LMFDB - Embedded newform 19.5.f.a.13.1

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			13.1
Character	$\chi$	$=$	19.13
Dual form			19.5.f.a.3.1

$q$-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 $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{18}\right)$

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	−0.795108	−	0.606467i	$-0.792586\pi$
$2$	−5.01717	−	5.97923i	−1.25429	−	1.49481i	−0.459185	−	0.888341i	$-0.651858\pi$
$3$	4.42557	−	12.1592i	0.491730	−	1.35102i	−0.407366	−	0.913265i	$-0.633553\pi$
$3$	4.42557	−	12.1592i	0.491730	−	1.35102i	0.899096	−	0.437752i	$-0.144225\pi$
$4$	−7.80084	+	44.2408i	−0.487552	+	2.76505i
$5$	−1.37942	−	7.82309i	−0.0551769	−	0.312924i	0.944711	−	0.327904i	$-0.106342\pi$
$5$	−1.37942	−	7.82309i	−0.0551769	−	0.312924i	−0.999888	+	0.0149808i	$0.995231\pi$
$6$	−94.9062	+	34.5430i	−2.63628	+	0.959529i
$7$	−2.12885	+	3.68728i	−0.0434460	+	0.0752506i	−0.886931	−	0.461903i	$-0.847167\pi$
$7$	−2.12885	+	3.68728i	−0.0434460	+	0.0752506i	0.843485	+	0.537153i	$0.180500\pi$
$8$	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	0.685202	−	0.728353i	$-0.259714\pi$
$11$	−34.8687	−	60.3943i	−0.288171	−	0.499127i	−0.973373	+	0.229226i	$0.926380\pi$
$12$	503.407	+	290.642i	3.49588	+	2.01835i
$13$	−46.7545	−	128.457i	−0.276654	−	0.760101i	−0.997736	−	0.0672511i	$-0.978577\pi$
$13$	−46.7545	−	128.457i	−0.276654	−	0.760101i	0.721082	−	0.692850i	$-0.243645\pi$
$14$	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	−0.340298	−	0.940318i	$-0.610528\pi$
$17$	152.200	−	127.711i	0.526642	−	0.441905i	0.866940	+	0.498413i	$0.166083\pi$
$18$			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	0.880052	+	0.474878i	$0.157508\pi$
$23$	−57.8431	+	328.044i	−0.109344	+	0.620122i	−0.989396	+	0.145244i	$0.953603\pi$
$24$	−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	−0.253937	−	0.967221i	$-0.581725\pi$
$29$	624.599	−	744.368i	0.742686	−	0.885098i	0.996622	+	0.0821227i	$0.0261699\pi$
$30$	401.149	+	694.811i	0.445721	+	0.772012i
$31$	43.5728	+	25.1568i	0.0453411	+	0.0261777i	0.522499	−	0.852640i	$-0.325000\pi$
$31$	43.5728	+	25.1568i	0.0453411	+	0.0261777i	−0.477158	+	0.878817i	$0.658333\pi$
$32$	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	$-0.994009\pi$
$37$		−	51.5297i		−	0.0376404i	0.999823	−	0.0188202i	$-0.00599100\pi$
$38$	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	−0.998758	−	0.0498257i	$-0.984133\pi$
$41$	−338.953	+	931.265i	−0.201638	+	0.553995i	0.797120	+	0.603821i	$0.206356\pi$
$42$	74.6715	−	423.483i	0.0423308	−	0.240070i
$43$	285.991	+	1621.94i	0.154673	+	0.877196i	0.959084	+	0.283122i	$0.0913703\pi$
$43$	285.991	+	1621.94i	0.154673	+	0.877196i	−0.804410	+	0.594074i	$0.797519\pi$
$44$	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	−0.999115	−	0.0420687i	$-0.986605\pi$
$47$	−2681.81	−	2250.31i	−1.21404	−	1.01870i	−0.214924	−	0.976631i	$-0.568950\pi$
$48$	−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	0.657281	−	0.753645i	$-0.271706\pi$
$53$	2857.21	+	503.803i	1.01716	+	0.179353i	0.359880	+	0.932998i	$0.382818\pi$
$54$	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	0.865979	−	0.500080i	$-0.166696\pi$
$59$	776.686	+	925.618i	0.223121	+	0.265906i	−0.642858	+	0.765985i	$0.722251\pi$
$60$	1579.31	−	4339.12i	0.438697	−	1.20531i
$61$	−888.240	+	5037.46i	−0.238710	+	1.35379i	0.595948	+	0.803023i	$0.296777\pi$
$61$	−888.240	+	5037.46i	−0.238710	+	1.35379i	−0.834658	+	0.550769i	$0.814335\pi$
$62$	−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	−0.488224	−	0.872718i	$-0.662355\pi$
$67$	2047.05	−	2439.58i	0.456015	−	0.543457i	0.944239	+	0.329261i	$0.106800\pi$
$68$	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	−0.777307	−	0.629122i	$-0.783415\pi$
$71$	−6515.81	+	1148.91i	−1.29256	+	0.227914i	−0.515257	+	0.857036i	$0.672303\pi$
