.7i	0.207393	+	0.128114i
$799$	−695559.			−1.08953
$800$	1.63666e6	−	1.95049e6i	2.55728	−	3.04764i
$801$	−170998.	−	469813.i	−0.266517	−	0.732251i
$802$	−355142.	−	2.01411e6i	−0.552145	−	3.13137i
$803$	−51530.0	+	292241.i	−0.0799151	+	0.453221i
$804$	1.73954e6	+	633142.i	2.69106	+	0.979466i
$805$	−5633.18	−	9756.95i	−0.00869284	−	0.0150564i
$806$	−46492.1	−	26842.2i	−0.0715664	−	0.0413189i
$807$	−78313.5	+	65712.8i	−0.120251	+	0.100903i
$808$	−609586.	−	726476.i	−0.933710	−	1.11275i
$809$	−372309.	+	644858.i	−0.568861	+	0.985297i	0.427818	+	0.903865i	$0.359283\pi$
$809$	−372309.	+	644858.i	−0.568861	+	0.985297i	−0.996679	+	0.0814316i	$0.974051\pi$
$810$	327102.	−	188852.i	0.498554	−	0.287841i
$811$	−160184.	+	440101.i	−0.243543	+	0.669130i	0.756345	+	0.654173i	$0.226983\pi$
$811$	−160184.	+	440101.i	−0.243543	+	0.669130i	−0.999888	+	0.0149565i	$0.995239\pi$
$812$	−183034.	−	32273.8i	−0.277600	−	0.0489484i
$813$	140349.	−	24747.2i	0.212338	−	0.0374408i
$814$	26357.2	−	9593.25i	0.0397788	−	0.0144783i
$815$	−218294.	−	183171.i	−0.328645	−	0.275766i
$816$		−	2.68223e6i		−	4.02825i
$817$	−368449.	−	466623.i	−0.551993	−	0.699072i
$818$	852994.			1.27479
$819$	−32335.7	+	38536.2i	−0.0482075	+	0.0574515i
$820$	−120959.	−	332331.i	−0.179891	−	0.494247i
$821$	131085.	+	743422.i	0.194477	+	1.10293i	0.913162	+	0.407597i	$0.133633\pi$
$821$	131085.	+	743422.i	0.194477	+	1.10293i	−0.718685	+	0.695336i	$0.755256\pi$
$822$	−456253.	+	2.58754e6i	−0.675246	+	3.82951i
$823$	−49041.1	−	17849.5i	−0.0724037	−	0.0263528i	0.305564	−	0.952171i	$-0.401155\pi$
$823$	−49041.1	−	17849.5i	−0.0724037	−	0.0263528i	−0.377968	+	0.925819i	$0.623377\pi$
$824$	−2.03803e6	−	3.52997e6i	−3.00162	−	5.19896i
$825$	−439106.	−	253518.i	−0.645152	−	0.372479i
$826$	30760.9	−	25811.4i	0.0450857	−	0.0378314i
$827$	177248.	+	211235.i	0.259161	+	0.308856i	0.879898	−	0.475163i	$-0.157611\pi$
$827$	177248.	+	211235.i	0.259161	+	0.308856i	−0.620737	+	0.784019i	$0.713167\pi$
$828$	646681.	−	1.12008e6i	0.943255	−	1.63377i
$829$	−279320.	+	161265.i	−0.406437	+	0.234656i	−0.689258	−	0.724516i	$-0.742063\pi$
$829$	−279320.	+	161265.i	−0.406437	+	0.234656i	0.282821	+	0.959173i	$0.408730\pi$
$830$	−18862.8	+	51825.2i	−0.0273811	+	0.0752289i
$831$	1.51872e6	+	267791.i	2.19926	+	0.387788i
$832$	−2.51424e6	+	443329.i	−3.63213	+	0.640442i
$833$	444883.	−	161924.i	0.641144	−	0.233357i
