LMFDB - Embedded newform 124.5.l.a.35.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [124,5,Mod(35,124)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(124, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([5, 6]))

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

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

chi := DirichletCharacter("124.35");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 124 = 2^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	124.l (of order $10$, degree $4$, 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:	$12.8178754224$
Analytic rank:	$0$
Dimension:	$248$
Relative dimension:	$62$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			35.15
Character	$\chi$	$=$	124.35
Dual form			124.5.l.a.39.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.10903 - 2.51673i) q^{2} +(-3.93487 - 1.27852i) q^{3} +(3.33209 + 15.6492i) q^{4} -23.8871 q^{5} +(9.01594 + 13.8780i) q^{6} +(-31.1843 - 42.9214i) q^{7} +(29.0253 - 57.0397i) q^{8} +(-51.6817 - 37.5490i) q^{9} +O(q^{10})$	\(q+(-3.10903 - 2.51673i) q^{2} +(-3.93487 - 1.27852i) q^{3} +(3.33209 + 15.6492i) q^{4} -23.8871 q^{5} +(9.01594 + 13.8780i) q^{6} +(-31.1843 - 42.9214i) q^{7} +(29.0253 - 57.0397i) q^{8} +(-51.6817 - 37.5490i) q^{9} +(74.2656 + 60.1175i) q^{10} +(-27.9360 - 38.4506i) q^{11} +(6.89640 - 65.8377i) q^{12} +(-62.6726 + 192.886i) q^{13} +(-11.0692 + 211.926i) q^{14} +(93.9927 + 30.5401i) q^{15} +(-233.794 + 104.289i) q^{16} +(245.519 + 178.380i) q^{17} +(66.1791 + 246.810i) q^{18} +(70.2816 - 22.8359i) q^{19} +(-79.5941 - 373.814i) q^{20} +(67.8303 + 208.760i) q^{21} +(-9.91619 + 189.851i) q^{22} +(266.727 - 367.118i) q^{23} +(-187.137 + 187.335i) q^{24} -54.4065 q^{25} +(680.294 - 441.959i) q^{26} +(352.337 + 484.950i) q^{27} +(567.777 - 631.027i) q^{28} +(54.8365 + 168.769i) q^{29} +(-215.365 - 331.505i) q^{30} +(955.887 - 98.9979i) q^{31} +(989.341 + 264.161i) q^{32} +(60.7648 + 187.015i) q^{33} +(-314.390 - 1172.49i) q^{34} +(744.901 + 1025.27i) q^{35} +(415.403 - 933.894i) q^{36} +504.705 q^{37} +(-275.979 - 105.883i) q^{38} +(493.217 - 678.855i) q^{39} +(-693.330 + 1362.51i) q^{40} +(539.572 + 1660.63i) q^{41} +(314.508 - 819.752i) q^{42} +(-313.499 + 101.862i) q^{43} +(508.635 - 565.296i) q^{44} +(1234.53 + 896.936i) q^{45} +(-1753.20 + 470.099i) q^{46} +(417.447 + 135.637i) q^{47} +(1053.29 - 111.454i) q^{48} +(-127.843 + 393.459i) q^{49} +(169.151 + 136.927i) q^{50} +(-738.023 - 1015.80i) q^{51} +(-3227.35 - 338.060i) q^{52} +(85.4576 + 62.0886i) q^{53} +(125.066 - 2394.46i) q^{54} +(667.309 + 918.473i) q^{55} +(-3353.36 + 532.935i) q^{56} -305.745 q^{57} +(254.260 - 662.717i) q^{58} +(3073.78 + 998.731i) q^{59} +(-164.735 + 1572.67i) q^{60} -7059.90 q^{61} +(-3221.03 - 2097.93i) q^{62} +3389.19i q^{63} +(-2411.07 - 3311.19i) q^{64} +(1497.07 - 4607.50i) q^{65} +(281.747 - 734.363i) q^{66} +4964.11i q^{67} +(-1973.41 + 4436.55i) q^{68} +(-1518.91 + 1103.55i) q^{69} +(264.411 - 5062.31i) q^{70} +(-172.545 + 237.488i) q^{71} +(-3641.86 + 1858.04i) q^{72} +(-3661.55 + 2660.27i) q^{73} +(-1569.14 - 1270.21i) q^{74} +(214.083 + 69.5597i) q^{75} +(591.548 + 1023.76i) q^{76} +(-779.191 + 2398.10i) q^{77} +(-3241.93 + 869.283i) q^{78} +(5124.44 - 7053.19i) q^{79} +(5584.67 - 2491.17i) q^{80} +(832.611 + 2562.51i) q^{81} +(2501.83 - 6520.91i) q^{82} +(-614.826 + 199.769i) q^{83} +(-3040.91 + 1757.10i) q^{84} +(-5864.73 - 4260.97i) q^{85} +(1231.04 + 472.302i) q^{86} -734.196i q^{87} +(-3004.06 + 477.422i) q^{88} +(2438.41 - 1771.61i) q^{89} +(-1580.83 - 5895.58i) q^{90} +(10233.4 - 3325.02i) q^{91} +(6633.86 + 2950.79i) q^{92} +(-3887.87 - 832.575i) q^{93} +(-956.491 - 1472.30i) q^{94} +(-1678.82 + 545.483i) q^{95} +(-3555.20 - 2304.33i) q^{96} +(-7765.61 + 5642.05i) q^{97} +(1387.70 - 901.529i) q^{98} +3036.16i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 248 q - 3 q^{2} - 31 q^{4} - 16 q^{5} - 10 q^{6} - 237 q^{8} + 1560 q^{9}+O(q^{10}) $ 248 * q - 3 * q^2 - 31 * q^4 - 16 * q^5 - 10 * q^6 - 237 * q^8 + 1560 * q^9	\( 248 q - 3 q^{2} - 31 q^{4} - 16 q^{5} - 10 q^{6} - 237 q^{8} + 1560 q^{9} - 250 q^{10} - 210 q^{12} + 346 q^{13} + 226 q^{14} + 73 q^{16} - 6 q^{17} + 818 q^{18} - 975 q^{20} + 102 q^{21} + 1540 q^{22} + 1023 q^{24} + 26248 q^{25} - 360 q^{26} + 160 q^{28} - 6 q^{29} - 4022 q^{30} + 6862 q^{32} + 1110 q^{33} + 3067 q^{34} - 4568 q^{36} - 2096 q^{37} + 5050 q^{38} - 3206 q^{40} - 6 q^{41} - 3884 q^{42} - 5660 q^{44} - 10272 q^{45} + 3185 q^{46} - 16516 q^{48} + 12392 q^{49} - 7878 q^{50} - 5935 q^{52} - 8454 q^{53} + 1362 q^{54} + 39536 q^{56} + 10892 q^{57} - 1105 q^{58} - 1267 q^{60} + 11696 q^{61} - 21020 q^{62} - 24493 q^{64} - 3756 q^{65} - 33182 q^{66} - 31014 q^{68} + 31734 q^{69} + 4205 q^{70} - 59598 q^{72} - 16646 q^{73} - 7683 q^{74} - 16019 q^{76} - 16618 q^{77} - 11625 q^{78} + 63150 q^{80} - 33864 q^{81} - 25974 q^{82} - 43055 q^{84} + 23956 q^{85} - 26357 q^{86} - 34700 q^{88} + 4170 q^{89} + 20102 q^{90} - 22738 q^{92} + 35990 q^{93} - 25646 q^{94} + 50490 q^{96} - 6614 q^{97} - 49748 q^{98}+O(q^{100}) \) 248 * q - 3 * q^2 - 31 * q^4 - 16 * q^5 - 10 * q^6 - 237 * q^8 + 1560 * q^9 - 250 * q^10 - 210 * q^12 + 346 * q^13 + 226 * q^14 + 73 * q^16 - 6 * q^17 + 818 * q^18 - 975 * q^20 + 102 * q^21 + 1540 * q^22 + 1023 * q^24 + 26248 * q^25 - 360 * q^26 + 160 * q^28 - 6 * q^29 - 4022 * q^30 + 6862 * q^32 + 1110 * q^33 + 3067 * q^34 - 4568 * q^36 - 2096 * q^37 + 5050 * q^38 - 3206 * q^40 - 6 * q^41 - 3884 * q^42 - 5660 * q^44 - 10272 * q^45 + 3185 * q^46 - 16516 * q^48 + 12392 * q^49 - 7878 * q^50 - 5935 * q^52 - 8454 * q^53 + 1362 * q^54 + 39536 * q^56 + 10892 * q^57 - 1105 * q^58 - 1267 * q^60 + 11696 * q^61 - 21020 * q^62 - 24493 * q^64 - 3756 * q^65 - 33182 * q^66 - 31014 * q^68 + 31734 * q^69 + 4205 * q^70 - 59598 * q^72 - 16646 * q^73 - 7683 * q^74 - 16019 * q^76 - 16618 * q^77 - 11625 * q^78 + 63150 * q^80 - 33864 * q^81 - 25974 * q^82 - 43055 * q^84 + 23956 * q^85 - 26357 * q^86 - 34700 * q^88 + 4170 * q^89 + 20102 * q^90 - 22738 * q^92 + 35990 * q^93 - 25646 * q^94 + 50490 * q^96 - 6614 * q^97 - 49748 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/124\mathbb{Z}\right)^\times$.

$n$	$63$	$65$
$\chi(n)$	$-1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−3.10903	−	2.51673i	−0.777257	−	0.629184i
$2$	−3.10903	−	2.51673i	−0.777257	−	0.629184i
$3$	−3.93487	−	1.27852i	−0.437208	−	0.142058i	0.0821390	−	0.996621i	$-0.473825\pi$
$3$	−3.93487	−	1.27852i	−0.437208	−	0.142058i	−0.519347	+	0.854563i	$0.673825\pi$
$4$	3.33209	+	15.6492i	0.208256	+	0.978074i
$5$	−23.8871			−0.955484			−0.477742	−	0.878500i	$-0.658545\pi$
$5$	−23.8871			−0.955484			−0.477742	+	0.878500i	$0.658545\pi$
$6$	9.01594	+	13.8780i	0.250443	+	0.385499i
$7$	−31.1843	−	42.9214i	−0.636413	−	0.875948i	0.362005	−	0.932176i	$-0.382092\pi$
$7$	−31.1843	−	42.9214i	−0.636413	−	0.875948i	−0.998418	+	0.0562286i	$0.982092\pi$
$8$	29.0253	−	57.0397i	0.453520	−	0.891246i
$9$	−51.6817	−	37.5490i	−0.638046	−	0.463568i
$10$	74.2656	+	60.1175i	0.742656	+	0.601175i
$11$	−27.9360	−	38.4506i	−0.230876	−	0.317773i	0.677823	−	0.735225i	$-0.262923\pi$
$11$	−27.9360	−	38.4506i	−0.230876	−	0.317773i	−0.908699	+	0.417451i	$0.862923\pi$
$12$	6.89640	−	65.8377i	0.0478917	−	0.457207i
$13$	−62.6726	+	192.886i	−0.370844	+	1.14134i	0.575397	+	0.817875i	$0.304848\pi$
$13$	−62.6726	+	192.886i	−0.370844	+	1.14134i	−0.946240	+	0.323465i	$0.895152\pi$
$14$	−11.0692	+	211.926i	−0.0564755	+	1.08126i
$15$	93.9927	+	30.5401i	0.417745	+	0.135734i
$16$	−233.794	+	104.289i	−0.913259	+	0.407379i
$17$	245.519	+	178.380i	0.849545	+	0.617231i	0.925021	−	0.379917i	$-0.124047\pi$
$17$	245.519	+	178.380i	0.849545	+	0.617231i	−0.0754753	+	0.997148i	$0.524047\pi$
$18$	66.1791	+	246.810i	0.204256	+	0.761759i
$19$	70.2816	−	22.8359i	0.194686	−	0.0632573i	−0.210051	−	0.977690i	$-0.567363\pi$
$19$	70.2816	−	22.8359i	0.194686	−	0.0632573i	0.404737	+	0.914433i	$0.367363\pi$
$20$	−79.5941	−	373.814i	−0.198985	−	0.934534i
$21$	67.8303	+	208.760i	0.153810	+	0.473379i
$22$	−9.91619	+	189.851i	−0.0204880	+	0.392255i
$23$	266.727	−	367.118i	0.504210	−	0.693986i	−0.478720	−	0.877968i	$-0.658899\pi$
$23$	266.727	−	367.118i	0.504210	−	0.693986i	0.982930	+	0.183982i	$0.0588989\pi$
$24$	−187.137	+	187.335i	−0.324891	+	0.325234i
$25$	−54.4065			−0.0870504
$26$	680.294	−	441.959i	1.00635	−	0.653785i
$27$	352.337	+	484.950i	0.483315	+	0.665227i
$28$	567.777	−	631.027i	0.724205	−	0.804881i
$29$	54.8365	+	168.769i	0.0652039	+	0.200677i	0.978351	−	0.206954i	$-0.0663550\pi$
$29$	54.8365	+	168.769i	0.0652039	+	0.200677i	−0.913147	+	0.407631i	$0.866355\pi$
$30$	−215.365	−	331.505i	−0.239294	−	0.368339i
$31$	955.887	−	98.9979i	0.994680	−	0.103015i
$31$	955.887	−	98.9979i	0.994680	−	0.103015i
$32$	989.341	+	264.161i	0.966153	+	0.257969i
$33$	60.7648	+	187.015i	0.0557987	+	0.171731i
$34$	−314.390	−	1172.49i	−0.271963	−	1.01427i
$35$	744.901	+	1025.27i	0.608083	+	0.836954i
$36$	415.403	−	933.894i	0.320527	−	0.720597i
$37$	504.705			0.368667			0.184333	−	0.982864i	$-0.440987\pi$
$37$	504.705			0.368667			0.184333	+	0.982864i	$0.440987\pi$
$38$	−275.979	−	105.883i	−0.191121	−	0.0733260i
$39$	493.217	−	678.855i	0.324272	−	0.446322i
$40$	−693.330	+	1362.51i	−0.433331	+	0.851571i
$41$	539.572	+	1660.63i	0.320983	+	0.987883i	0.973221	+	0.229870i	$0.0738300\pi$
$41$	539.572	+	1660.63i	0.320983	+	0.987883i	−0.652239	+	0.758014i	$0.726170\pi$
$42$	314.508	−	819.752i	0.178292	−	0.464712i
$43$	−313.499	+	101.862i	−0.169550	+	0.0550903i	−0.392562	−	0.919726i	$-0.628411\pi$
$43$	−313.499	+	101.862i	−0.169550	+	0.0550903i	0.223012	+	0.974816i	$0.428411\pi$
$44$	508.635	−	565.296i	0.262725	−	0.291992i