$72$	−19215.8	−	3388.26i	−3.70674	−	0.653599i
$73$	3998.62	+	1455.38i	0.750351	+	0.273105i	0.688753	−	0.724996i	$-0.258158\pi$
$73$	3998.62	+	1455.38i	0.750351	+	0.273105i	0.0615975	+	0.998101i	$0.480380\pi$
$74$	−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	0.755895	+	0.654692i	$0.227202\pi$
$79$	−1522.69	+	4183.56i	−0.243982	+	0.670336i	−0.999878	+	0.0156433i	$0.995020\pi$
$80$	−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	−0.896498	−	0.443048i	$-0.853897\pi$
$83$	−444.741	+	770.313i	−0.0645581	+	0.111818i	0.831940	+	0.554866i	$0.187230\pi$
$84$	−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	−0.999694	−	0.0247166i	$-0.992132\pi$
$89$	−1978.44	−	5435.72i	−0.249772	−	0.686242i	0.749923	−	0.661525i	$-0.230091\pi$
$90$	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	0.573636	−	0.819110i	$-0.305532\pi$
$97$	−3129.82	−	3729.97i	−0.332641	−	0.396426i	−0.906277	+	0.422684i	$0.861088\pi$
$98$	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	−0.528174	−	0.849136i	$-0.677123\pi$
$101$	−3947.43	+	1436.75i	−0.386965	+	0.140844i	0.141209	+	0.989980i	$0.454901\pi$
$102$	−10033.2	+	17378.0i	−0.964357	+	1.67032i
$103$	−15636.3	+	9027.60i	−1.47387	+	0.850938i	−0.999567	−	0.0294254i	$-0.990632\pi$
$103$	−15636.3	+	9027.60i	−1.47387	+	0.850938i	−0.474300	+	0.880363i	$0.657299\pi$
$104$	−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	0.983390	−	0.181507i	$-0.0580975\pi$
$107$	15088.6	+	8711.39i	1.31789	+	0.760887i	0.334505	+	0.942394i	$0.391431\pi$
$108$	−1079.66	−	2966.35i	−0.0925636	−	0.254316i
$109$	17653.1	−	3112.72i	1.48583	−	0.261992i	0.628924	−	0.777467i	$-0.283496\pi$
$109$	17653.1	−	3112.72i	1.48583	−	0.261992i	0.856905	+	0.515475i	$0.172384\pi$
$110$	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	$-0.888874\pi$
$113$		−	8735.60i		−	0.684126i	0.939677	−	0.342063i	$-0.111126\pi$
$114$	−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	0.998684	+	0.0512777i	$0.0163294\pi$
$127$	4300.13	+	11814.5i	0.266608	+	0.732501i	−0.732076	+	0.681223i	$0.761448\pi$
$128$	−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	−0.958279	−	0.285834i	$-0.907730\pi$
$131$	−14470.0	+	12141.8i	−0.843192	+	0.707522i	0.115088	+	0.993355i	$0.463285\pi$
$132$		−	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	0.589607	+	0.807690i	$0.299283\pi$
$137$	−4517.48	+	25619.9i	−0.240689	+	1.36501i	−0.830296	+	0.557323i	$0.811829\pi$
$138$	−5841.98	−	33131.5i	−0.306762	−	1.73974i
$139$	8171.00	−	2974.00i	0.422908	−	0.153926i	−0.121794	−	0.992555i	$-0.538865\pi$
$139$	8171.00	−	2974.00i	0.422908	−	0.153926i	0.544702	+	0.838629i	$0.316643\pi$
$140$	−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	0.133982	−	0.990984i	$-0.457224\pi$
$149$	−8888.72	−	3235.23i	−0.400375	−	0.145725i	−0.534356	+	0.845259i	$0.679446\pi$
$150$	−43473.0	+	36478.1i	−1.93213	+	1.62125i
$151$		−	15195.2i		−	0.666427i	−0.942851	−	0.333214i	$-0.891867\pi$
$151$		−	15195.2i		−	0.666427i	0.942851	−	0.333214i	$-0.108133\pi$
$152$	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	−0.981229	−	0.192848i	$-0.938227\pi$
$157$	−3084.41	−	17492.6i	−0.125133	−	0.709666i	0.856095	−	0.516818i	$-0.172884\pi$
$158$	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	−0.976445	−	0.215766i	$-0.930775\pi$
$163$	−17936.2	−	31066.5i	−0.675082	−	1.16928i	0.301364	−	0.953509i	$-0.402558\pi$
$164$	−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	0.270401	−	0.962748i	$-0.412844\pi$
$167$	5444.37	+	959.990i	0.195216	+	0.0344218i	−0.0751852	+	0.997170i	$0.523955\pi$
$168$	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	0.712489	−	0.701683i	$-0.247568\pi$
$173$	−3060.41	−	3647.26i	−0.102256	−	0.121864i	−0.814745	+	0.579819i	$0.803123\pi$