$834$	−672748.	−	564503.i	−0.967209	−	0.811585i
$835$			43916.1i			0.0629869i
$836$	995824.	−	536082.i	1.42485	−	0.767041i
$837$	−3535.49			−0.00504660
$838$	−1.20126e6	+	1.43160e6i	−1.71060	+	2.03861i
$839$	−191378.	−	525805.i	−0.271874	−	0.746966i	−0.998220	−	0.0596378i	$-0.981005\pi$
$839$	−191378.	−	525805.i	−0.271874	−	0.746966i	0.726347	−	0.687329i	$-0.241217\pi$
$840$	17156.5	+	97299.3i	0.0243148	+	0.137896i
$841$	−41141.7	+	233326.i	−0.0581688	+	0.329891i
$842$	1.66185e6	+	604864.i	2.34405	+	0.853166i
$843$	4662.56	+	8075.78i	0.00656098	+	0.0113640i
$844$	−1.00316e6	−	579174.i	−1.40827	−	0.813064i
$845$	−60084.9	+	50417.2i	−0.0841496	+	0.0706099i
$846$	1.51810e6	+	1.80920e6i	2.12109	+	2.52782i
$847$	20815.3	−	36053.1i	0.0290145	−	0.0502546i
$848$	−2.62144e6	+	1.51349e6i	−3.64543	+	2.10469i
$849$	226777.	−	623066.i	0.314618	−	0.864407i
$850$	−858141.	−	151313.i	−1.18774	−	0.209430i
$851$	16904.0	−	2980.63i	0.0233416	−	0.00411576i
$852$	−3.61403e6	+	1.31540e6i	−4.97866	+	1.81208i
$853$	−139634.	−	117167.i	−0.191908	−	0.161030i	0.541771	−	0.840526i	$-0.317754\pi$
$853$	−139634.	−	117167.i	−0.191908	−	0.161030i	−0.733679	+	0.679496i	$0.762198\pi$
$854$		−	169992.i		−	0.233083i
$855$	−242703.	−	50284.0i	−0.332004	−	0.0687856i
$856$	3.93329e6			5.36795
$857$	414126.	−	493537.i	0.563860	−	0.671982i	−0.406499	−	0.913651i	$-0.633250\pi$
$857$	414126.	−	493537.i	0.563860	−	0.671982i	0.970359	+	0.241669i	$0.0776949\pi$
$858$	329305.	+	904758.i	0.447325	+	1.22902i
$859$	−88618.4	−	502580.i	−0.120098	−	0.681112i	−0.984099	−	0.177621i	$-0.943160\pi$
$859$	−88618.4	−	502580.i	−0.120098	−	0.681112i	0.864000	−	0.503491i	$-0.167951\pi$
$860$	102059.	−	578804.i	0.137992	−	0.782591i
$861$	−51305.8	−	18673.8i	−0.0692086	−	0.0251899i
$862$	982788.	+	1.70224e6i	1.32265	+	2.29090i
$863$	−644366.	−	372025.i	−0.865189	−	0.499517i	0.000557497	−	1.00000i	$-0.499823\pi$
$863$	−644366.	−	372025.i	−0.865189	−	0.499517i	−0.865747	+	0.500483i	$0.833156\pi$
$864$	−243923.	+	204676.i	−0.326757	+	0.274182i
$865$	−24311.2	−	28973.0i	−0.0324919	−	0.0387223i
$866$	−776851.	+	1.34555e6i	−1.03586	+	1.79417i
$867$	493580.	−	284969.i	0.656628	−	0.379104i
$868$	−3291.42	+	9043.10i	−0.00436862	+	0.0120027i
$869$	305758.	+	53913.4i	0.404891	+	0.0713932i
$870$	767752.	−	135375.i	1.01434	−	0.178855i
$871$	−409090.	+	148897.i	−0.539241	+	0.196268i
$872$	3.10001e6	+	2.60122e6i	4.07690	+	3.42092i