$45$	1234.53	+	896.936i	0.609643	+	0.442932i
$46$	−1753.20	+	470.099i	−0.828545	+	0.222164i
$47$	417.447	+	135.637i	0.188975	+	0.0614018i	0.401976	−	0.915650i	$-0.368324\pi$
$47$	417.447	+	135.637i	0.188975	+	0.0614018i	−0.213000	+	0.977052i	$0.568324\pi$
$48$	1053.29	−	111.454i	0.457156	−	0.0483743i
$49$	−127.843	+	393.459i	−0.0532456	+	0.163873i
$50$	169.151	+	136.927i	0.0676605	+	0.0547707i
$51$	−738.023	−	1015.80i	−0.283746	−	0.390543i
$52$	−3227.35	−	338.060i	−1.19355	−	0.125022i
$53$	85.4576	+	62.0886i	0.0304228	+	0.0221035i	0.602893	−	0.797822i	$-0.294015\pi$
$53$	85.4576	+	62.0886i	0.0304228	+	0.0221035i	−0.572470	+	0.819926i	$0.694015\pi$
$54$	125.066	−	2394.46i	0.0428896	−	0.821146i
$55$	667.309	+	918.473i	0.220598	+	0.303627i
$56$	−3353.36	+	532.935i	−1.06931	+	0.169941i
$57$	−305.745			−0.0941044
$58$	254.260	−	662.717i	0.0755825	−	0.197003i
$59$	3073.78	+	998.731i	0.883015	+	0.286909i	0.715209	−	0.698911i	$-0.246332\pi$
$59$	3073.78	+	998.731i	0.883015	+	0.286909i	0.167807	+	0.985820i	$0.446332\pi$
$60$	−164.735	+	1572.67i	−0.0457597	+	0.436854i
$61$	−7059.90			−1.89731			−0.948657	−	0.316307i	$-0.897557\pi$
$61$	−7059.90			−1.89731			−0.948657	+	0.316307i	$0.897557\pi$
$62$	−3221.03	−	2097.93i	−0.837937	−	0.545767i
$63$			3389.19i			0.853916i
$64$	−2411.07	−	3311.19i	−0.588639	−	0.808396i
$65$	1497.07	−	4607.50i	0.354335	−	1.09053i
$66$	281.747	−	734.363i	0.0646803	−	0.168587i
$67$			4964.11i			1.10584i	0.833234	+	0.552920i	$0.186486\pi$
$67$			4964.11i			1.10584i	−0.833234	+	0.552920i	$0.813514\pi$
$68$	−1973.41	+	4436.55i	−0.426775	+	0.959461i
$69$	−1518.91	+	1103.55i	−0.319031	+	0.231789i
$70$	264.411	−	5062.31i	0.0539615	−	1.03312i
$71$	−172.545	+	237.488i	−0.0342284	+	0.0471113i	−0.825788	−	0.563980i	$-0.809269\pi$
$71$	−172.545	+	237.488i	−0.0342284	+	0.0471113i	0.791560	+	0.611092i	$0.209269\pi$
$72$	−3641.86	+	1858.04i	−0.702520	+	0.358419i
$73$	−3661.55	+	2660.27i	−0.687099	+	0.499207i	−0.875705	−	0.482846i	$-0.839603\pi$
$73$	−3661.55	+	2660.27i	−0.687099	+	0.499207i	0.188606	+	0.982053i	$0.439603\pi$
$74$	−1569.14	−	1270.21i	−0.286549	−	0.231959i
$75$	214.083	+	69.5597i	0.0380591	+	0.0123662i
$76$	591.548	+	1023.76i	0.102415	+	0.177244i
$77$	−779.191	+	2398.10i	−0.131420	+	0.404470i
$78$	−3241.93	+	869.283i	−0.532861	+	0.142880i
$79$	5124.44	−	7053.19i	0.821093	−	1.13014i	−0.168423	−	0.985715i	$-0.553867\pi$
$79$	5124.44	−	7053.19i	0.821093	−	1.13014i	0.989516	−	0.144423i	$-0.0461326\pi$
$80$	5584.67	−	2491.17i	0.872604	−	0.389245i
$81$	832.611	+	2562.51i	0.126903	+	0.390567i
$82$	2501.83	−	6520.91i	0.372074	−	0.969796i
$83$	−614.826	+	199.769i	−0.0892475	+	0.0289983i	−0.353300	−	0.935510i	$-0.614941\pi$
$83$	−614.826	+	199.769i	−0.0892475	+	0.0289983i	0.264053	+	0.964508i	$0.414941\pi$
$84$	−3040.91	+	1757.10i	−0.430968	+	0.249022i
$85$	−5864.73	−	4260.97i	−0.811727	−	0.589754i
$86$	1231.04	+	472.302i	0.166446	+	0.0638591i
$87$		−	734.196i		−	0.0970004i
$88$	−3004.06	+	477.422i	−0.387921	+	0.0616506i
$89$	2438.41	−	1771.61i	0.307841	−	0.223659i	−0.423129	−	0.906070i	$-0.639068\pi$
$89$	2438.41	−	1771.61i	0.307841	−	0.223659i	0.730969	+	0.682410i	$0.239068\pi$
$90$	−1580.83	−	5895.58i	−0.195164	−	0.727849i
$91$	10233.4	−	3325.02i	1.23576	−	0.401524i
$92$	6633.86	+	2950.79i	0.783774	+	0.348628i
$93$	−3887.87	−	832.575i	−0.449516	−	0.0962626i
$94$	−956.491	−	1472.30i	−0.108249	−	0.166625i
$95$	−1678.82	+	545.483i	−0.186019	+	0.0604413i
$96$	−3555.20	−	2304.33i	−0.385764	−	0.250036i
$97$	−7765.61	+	5642.05i	−0.825339	+	0.599644i	−0.918237	−	0.396032i	$-0.870387\pi$
$97$	−7765.61	+	5642.05i	−0.825339	+	0.599644i	0.0928980	+	0.995676i	$0.470387\pi$
$98$	1387.70	−	901.529i	0.144492	−	0.0938702i
$99$			3036.16i			0.309781i
$100$	−181.287	−	851.417i	−0.0181287	−	0.0851417i
$101$	9964.21	+	7239.42i	0.976788	+	0.709678i	0.956988	−	0.290126i	$-0.0936973\pi$
$101$	9964.21	+	7239.42i	0.976788	+	0.709678i	0.0197993	+	0.999804i	$0.493697\pi$
$102$	−261.970	+	5015.56i	−0.0251797	+	0.482080i
$103$	−18435.8	+	5990.14i	−1.73775	+	0.564629i	−0.994533	−	0.104424i	$-0.966700\pi$
$103$	−18435.8	+	5990.14i	−1.73775	+	0.564629i	−0.743215	+	0.669053i	$0.766700\pi$
$104$	9183.10	+	9173.41i	0.849029	+	0.848133i
$105$	−1620.27	−	4986.67i	−0.146963	−	0.452306i
$106$	−109.430	−	408.109i	−0.00973919	−	0.0363216i
$107$	−662.332	+	911.622i	−0.0578506	+	0.0796246i	−0.836962	−	0.547261i	$-0.815671\pi$
$107$	−662.332	+	911.622i	−0.0578506	+	0.0796246i	0.779111	+	0.626885i	$0.215671\pi$
$108$	−6415.06	+	7129.69i	−0.549988	+	0.611256i
$109$	115.008	−	353.958i	0.00967998	−	0.0297919i	−0.946100	−	0.323875i	$-0.895014\pi$
$109$	115.008	−	353.958i	0.00967998	−	0.0297919i	0.955780	+	0.294083i	$0.0950143\pi$
$110$	236.869	−	4535.00i	0.0195760	−	0.374793i
$111$	−1985.95	−	645.274i	−0.161184	−	0.0523719i
$112$	11766.9	+	6782.61i	0.938053	+	0.540705i
$113$	18433.4	−	13392.6i	1.44360	−	1.04884i	0.456328	−	0.889811i	$-0.349164\pi$
$113$	18433.4	−	13392.6i	1.44360	−	1.04884i	0.987274	−	0.159027i	$-0.0508358\pi$
$114$	950.570	+	769.480i	0.0731433	+	0.0592090i
$115$	−6371.34	+	8769.39i	−0.481765	+	0.663092i
$116$	−2458.38	+	1420.50i	−0.182698	+	0.105566i
$117$	10481.7	−	7615.41i	0.765703	−	0.556316i
$118$	−7042.91	−	10841.0i	−0.505811	−	0.778581i
$119$		−	16100.6i		−	1.13697i
$120$	4470.17	−	4474.89i	0.310428	−	0.310756i
$121$	3826.29	−	11776.1i	0.261341	−	0.804324i
$122$	21949.4	+	17767.9i	1.47470	+	1.19376i
$123$		−	7224.23i		−	0.477509i
$124$	4734.34	+	14629.0i	0.307905	+	0.951417i
$125$	16229.1			1.03866
$126$	8529.70	−	10537.1i	0.537270	−	0.663712i
$127$	−14161.1	−	4601.24i	−0.877993	−	0.285277i	−0.164869	−	0.986315i	$-0.552720\pi$
$127$	−14161.1	−	4601.24i	−0.877993	−	0.285277i	−0.713124	+	0.701038i	$0.752720\pi$
$128$	−837.322	+	16362.6i	−0.0511061	+	0.998693i
$129$	1363.81			0.0819548
$130$	−16250.3	+	10557.1i	−0.961554	+	0.624681i
$131$	−1170.38	−	1610.89i	−0.0682001	−	0.0938694i	0.773554	−	0.633730i	$-0.218477\pi$
$131$	−1170.38	−	1610.89i	−0.0682001	−	0.0938694i	−0.841754	+	0.539861i	$0.818477\pi$
$132$	−2724.16	+	1574.07i	−0.156345	+	0.0903392i
$133$	−3171.83	−	2304.47i	−0.179311	−	0.130277i
$134$	12493.4	−	15433.6i	0.695776	−	0.859521i
$135$	−8416.31	−	11584.1i	−0.461800	−	0.635613i
$136$	17301.0	−	8826.80i	0.935390	−	0.477227i
$137$	−11392.2	+	35061.5i	−0.606967	+	1.86805i	−0.124309	+	0.992244i	$0.539671\pi$
$137$	−11392.2	+	35061.5i	−0.606967	+	1.86805i	−0.482658	+	0.875809i	$0.660329\pi$
$138$	7499.66	+	391.717i	0.393807	+	0.0205691i
$139$	34357.5	+	11163.4i	1.77825	+	0.577788i	0.998814	−	0.0486969i	$-0.0155069\pi$
$139$	34357.5	+	11163.4i	1.77825	+	0.577788i	0.779434	+	0.626485i	$0.215507\pi$
$140$	−13562.5	+	15073.4i	−0.691967	+	0.769051i
$141$	−1469.19	−	1067.43i	−0.0738990	−	0.0536908i
$142$	1134.14	−	304.107i	0.0562459	−	0.0150817i
$143$	9167.41	−	2978.67i	0.448306	−	0.145663i
$144$	15998.9	+	3388.89i	0.771549	+	0.163430i
$145$	−1309.88	−	4031.41i	−0.0623013	−	0.191744i
$146$	18079.1	+	944.294i	0.848145	+	0.0442998i
$147$	1006.09	−	1384.76i	0.0465588	−	0.0640827i
$148$	1681.72	+	7898.22i	0.0767770	+	0.360584i
$149$	19413.5			0.874445			0.437222	−	0.899353i	$-0.355962\pi$
$149$	19413.5			0.874445			0.437222	+	0.899353i	$0.355962\pi$
$150$	−490.525	−	755.052i	−0.0218011	−	0.0335579i
$151$	−15994.4	−	22014.4i	−0.701477	−	0.965501i	−0.999939	−	0.0110788i	$-0.996473\pi$
$151$	−15994.4	−	22014.4i	−0.701477	−	0.965501i	0.298461	−	0.954422i	$-0.403527\pi$
$152$	737.391	−	4671.66i	0.0319162	−	0.202201i
$153$	−5990.85	−	18438.0i	−0.255921	−	0.787644i
$154$	8457.92	−	5494.75i	0.356633	−	0.231690i
$155$	−22833.4	+	2364.77i	−0.950401	+	0.0984296i
$156$	12267.0	+	5456.44i	0.504067	+	0.224213i
$157$	9236.27	+	28426.3i	0.374712	+	1.15324i	0.943673	+	0.330880i	$0.107346\pi$
$157$	9236.27	+	28426.3i	0.374712	+	1.15324i	−0.568961	+	0.822365i	$0.692654\pi$
$158$	−33683.0	+	9031.70i	−1.34926	+	0.361789i
$159$	−256.884	−	353.570i	−0.0101611	−	0.0139856i
$160$	−23632.5	−	6310.03i	−0.923144	−	0.246485i
$161$	−24074.9			−0.928781
$162$	3860.55	−	10062.4i	0.147102	−	0.383416i
$163$	−18375.8	+	25292.1i	−0.691625	+	0.951940i	0.308375	+	0.951265i	$0.400215\pi$
$163$	−18375.8	+	25292.1i	−0.691625	+	0.951940i	−1.00000		0.000674917i	$0.999785\pi$
$164$	−24189.6	+	13977.2i	−0.899377	+	0.519678i
$165$	−1451.49	−	4467.24i	−0.0533148	−	0.164086i
$166$	2414.28	+	926.267i	0.0876135	+	0.0336140i
$167$	−19931.9	+	6476.26i	−0.714686	+	0.232216i	−0.643718	−	0.765263i	$-0.722609\pi$
$167$	−19931.9	+	6476.26i	−0.714686	+	0.232216i	−0.0709685	+	0.997479i	$0.522609\pi$
$168$	13876.4	+	2190.30i	0.491653	+	0.0776042i
$169$	−10171.0	−	7389.63i	−0.356113	−	0.258731i
$170$	7509.85	+	28007.4i	0.259857	+	0.969116i
$171$	−4489.74	−	1458.80i	−0.153543	−	0.0498890i
$172$	−2638.66	−	4566.59i	−0.0891922	−	0.154360i
$173$	−4027.61	+	12395.7i	−0.134572	+	0.414170i	−0.995523	−	0.0945174i	$-0.969869\pi$
$173$	−4027.61	+	12395.7i	−0.134572	+	0.414170i	0.860951	+	0.508688i	$0.169869\pi$
$174$	−1847.78	+	2282.63i	−0.0610310	+	0.0753942i
$175$	1696.63	+	2335.20i	0.0554000	+	0.0762516i
$176$	10541.2	+	6076.11i	0.340304	+	0.196155i
$177$	−10818.0	−	7859.76i	−0.345304	−	0.250878i
$178$	−12039.7	−	628.852i	−0.379994	−	0.0198476i
$179$	−20880.2	−	28739.1i	−0.651671	−	0.896948i	0.347499	−	0.937680i	$-0.387031\pi$
$179$	−20880.2	−	28739.1i	−0.651671	−	0.896948i	−0.999170	+	0.0407322i	$0.987031\pi$
$180$	−9922.77	+	22308.0i	−0.306258	+	0.688519i
$181$	19389.4			0.591844			0.295922	−	0.955212i	$-0.404373\pi$
$181$	19389.4			0.591844			0.295922	+	0.955212i	$0.404373\pi$
$182$	−40184.0	−	15417.1i	−1.21314	−	0.465435i
$183$	27779.8	+	9026.22i	0.829521	+	0.269528i
$184$	−13198.5	−	25869.8i	−0.389842	−	0.764112i