$174$	−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	−0.821808	−	0.569765i	$-0.807034\pi$
$179$	−23687.3	+	13675.9i	−0.739281	+	0.426824i	0.0825266	+	0.996589i	$0.473701\pi$
$180$	−23627.6	−	19825.9i	−0.729247	−	0.611911i
$181$	−11843.8	+	14114.9i	−0.361521	+	0.430843i	−0.915891	−	0.401426i	$-0.868515\pi$
$181$	−11843.8	+	14114.9i	−0.361521	+	0.430843i	0.554371	+	0.832270i	$0.312959\pi$
$182$	−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	−0.519180	−	0.854665i	$-0.673762\pi$
$193$	15939.0	−	43792.0i	0.427903	−	1.17565i	0.947083	−	0.320989i	$-0.104015\pi$
$194$	−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	0.358916	+	0.933370i	$0.383146\pi$
$197$	−24405.6	+	42271.7i	−0.628864	+	1.08922i	−0.987780	+	0.155854i	$0.950187\pi$
$198$	40743.2	−	23523.1i	1.03926	−	0.600018i
$199$	6559.24	+	5503.86i	0.165633	+	0.138983i	0.721837	−	0.692063i	$-0.243298\pi$
$199$	6559.24	+	5503.86i	0.165633	+	0.138983i	−0.556204	+	0.831046i	$0.687743\pi$
$200$	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	0.919362	−	0.393412i	$-0.128706\pi$
$211$	16574.3	+	19752.5i	0.372281	+	0.443667i	−0.547081	+	0.837080i	$0.684261\pi$
$212$	−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	−0.0661848	−	0.997807i	$-0.521083\pi$
$223$	10586.9	−	1866.76i	0.212892	−	0.0375386i	0.279077	+	0.960269i	$0.409972\pi$
$224$	−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	$0.161770\pi$
$227$			50150.1i			0.973240i	−0.873614	+	0.486620i	$0.838230\pi$
$228$	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	0.987627	−	0.156818i	$-0.0501238\pi$
$233$	321.724	+	1824.59i	0.00592614	+	0.0336088i	−0.981701	+	0.190427i	$0.939013\pi$
$234$	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	0.841960	+	0.539541i	$0.181402\pi$
$239$	50736.9	+	87878.9i	0.888236	+	1.53847i	0.0462761	+	0.998929i	$0.485265\pi$
$240$	92874.1	+	53620.9i	1.61240	+	0.930919i
$241$	−30989.8	−	85143.9i	−0.533562	−	1.46595i	−0.854803	−	0.518953i	$-0.826322\pi$
$241$	−30989.8	−	85143.9i	−0.533562	−	1.46595i	0.321241	−	0.946998i	$-0.395900\pi$
$242$	−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	0.850872	+	0.525372i	$0.176074\pi$
$251$	−8087.69	+	45867.6i	−0.128374	+	0.728045i	−0.979246	+	0.202673i	$0.935037\pi$
$252$	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	−0.0904115	−	0.995904i	$-0.528818\pi$
$257$	59844.5	−	71319.9i	0.906063	−	1.07980i	0.996474	−	0.0838990i	$-0.0267373\pi$
$258$	−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	0.374491	−	0.927231i	$-0.377818\pi$
$263$	4520.53	+	1645.34i	0.0653549	+	0.0237872i	−0.309136	+	0.951018i	$0.600040\pi$
$264$	−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	−0.919620	−	0.392810i	$-0.871503\pi$
$269$	2702.20	−	7424.22i	0.0373433	−	0.102600i	0.956963	+	0.290210i	$0.0937252\pi$
$270$	756.578	−	4290.77i	0.0103783	−	0.0588582i
$271$	1912.53	+	10846.5i	0.0260418	+	0.147690i	0.995056	−	0.0993142i	$-0.0316649\pi$
$271$	1912.53	+	10846.5i	0.0260418	+	0.147690i	−0.969014	+	0.247004i	$0.920554\pi$
$272$	−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	0.933868	+	0.357617i	$0.116411\pi$
$277$	59590.8	+	103214.i	0.776640	+	1.34518i	−0.157229	+	0.987562i	$0.550256\pi$
$278$	−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	0.178140	−	0.984005i	$-0.442992\pi$
$281$	709.722	+	125.143i	0.00898826	+	0.00158487i	−0.169152	+	0.985590i	$0.554103\pi$
$282$	332253.	+	120930.i	4.17802	+	1.52068i
$283$	−39254.1	+	32938.1i	−0.490130	+	0.411268i	−0.854073	−	0.520153i	$-0.825875\pi$
$283$	−39254.1	+	32938.1i	−0.490130	+	0.411268i	0.363943	+	0.931421i	$0.381430\pi$
$284$		−	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	−0.421583	−	0.906790i	$-0.638525\pi$
$293$	13128.7	−	7579.87i	0.152928	−	0.0882930i	0.574511	+	0.818497i	$0.305192\pi$
$294$	−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	−0.355895	−	0.934526i	$-0.615824\pi$