$873$		−	420842.i		−	0.552193i
$874$	891156.	−	294633.i	1.16662	−	0.385708i
$875$	40143.5			0.0524323
$876$	1.58994e6	−	1.89481e6i	2.07192	−	2.46921i
$877$	−510836.	−	1.40351e6i	−0.664175	−	1.82481i	−0.556904	−	0.830577i	$-0.688011\pi$
$877$	−510836.	−	1.40351e6i	−0.664175	−	1.82481i	−0.107271	−	0.994230i	$-0.534211\pi$
$878$	−188194.	−	1.06730e6i	−0.244128	−	1.38452i
$879$	−34062.7	+	193179.i	−0.0440861	+	0.250025i
$880$	543123.	+	197681.i	0.701347	+	0.255269i
$881$	−732791.	−	1.26923e6i	−0.944122	−	1.63527i	−0.757499	−	0.652836i	$-0.773579\pi$
$881$	−732791.	−	1.26923e6i	−0.944122	−	1.63527i	−0.186623	−	0.982432i	$-0.559754\pi$
$882$	−1.39216e6	−	803766.i	−1.78959	−	1.03322i
$883$	1.03723e6	−	870340.i	1.33031	−	1.11627i	0.346309	−	0.938121i	$-0.387435\pi$
$883$	1.03723e6	−	870340.i	1.33031	−	1.11627i	0.984004	−	0.178145i	$-0.0570095\pi$
$884$	784278.	+	934666.i	1.00361	+	1.19606i
$885$	−62100.1	+	107561.i	−0.0792877	+	0.137330i
$886$	620852.	−	358449.i	0.790899	−	0.456626i
$887$	−151436.	+	416067.i	−0.192478	+	0.528830i	−0.997964	−	0.0637859i	$-0.979683\pi$
$887$	−151436.	+	416067.i	−0.192478	+	0.528830i	0.805485	+	0.592616i	$0.201905\pi$
$888$	−148240.	−	26138.7i	−0.187992	−	0.0331480i
$889$	−52717.7	+	9295.56i	−0.0667042	+	0.0117617i
$890$	337035.	−	122671.i	0.425496	−	0.154868i
$891$	−325427.	−	273065.i	−0.409919	−	0.343962i
$892$		−	482935.i		−	0.606958i
$893$	−37605.3	+	1.26325e6i	−0.0471569	+	1.58411i
$894$	955350.			1.19533
$895$	139662.	−	166443.i	0.174355	−	0.207788i
$896$	106697.	+	293148.i	0.132903	+	0.365149i
$897$	102315.	+	580259.i	0.127162	+	0.721169i
$898$	294547.	−	1.67046e6i	0.365260	−	2.07149i
$899$	45941.4	+	16721.3i	0.0568441	+	0.0206895i
$900$	1.09085e6	+	1.88941e6i	1.34673	+	2.33260i
$901$	499206.	+	288217.i	0.614937	+	0.355034i
$902$	−413236.	+	346746.i	−0.507908	+	0.426186i
$903$	−58323.4	−	69507.1i	−0.0715265	−	0.0852420i
$904$	−986055.	+	1.70790e6i	−1.20660	+	2.08990i
$905$	126759.	−	73184.6i	0.154769	−	0.0893557i
$906$	524889.	−	1.44212e6i	0.639456	−	1.75689i
$907$	35090.0	+	6187.31i	0.0426549	+	0.00752121i	0.194935	−	0.980816i	$-0.437550\pi$
$907$	35090.0	+	6187.31i	0.0426549	+	0.00752121i	−0.152280	+	0.988337i	$0.548662\pi$
$908$	−2.21868e6	+	391213.i	−2.69105	+	0.474505i
$909$	341179.	−	124179.i	0.412909	−	0.150287i
$910$	−27645.2	−	23197.1i	−0.0333839	−	0.0280124i