$185$	−12055.9			−0.352255
$186$	9992.11	+	12373.2i	0.288823	+	0.357649i
$187$		−	14423.5i		−	0.412467i
$188$	−731.632	+	6984.65i	−0.0207003	+	0.197619i
$189$	9827.40	−	30245.6i	0.275115	−	0.846718i
$190$	6592.34	+	2529.23i	0.182613	+	0.0700618i
$191$		−	17124.7i		−	0.469414i	−0.972066	−	0.234707i	$-0.924587\pi$
$191$		−	17124.7i		−	0.469414i	0.972066	−	0.234707i	$-0.0754131\pi$
$192$	5253.82	+	16111.7i	0.142519	+	0.437058i
$193$	22649.4	−	16455.8i	0.608055	−	0.441778i	−0.240674	−	0.970606i	$-0.577368\pi$
$193$	22649.4	−	16455.8i	0.608055	−	0.441778i	0.848729	+	0.528828i	$0.177368\pi$
$194$	38343.0	+	2002.71i	1.01879	+	0.0532126i
$195$	−11781.5	+	16215.9i	−0.309836	+	0.426453i
$196$	−6583.30	−	689.591i	−0.171369	−	0.0179506i
$197$	16637.8	−	12088.1i	0.428710	−	0.311476i	−0.352423	−	0.935841i	$-0.614642\pi$
$197$	16637.8	−	12088.1i	0.428710	−	0.311476i	0.781133	+	0.624365i	$0.214642\pi$
$198$	7641.21	−	9439.50i	0.194909	−	0.240779i
$199$	36219.5	+	11768.4i	0.914611	+	0.297175i	0.728254	−	0.685307i	$-0.240332\pi$
$199$	36219.5	+	11768.4i	0.914611	+	0.297175i	0.186357	+	0.982482i	$0.440332\pi$
$200$	−1579.16	+	3103.33i	−0.0394791	+	0.0775833i
$201$	6346.71	−	19533.2i	0.157093	−	0.483482i
$202$	−12759.3	−	47584.8i	−0.312697	−	1.16618i
$203$	5533.79	−	7616.61i	0.134286	−	0.184829i
$204$	13437.3	−	14934.2i	0.322888	−	0.358857i
$205$	−12888.8	−	39667.7i	−0.306694	−	0.943907i
$206$	72392.9	+	27774.4i	1.70593	+	0.654501i
$207$	−27569.8	+	8957.99i	−0.643419	+	0.209059i
$208$	−5463.46	−	51631.8i	−0.126282	−	1.19341i
$209$	−2841.44	−	2064.42i	−0.0650497	−	0.0472614i
$210$	−7512.68	+	19581.5i	−0.170355	+	0.444025i
$211$			48934.0i			1.09912i	0.835454	+	0.549560i	$0.185205\pi$
$211$			48934.0i			1.09912i	−0.835454	+	0.549560i	$0.814795\pi$
$212$	−686.884	+	1544.23i	−0.0152831	+	0.0343589i
$213$	982.577	−	713.884i	0.0216575	−	0.0157351i
$214$	4353.52	−	1167.34i	0.0950633	−	0.0254901i
$215$	7488.57	−	2433.19i	0.162003	−	0.0526379i
$216$	37888.1	−	6021.39i	0.812074	−	0.129059i
$217$	−34057.8	−	37940.9i	−0.723264	−	0.805727i
$218$	−1248.38	+	811.020i	−0.0262684	+	0.0170655i
$219$	17809.0	−	5786.48i	0.371322	−	0.120650i
$220$	−12149.8	+	13503.3i	−0.251029	+	0.278994i
$221$	−49794.3	+	36177.7i	−1.01952	+	0.740723i
$222$	4550.39	+	7004.29i	0.0923299	+	0.142121i
$223$		−	16048.4i		−	0.322717i	−0.986896	−	0.161359i	$-0.948412\pi$
$223$		−	16048.4i		−	0.322717i	0.986896	−	0.161359i	$-0.0515876\pi$
$224$	−19513.7	−	50701.6i	−0.388905	−	1.01047i
$225$	2811.82	+	2042.91i	0.0555422	+	0.0403537i
$226$	−91015.5	−	4753.86i	−1.78196	−	0.0930743i
$227$	−11425.4	+	3712.35i	−0.221728	+	0.0720438i	−0.417774	−	0.908551i	$-0.637190\pi$
$227$	−11425.4	+	3712.35i	−0.221728	+	0.0720438i	0.196046	+	0.980595i	$0.437190\pi$
$228$	−1018.77	−	4784.67i	−0.0195978	−	0.0920411i
$229$	1688.16	+	5195.62i	0.0321916	+	0.0990755i	0.965861	−	0.259060i	$-0.0834127\pi$
$229$	1688.16	+	5195.62i	0.0321916	+	0.0990755i	−0.933670	+	0.358135i	$0.883413\pi$
$230$	41878.9	−	11229.3i	0.791661	−	0.212274i
$231$	6132.04	−	8440.03i	0.114916	−	0.158169i
$232$	11218.2	+	1770.72i	0.208424	+	0.0328983i
$233$	−16431.4	+	50570.5i	−0.302665	+	0.931506i	0.677874	+	0.735178i	$0.262902\pi$
$233$	−16431.4	+	50570.5i	−0.302665	+	0.931506i	−0.980538	+	0.196327i	$0.937098\pi$
$234$	−51753.9	−	2703.18i	−0.945173	−	0.0493677i
$235$	−9971.59	−	3239.96i	−0.180563	−	0.0586684i
$236$	−5387.21	+	51430.0i	−0.0967253	+	0.923405i
$237$	−29181.7	+	21201.7i	−0.519533	+	0.377463i
$238$	−40521.1	+	50057.3i	−0.715364	+	0.883718i
$239$	−28089.3	+	38661.6i	−0.491751	+	0.676837i	−0.980710	−	0.195470i	$-0.937377\pi$
$239$	−28089.3	+	38661.6i	−0.491751	+	0.676837i	0.488959	+	0.872307i	$0.337377\pi$
$240$	−25160.0	+	2662.32i	−0.436805	+	0.0462209i
$241$	−26061.7	+	18934.9i	−0.448712	+	0.326009i	−0.789087	−	0.614281i	$-0.789446\pi$
$241$	−26061.7	+	18934.9i	−0.448712	+	0.326009i	0.340375	+	0.940290i	$0.389446\pi$
$242$	−41533.4	+	26982.5i	−0.709196	+	0.460735i
$243$		−	59701.6i		−	1.01105i
$244$	−23524.3	−	110482.i	−0.395127	−	1.85571i
$245$	3053.79	−	9398.60i	0.0508753	−	0.156578i
$246$	−18181.5	+	22460.3i	−0.300441	+	0.371147i
$247$			14987.5i			0.245661i
$248$	22098.1	−	57397.0i	0.359295	−	0.933224i
$249$	2674.67			0.0431392
$250$	−50456.5	−	40844.2i	−0.807305	−	0.653507i
$251$	94798.4	+	30801.9i	1.50471	+	0.488911i	0.941388	−	0.337325i	$-0.109522\pi$
$251$	94798.4	+	30801.9i	1.50471	+	0.488911i	0.563325	+	0.826236i	$0.309522\pi$
$252$	−53038.1	+	11293.1i	−0.835193	+	0.177833i
$253$	−21567.2			−0.336940
$254$	32447.3	+	49945.2i	0.502934	+	0.774152i
$255$	17629.2	+	24264.6i	0.271115	+	0.373157i
$256$	43783.6	−	48764.4i	0.668084	−	0.744086i
$257$	71597.1	+	52018.3i	1.08400	+	0.787572i	0.978376	−	0.206834i	$-0.0663160\pi$
$257$	71597.1	+	52018.3i	1.08400	+	0.787572i	0.105624	+	0.994406i	$0.466316\pi$
$258$	−4240.12	−	3432.35i	−0.0636999	−	0.0515646i
$259$	−15738.8	−	21662.7i	−0.234624	−	0.322933i
$260$	77091.9	+	8075.26i	1.14041	+	0.119457i
$261$	3503.07	−	10781.4i	0.0514243	−	0.158268i
$262$	−415.440	+	7953.85i	−0.00605210	+	0.115871i
$263$	129540.	+	42090.1i	1.87280	+	0.608511i	0.990440	+	0.137943i	$0.0440489\pi$
$263$	129540.	+	42090.1i	1.87280	+	0.608511i	0.882364	+	0.470568i	$0.155951\pi$
$264$	12431.0	+	1962.15i	0.178360	+	0.0281530i
$265$	−2041.34	−	1483.12i	−0.0290685	−	0.0211195i
$266$	4061.56	+	15147.3i	0.0574024	+	0.214078i
$267$	−11859.9	+	3853.50i	−0.166363	+	0.0540546i
$268$	−77684.4	+	16540.9i	−1.08159	+	0.230298i
$269$	22054.4	+	67876.4i	0.304783	+	0.938024i	0.979758	+	0.200184i	$0.0641541\pi$
$269$	22054.4	+	67876.4i	0.304783	+	0.938024i	−0.674976	+	0.737840i	$0.735846\pi$
$270$	−2987.46	+	57196.7i	−0.0409803	+	0.784592i
$271$	−20096.9	+	27661.0i	−0.273647	+	0.376642i	−0.923617	−	0.383318i	$-0.874781\pi$
$271$	−20096.9	+	27661.0i	−0.273647	+	0.376642i	0.649970	+	0.759960i	$0.274781\pi$
$272$	−76003.9	−	16099.2i	−1.02730	−	0.217604i
$273$	−44518.1			−0.597325
$274$	123659.	−	80336.0i	1.64712	−	1.07006i
$275$	1519.90	+	2091.96i	0.0200978	+	0.0276623i
$276$	−22330.8	−	20092.5i	−0.293147	−	0.263764i
$277$	27534.3	+	84741.8i	0.358851	+	1.10443i	0.953743	+	0.300624i	$0.0971950\pi$
$277$	27534.3	+	84741.8i	0.358851	+	1.10443i	−0.594892	+	0.803806i	$0.702805\pi$
$278$	−78723.0	−	121176.i	−1.01862	−	1.56793i
$279$	−53119.2	−	30776.2i	−0.682406	−	0.395373i
$280$	80102.0	−	12730.3i	1.02171	−	0.162376i
$281$	28782.4	+	88583.3i	0.364515	+	1.12186i	0.950284	+	0.311383i	$0.100792\pi$
$281$	28782.4	+	88583.3i	0.364515	+	1.12186i	−0.585770	+	0.810478i	$0.699208\pi$
$282$	1881.31	+	7016.21i	0.0236571	+	0.0882275i
$283$	78262.3	+	107719.i	0.977191	+	1.34499i	0.938329	+	0.345744i	$0.112373\pi$
$283$	78262.3	+	107719.i	0.977191	+	1.34499i	0.0388625	+	0.999245i	$0.487627\pi$
$284$	−4291.44	−	1908.86i	−0.0532067	−	0.0236667i
$285$	7303.37			0.0899153
$286$	−35998.2	−	13811.2i	−0.440098	−	0.168849i
$287$	54450.6	−	74944.8i	0.661056	−	0.909866i
$288$	−41211.9	−	50801.0i	−0.496864	−	0.612474i
$289$	2650.66	+	8157.89i	0.0317364	+	0.0976747i
$290$	−6073.52	+	15830.4i	−0.0722179	+	0.188233i
$291$	37770.2	−	12272.3i	0.446029	−	0.144924i
$292$	−53831.8	−	48436.0i	−0.631354	−	0.568072i
$293$	−112384.	−	81651.9i	−1.30909	−	0.951111i	−1.00000		7.89677e-5i	$-0.999975\pi$
$293$	−112384.	−	81651.9i	−1.30909	−	0.951111i	−0.309092	−	0.951032i	$-0.600025\pi$
$294$	−6613.04	+	1773.21i	−0.0765079	+	0.0205147i
$295$	−73423.6	−	23856.8i	−0.843707	−	0.274137i
$296$	14649.2	−	28788.2i	0.167198	−	0.328573i
$297$	8803.74	−	27095.1i	0.0998054	−	0.307169i
$298$	−60357.2	−	48858.7i	−0.679668	−	0.550186i
$299$	54095.6	+	74456.3i	0.605090	+	0.832835i
$300$	−375.209	+	3582.00i	−0.00416899	+	0.0398000i
$301$	14148.3	+	10279.3i	0.156160	+	0.113457i
$302$	−5677.39	+	108697.i	−0.0622493	+	1.19180i
$303$	−29952.2	−	41225.6i	−0.326245	−	0.449037i
$304$	−14049.9	+	12668.5i	−0.152029	+	0.137081i
$305$	168641.			1.81285
$306$	−27777.7	+	72401.5i	−0.296656	+	0.773223i
$307$	128769.	+	41839.7i	1.36627	+	0.443927i	0.898131	−	0.439729i	$-0.144925\pi$
$307$	128769.	+	41839.7i	1.36627	+	0.443927i	0.468137	+	0.883656i	$0.344925\pi$
$308$	−40124.7	−	4203.01i	−0.422971	−	0.0443056i
$309$	80200.9			0.839968
$310$	76941.1	+	50113.4i	0.800635	+	0.521471i
$311$		−	42302.6i		−	0.437368i	−0.975796	−	0.218684i	$-0.929824\pi$
$311$		−	42302.6i		−	0.437368i	0.975796	−	0.218684i	$-0.0701763\pi$
$312$	−24406.0	−	47837.0i	−0.250719	−	0.491422i
$313$	−20482.4	+	63038.3i	−0.209070	+	0.643452i	0.790451	+	0.612525i	$0.209846\pi$
$313$	−20482.4	+	63038.3i	−0.209070	+	0.643452i	−0.999522	+	0.0309271i	$0.990154\pi$
$314$	42825.7	−	111623.i	0.434355	−	1.13213i
$315$		−	80958.0i		−	0.815903i
$316$	127452.	+	56691.5i	1.27636	+	0.567732i
$317$	−39669.6	+	28821.6i	−0.394765	+	0.286814i	−0.767405	−	0.641162i	$-0.778453\pi$
$317$	−39669.6	+	28821.6i	−0.394765	+	0.286814i	0.372640	+	0.927976i	$0.378453\pi$
$318$	−91.1838	+	1745.77i	−0.000901703	+	0.0172636i
$319$	4957.37	−	6823.23i	0.0487158	−	0.0670515i
$320$	57593.4	+	79094.7i	0.562435	+	0.772409i
$321$	3771.72	−	2740.31i	0.0366040	−	0.0265944i
$322$	74849.6	+	60590.2i	0.721901	+	0.584374i
$323$	21328.9	+	6930.18i	0.204439	+	0.0664262i
$324$	−37326.9	+	21568.2i	−0.355576	+	0.205458i
$325$	3409.79	−	10494.3i	0.0322821	−	0.0993540i
$326$	120784.	−	32386.8i	1.13651	−	0.304743i
$327$	−905.083	+	1245.74i	−0.00846433	+	0.0116502i
$328$	110383.	+	17423.3i	1.02602	+	0.161950i
$329$	−7196.04	−	22147.1i	−0.0664816	−	0.204609i
$330$	−6730.13	+	17541.8i	−0.0618010	+	0.161082i
$331$	−33962.9	+	11035.2i	−0.309991	+	0.100722i	−0.459881	−	0.887980i	$-0.652108\pi$
$331$	−33962.9	+	11035.2i	−0.309991	+	0.100722i	0.149890	+	0.988703i	$0.452108\pi$