$307$	48768.0	−	133989.i	0.517438	−	1.42165i	0.873333	−	0.487124i	$-0.161954\pi$
$308$	−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	−0.725906	−	0.687794i	$-0.758579\pi$
$311$	22506.4	−	38982.3i	0.232694	−	0.403038i	0.958600	+	0.284756i	$0.0919125\pi$
$312$	−345827.	+	199663.i	−3.55262	+	2.05111i
$313$	119802.	+	100526.i	1.22286	+	1.02610i	0.998670	+	0.0515563i	$0.0164182\pi$
$313$	119802.	+	100526.i	1.22286	+	1.02610i	0.224190	+	0.974545i	$0.428026\pi$
$314$	−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	0.788041	−	0.615623i	$-0.211095\pi$
$317$	−21238.2	−	58351.4i	−0.211348	−	0.580674i	−0.999389	+	0.0349486i	$0.988873\pi$
$318$	−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	−0.652427	−	0.757851i	$-0.726249\pi$
$331$	−35314.0	+	20388.5i	−0.322322	+	0.186093i	0.330105	+	0.943944i	$0.392916\pi$
$332$	−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	−0.116368	−	0.993206i	$-0.537125\pi$
$337$	12944.4	−	2282.45i	0.113978	−	0.0200975i	0.230346	+	0.973109i	$0.426014\pi$
$338$	−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	−0.928996	−	0.370089i	$-0.879327\pi$
$347$	−21987.1	−	124695.i	−0.182603	−	1.03559i	0.746393	−	0.665505i	$-0.231784\pi$
$348$	530772.	−	193185.i	4.38278	−	1.59520i
$349$	−56618.7	+	98066.5i	−0.464846	+	0.805137i	−0.999195	−	0.0401271i	$-0.987224\pi$
$349$	−56618.7	+	98066.5i	−0.464846	+	0.805137i	0.534348	+	0.845264i	$0.320557\pi$
$350$	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	0.726150	−	0.687537i	$-0.241308\pi$
$353$	−28952.8	−	50147.7i	−0.232349	−	0.402441i	−0.958499	+	0.285096i	$0.907975\pi$
$354$	−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	−0.403311	+	0.915063i	$0.632141\pi$
$359$	−177148.	+	148645.i	−1.37451	+	1.15335i	−0.971195	+	0.238285i	$0.923415\pi$
$360$			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	−0.896777	−	0.442483i	$-0.854098\pi$
$367$	−175005.	+	63696.5i	−1.29932	+	0.472915i	−0.402548	+	0.915399i	$0.631875\pi$
$368$	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	0.167246	−	0.985915i	$-0.446513\pi$
$373$	−83889.0	−	48433.4i	−0.602959	−	0.348118i	−0.770205	+	0.637797i	$0.779846\pi$
$374$	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	$0.254088\pi$
$379$			205731.i			1.43226i	−0.697967	+	0.716130i	$0.745912\pi$
$380$	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	−0.0377575	−	0.999287i	$-0.512021\pi$
$383$	92926.8	−	255314.i	0.633496	−	1.74052i	0.671253	−	0.741228i	$-0.265756\pi$
$384$	−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	0.963685	−	0.267041i	$-0.0860460\pi$
$389$	131353.	+	110218.i	0.868043	+	0.728375i	−0.0956421	+	0.995416i	$0.530490\pi$
$390$	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	−0.359037	−	0.933323i	$-0.616895\pi$
$397$	78451.6	−	65828.7i	0.497761	−	0.417671i	0.856798	+	0.515652i	$0.172450\pi$
$398$		−	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	−0.967876	−	0.251428i	$-0.919100\pi$
$401$	−168425.	−	200721.i	−1.04741	−	1.24826i	−0.0795388	−	0.996832i	$-0.525345\pi$
$402$	−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	−0.933989	−	0.357303i	$-0.883696\pi$
$409$	−70246.1	+	83716.0i	−0.419928	+	0.500451i	0.514060	+	0.857754i	$0.328141\pi$
$410$	−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	0.504070	+	0.863663i	$0.331835\pi$
$421$	−77493.6	+	212912.i	−0.437222	+	1.20126i	−0.941292	+	0.337594i	$0.890387\pi$
$422$	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	0.922717	+	0.385479i	$0.125964\pi$
$431$	86129.1	+	236638.i	0.463656	+	1.27388i	−0.459061	+	0.888405i	$0.651814\pi$
$432$	72199.8	−	12730.8i	0.386873	−	0.0682162i
$433$	196032.	+	34565.8i	1.04557	+	0.184362i	0.669945	−	0.742411i	$-0.266318\pi$
$433$	196032.	+	34565.8i	1.04557	+	0.184362i	0.375623	+	0.926773i	$0.377429\pi$