$911$		−	65460.3i		−	0.0788754i	−0.999222	−	0.0394377i	$-0.987443\pi$
$911$		−	65460.3i		−	0.0788754i	0.999222	−	0.0394377i	$-0.0125567\pi$
$912$	−4.87138e6	−	145015.i	−5.85683	−	0.174350i
$913$	62030.1			0.0744150
$914$	−476579.	+	567965.i	−0.570483	+	0.679875i
$915$	179828.	+	494072.i	0.214790	+	0.590131i
$916$	31073.9	+	176229.i	0.0370344	+	0.210032i
$917$	−13965.6	+	79203.0i	−0.0166082	+	0.0941897i
$918$	102400.	+	37270.7i	0.121511	+	0.0442265i
$919$	−53218.2	−	92176.7i	−0.0630129	−	0.109142i	0.832798	−	0.553577i	$-0.186738\pi$
$919$	−53218.2	−	92176.7i	−0.0630129	−	0.109142i	−0.895811	+	0.444436i	$0.853404\pi$
$920$	517341.	+	298687.i	0.611226	+	0.352891i
$921$	−1.41337e6	+	1.18596e6i	−1.66623	+	1.39814i
$922$	−1.14159e6	−	1.36049e6i	−1.34291	−	1.60042i
$923$	452230.	−	783285.i	0.530830	−	0.919425i
$924$	149472.	−	86297.7i	0.175072	−	0.101078i
$925$	−9902.97	+	27208.2i	−0.0115740	+	0.0317992i
$926$	−1.43084e6	−	252296.i	−1.66867	−	0.294231i
$927$	1.53681e6	−	270982.i	1.78839	−	0.315341i
$928$	4.13765e6	−	1.50598e6i	4.80460	−	1.74873i
$929$	−99430.9	−	83432.4i	−0.115210	−	0.0966726i	0.583363	−	0.812212i	$-0.301737\pi$
$929$	−99430.9	−	83432.4i	−0.115210	−	0.0966726i	−0.698573	+	0.715539i	$0.746181\pi$
$930$		−	40366.5i		−	0.0466719i
$931$	−270029.	−	816736.i	−0.311538	−	0.942285i
$932$	−83230.9			−0.0958193
$933$	−374388.	+	446178.i	−0.430089	+	0.512560i
$934$	173394.	+	476397.i	0.198766	+	0.546104i
$935$	−19112.7	−	108393.i	−0.0218624	−	0.123988i
$936$	463178.	−	2.62681e6i	0.528684	−	2.99832i
$937$	344949.	+	125551.i	0.392894	+	0.143002i	0.530910	−	0.847428i	$-0.321850\pi$
$937$	344949.	+	125551.i	0.392894	+	0.143002i	−0.138016	+	0.990430i	$0.544072\pi$
$938$	52917.4	+	91655.5i	0.0601440	+	0.104172i
$939$	1.75251e6	+	1.01181e6i	1.98760	+	1.14754i
$940$	−957032.	+	803045.i	−1.08310	+	0.908833i
$941$	880079.	+	1.04884e6i	0.993899	+	1.18448i	0.982824	+	0.184545i	$0.0590810\pi$
$941$	880079.	+	1.04884e6i	0.993899	+	1.18448i	0.0110754	+	0.999939i	$0.496475\pi$
$942$	896976.	−	1.55361e6i	1.01083	−	1.75081i
$943$	−285890.	+	165059.i	−0.321496	+	0.185616i
$944$	−431171.	+	1.18463e6i	−0.483844	+	1.32935i
$945$	−2340.55	−	412.703i	−0.00262093	−	0.000462140i
$946$	−882858.	+	155672.i	−0.986526	+	0.173951i
$947$	508404.	−	185044.i	0.566904	−	0.206336i	−0.0426374	−	0.999091i	$-0.513576\pi$
$947$	508404.	−	185044.i	0.566904	−	0.206336i	0.609541	+	0.792755i	$0.291354\pi$