$332$	−5174.88	−	8955.88i	−0.0469488	−	0.0812517i
$333$	−26084.0	−	18951.2i	−0.235227	−	0.170902i
$334$	78267.8	+	30028.4i	0.701601	+	0.269178i
$335$		−	118578.i		−	1.05661i
$336$	−37629.7	−	41733.0i	−0.333313	−	0.369658i
$337$	117397.	−	85293.8i	1.03371	−	0.751031i	0.0646584	−	0.997907i	$-0.479404\pi$
$337$	117397.	−	85293.8i	1.03371	−	0.751031i	0.969047	+	0.246877i	$0.0794042\pi$
$338$	13024.0	+	48572.1i	0.114002	+	0.425161i
$339$	−89655.7	+	29130.9i	−0.780151	+	0.253486i
$340$	47139.0	−	105976.i	0.407777	−	0.916749i
$341$	−30510.2	−	33988.8i	−0.262383	−	0.292299i
$342$	10287.3	+	15834.9i	0.0879527	+	0.135383i
$343$	−100273.	+	32580.7i	−0.852308	+	0.276932i
$344$	−3289.21	+	20838.5i	−0.0277955	+	0.176096i
$345$	36282.2	−	26360.6i	0.304829	−	0.221471i
$346$	43718.6	−	28402.1i	0.365186	−	0.237246i
$347$			58224.6i			0.483557i	0.970331	+	0.241779i	$0.0777308\pi$
$347$			58224.6i			0.483557i	−0.970331	+	0.241779i	$0.922269\pi$
$348$	11489.6	−	2446.41i	0.0948736	−	0.0202009i
$349$	−45895.4	−	33344.9i	−0.376806	−	0.273766i	0.383221	−	0.923657i	$-0.374815\pi$
$349$	−45895.4	−	33344.9i	−0.376806	−	0.273766i	−0.760028	+	0.649891i	$0.774815\pi$
$350$	602.236	−	11530.2i	0.00491622	−	0.0941238i
$351$	−115622.	+	37567.9i	−0.938484	+	0.304932i
$352$	−17481.1	−	45420.3i	−0.141086	−	0.366577i
$353$	20669.3	+	63613.6i	0.165873	+	0.510506i	0.999100	−	0.0424264i	$-0.0135088\pi$
$353$	20669.3	+	63613.6i	0.165873	+	0.510506i	−0.833226	+	0.552932i	$0.813509\pi$
$354$	13852.6	+	51662.3i	0.110541	+	0.412256i
$355$	4121.61	−	5672.91i	0.0327047	−	0.0450141i
$356$	35849.2	+	32255.9i	0.282865	+	0.254513i
$357$	−20585.0	+	63354.0i	−0.161515	+	0.497093i
$358$	−7411.66	+	141901.i	−0.0578295	+	1.10718i
$359$	58674.7	+	19064.6i	0.455263	+	0.147924i	0.527667	−	0.849452i	$-0.323067\pi$
$359$	58674.7	+	19064.6i	0.455263	+	0.147924i	−0.0724038	+	0.997375i	$0.523067\pi$
$360$	86993.5	−	44383.3i	0.671246	−	0.342464i
$361$	−101014.	+	73390.9i	−0.775116	+	0.563155i
$362$	−60282.1	−	48798.0i	−0.460015	−	0.372378i
$363$	−30111.9	+	41445.5i	−0.228521	+	0.314532i
$364$	86132.4	+	149064.i	0.650075	+	1.12505i
$365$	87463.9	−	63546.2i	0.656512	−	0.476984i
$366$	−63651.7	−	97977.2i	−0.475168	−	0.731413i
$367$		−	210188.i		−	1.56054i	−0.625441	−	0.780272i	$-0.715081\pi$
$367$		−	210188.i		−	1.56054i	0.625441	−	0.780272i	$-0.284919\pi$
$368$	−24072.8	+	113647.i	−0.177759	+	0.839193i
$369$	34469.0	−	106085.i	0.253149	−	0.779113i
$370$	37482.2	+	30341.6i	0.273793	+	0.221633i
$371$		−	5604.15i		−	0.0407157i
$372$	74.3885	−	63616.2i	0.000537551	−	0.459708i
$373$	−233994.			−1.68185			−0.840926	−	0.541150i	$-0.817989\pi$
$373$	−233994.			−1.68185			−0.840926	+	0.541150i	$0.817989\pi$
$374$	−36300.2	+	44843.2i	−0.259517	+	0.320592i
$375$	−63859.3	−	20749.1i	−0.454110	−	0.147549i
$376$	19853.2	−	19874.2i	0.140428	−	0.140577i
$377$	−35990.0			−0.253221
$378$	−106674.	+	69301.5i	−0.746576	+	0.485019i
$379$	119230.	+	164106.i	0.830057	+	1.14248i	0.987912	+	0.155014i	$0.0495422\pi$
$379$	119230.	+	164106.i	0.830057	+	1.14248i	−0.157855	+	0.987462i	$0.550458\pi$
$380$	−14130.4	−	24454.6i	−0.0978557	−	0.169353i
$381$	49839.6	+	36210.6i	0.343340	+	0.249451i
$382$	−43098.3	+	53241.1i	−0.295348	+	0.364855i
$383$	−157294.	−	216496.i	−1.07229	−	1.47588i	−0.867733	−	0.497030i	$-0.834424\pi$
$383$	−157294.	−	216496.i	−1.07229	−	1.47588i	−0.204559	−	0.978854i	$-0.565576\pi$
$384$	24214.6	−	63314.2i	0.164216	−	0.429377i
$385$	18612.6	−	57283.8i	0.125570	−	0.386465i
$386$	−111833.	−	5841.17i	−0.750574	−	0.0392035i
$387$	20027.0	+	6507.16i	0.133719	+	0.0434480i
$388$	−114169.	−	102726.i	−0.758378	−	0.682363i
$389$	−84997.3	−	61754.2i	−0.561702	−	0.408101i	0.270379	−	0.962754i	$-0.412851\pi$
$389$	−84997.3	−	61754.2i	−0.561702	−	0.408101i	−0.832082	+	0.554653i	$0.812851\pi$
$390$	77440.2	−	20764.6i	0.509140	−	0.136520i
$391$	130973.	−	42555.7i	0.856699	−	0.278358i
$392$	18732.1	+	18712.4i	0.121903	+	0.121775i
$393$	2545.75	+	7835.02i	0.0164828	+	0.0507288i
$394$	−82149.9	−	4290.80i	−0.529194	−	0.0276405i
$395$	−122408.	+	168480.i	−0.784541	+	1.07983i
$396$	−47513.5	+	10116.8i	−0.302989	+	0.0645136i
$397$	202771.			1.28655			0.643273	−	0.765637i	$-0.277576\pi$
$397$	202771.			1.28655			0.643273	+	0.765637i	$0.277576\pi$
$398$	−82989.4	−	127743.i	−0.523910	−	0.806440i
$399$	9534.44	+	13123.0i	0.0598893	+	0.0824306i
$400$	12719.9	−	5674.00i	0.0794995	−	0.0354625i
$401$	−8648.57	−	26617.6i	−0.0537843	−	0.165531i	0.920556	−	0.390610i	$-0.127736\pi$
$401$	−8648.57	−	26617.6i	−0.0537843	−	0.165531i	−0.974340	+	0.225079i	$0.927736\pi$
$402$	−68891.9	+	44756.1i	−0.426301	+	0.276949i
$403$	−40812.6	+	190582.i	−0.251295	+	1.17347i
$404$	−80089.4	+	180054.i	−0.490696	+	1.10317i
$405$	−19888.7	−	61211.0i	−0.121254	−	0.373181i
$406$	−36373.7	+	9753.16i	−0.220666	+	0.0591688i
$407$	−14099.4	−	19406.2i	−0.0851163	−	0.117152i
$408$	−79362.4	+	12612.7i	−0.476754	+	0.0757684i
$409$	−93881.0			−0.561218			−0.280609	−	0.959822i	$-0.590536\pi$
$409$	−93881.0			−0.561218			−0.280609	+	0.959822i	$0.590536\pi$
$410$	−59761.4	+	155766.i	−0.355511	+	0.926625i
$411$	89653.5	−	123397.i	0.530742	−	0.730504i
$412$	−155171.	−	268545.i	−0.914145	−	1.58206i
$413$	−52986.5	−	163076.i	−0.310645	−	0.956068i
$414$	108260.	+	41535.4i	0.631638	+	0.242336i
$415$	14686.4	−	4771.91i	0.0852746	−	0.0277074i
$416$	−112957.	+	174275.i	−0.652722	+	1.00704i
$417$	−120920.	−	87853.4i	−0.695385	−	0.505227i
$418$	3638.49	+	13569.5i	0.0208242	+	0.0776625i
$419$	−277918.	−	90301.2i	−1.58303	−	0.514358i	−0.620195	−	0.784448i	$-0.712947\pi$
$419$	−277918.	−	90301.2i	−1.58303	−	0.514358i	−0.962835	+	0.270090i	$0.912947\pi$
$420$	72638.5	−	41972.0i	0.411783	−	0.237936i
$421$	927.086	−	2853.28i	0.00523065	−	0.0160983i	−0.948407	−	0.317055i	$-0.897306\pi$
$421$	927.086	−	2853.28i	0.00523065	−	0.0160983i	0.953638	+	0.300957i	$0.0973060\pi$
$422$	123154.	−	152137.i	0.691549	−	0.854299i
$423$	−16481.3	−	22684.6i	−0.0921111	−	0.126780i
$424$	6021.95	−	3072.34i	0.0334970	−	0.0170898i
$425$	−13357.8	−	9705.01i	−0.0739532	−	0.0537302i
$426$	−4851.52	−	253.401i	−0.0267336	−	0.00139633i
$427$	220158.	+	303021.i	1.20748	+	1.66195i
$428$	−16473.1	−	7327.35i	−0.0899265	−	0.0399999i
$429$	−39880.9			−0.216696
$430$	−29405.9	−	11281.9i	−0.159037	−	0.0610163i
$431$	−307191.	−	99812.5i	−1.65369	−	0.537317i	−0.674156	−	0.738589i	$-0.735492\pi$
$431$	−307191.	−	99812.5i	−1.65369	−	0.537317i	−0.979535	+	0.201273i	$0.935492\pi$
$432$	−132949.	−	76633.7i	−0.712392	−	0.410631i
$433$	−146831.			−0.783146			−0.391573	−	0.920147i	$-0.628069\pi$
$433$	−146831.			−0.783146			−0.391573	+	0.920147i	$0.628069\pi$
$434$	10399.3	+	203674.i	0.0552111	+	1.08132i
$435$			17537.8i			0.0926823i
$436$	5922.37	+	620.359i	0.0311546	+	0.00326340i
$437$	10362.5	−	31892.6i	0.0542629	−	0.167004i
$438$	−69931.6	−	26830.1i	−0.364523	−	0.139854i
$439$		−	204455.i		−	1.06089i	−0.847721	−	0.530443i	$-0.822026\pi$
$439$		−	204455.i		−	1.06089i	0.847721	−	0.530443i	$-0.177974\pi$
$440$	71758.3	−	11404.2i	0.370652	−	0.0589061i
$441$	21381.1	−	15534.3i	0.109939	−	0.0798756i
$442$	245861.	+	12841.7i	1.25848	+	0.0657320i
$443$	79876.4	−	109940.i	0.407015	−	0.560209i	−0.555472	−	0.831535i	$-0.687462\pi$
$443$	79876.4	−	109940.i	0.407015	−	0.560209i	0.962487	+	0.271327i	$0.0874624\pi$
$444$	3480.65	−	33228.6i	0.0176561	−	0.168557i
$445$	−58246.5	+	42318.5i	−0.294137	+	0.213703i
$446$	−40389.6	+	49895.0i	−0.203049	+	0.250834i
$447$	−76389.9	−	24820.6i	−0.382314	−	0.124221i
$448$	−66933.8	+	206743.i	−0.333495	+	1.03009i
$449$	−9320.85	+	28686.6i	−0.0462342	+	0.142294i	−0.971509	−	0.237004i	$-0.923835\pi$
$449$	−9320.85	+	28686.6i	−0.0462342	+	0.142294i	0.925275	+	0.379298i	$0.123835\pi$
$450$	−3600.57	−	13428.1i	−0.0177806	−	0.0663114i
$451$	48778.8	−	67138.2i	0.239816	−	0.330078i
$452$	271005.	+	243842.i	1.32648	+	1.19352i
$453$	34790.1	+	107073.i	0.169535	+	0.521775i
$454$	44864.9	+	17213.0i	0.217668	+	0.0835111i
$455$	−244445.	+	79425.1i	−1.18075	+	0.383650i
$456$	−8874.35	+	17439.6i	−0.0426783	+	0.0838702i
$457$	94902.6	+	68950.7i	0.454408	+	0.330146i	0.791333	−	0.611385i	$-0.209387\pi$
$457$	94902.6	+	68950.7i	0.454408	+	0.330146i	−0.336926	+	0.941531i	$0.609387\pi$
$458$	7827.46	−	20402.0i	0.0373156	−	0.0972615i
$459$			181914.i			0.863457i
$460$	−158464.	−	70485.8i	−0.748884	−	0.333109i
$461$	143439.	−	104215.i	0.674940	−	0.490373i	−0.196735	−	0.980457i	$-0.563034\pi$
$461$	143439.	−	104215.i	0.674940	−	0.490373i	0.871675	+	0.490084i	$0.163034\pi$
$462$	−40306.0	+	10807.6i	−0.188836	+	0.0506342i
$463$	−313984.	+	102020.i	−1.46469	+	0.475907i	−0.929499	−	0.368824i	$-0.879760\pi$
$463$	−313984.	+	102020.i	−1.46469	+	0.475907i	−0.535191	+	0.844731i	$0.679760\pi$
$464$	−30421.3	−	33738.5i	−0.141300	−	0.156707i
$465$	92869.9	+	19887.8i	0.429506	+	0.0919774i
$466$	178358.	−	115872.i	0.821336	−	0.533587i
$467$	−117825.	+	38283.8i	−0.540263	+	0.175542i	−0.566421	−	0.824116i	$-0.691673\pi$
$467$	−117825.	+	38283.8i	−0.540263	+	0.175542i	0.0261586	+	0.999658i	$0.491673\pi$
$468$	154101.	+	138655.i	0.703581	+	0.633059i
$469$	213067.	−	154802.i	0.968658	−	0.703771i
$470$	22847.8	+	35169.0i	0.103431	+	0.159208i
$471$		−	123663.i		−	0.557439i
$472$	146185.	−	146339.i	0.656172	−	0.656865i
$473$	12674.5	+	9208.59i	0.0566513	+	0.0411596i
$474$	144086.	+	7525.79i	0.641304	+	0.0334962i
$475$	−3823.77	+	1242.42i	−0.0169475	+	0.00550657i
$476$	251962.	−	53648.9i	1.11204	−	0.236781i
$477$	−2085.24	−	6417.70i	−0.00916470	−	0.0282061i
$478$	184631.	−	49506.6i	0.808071	−	0.216674i
$479$	125117.	−	172209.i	0.545313	−	0.750560i	−0.444053	−	0.896000i	$-0.646460\pi$
$479$	125117.	−	172209.i	0.545313	−	0.750560i	0.989367	+	0.145441i	$0.0464600\pi$