$434$	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	0.483060	−	0.875588i	$-0.339525\pi$
$439$	−89250.7	−	106365.i	−0.463108	−	0.551911i	−0.946168	+	0.323677i	$0.895081\pi$
$440$	−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	−0.552418	−	0.833567i	$-0.686295\pi$
$443$	−86308.2	+	31413.6i	−0.439789	+	0.160070i	0.112629	+	0.993637i	$0.464073\pi$
$444$	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	−0.0456084	−	0.998959i	$-0.514523\pi$
$449$	−188202.	−	108658.i	−0.933537	−	0.538978i	−0.887928	+	0.459982i	$0.847856\pi$
$450$	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	−0.924772	−	0.380522i	$-0.875744\pi$
$461$	−39511.2	−	224079.i	−0.185917	−	1.05439i	0.738855	−	0.673864i	$-0.235367\pi$
$462$	−28179.7	+	10256.6i	−0.132024	+	0.0480527i
$463$	93072.0	−	161206.i	0.434167	−	0.752000i	−0.563060	−	0.826416i	$-0.690376\pi$
$463$	93072.0	−	161206.i	0.434167	−	0.752000i	0.997227	+	0.0744161i	$0.0237093\pi$
$464$	−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	0.930825	−	0.365464i	$-0.119090\pi$
$467$	32476.0	+	56250.0i	0.148912	+	0.257922i	−0.781914	+	0.623386i	$0.785756\pi$
$468$	−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	−0.793946	−	0.607989i	$-0.791976\pi$
$479$	36725.2	−	208279.i	0.160064	−	0.907766i	0.954009	−	0.299777i	$-0.0969124\pi$
$480$	−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	−0.118980	−	0.992897i	$-0.537962\pi$
$487$	−246263.	−	142180.i	−1.03834	−	0.599488i	−0.919364	+	0.393409i	$0.871296\pi$
$488$	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	0.951937	−	0.306293i	$-0.0990888\pi$
$491$	357832.	+	130240.i	1.48428	+	0.540234i	0.532345	+	0.846528i	$0.321311\pi$
$492$	−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	−0.998048	−	0.0624499i	$-0.980109\pi$
$499$	−20305.7	−	115160.i	−0.0815488	−	0.462486i	0.916499	−	0.400036i	$-0.131002\pi$
$500$	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	0.563670	−	0.826000i	$-0.309389\pi$
$503$	−38432.2	−	32248.5i	−0.151901	−	0.127460i	−0.715571	+	0.698540i	$0.753833\pi$
$504$	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	0.0373256	−	0.999303i	$-0.488116\pi$
$509$	−69791.6	−	12306.1i	−0.269382	−	0.0474992i	−0.306707	+	0.951804i	$0.599227\pi$
$510$	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	−0.719822	−	0.694158i	$-0.755777\pi$
$521$	−129905.	+	75000.6i	−0.478575	+	0.276305i	0.241247	+	0.970464i	$0.422443\pi$
$522$	502165.	+	421366.i	1.84292	+	1.54639i
$523$	195955.	−	233530.i	0.716394	−	0.853765i	−0.277881	−	0.960615i	$-0.589632\pi$
$523$	195955.	−	233530.i	0.716394	−	0.853765i	0.994275	+	0.106850i	$0.0340766\pi$
$524$	−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	0.352779	−	0.935707i	$-0.385237\pi$
$541$	−148522.	−	124625.i	−0.507453	−	0.425804i	−0.860232	+	0.509903i	$0.829681\pi$
$542$	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	−0.350764	−	0.936464i	$-0.614078\pi$
$547$	−299408.	−	52793.7i	−1.00066	−	0.176444i	−0.649900	+	0.760020i	$0.725189\pi$
$548$	−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	−0.314767	−	0.949169i	$-0.601927\pi$
$557$	16821.9	−	6122.67i	0.0542206	−	0.0197347i	0.368988	+	0.929434i	$0.379704\pi$
$558$	−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	0.914440	−	0.404721i	$-0.132631\pi$
$563$	323677.	+	186875.i	1.02116	+	0.589568i	0.106721	+	0.994289i	$0.465965\pi$
$564$	−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	$0.212365\pi$
$569$			400661.i			1.23752i	−0.785580	+	0.618760i	$0.787635\pi$
$570$	−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	0.210272	+	0.977643i	$0.432565\pi$
$577$	−246876.	+	427602.i	−0.741528	+	1.28436i	−0.951799	+	0.306721i	$0.900768\pi$
$578$	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	−0.889332	−	0.457262i	$-0.848830\pi$
$587$	−204484.	+	171582.i	−0.593448	+	0.497962i	0.295884	+	0.955224i	$0.404386\pi$