$948$	−1.98245e6	−	1.66348e6i	−2.20590	−	1.85097i
$949$			581696.i			0.645898i
$950$	−321205.	+	1.55035e6i	−0.355906	+	1.71783i
$951$	−803494.			−0.888427
$952$	122755.	−	146294.i	0.135446	−	0.161419i
$953$	319968.	+	879104.i	0.352306	+	0.967953i	0.981627	+	0.190808i	$0.0611107\pi$
$953$	319968.	+	879104.i	0.352306	+	0.967953i	−0.629321	+	0.777145i	$0.716667\pi$
$954$	−339875.	−	1.92753e6i	−0.373442	−	2.11789i
$955$	19807.8	−	112336.i	0.0217185	−	0.123172i
$956$	−4.28362e6	−	1.55911e6i	−4.68700	−	1.70593i
$957$	−438416.	−	759359.i	−0.478699	−	0.829131i
$958$	−1.42960e6	−	825382.i	−1.55770	−	0.899340i
$959$	−84850.8	+	71198.3i	−0.0922611	+	0.0774163i
$960$	−1.23395e6	−	1.47056e6i	−1.33892	−	1.59566i
$961$	−460495.	+	797600.i	−0.498629	+	0.863652i
$962$	47615.8	−	27491.0i	0.0514519	−	0.0297058i
$963$	−515035.	+	1.41505e6i	−0.555372	+	1.52587i
$964$	4.00858e6	+	706820.i	4.31356	+	0.760597i
$965$	−364575.	+	64284.4i	−0.391500	+	0.0690321i
$966$	134602.	−	48991.1i	0.144244	−	0.0525005i
$967$	697564.	+	585325.i	0.745986	+	0.625957i	0.934438	−	0.356126i	$-0.115902\pi$
$967$	697564.	+	585325.i	0.745986	+	0.625957i	−0.188452	+	0.982082i	$0.560347\pi$
$968$			2.20737e6i			2.35572i
$969$	439917.	+	817190.i	0.468515	+	0.870313i
$970$	301905.			0.320868
$971$	870573.	−	1.03751e6i	0.923350	−	1.10041i	−0.0713357	−	0.997452i	$-0.522726\pi$
$971$	870573.	−	1.03751e6i	0.923350	−	1.10041i	0.994686	−	0.102954i	$-0.0328294\pi$
$972$	1.29854e6	+	3.56770e6i	1.37443	+	3.77620i
$973$	−6428.88	−	36460.0i	−0.00679062	−	0.0385115i
$974$	385416.	−	2.18580e6i	0.406268	−	2.30406i
$975$	−933967.	−	339936.i	−0.982477	−	0.357592i
$976$	2.66840e6	+	4.62180e6i	2.80124	+	4.85189i
$977$	−509913.	−	294398.i	−0.534204	−	0.308423i	0.208523	−	0.978017i	$-0.433134\pi$
$977$	−509913.	−	294398.i	−0.534204	−	0.308423i	−0.742727	+	0.669595i	$0.766468\pi$
$978$	2.77539e6	−	2.32883e6i	2.90166	−	2.43478i
$979$	−259301.	−	309023.i	−0.270545	−	0.322423i
$980$	425176.	−	736426.i	0.442707	−	0.766791i
$981$	−1.34174e6	+	774654.i	−1.39422	+	0.804952i
$982$	−1.01657e6	+	2.79300e6i	−1.05418	+	2.89633i
$983$	−1.39988e6	−	246837.i	−1.44872	−	0.255449i	−0.606716	−	0.794918i	$-0.707514\pi$
$983$	−1.39988e6	−	246837.i	−1.44872	−	0.255449i	−0.842005	+	0.539470i	$0.818625\pi$
$984$	2.85098e6	−	502706.i	2.94445	−	0.519187i
$985$	364361.	−	132617.i	0.375543	−	0.136686i