$480$	84923.4	+	55043.7i	0.368591	+	0.238905i
$481$	−31631.2	+	97350.7i	−0.136718	+	0.420774i
$482$	128681.	+	6721.16i	0.553884	+	0.0289301i
$483$	94731.8	+	30780.2i	0.406071	+	0.131940i
$484$	197036.	+	20639.2i	0.841115	+	0.0881055i
$485$	185498.	−	134772.i	0.788598	−	0.572950i
$486$	−150253.	+	185614.i	−0.636137	+	0.785847i
$487$	−81533.8	+	112222.i	−0.343779	+	0.473172i	−0.945541	−	0.325504i	$-0.894466\pi$
$487$	−81533.8	+	112222.i	−0.343779	+	0.473172i	0.601761	+	0.798676i	$0.294466\pi$
$488$	−204916.	+	402695.i	−0.860470	+	1.69097i
$489$	104643.	−	76027.4i	0.437614	−	0.317945i
$490$	−33148.1	+	21534.9i	−0.138060	+	0.0896914i
$491$		−	51081.0i		−	0.211883i	−0.994372	−	0.105942i	$-0.966214\pi$
$491$		−	51081.0i		−	0.211883i	0.994372	−	0.105942i	$-0.0337856\pi$
$492$	113053.	−	24071.8i	0.467039	−	0.0994440i
$493$	−16641.7	+	51217.7i	−0.0684704	+	0.210730i
$494$	37719.7	−	46596.7i	0.154566	−	0.190942i
$495$		−	72525.1i		−	0.295990i
$496$	−213157.	+	122834.i	−0.866434	+	0.499292i
$497$	15574.0			0.0630505
$498$	−8315.63	−	6731.44i	−0.0335302	−	0.0271425i
$499$	82840.9	+	26916.6i	0.332693	+	0.108099i	0.470600	−	0.882347i	$-0.344037\pi$
$499$	82840.9	+	26916.6i	0.332693	+	0.108099i	−0.137907	+	0.990445i	$0.544037\pi$
$500$	54076.7	+	253971.i	0.216307	+	1.01589i
$501$	86709.5			0.345455
$502$	−217211.	−	334346.i	−0.861933	−	1.32675i
$503$	−174942.	−	240788.i	−0.691448	−	0.951696i	−1.00000		0.000488693i	$-0.999844\pi$
$503$	−174942.	−	240788.i	−0.691448	−	0.951696i	0.308552	−	0.951207i	$-0.400156\pi$
$504$	193319.	+	98372.3i	0.761049	+	0.387268i
$505$	−238016.	−	172929.i	−0.933305	−	0.678086i
$506$	67053.0	+	54278.9i	0.261889	+	0.211997i
$507$	30573.6	+	42081.0i	0.118941	+	0.163708i
$508$	24819.3	−	236942.i	0.0961751	−	0.918153i
$509$	−23464.3	+	72215.7i	−0.0905675	+	0.278738i	−0.986073	−	0.166312i	$-0.946814\pi$
$509$	−23464.3	+	72215.7i	−0.0905675	+	0.278738i	0.895506	+	0.445050i	$0.146814\pi$
$510$	6257.70	−	119807.i	0.0240588	−	0.460620i
$511$	228366.	+	74200.5i	0.874558	+	0.284161i
$512$	−258851.	+	41418.3i	−0.987439	+	0.157998i
$513$	35837.1	+	26037.1i	0.136175	+	0.0989370i
$514$	−91681.0	−	341917.i	−0.347019	−	1.29418i
$515$	440377.	−	143087.i	1.66039	−	0.539494i
$516$	4544.34	+	21342.5i	0.0170676	+	0.0801579i
$517$	−6446.47	−	19840.2i	−0.0241180	−	0.0742275i
$518$	−5586.68	+	106960.i	−0.0208207	+	0.398624i
$519$	31696.3	−	43626.2i	0.117672	−	0.161962i
$520$	−219358.	−	219126.i	−0.811234	−	0.810378i
$521$	464127.			1.70986			0.854932	−	0.518741i	$-0.173599\pi$
$521$	464127.			1.70986			0.854932	+	0.518741i	$0.173599\pi$
$522$	−38024.9	+	24703.2i	−0.139549	+	0.0906593i
$523$	177809.	+	244733.i	0.650055	+	0.894723i	0.999101	−	0.0423818i	$-0.0134946\pi$
$523$	177809.	+	244733.i	0.650055	+	0.894723i	−0.349047	+	0.937105i	$0.613495\pi$
$524$	21309.3	−	23683.2i	0.0776082	−	0.0862536i
$525$	−3690.41	−	11357.9i	−0.0133892	−	0.0412078i
$526$	−296814.	−	456877.i	−1.07278	−	1.65131i
$527$	252347.	+	146205.i	0.908610	+	0.526431i
$528$	−33710.1	−	37385.9i	−0.120918	−	0.134103i
$529$	22843.1	+	70303.8i	0.0816288	+	0.251228i
$530$	2613.95	+	9748.55i	0.00930564	+	0.0347047i
$531$	−121357.	−	167033.i	−0.430403	−	0.592399i
$532$	25494.2	−	57315.2i	0.0900779	−	0.202510i
$533$	−354130.			−1.24654
$534$	46570.8	+	17867.5i	0.163317	+	0.0626586i
$535$	15821.2	−	21776.0i	0.0552754	−	0.0760800i
$536$	283152.	+	144085.i	0.985575	+	0.501521i
$537$	45417.4	+	139781.i	0.157498	+	0.484728i
$538$	102259.	−	266535.i	0.353295	−	0.920850i
$539$	18700.1	−	6076.04i	0.0643676	−	0.0209143i
$540$	153237.	−	170308.i	0.525505	−	0.584045i
$541$	239669.	+	174130.i	0.818875	+	0.594947i	0.916390	−	0.400287i	$-0.131089\pi$
$541$	239669.	+	174130.i	0.818875	+	0.594947i	−0.0975153	+	0.995234i	$0.531089\pi$
$542$	132097.	−	35420.2i	0.449671	−	0.120574i
$543$	−76294.8	−	24789.7i	−0.258759	−	0.0840759i
$544$	195781.	+	241335.i	0.661564	+	0.815496i
$545$	−2747.20	+	8455.02i	−0.00924906	+	0.0284657i
$546$	138408.	+	112040.i	0.464275	+	0.375827i
$547$	269172.	+	370484.i	0.899612	+	1.23821i	0.970592	+	0.240732i	$0.0773875\pi$
$547$	269172.	+	370484.i	0.899612	+	1.23821i	−0.0709794	+	0.997478i	$0.522612\pi$
$548$	−586643.	−	61450.0i	−1.95350	−	0.204626i
$549$	364868.	+	265092.i	1.21057	+	0.879533i
$550$	539.505	−	10329.1i	0.00178349	−	0.0341459i
$551$	7707.99	+	10609.1i	0.0253886	+	0.0349443i
$552$	18859.5	+	118669.i	0.0618945	+	0.389456i
$553$	−462535.			−1.51250
$554$	127668.	−	332761.i	0.415970	−	1.08421i
$555$	47438.6	+	15413.7i	0.154009	+	0.0500405i
$556$	−60216.2	+	574865.i	−0.194789	+	1.85959i
$557$	−57074.4			−0.183963			−0.0919816	−	0.995761i	$-0.529320\pi$
$557$	−57074.4			−0.183963			−0.0919816	+	0.995761i	$0.529320\pi$
$558$	87693.4	+	229371.i	0.281643	+	0.736665i
$559$		−	66853.6i		−	0.213944i
$560$	−281078.	−	162017.i	−0.896295	−	0.516635i
$561$	−18440.8	+	56754.8i	−0.0585940	+	0.180334i
$562$	133455.	−	347845.i	0.422535	−	1.10132i
$563$		−	194826.i		−	0.614654i	−0.951604	−	0.307327i	$-0.900565\pi$
$563$		−	194826.i		−	0.614654i	0.951604	−	0.307327i	$-0.0994345\pi$
$564$	11808.9	−	26548.3i	0.0371237	−	0.0834601i
$565$	−440320.	+	319911.i	−1.37934	+	1.00215i
$566$	27780.1	−	531866.i	0.0867163	−	1.66023i
$567$	84022.4	−	115647.i	0.261354	−	0.359723i
$568$	8538.09	+	16735.1i	0.0264645	+	0.0518719i
$569$	−84320.0	+	61262.1i	−0.260439	+	0.189220i	−0.710341	−	0.703858i	$-0.751459\pi$
$569$	−84320.0	+	61262.1i	−0.260439	+	0.189220i	0.449902	+	0.893078i	$0.351459\pi$
$570$	−22706.4	−	18380.6i	−0.0698872	−	0.0565732i
$571$	−177030.	−	57520.7i	−0.542970	−	0.176422i	0.0246744	−	0.999696i	$-0.492145\pi$
$571$	−177030.	−	57520.7i	−0.542970	−	0.176422i	−0.567644	+	0.823274i	$0.692145\pi$
$572$	77160.5	+	133537.i	0.235832	+	0.408141i
$573$	−21894.2	+	67383.5i	−0.0666838	+	0.205232i
$574$	−357904.	+	95967.7i	−1.08628	+	0.291274i
$575$	−14511.7	+	19973.6i	−0.0438917	+	0.0604117i
$576$	276.214	+	261661.i	0.000832531	+	0.788668i
$577$	118813.	+	365668.i	0.356871	+	1.09834i	0.954917	+	0.296874i	$0.0959442\pi$
$577$	118813.	+	365668.i	0.356871	+	1.09834i	−0.598045	+	0.801462i	$0.704056\pi$
$578$	12290.3	−	32034.1i	0.0367880	−	0.0958863i
$579$	−110162.	+	35793.7i	−0.328605	+	0.106770i
$580$	58723.6	−	33931.7i	0.174565	−	0.100867i
$581$	27747.3	+	20159.6i	0.0821993	+	0.0597213i
$582$	−148315.	−	56902.7i	−0.437862	−	0.167991i
$583$		−	5020.40i		−	0.0147707i
$584$	45463.7	+	286069.i	0.133303	+	0.838775i
$585$	−250378.	+	181910.i	−0.731617	+	0.531551i
$586$	143909.	+	536699.i	0.419077	+	1.56292i
$587$	−108150.	+	35140.1i	−0.313871	+	0.101983i	−0.461716	−	0.887028i	$-0.652766\pi$
$587$	−108150.	+	35140.1i	−0.313871	+	0.101983i	0.147846	+	0.989010i	$0.452766\pi$
$588$	25022.8	+	11130.3i	0.0723738	+	0.0321924i
$589$	64920.6	−	28786.2i	0.187134	−	0.0829764i
$590$	168235.	+	258959.i	0.483294	+	0.743922i
$591$	−80922.5	+	26293.3i	−0.231683	+	0.0752784i
$592$	−117997.	+	52635.2i	−0.336688	+	0.150187i
$593$	−31735.8	+	23057.4i	−0.0902485	+	0.0655694i	−0.631994	−	0.774973i	$-0.717763\pi$
$593$	−31735.8	+	23057.4i	−0.0902485	+	0.0655694i	0.541746	+	0.840542i	$0.317763\pi$
$594$	−95562.2	+	62082.8i	−0.270840	+	0.175954i
$595$			384598.i			1.08636i
$596$	64687.8	+	303806.i	0.182108	+	0.855272i
$597$	−127473.	−	92614.6i	−0.357659	−	0.259855i
$598$	19201.9	−	367631.i	0.0536959	−	1.02804i
$599$	316988.	−	102996.i	0.883463	−	0.287055i	0.168069	−	0.985775i	$-0.446247\pi$
$599$	316988.	−	102996.i	0.883463	−	0.287055i	0.715395	+	0.698721i	$0.246247\pi$
$600$	10181.5	−	10192.2i	0.0282819	−	0.0283118i
$601$	−28130.4	−	86576.3i	−0.0778801	−	0.239690i	0.904535	−	0.426399i	$-0.140218\pi$
$601$	−28130.4	−	86576.3i	−0.0778801	−	0.239690i	−0.982415	+	0.186709i	$0.940218\pi$
$602$	−18117.0	−	67566.2i	−0.0499913	−	0.186439i
$603$	186397.	−	256554.i	0.512632	−	0.705577i
$604$	291212.	−	323653.i	0.798245	−	0.887168i
$605$	−91399.0	+	281297.i	−0.249707	+	0.768519i
$606$	−10631.9	+	203553.i	−0.0289511	+	0.554285i
$607$	556494.	+	180816.i	1.51037	+	0.490749i	0.943022	−	0.332730i	$-0.107970\pi$
$607$	556494.	+	180816.i	1.51037	+	0.490749i	0.567347	+	0.823479i	$0.307970\pi$
$608$	75564.8	−	4026.84i	0.204415	−	0.0108932i
$609$	−31512.7	+	22895.3i	−0.0849672	+	0.0617323i
$610$	−524308.	−	424424.i	−1.40905	−	1.14062i
$611$	−52324.9	+	72019.0i	−0.140161	+	0.192915i
$612$	268577.	−	155189.i	0.717077	−	0.414341i
$613$	−272154.	+	197731.i	−0.724259	+	0.526205i	−0.887742	−	0.460341i	$-0.847727\pi$
$613$	−272154.	+	197731.i	−0.724259	+	0.526205i	0.163483	+	0.986546i	$0.447727\pi$
$614$	−295048.	−	454159.i	−0.782629	−	1.20468i
$615$			172566.i			0.456252i
$616$	114171.	+	114051.i	0.300881	+	0.300563i
$617$	182632.	−	562083.i	0.479740	−	1.47649i	−0.359716	−	0.933062i	$-0.617127\pi$
$617$	182632.	−	562083.i	0.479740	−	1.47649i	0.839457	−	0.543427i	$-0.182873\pi$
$618$	−249347.	−	201844.i	−0.652870	−	0.528494i
$619$		−	531701.i		−	1.38767i	−0.720134	−	0.693835i	$-0.755920\pi$
$619$		−	531701.i		−	1.38767i	0.720134	−	0.693835i	$-0.244080\pi$
$620$	−113090.	−	349444.i	−0.294198	−	0.909064i
$621$	272012.			0.705350
$622$	−106464.	+	131520.i	−0.275185	+	0.339947i
$623$	−152080.	−	49413.7i	−0.391828	−	0.127313i
$624$	−44514.2	+	210150.i	−0.114322	+	0.539709i
$625$	−353661.			−0.905372
$626$	222331.	−	144439.i	0.567350	−	0.368584i
$627$	8541.29	+	11756.1i	0.0217264	+	0.0299039i
$628$	−414073.	+	239259.i	−1.04992	+	0.606666i
$629$	123914.	+	90029.1i	0.313199	+	0.227553i
$630$	−203750.	+	251700.i	−0.513353	+	0.634166i
$631$	82679.8	+	113799.i	0.207654	+	0.285811i	0.900123	−	0.435637i	$-0.143477\pi$
$631$	82679.8	+	113799.i	0.207654	+	0.285811i	−0.692468	+	0.721448i	$0.743477\pi$
$632$	−253574.	−	497018.i	−0.634849	−	1.24434i