$588$			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	0.440368	+	0.897817i	$0.354848\pi$
$593$	−98642.5	+	559430.i	−0.280514	+	1.59087i	−0.720882	+	0.693058i	$0.756263\pi$
$594$	−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	−0.857115	−	0.515126i	$-0.827745\pi$
$599$	−72111.2	+	85938.8i	−0.200978	+	0.239517i	0.656136	+	0.754642i	$0.272190\pi$
$600$	−820696.	−	1.42149e6i	−2.27971	−	3.94857i
$601$	−398665.	−	230169.i	−1.10372	−	0.637233i	−0.166524	−	0.986037i	$-0.553254\pi$
$601$	−398665.	−	230169.i	−1.10372	−	0.637233i	−0.937196	+	0.348804i	$0.886588\pi$
$602$	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	$-0.802627\pi$
$607$		−	428202.i		−	1.16218i	0.813841	−	0.581088i	$-0.197373\pi$
$608$	−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	−0.986968	−	0.160915i	$-0.948556\pi$
$613$	−43047.2	−	244133.i	−0.114558	−	0.649689i	0.872411	−	0.488774i	$-0.162556\pi$
$614$	−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	0.346444	−	0.938071i	$-0.387389\pi$
$617$	−196898.	−	165217.i	−0.517216	−	0.433995i	−0.863660	+	0.504075i	$0.831833\pi$
$618$	1.17214e6	−	1.39690e6i	3.06903	−	3.65753i
$619$	44579.7	+	77214.3i	0.116347	+	0.201519i	0.918317	−	0.395845i	$-0.129548\pi$
$619$	44579.7	+	77214.3i	0.116347	+	0.201519i	−0.801970	+	0.597364i	$0.796215\pi$
$620$	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	0.921056	+	0.389430i	$0.127328\pi$
$631$	−30915.8	+	175332.i	−0.0776465	+	0.440355i	−0.998702	+	0.0509251i	$0.983783\pi$
$632$	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	−0.190748	−	0.981639i	$-0.561091\pi$
$641$	−14073.2	+	2481.49i	−0.0342514	+	0.00603944i	0.156496	+	0.987679i	$0.449980\pi$
$642$	−1.73292e6	−	305560.i	−4.20444	−	0.741356i
$643$	−687644.	−	250282.i	−1.66319	−	0.605351i	−0.672330	−	0.740252i	$-0.734706\pi$
$643$	−687644.	−	250282.i	−1.66319	−	0.605351i	−0.990859	+	0.134901i	$0.956929\pi$
$644$	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	−0.735354	−	0.677683i	$-0.762984\pi$
$653$	93474.8	−	161903.i	0.219214	−	0.379690i	0.954568	+	0.297994i	$0.0963174\pi$
$654$	−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	0.862299	−	0.506400i	$-0.169024\pi$
$659$	−53750.1	−	147677.i	−0.123768	−	0.340050i	−0.986067	+	0.166350i	$0.946802\pi$
$660$	−317126.	+	55917.9i	−0.728022	+	0.128370i
$661$	652968.	+	115136.i	1.49448	+	0.263516i	0.860346	−	0.509711i	$-0.170248\pi$
$661$	652968.	+	115136.i	1.49448	+	0.263516i	0.634129	+	0.773227i	$0.281359\pi$
$662$	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	−0.901439	−	0.432905i	$-0.857488\pi$
$673$	−442626.	+	255550.i	−0.977252	+	0.564217i	−0.0758125	+	0.997122i	$0.524155\pi$
$674$	−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	−0.165737	−	0.986170i	$-0.553000\pi$
$677$	−505379.	−	291780.i	−1.10265	−	0.636618i	−0.936917	+	0.349552i	$0.886334\pi$
$678$	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	$0.168299\pi$
$683$			470626.i			1.00887i	−0.863450	+	0.504434i	$0.831701\pi$
$684$	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	−0.913323	−	0.407236i	$-0.866493\pi$
$691$	−49650.9	+	85997.9i	−0.103985	+	0.180107i	0.809338	+	0.587343i	$0.199826\pi$
$692$	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	−0.968377	−	0.249492i	$-0.919736\pi$
$701$	−437756.	+	367321.i	−0.890833	+	0.747497i	0.0775444	+	0.996989i	$0.475292\pi$
$702$		−	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	−0.112812	−	0.993616i	$-0.535986\pi$
$709$	220905.	−	80402.8i	0.439453	−	0.159948i	0.552265	+	0.833668i	$0.313764\pi$
$710$	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	0.700247	−	0.713901i	$-0.253073\pi$
$719$	402082.	+	146346.i	0.777780	+	0.283089i	0.0775335	+	0.996990i	$0.475296\pi$
$720$	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	−0.852386	−	0.522913i	$-0.824845\pi$