$986$	−1.15435e6	−	968616.i	−1.18737	−	0.996318i
$987$			192871.i			0.197985i
$988$	1.73991e6	−	1.37385e6i	1.78243	−	1.40742i
$989$	−548610.			−0.560881
$990$	−240225.	+	286289.i	−0.245103	+	0.292102i
$991$	−106525.	−	292676.i	−0.108469	−	0.298016i	0.873569	−	0.486701i	$-0.161800\pi$
$991$	−106525.	−	292676.i	−0.108469	−	0.298016i	−0.982038	+	0.188685i	$0.939578\pi$
$992$	−39590.4	−	224528.i	−0.0402315	−	0.228164i
$993$	91622.8	−	519618.i	0.0929191	−	0.526970i
$994$	−206619.	−	75203.1i	−0.209121	−	0.0761137i
$995$	34009.2	+	58905.7i	0.0343519	+	0.0594992i
$996$	−447771.	−	258521.i	−0.451375	−	0.260601i
$997$	−933415.	+	783228.i	−0.939041	+	0.787949i	−0.977418	−	0.211314i	$-0.932226\pi$
$997$	−933415.	+	783228.i	−0.939041	+	0.787949i	0.0383772	+	0.999263i	$0.487781\pi$
$998$	−586688.	−	699188.i	−0.589042	−	0.701993i
$999$	1810.47	−	3135.83i	0.00181410	−	0.00314211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.5.f.a.3.1	✓	36
19.13	odd	18	inner	19.5.f.a.13.1	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.5.f.a.3.1	✓	36	1.1	even	1	trivial
19.5.f.a.13.1	yes	36	19.13	odd	18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	19.f (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.01717 + 5.97923i) q^{2} +(4.42557 + 12.1592i) q^{3} +(-7.80084 - 44.2408i) q^{4} +(-1.37942 + 7.82309i) q^{5} +(-94.9062 - 34.5430i) q^{6} +(-2.12885 - 3.68728i) q^{7} +(195.510 + 112.878i) q^{8} +(-66.2097 + 55.5565i) q^{9} +O(q^{10})\)	\(q+(-5.01717 + 5.97923i) q^{2} +(4.42557 + 12.1592i) q^{3} +(-7.80084 - 44.2408i) q^{4} +(-1.37942 + 7.82309i) q^{5} +(-94.9062 - 34.5430i) q^{6} +(-2.12885 - 3.68728i) q^{7} +(195.510 + 112.878i) q^{8} +(-66.2097 + 55.5565i) q^{9} +(-39.8553 - 47.4977i) q^{10} +(-34.8687 + 60.3943i) q^{11} +(503.407 - 290.642i) q^{12} +(-46.7545 + 128.457i) q^{13} +(32.7279 + 5.77082i) q^{14} +(-101.227 + 17.8490i) q^{15} +(-980.405 + 356.838i) q^{16} +(152.200 + 127.711i) q^{17} -674.620i q^{18} +(240.172 - 269.515i) q^{19} +356.860 q^{20} +(35.4128 - 42.2033i) q^{21} +(-186.170 - 511.497i) q^{22} +(-57.8431 - 328.044i) q^{23} +(-507.255 + 2876.78i) q^{24} +(528.010 + 192.180i) q^{25} +(-533.499 - 924.047i) q^{26} +(-60.8549 - 35.1346i) q^{27} +(-146.521 + 122.946i) q^{28} +(624.599 + 744.368i) q^{29} +(401.149 - 694.811i) q^{30} +(43.5728 - 25.1568i) q^{31} +(1549.84 - 4258.14i) q^{32} +(-888.657 - 156.694i) q^{33} +(-1527.22 + 