$633$	62563.0	−	192549.i	0.156138	−	0.480545i
$634$	195870.	+	10230.6i	0.487293	+	0.0254520i
$635$	338269.	+	109910.i	0.838908	+	0.272578i
$636$	4677.12	−	5198.15i	0.0115628	−	0.0128509i
$637$	−67880.7	−	49318.2i	−0.167289	−	0.121543i
$638$	−32584.8	+	8737.23i	−0.0800524	+	0.0214651i
$639$	17834.9	−	5794.91i	0.0436786	−	0.0141920i
$640$	20001.2	−	390855.i	0.0488310	−	0.954235i
$641$	−70509.0	−	217004.i	−0.171604	−	0.528144i	0.827858	−	0.560938i	$-0.189559\pi$
$641$	−70509.0	−	217004.i	−0.171604	−	0.528144i	−0.999462	+	0.0327940i	$0.989559\pi$
$642$	−18623.0	−	972.705i	−0.0451835	−	0.00236000i
$643$	−392586.	+	540349.i	−0.949540	+	1.30693i	0.00219110	+	0.999998i	$0.499303\pi$
$643$	−392586.	+	540349.i	−0.949540	+	1.30693i	−0.951731	+	0.306932i	$0.900697\pi$
$644$	−80219.9	−	376753.i	−0.193424	−	0.908417i
$645$	−32577.5			−0.0783065
$646$	−48870.7	−	75225.3i	−0.117107	−	0.180260i
$647$	−210928.	−	290318.i	−0.503879	−	0.693530i	0.478993	−	0.877819i	$-0.341002\pi$
$647$	−210928.	−	290318.i	−0.503879	−	0.693530i	−0.982872	+	0.184288i	$0.941002\pi$
$648$	170332.	+	26885.8i	0.405645	+	0.0640283i
$649$	−47467.2	−	146089.i	−0.112695	−	0.346839i
$650$	−37012.4	+	24045.4i	−0.0876034	+	0.0569122i
$651$	85504.9	+	192836.i	0.201757	+	0.455016i
$652$	−457031.	−	203290.i	−1.07510	−	0.478213i
$653$	−126823.	−	390321.i	−0.297421	−	0.915368i	−0.982397	−	0.186803i	$-0.940187\pi$
$653$	−126823.	−	390321.i	−0.297421	−	0.915368i	0.684976	−	0.728565i	$-0.259813\pi$
$654$	5949.12	−	1595.18i	0.0139090	−	0.00372954i
$655$	27957.0	+	38479.6i	0.0651641	+	0.0896907i
$656$	−299335.	−	331975.i	−0.695584	−	0.771432i
$657$	289126.			0.669817
$658$	−33365.8	+	86966.5i	−0.0770636	+	0.200863i
$659$	−265767.	+	365797.i	−0.611971	+	0.842306i	−0.996738	−	0.0807082i	$-0.974282\pi$
$659$	−265767.	+	365797.i	−0.611971	+	0.842306i	0.384767	+	0.923014i	$0.374282\pi$
$660$	65072.2	−	37600.0i	0.149385	−	0.0863177i
$661$	18970.6	+	58385.4i	0.0434187	+	0.133629i	0.970416	−	0.241439i	$-0.0776194\pi$
$661$	18970.6	+	58385.4i	0.0434187	+	0.133629i	−0.926997	+	0.375068i	$0.877619\pi$
$662$	133364.	+	51166.9i	0.304315	+	0.116754i
$663$	242188.	−	78691.7i	0.550967	−	0.179020i
$664$	−6450.73	+	40867.9i	−0.0146310	+	0.0926928i
$665$	75765.7	+	55047.0i	0.171329	+	0.124477i
$666$	33400.9	+	124566.i	0.0753026	+	0.280835i
$667$	76584.7	+	24883.9i	0.172143	+	0.0559328i
$668$	−167763.	−	290338.i	−0.375962	−	0.650656i
$669$	−20518.2	+	63148.5i	−0.0458445	+	0.141095i
$670$	−298430.	+	368663.i	−0.664803	+	0.821259i
$671$	197225.	+	271457.i	0.438044	+	0.602916i
$672$	11961.1	+	224453.i	0.0264869	+	0.497035i
$673$	205740.	+	149479.i	0.454243	+	0.330027i	0.791269	−	0.611469i	$-0.209421\pi$
$673$	205740.	+	149479.i	0.454243	+	0.330027i	−0.337026	+	0.941495i	$0.609421\pi$
$674$	−579652.	−	30276.0i	−1.27599	−	0.0666467i
$675$	−19169.4	−	26384.4i	−0.0420728	−	0.0579082i
$676$	81751.2	−	183790.i	0.178896	−	0.402188i
$677$	−230683.			−0.503314			−0.251657	−	0.967817i	$-0.580975\pi$
$677$	−230683.			−0.503314			−0.251657	+	0.967817i	$0.580975\pi$
$678$	352057.	+	135071.i	0.765867	+	0.293834i
$679$	484330.	+	157368.i	1.05051	+	0.341332i
$680$	−413270.	+	210847.i	−0.893751	+	0.455983i
$681$	49703.9			0.107176
$682$	9316.11	+	182458.i	0.0200293	+	0.392278i
$683$			277758.i			0.595422i	0.954656	+	0.297711i	$0.0962232\pi$
$683$			277758.i			0.595422i	−0.954656	+	0.297711i	$0.903777\pi$
$684$	7868.88	−	75121.7i	0.0168190	−	0.160566i
$685$	272126.	−	837517.i	0.579947	−	1.78489i
$686$	393749.	+	151067.i	0.836703	+	0.321011i
$687$		−	22602.4i		−	0.0478897i
$688$	62671.1	−	56509.2i	0.132401	−	0.119383i
$689$	−17331.9	+	12592.4i	−0.0365096	+	0.0265258i
$690$	−179145.	−	9356.99i	−0.376276	−	0.0196534i
$691$	−131498.	+	180992.i	−0.275400	+	0.379055i	−0.924203	−	0.381901i	$-0.875270\pi$
$691$	−131498.	+	180992.i	−0.275400	+	0.379055i	0.648804	+	0.760956i	$0.275270\pi$
$692$	−207403.	−	21725.2i	−0.433115	−	0.0453681i
$693$	130316.	−	94680.4i	0.271352	−	0.197149i
$694$	146536.	−	181022.i	0.304246	−	0.375848i
$695$	−820701.	−	266662.i	−1.69909	−	0.552067i
$696$	−41878.3	−	21310.2i	−0.0864512	−	0.0439916i
$697$	−163748.	+	503965.i	−0.337063	+	1.03737i
$698$	58769.6	+	219177.i	0.120626	+	0.449867i
$699$	129311.	−	177981.i	0.264655	−	0.364266i
$700$	−30890.7	+	34331.9i	−0.0630423	+	0.0700652i
$701$	−145449.	−	447646.i	−0.295989	−	0.910959i	−0.982888	−	0.184206i	$-0.941029\pi$
$701$	−145449.	−	447646.i	−0.295989	−	0.910959i	0.686899	−	0.726753i	$-0.258971\pi$
$702$	454021.	+	174191.i	0.921301	+	0.353468i
$703$	35471.5	−	11525.4i	0.0717742	−	0.0233209i
$704$	−59961.7	+	185208.i	−0.120984	+	0.373693i
$705$	35094.6	+	25497.7i	0.0706093	+	0.0513007i
$706$	95837.2	−	249796.i	0.192276	−	0.501159i
$707$		−	653434.i		−	1.30726i
$708$	86952.2	−	195483.i	0.173466	−	0.389980i
$709$	−482182.	+	350326.i	−0.959222	+	0.696915i	−0.952970	−	0.303065i	$-0.901990\pi$
$709$	−482182.	+	350326.i	−0.959222	+	0.696915i	−0.00625170	+	0.999980i	$0.501990\pi$
$710$	−27091.4	+	7264.22i	−0.0537421	+	0.0144103i
$711$	−529680.	+	172104.i	−1.04779	+	0.340448i
$712$	−30276.5	−	190507.i	−0.0597236	−	0.375796i
$713$	218617.	−	377329.i	0.430036	−	0.742235i
$714$	223445.	−	145162.i	0.438302	−	0.284746i
$715$	−218983.	+	71151.8i	−0.428349	+	0.139179i
$716$	380169.	−	422519.i	0.741568	−	0.824177i
$717$	159957.	−	116216.i	0.311147	−	0.226062i
$718$	−134441.	−	206941.i	−0.260785	−	0.401419i
$719$			670466.i			1.29694i	0.761242	+	0.648468i	$0.224590\pi$
$719$			670466.i			1.29694i	−0.761242	+	0.648468i	$0.775410\pi$
$720$	−382166.	−	80950.9i	−0.737203	−	0.156155i
$721$	832011.	+	604492.i	1.60051	+	1.16284i
$722$	498760.	+	26050.9i	0.956792	+	0.0499745i
$723$	126758.	−	41186.2i	0.242493	−	0.0787907i
$724$	64607.3	+	303428.i	0.123255	+	0.578867i
$725$	−2983.46	−	9182.15i	−0.00567602	−	0.0174690i
$726$	197926.	−	53071.5i	0.375517	−	0.100690i
$727$	527671.	−	726277.i	0.998378	−	1.37415i	0.0720620	−	0.997400i	$-0.477042\pi$
$727$	527671.	−	726277.i	0.998378	−	1.37415i	0.926316	−	0.376749i	$-0.122958\pi$
$728$	107368.	−	680218.i	0.202587	−	1.28347i
$729$	−8888.14	+	27354.9i	−0.0167246	+	0.0514730i
$730$	−431856.	−	22556.5i	−0.810389	−	0.0423277i
$731$	−95139.9	−	30912.8i	−0.178044	−	0.0578501i
$732$	−48687.9	+	464808.i	−0.0908656	+	0.867464i
$733$	−382088.	+	277603.i	−0.711141	+	0.516674i	−0.883542	−	0.468353i	$-0.844848\pi$
$733$	−382088.	+	277603.i	−0.711141	+	0.516674i	0.172401	+	0.985027i	$0.444848\pi$
$734$	−528987.	+	653480.i	−0.981868	+	1.21294i
$735$	−24032.6	+	33078.0i	−0.0444862	+	0.0612300i
$736$	360862.	−	292746.i	0.666171	−	0.540426i
$737$	190873.	−	138677.i	0.351406	−	0.255312i
$738$	−374152.	+	243071.i	−0.686967	+	0.446293i
$739$		−	687813.i		−	1.25945i	−0.776817	−	0.629726i	$-0.783167\pi$
$739$		−	687813.i		−	1.25945i	0.776817	−	0.629726i	$-0.216833\pi$
$740$	−40171.5	−	188666.i	−0.0733592	−	0.344532i
$741$	19161.8	−	58974.1i	0.0348980	−	0.107405i
$742$	−14104.2	+	17423.5i	−0.0256177	+	0.0316466i
$743$			266579.i			0.482890i	0.970414	+	0.241445i	$0.0776214\pi$
$743$			266579.i			0.482890i	−0.970414	+	0.241445i	$0.922379\pi$
$744$	−160336.	+	197597.i	−0.289658	+	0.356973i
$745$	−463733.			−0.835518
$746$	727495.	+	588902.i	1.30723	+	1.05819i
$747$	39276.4	+	12761.7i	0.0703867	+	0.0228700i
$748$	225717.	−	48060.6i	0.403423	−	0.0858986i
$749$	59782.4			0.106564
$750$	146320.	+	225226.i	0.260125	+	0.400403i
$751$	−370737.	−	510275.i	−0.657333	−	0.904742i	0.342056	−	0.939679i	$-0.388877\pi$
$751$	−370737.	−	510275.i	−0.657333	−	0.904742i	−0.999389	+	0.0349379i	$0.988877\pi$
$752$	−111742.	+	11824.1i	−0.197597	+	0.0209089i
$753$	−333639.	−	242403.i	−0.588419	−	0.427512i
$754$	111894.	+	90577.4i	0.196818	+	0.159323i
$755$	382059.	+	525860.i	0.670250	+	0.922520i
$756$	506065.	+	53009.6i	0.885448	+	0.0927493i
$757$	−282068.	+	868116.i	−0.492223	+	1.51491i	0.329016	+	0.944324i	$0.393283\pi$
$757$	−282068.	+	868116.i	−0.492223	+	1.51491i	−0.821240	+	0.570583i	$0.806717\pi$
$758$	42322.1	−	810282.i	0.0736596	−	1.41026i
$759$	84864.2	+	27574.0i	0.147313	+	0.0478649i
$760$	−17614.1	+	111592.i	−0.0304954	+	0.193200i
$761$	233670.	+	169771.i	0.403491	+	0.293153i	0.770961	−	0.636882i	$-0.219776\pi$
$761$	233670.	+	169771.i	0.403491	+	0.293153i	−0.367470	+	0.930035i	$0.619776\pi$
$762$	−63820.2	−	238013.i	−0.109913	−	0.409911i
$763$	−18778.8	+	6101.60i	−0.0322566	+	0.0104808i
$764$	267988.	−	57061.1i	0.459122	−	0.0977582i
$765$	143104.	+	440429.i	0.244528	+	0.752581i
$766$	−55833.1	+	1.06896e6i	−0.0951556	+	1.82181i
$767$	−385283.	+	530296.i	−0.654921	+	0.901422i
$768$	−234629.	+	135904.i	−0.397795	+	0.230414i
$769$	−794267.			−1.34312			−0.671558	−	0.740952i	$-0.734375\pi$
$769$	−794267.			−1.34312			−0.671558	+	0.740952i	$0.734375\pi$
$770$	−202035.	+	131254.i	−0.340758	+	0.221376i
$771$	−215219.	−	296224.i	−0.362053	−	0.498323i
$772$	332990.	+	299613.i	0.558723	+	0.502720i
$773$	−225677.	−	694561.i	−0.377683	−	1.16239i	−0.941650	−	0.336592i	$-0.890726\pi$
$773$	−225677.	−	694561.i	−0.377683	−	1.16239i	0.563967	−	0.825797i	$-0.309274\pi$
$774$	−45887.6	−	70633.5i	−0.0765973	−	0.117904i
$775$	−52006.5	+	5386.13i	−0.0865872	+	0.00896753i
$776$	96421.8	+	606711.i	0.160122	+	1.00753i
$777$	34234.3	+	105362.i	0.0567047	+	0.174519i
$778$	108840.	+	405911.i	0.179817	+	0.670613i
$779$	75844.0	+	104390.i	0.124982	+	0.172022i
$780$	−293023.	−	130339.i	−0.481628	−	0.214232i
$781$	13951.8			0.0228732
$782$	−514300.	−	197317.i	−0.841013	−	0.322665i
$783$	−62523.8	+	86056.6i	−0.101982	+	0.140366i
$784$	−11144.6	−	105321.i	−0.0181315	−	0.171350i
$785$	−220628.	−	679023.i	−0.358031	−	1.10191i
$786$	11803.8	−	30766.3i	0.0191064	−	0.0498000i
$787$	407212.	−	132311.i	0.657463	−	0.213623i	0.0387610	−	0.999249i	$-0.487659\pi$