$727$	−121695.	−	690166.i	−0.230252	−	1.30582i	0.622134	−	0.782911i	$-0.286266\pi$
$728$	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	0.687983	−	0.725727i	$-0.258496\pi$
$733$	−152862.	−	264765.i	−0.284506	−	0.492779i	−0.972489	+	0.232948i	$0.925163\pi$
$734$	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	−0.560771	−	0.827971i	$-0.689495\pi$
$739$	85874.1	−	72056.9i	0.157244	−	0.131943i	0.718015	+	0.696028i	$0.245051\pi$
$740$		−	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	0.640988	−	0.767551i	$-0.278525\pi$
$743$	−124878.	−	148824.i	−0.226208	−	0.269585i	−0.867196	+	0.497966i	$0.834080\pi$
$744$	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	−0.996751	−	0.0805404i	$-0.974335\pi$
$751$	−419814.	+	500315.i	−0.744351	+	0.887082i	0.252401	+	0.967623i	$0.418780\pi$
$752$	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	0.497974	−	0.867192i	$-0.334077\pi$
$757$	184536.	+	67165.5i	0.322024	+	0.117207i	−0.175950	+	0.984399i	$0.556300\pi$
$758$	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	0.997995	+	0.0632951i	$0.0201609\pi$
$769$	729520.	+	612140.i	1.23363	+	1.03514i	0.235634	+	0.971842i	$0.424284\pi$
$770$	−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	0.998536	−	0.0540916i	$-0.0172263\pi$
$773$	118815.	+	326441.i	0.198844	+	0.546318i	−0.799692	+	0.600410i	$0.795004\pi$
$774$	−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	−0.226795	−	0.973943i	$-0.572825\pi$
$787$	311708.	−	179965.i	0.503267	−	0.290561i	0.730062	+	0.683381i	$0.239491\pi$
$788$	−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	$0.0203321\pi$
$797$			81093.2i			0.127664i	−0.997961	+	0.0638319i	$0.979668\pi$
$798$	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	−0.996679	−	0.0814316i	$-0.974051\pi$
$809$	−372309.	−	644858.i	−0.568861	−	0.985297i	0.427818	−	0.903865i	$-0.359283\pi$
$810$	327102.	+	188852.i	0.498554	+	0.287841i
$811$	−160184.	−	440101.i	−0.243543	−	0.669130i	−0.999888	−	0.0149565i	$-0.995239\pi$
$811$	−160184.	−	440101.i	−0.243543	−	0.669130i	0.756345	−	0.654173i	$-0.226983\pi$
$812$	−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	−0.718685	−	0.695336i	$-0.755256\pi$
$821$	131085.	−	743422.i	0.194477	−	1.10293i	0.913162	−	0.407597i	$-0.133633\pi$
$822$	−456253.	−	2.58754e6i	−0.675246	−	3.82951i
$823$	−49041.1	+	17849.5i	−0.0724037	+	0.0263528i	−0.377968	−	0.925819i	$-0.623377\pi$
$823$	−49041.1	+	17849.5i	−0.0724037	+	0.0263528i	0.305564	+	0.952171i	$0.401155\pi$
$824$	−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	−0.620737	−	0.784019i	$-0.713167\pi$
$827$	177248.	−	211235.i	0.259161	−	0.308856i	0.879898	+	0.475163i	$0.157611\pi$
$828$	646681.	+	1.12008e6i	0.943255	+	1.63377i
$829$	−279320.	−	161265.i	−0.406437	−	0.234656i	0.282821	−	0.959173i	$-0.408730\pi$
$829$	−279320.	−	161265.i	−0.406437	−	0.234656i	−0.689258	+	0.724516i	$0.742063\pi$
$830$	−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	0.726347	+	0.687329i	$0.241217\pi$
$839$	−191378.	+	525805.i	−0.271874	+	0.746966i	−0.998220	+	0.0596378i	$0.981005\pi$
$840$	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	−0.733679	−	0.679496i	$-0.762198\pi$
$853$	−139634.	+	117167.i	−0.191908	+	0.161030i	0.541771	+	0.840526i	$0.317754\pi$
$854$			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	0.970359	−	0.241669i	$-0.0776949\pi$
$857$	414126.	+	493537.i	0.563860	+	0.671982i	−0.406499	+	0.913651i	$0.633250\pi$
$858$	329305.	−	904758.i	0.447325	−	1.22902i
$859$	−88618.4	+	502580.i	−0.120098	+	0.681112i	0.864000	+	0.503491i	$0.167951\pi$
$859$	−88618.4	+	502580.i	−0.120098	+	0.681112i	−0.984099	+	0.177621i	$0.943160\pi$
$860$	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	−0.865747	−	0.500483i	$-0.833156\pi$