269.291i) q^{34} +(31.7825 - 11.5679i) q^{35} +(2974.35 + 2495.78i) q^{36} +51.5297i q^{37} +(406.507 + 2788.25i) q^{38} -1768.84 q^{39} +(-1152.74 + 1373.79i) q^{40} +(-338.953 - 931.265i) q^{41} +(74.6715 + 423.483i) q^{42} +(285.991 - 1621.94i) q^{43} +(2943.90 + 1071.49i) q^{44} +(-343.293 - 594.600i) q^{45} +(2251.66 + 1300.00i) q^{46} +(-2681.81 + 2250.31i) q^{47} +(-8677.70 - 10341.7i) q^{48} +(1191.44 - 2063.63i) q^{49} +(-3798.21 + 2192.89i) q^{50} +(-879.283 + 2415.81i) q^{51} +(6047.76 + 1066.38i) q^{52} +(2857.21 - 503.803i) q^{53} +(515.397 - 187.589i) q^{54} +(-424.372 - 356.090i) q^{55} -961.200i q^{56} +(4339.97 + 1727.53i) q^{57} -7584.47 q^{58} +(776.686 - 925.618i) q^{59} +(1579.31 + 4339.12i) q^{60} +(-888.240 - 5037.46i) q^{61} +(-68.1941 + 386.748i) q^{62} +(345.803 + 125.862i) q^{63} +(9338.00 + 16173.9i) q^{64} +(-940.437 - 542.961i) q^{65} +(5395.46 - 4527.33i) q^{66} +(2047.05 + 2439.58i) q^{67} +(4462.73 - 7729.67i) q^{68} +(3732.75 - 2155.11i) q^{69} +(-90.2912 + 248.073i) q^{70} +(-6515.81 - 1148.91i) q^{71} +(-19215.8 + 3388.26i) q^{72} +(3998.62 - 1455.38i) q^{73} +(-308.108 - 258.533i) q^{74} +7270.66i q^{75} +(-13797.1 - 8522.96i) q^{76} +296.921 q^{77} +(8874.59 - 10576.3i) q^{78} +(-1522.69 - 4183.56i) q^{79} +(-1439.19 - 8162.03i) q^{80} +(-1057.80 + 5999.08i) q^{81} +(7268.84 + 2645.64i) q^{82} +(-444.741 - 770.313i) q^{83} +(-2143.36 - 1237.47i) q^{84} +(-1209.04 + 1014.50i) q^{85} +(8263.07 + 9847.54i) q^{86} +(-6286.67 + 10888.8i) q^{87} +(-13634.4 + 7871.80i) q^{88} +(-1978.44 + 5435.72i) q^{89} +(5277.61 + 930.585i) q^{90} +(573.191 - 101.069i) q^{91} +(-14061.7 + 5118.04i) q^{92} +(498.720 + 418.476i) q^{93} -27325.4i q^{94} +(1777.14 + 2250.66i) q^{95} +58634.2 q^{96} +(-3129.82 + 3729.97i) q^{97} +(6361.27 + 17477.4i) q^{98} +(-1046.65 - 5935.87i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{2} - 18 q^{3} - 48 q^{4} - 6 q^{5} - 48 q^{7} - 9 q^{8} + 246 q^{9}+O(q^{10}) \) 36 * q - 6 * q^2 - 18 * q^3 - 48 * q^4 - 6 * q^5 - 48 * q^7 - 9 * q^8 + 246 * q^9	\( 36 q - 6 q^{2} - 18 q^{3} - 48 q^{4} - 6 q^{5} - 48 q^{7} - 9 q^{8} + 246 q^{9} - 153 q^{10} - 48 q^{11} + 855 q^{12} + 555 q^{13} - 399 q^{14} - 1647 q^{15} - 2112 q^{16} + 39 q^{17} - 12 q^{19} + 2886 q^{20} + 912 q^{21} + 1386 q^{22} + 1074 q^{23} + 168 q^{24} + 2448 q^{25} - 3675 q^{26} + 1215 q^{27} + 2316 q^{28} - 1743 q^{29} + 2580 