$787$	407212.	−	132311.i	0.657463	−	0.213623i	0.618702	+	0.785626i	$0.287659\pi$
$788$	244607.	+	220090.i	0.393928	+	0.354444i
$789$	−455911.	−	331238.i	−0.732362	−	0.532092i
$790$	804590.	−	215741.i	1.28920	−	0.345683i
$791$	−1.14966e6	−	373548.i	−1.83746	−	0.597026i
$792$	173182.	+	88125.4i	0.276091	+	0.140492i
$793$	442462.	−	1.36176e6i	0.703607	−	2.16548i
$794$	−630421.	−	510321.i	−0.999977	−	0.809474i
$795$	6136.21	+	8445.76i	0.00970880	+	0.0133630i
$796$	−63479.6	+	606019.i	−0.100186	+	0.956446i
$797$	927703.	+	674016.i	1.46047	+	1.06109i	0.983240	+	0.182314i	$0.0583588\pi$
$797$	927703.	+	674016.i	1.46047	+	1.06109i	0.477229	+	0.878779i	$0.341641\pi$
$798$	3384.36	−	64795.5i	0.00531460	−	0.101751i
$799$	78296.1	+	107765.i	0.122644	+	0.168805i
$800$	−53826.5	−	14372.0i	−0.0841040	−	0.0224563i
$801$	−192543.			−0.300098
$802$	−40100.7	+	104521.i	−0.0623452	+	0.162500i
$803$	204578.	+	66471.4i	0.317269	+	0.103087i
$804$	326826.	+	34234.5i	0.505597	+	0.0529605i
$805$	575080.			0.887435
$806$	606532.	−	489810.i	0.933649	−	0.753976i
$807$		−	295282.i		−	0.453409i
$808$	702149.	−	358230.i	1.07549	−	0.548705i
$809$	−369307.	+	1.13661e6i	−0.564274	+	1.73666i	0.105824	+	0.994385i	$0.466252\pi$
$809$	−369307.	+	1.13661e6i	−0.564274	+	1.73666i	−0.670098	+	0.742273i	$0.733748\pi$
$810$	−92217.4	+	240361.i	−0.140554	+	0.366348i
$811$		−	785831.i		−	1.19478i	−0.801952	−	0.597389i	$-0.796205\pi$
$811$		−	785831.i		−	1.19478i	0.801952	−	0.597389i	$-0.203795\pi$
$812$	137633.	+	61220.1i	0.208742	+	0.0928500i
$813$	114444.	−	83148.3i	0.173146	−	0.125798i
$814$	−5004.75	+	95818.9i	−0.00755325	+	0.144611i
$815$	438944.	−	604155.i	0.660836	−	0.909563i
$816$	278483.	+	160521.i	0.418233	+	0.241074i
$817$	−19707.1	+	14318.0i	−0.0295242	+	0.0214506i
$818$	291879.	+	236274.i	0.436210	+	0.353109i
$819$	−653729.	−	212409.i	−0.974608	−	0.316669i
$820$	577820.	−	333876.i	0.859340	−	0.496544i
$821$	305952.	−	941623.i	0.453907	−	1.39698i	−0.418507	−	0.908214i	$-0.637446\pi$
$821$	305952.	−	941623.i	0.453907	−	1.39698i	0.872414	−	0.488768i	$-0.162554\pi$
$822$	−589294.	+	158012.i	−0.872144	+	0.233855i
$823$	−199105.	+	274045.i	−0.293956	+	0.404596i	−0.930294	−	0.366814i	$-0.880448\pi$
$823$	−199105.	+	274045.i	−0.293956	+	0.404596i	0.636338	+	0.771410i	$0.280448\pi$
$824$	−193427.	+	1.22544e6i	−0.284881	+	1.80483i
$825$	−3306.00	−	10174.8i	−0.00485730	−	0.0149492i
$826$	−245682.	+	640359.i	−0.360091	+	0.938563i
$827$	−90293.3	+	29338.1i	−0.132021	+	0.0428964i	−0.374283	−	0.927315i	$-0.622111\pi$
$827$	−90293.3	+	29338.1i	−0.132021	+	0.0428964i	0.242261	+	0.970211i	$0.422111\pi$
$828$	−232051.	−	401597.i	−0.338471	−	0.585773i
$829$	743936.	+	540501.i	1.08250	+	0.786480i	0.978117	−	0.208057i	$-0.0667141\pi$
$829$	743936.	+	540501.i	1.08250	+	0.786480i	0.104380	+	0.994537i	$0.466714\pi$
$830$	−57670.1	−	22125.8i	−0.0837133	−	0.0321176i
$831$		−	368651.i		−	0.533843i
$832$	789791.	−	257541.i	1.14095	−	0.372048i
$833$	−101573.	+	73797.0i	−0.146382	+	0.106353i
$834$	154839.	+	577462.i	0.222612	+	0.830216i
$835$	476115.	−	154699.i	0.682871	−	0.221878i
$836$	22838.6	−	51345.0i	0.0326782	−	0.0734659i
$837$	384803.	+	428677.i	0.549273	+	0.611898i
$838$	636792.	+	980195.i	0.906795	+	1.39580i
$839$	77867.3	−	25300.6i	0.110619	−	0.0359424i	−0.253184	−	0.967418i	$-0.581478\pi$
$839$	77867.3	−	25300.6i	0.110619	−	0.0359424i	0.363804	+	0.931476i	$0.381478\pi$
$840$	−331467.	−	52319.9i	−0.469767	−	0.0741496i
$841$	546726.	−	397220.i	0.772997	−	0.561615i
$842$	−10063.3	+	6537.69i	−0.0141943	+	0.00922147i
$843$		−	385363.i		−	0.542269i
$844$	−765777.	+	163053.i	−1.07502	+	0.228898i
$845$	242955.	+	176517.i	0.340261	+	0.247214i
$846$	−5850.24	+	112006.i	−0.00817397	+	0.156495i
$847$	−624768.	+	202999.i	−0.870867	+	0.282962i
$848$	−26454.7	−	5603.66i	−0.0367884	−	0.00779256i
$849$	−170232.	−	523920.i	−0.236170	−	0.726858i
$850$	17104.8	+	63791.2i	0.0236745	+	0.0882923i
$851$	134618.	−	185286.i	0.185886	−	0.255849i
$852$	14445.7	+	12997.8i	0.0199004	+	0.0179057i
$853$	176346.	−	542737.i	0.242364	−	0.745919i	−0.753695	−	0.657224i	$-0.771730\pi$
$853$	176346.	−	542737.i	0.242364	−	0.745919i	0.996059	−	0.0886948i	$-0.0282696\pi$
$854$	78147.5	−	1.49618e6i	0.107152	−	2.05148i
$855$	107247.	+	34846.6i	0.146707	+	0.0476682i
$856$	32774.3	+	64239.3i	0.0447287	+	0.0876705i
$857$	−170288.	+	123722.i	−0.231859	+	0.168455i	−0.697648	−	0.716440i	$-0.745770\pi$
$857$	−170288.	+	123722.i	−0.231859	+	0.168455i	0.465790	+	0.884895i	$0.345770\pi$
$858$	123991.	+	100370.i	0.168428	+	0.136341i
$859$	−488681.	+	672611.i	−0.662276	+	0.911544i	−0.999554	−	0.0298608i	$-0.990494\pi$
$859$	−488681.	+	672611.i	−0.662276	+	0.911544i	0.337279	+	0.941405i	$0.390494\pi$
$860$	63030.0	+	109083.i	0.0852217	+	0.147489i
$861$	−310074.	+	225282.i	−0.418273	+	0.303893i
$862$	703864.	+	1.08344e6i	0.947271	+	1.45811i
$863$			347799.i			0.466990i	0.972358	+	0.233495i	$0.0750162\pi$
$863$			347799.i			0.466990i	−0.972358	+	0.233495i	$0.924984\pi$
$864$	220477.	+	572854.i	0.295349	+	0.767391i
$865$	96207.9	−	296097.i	0.128581	−	0.395733i
$866$	456502.	+	369535.i	0.608705	+	0.492742i
$867$		−	35489.2i		−	0.0472126i
$868$	480260.	−	659399.i	0.637437	−	0.875203i
$869$	−414356.			−0.548698
$870$	44138.0	−	54525.5i	0.0583142	−	0.0720379i
$871$	−957510.	−	311114.i	−1.26214	−	0.410094i
$872$	−16851.5	−	16833.7i	−0.0221619	−	0.0221385i
$873$	613194.			0.804580
$874$	−112483.	+	73075.2i	−0.147252	+	0.0956637i
$875$	−506091.	−	696574.i	−0.661017	−	0.909811i
$876$	149895.	+	259415.i	0.195334	+	0.338054i
$877$	546117.	+	396777.i	0.710046	+	0.515879i	0.883189	−	0.469018i	$-0.155392\pi$
$877$	546117.	+	396777.i	0.710046	+	0.515879i	−0.173142	+	0.984897i	$0.555392\pi$
$878$	−514559.	+	635656.i	−0.667492	+	0.824580i
$879$	337824.	+	464975.i	0.437233	+	0.601800i
$880$	−251800.	−	145141.i	−0.325155	−	0.187423i
$881$	−49916.7	+	153628.i	−0.0643123	+	0.197933i	−0.978049	−	0.208373i	$-0.933183\pi$
$881$	−49916.7	+	153628.i	−0.0643123	+	0.197933i	0.913737	+	0.406306i	$0.133183\pi$
$882$	−105570.	−	5514.07i	−0.135708	−	0.00708819i
$883$	−761032.	−	247274.i	−0.976072	−	0.317145i	−0.222807	−	0.974863i	$-0.571522\pi$
$883$	−761032.	−	247274.i	−0.976072	−	0.317145i	−0.753265	+	0.657718i	$0.771522\pi$
$884$	−732070.	−	658693.i	−0.936803	−	0.842905i
$885$	258411.	+	187747.i	0.329932	+	0.239710i
$886$	−525028.	+	140780.i	−0.668829	+	0.179338i
$887$	−472453.	+	153509.i	−0.600498	+	0.195114i	−0.593463	−	0.804862i	$-0.702240\pi$
$887$	−472453.	+	153509.i	−0.600498	+	0.195114i	−0.00703561	+	0.999975i	$0.502240\pi$
$888$	−94449.1	+	94548.8i	−0.119777	+	0.119903i
$889$	244113.	+	751303.i	0.308878	+	0.950630i
$890$	287594.	+	15021.4i	0.363078	+	0.0189641i
$891$	75270.3	−	103601.i	0.0948130	−	0.130499i
$892$	251145.	−	53474.8i	0.315642	−	0.0672078i
$893$	32436.2			0.0406749
$894$	175031.	+	269421.i	0.218998	+	0.337098i
$895$	498767.	+	686494.i	0.622661	+	0.857020i
$896$	728417.	−	474316.i	0.907328	−	0.590815i
$897$	−117666.	−	362138.i	−0.146240	−	0.450080i
$898$	101175.	−	65729.4i	0.125465	−	0.0815093i
$899$	69125.3	+	155896.i	0.0855298	+	0.192892i
$900$	−22600.6	+	50809.9i	−0.0279020	+	0.0627283i
$901$	9906.09	+	30487.8i	0.0122026	+	0.0375558i
$902$	−320624.	+	85971.3i	−0.394078	+	0.105667i
$903$	−42529.4	−	58536.7i	−0.0521571	−	0.0717881i
$904$	−228878.	−	1.44016e6i	−0.280070	−	1.76227i
$905$	−463156.			−0.565497
$906$	161311.	−	420450.i	0.196520	−	0.512222i
$907$	−796940.	+	1.09689e6i	−0.968749	+	1.33337i	−0.0260724	+	0.999660i	$0.508300\pi$
$907$	−796940.	+	1.09689e6i	−0.968749	+	1.33337i	−0.942676	+	0.333708i	$0.891700\pi$
$908$	−96165.8	−	166429.i	−0.116640	−	0.201863i
$909$	−243135.	−	748292.i	−0.294252	−	0.905615i
$910$	959878.	+	368269.i	1.15913	+	0.444716i
$911$	1.08393e6	−	352190.i	1.30606	−	0.424366i	0.428377	−	0.903600i	$-0.359085\pi$
$911$	1.08393e6	−	352190.i	1.30606	−	0.424366i	0.877687	+	0.479234i	$0.159085\pi$
$912$	71481.5	−	31885.9i	0.0859417	−	0.0383362i
$913$	24857.0	+	18059.7i	0.0298200	+	0.0216655i
$914$	−121524.	−	453214.i	−0.145469	−	0.542514i
$915$	−663580.	−	215610.i	−0.792594	−	0.257529i
$916$	−75682.1	+	43730.6i	−0.0901991	+	0.0521188i
$917$	−32644.4	+	100469.i	−0.0388212	+	0.119479i
$918$	457829.	−	565576.i	0.543273	−	0.671128i
$919$	60062.9	+	82669.5i	0.0711173	+	0.0978846i	0.843094	−	0.537766i	$-0.180732\pi$
$919$	60062.9	+	82669.5i	0.0711173	+	0.0978846i	−0.771977	+	0.635651i	$0.780732\pi$
$920$	315274.	+	617954.i	0.372488	+	0.730096i
$921$	−453198.	−	329268.i	−0.534280	−	0.388177i
$922$	−708236.	−	36992.1i	−0.833136	−	0.0435158i
$923$	−34994.4	−	48165.6i	−0.0410766	−	0.0565371i
$924$	152512.	+	67838.5i	0.178633	+	0.0794570i
$925$	−27459.2			−0.0320926
$926$	1.23294e6	+	473033.i	1.43787	+	0.551658i
$927$	1.17772e6	+	382663.i	1.37051	+	0.445305i
$928$	9669.78	+	181456.i	0.0112285	+	0.210705i
$929$	−226553.			−0.262505			−0.131253	−	0.991349i	$-0.541900\pi$
$929$	−226553.			−0.262505			−0.131253	+	0.991349i	$0.541900\pi$
$930$	−238683.	−	295561.i	−0.275965	−	0.341728i
$931$			30572.3i			0.0352719i
$932$	−846138.	−	88631.7i	−0.974113	−	0.102037i
$933$	−54084.7	+	166456.i	−0.0621314	+	0.191221i
$934$	462672.	+	177510.i	0.530371	+	0.203483i
$935$			344537.i			0.394105i
$936$	−130146.	−	818914.i	−0.148553	−	0.934731i
$937$	632509.	−	459545.i	0.720423	−	0.523418i	−0.166096	−	0.986110i	$-0.553116\pi$
$937$	632509.	−	459545.i	0.720423	−	0.523418i	0.886519	+	0.462691i	$0.153116\pi$
$938$	−1.05203e6	−	54948.8i	−1.19570	−	0.0624529i
$939$	161191.	−	221861.i	0.182814	−	0.251622i
$940$	17476.6	−	166843.i	0.0197788	−	0.188822i
$941$	−29399.4	+	21359.9i	−0.0332016	+	0.0241224i	−0.604262	−	0.796785i	$-0.706532\pi$