$863$	−644366.	+	372025.i	−0.865189	+	0.499517i	0.000557497		1.00000i	$0.499823\pi$
$864$	−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	−0.107271	+	0.994230i	$0.534211\pi$
$877$	−510836.	+	1.40351e6i	−0.664175	+	1.82481i	−0.556904	+	0.830577i	$0.688011\pi$
$878$	−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	−0.186623	+	0.982432i	$0.559754\pi$
$881$	−732791.	+	1.26923e6i	−0.944122	+	1.63527i	−0.757499	+	0.652836i	$0.773579\pi$
$882$	−1.39216e6	+	803766.i	−1.78959	+	1.03322i
$883$	1.03723e6	+	870340.i	1.33031	+	1.11627i	0.984004	+	0.178145i	$0.0570095\pi$
$883$	1.03723e6	+	870340.i	1.33031	+	1.11627i	0.346309	+	0.938121i	$0.387435\pi$
$884$	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	0.805485	−	0.592616i	$-0.201905\pi$
$887$	−151436.	−	416067.i	−0.192478	−	0.528830i	−0.997964	+	0.0637859i	$0.979683\pi$
$888$	−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	−0.152280	−	0.988337i	$-0.548662\pi$
$907$	35090.0	−	6187.31i	0.0426549	−	0.00752121i	0.194935	+	0.980816i	$0.437550\pi$
$908$	−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	$0.0125567\pi$
$911$			65460.3i			0.0788754i	−0.999222	+	0.0394377i	$0.987443\pi$
$912$	−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	−0.895811	−	0.444436i	$-0.853404\pi$
$919$	−53218.2	+	92176.7i	−0.0630129	+	0.109142i	0.832798	+	0.553577i	$0.186738\pi$
$920$	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	−0.698573	−	0.715539i	$-0.746181\pi$
$929$	−99430.9	+	83432.4i	−0.115210	+	0.0966726i	0.583363	+	0.812212i	$0.301737\pi$
$930$			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	−0.138016	−	0.990430i	$-0.544072\pi$
$937$	344949.	−	125551.i	0.392894	−	0.143002i	0.530910	+	0.847428i	$0.321850\pi$
$938$	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	0.0110754	−	0.999939i	$-0.496475\pi$
$941$	880079.	−	1.04884e6i	0.993899	−	1.18448i	0.982824	−	0.184545i	$-0.0590810\pi$
$942$	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	0.609541	−	0.792755i	$-0.291354\pi$
$947$	508404.	+	185044.i	0.566904	+	0.206336i	−0.0426374	+	0.999091i	$0.513576\pi$
$948$	−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	−0.629321	−	0.777145i	$-0.716667\pi$
$953$	319968.	−	879104.i	0.352306	−	0.967953i	0.981627	−	0.190808i	$-0.0611107\pi$
$954$	−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	−0.188452	−	0.982082i	$-0.560347\pi$
$967$	697564.	−	585325.i	0.745986	−	0.625957i	0.934438	+	0.356126i	$0.115902\pi$
$968$		−	2.20737e6i		−	2.35572i
$969$	439917.	−	817190.i	0.468515	−	0.870313i
$970$	301905.			0.320868
$971$	870573.	+	1.03751e6i	0.923350	+	1.10041i	0.994686	+	0.102954i	$0.0328294\pi$
$971$	870573.	+	1.03751e6i	0.923350	+	1.10041i	−0.0713357	+	0.997452i	$0.522726\pi$
$972$	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	−0.742727	−	0.669595i	$-0.766468\pi$
$977$	−509913.	+	294398.i	−0.534204	+	0.308423i	0.208523	+	0.978017i	$0.433134\pi$
$978$	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	−0.842005	−	0.539470i	$-0.818625\pi$
$983$	−1.39988e6	+	246837.i	−1.44872	+	0.255449i	−0.606716	+	0.794918i	$0.707514\pi$
$984$	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	−0.982038	−	0.188685i	$-0.939578\pi$
$991$	−106525.	+	292676.i	−0.108469	+	0.298016i	0.873569	+	0.486701i	$0.161800\pi$
$992$	−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	0.0383772	−	0.999263i	$-0.487781\pi$
$997$	−933415.	−	783228.i	−0.939041	−	0.787949i	−0.977418	+	0.211314i	$0.932226\pi$
$998$	−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.13.1	yes	36
19.3	odd	18	inner	19.5.f.a.3.1	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.5.f.a.3.1	✓	36	19.3	odd	18	inner
19.5.f.a.13.1	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 19 \)
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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