q^{30} - 2817 q^{31} - 6039 q^{32} - 7368 q^{33} - 8460 q^{34} - 1326 q^{35} - 4581 q^{36} + 2892 q^{38} + 7164 q^{39} + 4482 q^{40} + 6150 q^{41} + 22299 q^{42} + 2091 q^{43} + 34053 q^{44} + 3165 q^{45} + 7326 q^{46} + 4539 q^{47} - 44943 q^{48} + 102 q^{49} - 51876 q^{50} - 25836 q^{51} - 3279 q^{52} - 11607 q^{53} + 6069 q^{54} - 7044 q^{55} + 2532 q^{57} + 13644 q^{58} - 681 q^{59} + 63654 q^{60} + 44346 q^{61} + 14796 q^{62} + 53388 q^{63} + 939 q^{64} + 3636 q^{65} + 11148 q^{66} - 52089 q^{67} + 5262 q^{68} - 54954 q^{69} - 69999 q^{70} - 24504 q^{71} - 101118 q^{72} - 6666 q^{73} - 9675 q^{74} - 6462 q^{76} + 48918 q^{77} + 56871 q^{78} + 41043 q^{79} + 65649 q^{80} + 2919 q^{81} + 114711 q^{82} - 17598 q^{83} + 11115 q^{84} + 52344 q^{85} - 55716 q^{86} + 2121 q^{87} - 69057 q^{88} - 11706 q^{89} - 41394 q^{90} - 84249 q^{91} - 88668 q^{92} - 60321 q^{93} + 93405 q^{95} + 167166 q^{96} + 4401 q^{97} + 69381 q^{98} + 58386 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 - 18 * q^3 - 48 * q^4 - 6 * q^5 - 48 * q^7 - 9 * q^8 + 246 * q^9 - 153 * q^10 - 48 * q^11 + 855 * q^12 + 555 * q^13 - 399 * q^14 - 1647 * q^15 - 2112 * q^16 + 39 * q^17 - 12 * q^19 + 2886 * q^20 + 912 * q^21 + 1386 * q^22 + 1074 * q^23 + 168 * q^24 + 2448 * q^25 - 3675 * q^26 + 1215 * q^27 + 2316 * q^28 - 1743 * q^29 + 2580 * q^30 - 2817 * q^31 - 6039 * q^32 - 7368 * q^33 - 8460 * q^34 - 1326 * q^35 - 4581 * q^36 + 2892 * q^38 + 7164 * q^39 + 4482 * q^40 + 6150 * q^41 + 22299 * q^42 + 2091 * q^43 + 34053 * q^44 + 3165 * q^45 + 7326 * q^46 + 4539 * q^47 - 44943 * q^48 + 102 * q^49 - 51876 * q^50 - 25836 * q^51 - 3279 * q^52 - 11607 * q^53 + 6069 * q^54 - 7044 * q^55 + 2532 * q^57 + 13644 * q^58 - 681 * q^59 + 63654 * q^60 + 44346 * q^61 + 14796 * q^62 + 53388 * q^63 + 939 * q^64 + 3636 * q^65 + 11148 * q^66 - 52089 * q^67 + 5262 * q^68 - 54954 * q^69 - 69999 * q^70 - 24504 * q^71 - 101118 * q^72 - 6666 * q^73 - 9675 * q^74 - 6462 * q^76 + 48918 * q^77 + 56871 * q^78 + 41043 * q^79 + 65649 * q^80 + 2919 * q^81 + 114711 * q^82 - 17598 * q^83 + 11115 * q^84 + 52344 * q^85 - 55716 * q^86 + 2121 * q^87 - 69057 * q^88 - 11706 * q^89 - 41394 * q^90 - 84249 * q^91 - 88668 * q^92 - 60321 * q^93 + 93405 * q^95 + 167166 * q^96 + 4401 * q^97 + 69381 * q^98 + 58386 * q^99

Introduction

L-functions

Modular forms

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