$941$	−29399.4	+	21359.9i	−0.0332016	+	0.0241224i	0.571061	+	0.820908i	$0.306532\pi$
$942$	−311226.	+	384471.i	−0.350731	+	0.433273i
$943$	753567.	+	244849.i	0.847420	+	0.275343i
$944$	−822788.	+	87064.0i	−0.923303	+	0.0977000i
$945$	−234748.	+	722480.i	−0.262868	+	0.809025i
$946$	−16229.9	−	60528.2i	−0.0181357	−	0.0676356i
$947$	187033.	−	257428.i	0.208553	−	0.287049i	−0.691907	−	0.721986i	$-0.743229\pi$
$947$	187033.	−	257428.i	0.208553	−	0.287049i	0.900461	+	0.434937i	$0.143229\pi$
$948$	−429026.	−	386023.i	−0.477383	−	0.429533i
$949$	−283652.	−	872990.i	−0.314958	−	0.969341i
$950$	15015.1	+	5760.71i	0.0166372	+	0.00638306i
$951$	192944.	−	62691.2i	0.213339	−	0.0693180i
$952$	−918377.	−	467326.i	−1.01332	−	0.515639i
$953$	349383.	+	253841.i	0.384694	+	0.279497i	0.763278	−	0.646070i	$-0.223589\pi$
$953$	349383.	+	253841.i	0.384694	+	0.279497i	−0.378584	+	0.925567i	$0.623589\pi$
$954$	−9668.58	+	25200.8i	−0.0106235	+	0.0276896i
$955$			409059.i			0.448518i
$956$	−698619.	−	310751.i	−0.764407	−	0.340014i
$957$	−28230.2	+	20510.5i	−0.0308241	+	0.0223950i
$958$	−822398.	+	220516.i	−0.896088	+	0.240275i
$959$	1.86015e6	−	604398.i	2.02260	−	0.657182i
$960$	−125499.	−	384862.i	−0.136175	−	0.417602i
$961$	903920.	−	189262.i	0.978776	−	0.204935i
$962$	343348.	−	223059.i	0.371009	−	0.241029i
$963$	68460.9	−	22244.3i	0.0738228	−	0.0239865i
$964$	−383156.	−	344751.i	−0.412308	−	0.370981i
$965$	−541030.	+	393081.i	−0.580987	+	0.422112i
$966$	−217058.	−	334111.i	−0.232606	−	0.358045i
$967$		−	847584.i		−	0.906421i	−0.891403	−	0.453211i	$-0.850279\pi$
$967$		−	847584.i		−	0.906421i	0.891403	−	0.453211i	$-0.149721\pi$
$968$	−560647.	−	560056.i	−0.598327	−	0.597696i
$969$	−75066.2	−	54538.8i	−0.0799460	−	0.0580842i
$970$	−915904.	−	47838.9i	−0.973434	−	0.0508438i
$971$	739946.	−	240423.i	0.784805	−	0.254998i	0.110914	−	0.993830i	$-0.464622\pi$
$971$	739946.	−	240423.i	0.784805	−	0.254998i	0.673890	+	0.738832i	$0.264622\pi$
$972$	934282.	−	198931.i	0.988884	−	0.210557i
$973$	−592263.	−	1.82280e6i	−0.625589	−	1.92536i
$974$	535923.	−	143701.i	0.564917	−	0.151476i
$975$	−26834.2	+	36934.1i	−0.0282280	+	0.0388525i
$976$	1.65057e6	−	736271.i	1.73274	−	0.772927i
$977$	−449076.	+	1.38211e6i	−0.470469	+	1.44795i	0.381503	+	0.924367i	$0.375407\pi$
$977$	−449076.	+	1.38211e6i	−0.470469	+	1.44795i	−0.851972	+	0.523587i	$0.824593\pi$
$978$	−516678.	−	26986.8i	−0.540185	−	0.0282146i
$979$	−136239.	−	44266.6i	−0.142146	−	0.0461860i
$980$	157256.	+	16472.3i	0.163740	+	0.0171515i
$981$	−19234.6	+	13974.7i	−0.0199868	+	0.0145213i
$982$	−128557.	+	158812.i	−0.133313	+	0.164688i
$983$	−1.03851e6	+	1.42938e6i	−1.07474	+	1.47925i	−0.209556	+	0.977797i	$0.567202\pi$
$983$	−1.03851e6	+	1.42938e6i	−1.07474	+	1.47925i	−0.865184	+	0.501455i	$0.832798\pi$
$984$	−412068.	−	209685.i	−0.425578	−	0.216560i
$985$	−397429.	+	288749.i	−0.409626	+	0.297611i
$986$	180641.	−	117355.i	0.185807	−	0.120711i
$987$			96346.4i			0.0989012i
$988$	−234543.	+	49939.9i	−0.240275	+	0.0511604i
$989$	−46223.2	+	142260.i	−0.0472572	+	0.145443i
$990$	−182526.	+	225482.i	−0.186232	+	0.230061i
$991$		−	539028.i		−	0.548864i	−0.961607	−	0.274432i	$-0.911510\pi$
$991$		−	539028.i		−	0.548864i	0.961607	−	0.274432i	$-0.0884897\pi$
$992$	971850.	+	154565.i	0.987588	+	0.157068i
$993$	147749.			0.149839
$994$	−48420.1	−	39195.7i	−0.0490064	−	0.0396703i
$995$	−865179.	−	281114.i	−0.873896	−	0.283946i
$996$	8912.26	+	41856.5i	0.00898399	+	0.0421933i
$997$	981734.			0.987651			0.493826	−	0.869561i	$-0.335598\pi$
$997$	981734.			0.987651			0.493826	+	0.869561i	$0.335598\pi$
$998$	−189813.	−	292173.i	−0.190574	−	0.293345i
$999$	177826.	+	244757.i	0.178182	+	0.245247i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	124.5.l.a.35.15	✓	248
4.3	odd	2	inner	124.5.l.a.35.36	yes	248
31.8	even	5	inner	124.5.l.a.39.36	yes	248
124.39	odd	10	inner	124.5.l.a.39.15	yes	248

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
124.5.l.a.35.15	✓	248	1.1	even	1	trivial
124.5.l.a.35.36	yes	248	4.3	odd	2	inner
124.5.l.a.39.15	yes	248	124.39	odd	10	inner
124.5.l.a.39.36	yes	248	31.8	even	5	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:	\( N \)	\(=\)	\( 124 = 2^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	124.l (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.10903 - 2.51673i) q^{2} +(-3.93487 - 1.27852i) q^{3} +(3.33209 + 15.6492i) q^{4} -23.8871 q^{5} +(9.01594 + 13.8780i) q^{6} +(-31.1843 - 42.9214i) q^{7} +(29.0253 - 57.0397i) q^{8} +(-51.6817 - 37.5490i) q^{9} +O(q^{10})\)	\(q+(-3.10903 - 2.51673i) q^{2} +(-3.93487 - 1.27852i) q^{3} +(3.33209 + 15.6492i) q^{4} -23.8871 q^{5} +(9.01594 + 13.8780i) q^{6} +(-31.1843 - 42.9214i) q^{7} +(29.0253 - 57.0397i) q^{8} +(-51.6817 - 37.5490i) q^{9} +(74.2656 + 60.1175i) q^{10} +(-27.9360 - 38.4506i) q^{11} +(6.89640 - 65.8377i) q^{12} +(-62.6726 + 192.886i) q^{13} +(-11.0692 + 211.926i) q^{14} +(93.9927 + 30.5401i) q^{15} +(-233.794 + 104.289i) q^{16} +(245.519 + 178.380i) q^{17} +(66.1791 + 246.810i) q^{18} +(70.2816 - 22.8359i) q^{19} +(-79.5941 - 373.814i) q^{20} +(67.8303 + 208.760i) q^{21} +(-9.91619 + 189.851i) q^{22} +(266.727 - 367.118i) q^{23} +(-187.137 + 187.335i) q^{24} -54.4065 q^{25} +(680.294 - 441.959i) q^{26} +(352.337 + 484.950i) q^{27} +(567.777 - 631.027i) q^{28} +(54.8365 + 168.769i) q^{29} +(-215.365 - 331.505i) q^{30} +(955.887 - 98.9979i) q^{31} +(989.341 + 264.161i) q^{32} +(60.7648 + 187.015i) q^{33} +(-314.390 - 1172.49i) q^{34} +(744.901 + 1025.27i) q^{35} +(415.403 - 933.894i) q^{36} +504.705 q^{37} +(-275.979 - 105.883i) q^{38} +(493.217 - 678.855i) q^{39} +(-693.330 + 1362.51i) q^{40} +(539.572 + 1660.63i) q^{41} +(314.508 - 819.752i) q^{42} +(-313.499 + 101.862i) q^{43} +(508.635 - 565.296i) q^{44} +(1234.53 + 896.936i) q^{45} +(-1753.20 + 470.099i) q^{46} +(417.447 + 135.637i) q^{47} +(1053.29 - 111.454i) q^{48} +(-127.843 + 393.459i) q^{49} +(169.151 + 136.927i) q^{50} +(-738.023 - 1015.80i) q^{51} +(-3227.35 - 338.060i) q^{52} +(85.4576 + 62.0886i) q^{53} +(125.066 - 2394.46i) q^{54} +(667.309 + 918.473i) q^{55} +(-3353.36 + 532.935i) q^{56} -305.745 q^{57} +(254.260 - 662.717i) q^{58} +(3073.78 + 998.731i) q^{59} +(-164.735 + 1572.67i) q^{60} -7059.90 q^{61} +(-3221.03 - 2097.93i) q^{62} +3389.19i q^{63} +(-2411.07 - 3311.19i) q^{64} +(1497.07 - 4607.50i) q^{65} +(281.747 - 734.363i) q^{66} +4964.11i q^{67} +(-1973.41 + 4436.55i) q^{68} +(-1518.91 + 1103.55i) q^{69} +(264.411 - 5062.31i) q^{70} +(-172.545 + 237.488i) q^{71} +(-3641.86 + 1858.04i) q^{72} +(-3661.55 + 2660.27i) q^{73} +(-1569.14 - 1270.21i) q^{74} +(214.083 + 69.5597i) q^{75} +(591.548 + 1023.76i) q^{76} +(-779.191 + 2398.10i) q^{77} +(-3241.93 + 869.283i) q^{78} +(5124.44 - 7053.19i) q^{79} +(5584.67 - 2491.17i) q^{80} +(832.611 + 2562.51i) q^{81} +(2501.83 - 6520.91i) q^{82} +(-614.826 + 199.769i) q^{83} +(-3040.91 + 1757.10i) q^{84} +(-5864.73 - 4260.97i) q^{85} +(1231.04 + 472.302i) q^{86} -734.196i q^{87} +(-3004.06 + 477.422i) q^{88} +(2438.41 - 1771.61i) q^{89} +(-1580.83 - 5895.58i) q^{90} +(10233.4 - 3325.02i) q^{91} +(6633.86 + 2950.79i) q^{92} +(-3887.87 - 832.575i) q^{93} +(-956.491 - 1472.30i) q^{94} +(-1678.82 + 545.483i) q^{95} +(-3555.20 - 2304.33i) q^{96} +(-7765.61 + 5642.05i) q^{97} +(1387.70 - 901.529i) q^{98} +3036.16i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 248 q - 3 q^{2} - 31 q^{4} - 16 q^{5} - 10 q^{6} - 237 q^{8} + 1560 q^{9}+O(q^{10}) \) 248 * q - 3 * q^2 - 31 * q^4 - 16 * q^5 - 10 * q^6 - 237 * q^8 + 1560 * q^9	\( 248 q - 3 q^{2} - 31 q^{4} - 16 q^{5} - 10 q^{6} - 237 q^{8} + 1560 q^{9} - 250 q^{10} - 210 q^{12} + 346 q^{13} + 226 q^{14} + 73 q^{16} - 6 q^{17} + 818 q^{18} - 975 q^{20} + 102 q^{21} + 1540 q^{22} + 1023 q^{24} + 26248 q^{25} - 360 q^{26} + 160 q^{28} - 6 q^{29} - 4022 q^{30} + 6862 q^{32} + 1110 q^{33} + 3067 q^{34} - 4568 q^{36} - 2096 q^{37} + 5050 q^{38} - 3206 q^{40} - 6 q^{41} - 3884 q^{42} - 5660 q^{44} - 10272 q^{45} + 3185 q^{46} - 16516 q^{48} + 12392 q^{49} - 7878 q^{50} - 5935 q^{52} - 8454 q^{53} + 1362 q^{54} + 39536 q^{56} + 10892 q^{57} - 1105 q^{58} - 1267 q^{60} + 11696 q^{61} - 21020 q^{62} - 24493 q^{64} - 3756 q^{65} - 33182 q^{66} - 31014 q^{68} + 31734 q^{69} + 4205 q^{70} - 59598 q^{72} - 16646 q^{73} - 7683 q^{74} - 16019 q^{76} - 16618 q^{77} - 11625 q^{78} + 63150 q^{80} - 33864 q^{81} - 25974 q^{82} - 43055 q^{84} + 23956 q^{85} - 26357 q^{86} - 34700 q^{88} + 4170 q^{89} + 20102 q^{90} - 22738 q^{92} + 35990 q^{93} - 25646 q^{94} + 50490 q^{96} - 6614 q^{97} - 49748 q^{98}+O(q^{100}) \) 248 * q - 3 * q^2 - 31 * q^4 - 16 * q^5 - 10 * q^6 - 237 * q^8 + 1560 * q^9 - 250 * q^10 - 210 * q^12 + 346 * q^13 + 226 * q^14 + 73 * q^16 - 6 * q^17 + 818 * q^18 - 975 * q^20 + 102 * q^21 + 1540 * q^22 + 1023 * q^24 + 26248 * q^25 - 360 * q^26 + 160 * q^28 - 6 * q^29 - 4022 * q^30 + 6862 * q^32 + 1110 * q^33 + 3067 * q^34 - 4568 * q^36 - 2096 * q^37 + 5050 * q^38 - 3206 * q^40 - 6 * q^41 - 3884 * q^42 - 5660 * q^44 - 10272 * q^45 + 3185 * q^46 - 16516 * q^48 + 12392 * q^49 - 7878 * q^50 - 5935 * q^52 - 8454 * q^53 + 1362 * q^54 + 39536 * q^56 + 10892 * q^57 - 1105 * q^58 - 1267 * q^60 + 11696 * q^61 - 21020 * q^62 - 24493 * q^64 - 3756 * q^65 - 33182 * q^66 - 31014 * q^68 + 31734 * q^69 + 4205 * q^70 - 59598 * q^72 - 16646 * q^73 - 7683 * q^74 - 16019 * q^76 - 16618 * q^77 - 11625 * q^78 + 63150 * q^80 - 33864 * q^81 - 25974 * q^82 - 43055 * q^84 + 23956 * q^85 - 26357 * q^86 - 34700 * q^88 + 4170 * q^89 + 20102 * q^90 - 22738 * q^92 + 35990 * q^93 - 25646 * q^94 + 50490 * q^96 - 6614 * q^97 - 49748 * q^98

Introduction

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