LMFDB - Embedded newform 95.4.e.c.26.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [95,4,Mod(11,95)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(95, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("95.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 95 = 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	95.e (of order $3$, degree $2$, 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:	$5.60518145055$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 3 x^{19} + 66 x^{18} - 125 x^{17} + 2555 x^{16} - 3995 x^{15} + 60229 x^{14} + \cdots + 2336368896 $ x^20 - 3x^19 + 66x^18 - 125x^17 + 2555x^16 - 3995x^15 + 60229x^14 - 60298x^13 + 973502x^12 - 718952x^11 + 10405341x^10 - 2780554x^9 + 75565678x^8 - 3086948x^7 + 383106268x^6 + 101986984x^5 + 1262984080x^4 + 373132800x^3 + 2532879168x^2 + 1338713856*x + 2336368896
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.7
Root			$-1.09984 + 1.90498i$ of defining polynomial
Character	$\chi$	$=$	95.26
Dual form			95.4.e.c.11.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.09984 + 1.90498i) q^{2} +(-4.37756 - 7.58215i) q^{3} +(1.58071 - 2.73786i) q^{4} +(2.50000 + 4.33013i) q^{5} +(9.62922 - 16.6783i) q^{6} -33.5680 q^{7} +24.5515 q^{8} +(-24.8260 + 43.0000i) q^{9} +O(q^{10})$	\(q+(1.09984 + 1.90498i) q^{2} +(-4.37756 - 7.58215i) q^{3} +(1.58071 - 2.73786i) q^{4} +(2.50000 + 4.33013i) q^{5} +(9.62922 - 16.6783i) q^{6} -33.5680 q^{7} +24.5515 q^{8} +(-24.8260 + 43.0000i) q^{9} +(-5.49920 + 9.52489i) q^{10} -52.8293 q^{11} -27.6785 q^{12} +(23.5896 - 40.8584i) q^{13} +(-36.9194 - 63.9463i) q^{14} +(21.8878 - 37.9108i) q^{15} +(14.3571 + 24.8672i) q^{16} +(-19.3309 - 33.4821i) q^{17} -109.219 q^{18} +(-57.7308 + 59.3814i) q^{19} +15.8071 q^{20} +(146.946 + 254.518i) q^{21} +(-58.1037 - 100.639i) q^{22} +(94.9663 - 164.486i) q^{23} +(-107.476 - 186.153i) q^{24} +(-12.5000 + 21.6506i) q^{25} +103.779 q^{26} +198.322 q^{27} +(-53.0611 + 91.9045i) q^{28} +(51.2938 - 88.8434i) q^{29} +96.2922 q^{30} +62.8629 q^{31} +(66.6251 - 115.398i) q^{32} +(231.263 + 400.560i) q^{33} +(42.5218 - 73.6500i) q^{34} +(-83.9199 - 145.354i) q^{35} +(78.4853 + 135.941i) q^{36} -121.050 q^{37} +(-176.615 - 44.6659i) q^{38} -413.060 q^{39} +(61.3788 + 106.311i) q^{40} +(18.6460 + 32.2958i) q^{41} +(-323.234 + 559.857i) q^{42} +(-92.8180 - 160.765i) q^{43} +(-83.5076 + 144.639i) q^{44} -248.260 q^{45} +417.791 q^{46} +(-142.854 + 247.430i) q^{47} +(125.698 - 217.715i) q^{48} +783.809 q^{49} -54.9920 q^{50} +(-169.245 + 293.140i) q^{51} +(-74.5765 - 129.170i) q^{52} +(139.396 - 241.441i) q^{53} +(218.122 + 377.798i) q^{54} +(-132.073 - 228.758i) q^{55} -824.145 q^{56} +(702.959 + 177.778i) q^{57} +225.660 q^{58} +(49.5587 + 85.8381i) q^{59} +(-69.1963 - 119.852i) q^{60} +(192.118 - 332.758i) q^{61} +(69.1391 + 119.752i) q^{62} +(833.360 - 1443.42i) q^{63} +522.821 q^{64} +235.896 q^{65} +(-508.705 + 881.103i) q^{66} +(275.126 - 476.532i) q^{67} -122.226 q^{68} -1662.88 q^{69} +(184.597 - 319.731i) q^{70} +(-446.673 - 773.660i) q^{71} +(-609.517 + 1055.71i) q^{72} +(97.1143 + 168.207i) q^{73} +(-133.135 - 230.597i) q^{74} +218.878 q^{75} +(71.3227 + 251.924i) q^{76} +1773.37 q^{77} +(-454.299 - 786.869i) q^{78} +(318.203 + 551.144i) q^{79} +(-71.7854 + 124.336i) q^{80} +(-197.861 - 342.705i) q^{81} +(-41.0152 + 71.0405i) q^{82} -465.318 q^{83} +929.112 q^{84} +(96.6546 - 167.411i) q^{85} +(204.170 - 353.632i) q^{86} -898.166 q^{87} -1297.04 q^{88} +(-617.121 + 1068.88i) q^{89} +(-273.047 - 472.930i) q^{90} +(-791.855 + 1371.53i) q^{91} +(-300.228 - 520.010i) q^{92} +(-275.186 - 476.636i) q^{93} -628.464 q^{94} +(-401.456 - 101.528i) q^{95} -1166.62 q^{96} +(-355.282 - 615.367i) q^{97} +(862.064 + 1493.14i) q^{98} +(1311.54 - 2271.66i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 3 q^{2} - 5 q^{3} - 43 q^{4} + 50 q^{5} + 9 q^{6} + 6 q^{7} + 96 q^{8} - 97 q^{9}+O(q^{10}) $ 20 * q - 3 * q^2 - 5 * q^3 - 43 * q^4 + 50 * q^5 + 9 * q^6 + 6 * q^7 + 96 * q^8 - 97 * q^9	\( 20 q - 3 q^{2} - 5 q^{3} - 43 q^{4} + 50 q^{5} + 9 q^{6} + 6 q^{7} + 96 q^{8} - 97 q^{9} + 15 q^{10} - 36 q^{11} + 186 q^{12} + 14 q^{13} + 68 q^{14} + 25 q^{15} + 9 q^{16} - 144 q^{17} - 22 q^{18} + 96 q^{19} - 430 q^{20} + 46 q^{21} - 136 q^{22} + 321 q^{23} - 416 q^{24} - 250 q^{25} - 46 q^{26} + 1006 q^{27} + 130 q^{28} - 178 q^{29} + 90 q^{30} + 604 q^{31} - 202 q^{32} + 1099 q^{33} - 751 q^{34} + 15 q^{35} - 526 q^{36} - 774 q^{37} - 12 q^{38} - 1216 q^{39} + 240 q^{40} - 388 q^{41} + 143 q^{42} - 514 q^{43} - 1246 q^{44} - 970 q^{45} + 3650 q^{46} + 522 q^{47} + 4 q^{48} + 1582 q^{49} + 150 q^{50} - 1080 q^{51} + 569 q^{52} - 681 q^{53} - 321 q^{54} - 90 q^{55} - 3184 q^{56} + 514 q^{57} + 1198 q^{58} - 891 q^{59} + 465 q^{60} + 1110 q^{61} - 1921 q^{62} - 727 q^{63} + 952 q^{64} + 140 q^{65} + 3312 q^{66} - 691 q^{67} - 228 q^{68} + 172 q^{69} - 340 q^{70} + 382 q^{71} - 2678 q^{72} - 797 q^{73} + 404 q^{74} + 250 q^{75} + 462 q^{76} + 2390 q^{77} + 1000 q^{78} - 660 q^{79} - 45 q^{80} - 2454 q^{81} - 1155 q^{82} - 2026 q^{83} + 10756 q^{84} + 720 q^{85} + 858 q^{86} + 312 q^{87} - 98 q^{88} - 2957 q^{89} - 55 q^{90} - 3110 q^{91} + 98 q^{92} + 1500 q^{93} - 6374 q^{94} + 945 q^{95} - 584 q^{96} - 2881 q^{97} + 4062 q^{98} + 2723 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 - 5 * q^3 - 43 * q^4 + 50 * q^5 + 9 * q^6 + 6 * q^7 + 96 * q^8 - 97 * q^9 + 15 * q^10 - 36 * q^11 + 186 * q^12 + 14 * q^13 + 68 * q^14 + 25 * q^15 + 9 * q^16 - 144 * q^17 - 22 * q^18 + 96 * q^19 - 430 * q^20 + 46 * q^21 - 136 * q^22 + 321 * q^23 - 416 * q^24 - 250 * q^25 - 46 * q^26 + 1006 * q^27 + 130 * q^28 - 178 * q^29 + 90 * q^30 + 604 * q^31 - 202 * q^32 + 1099 * q^33 - 751 * q^34 + 15 * q^35 - 526 * q^36 - 774 * q^37 - 12 * q^38 - 1216 * q^39 + 240 * q^40 - 388 * q^41 + 143 * q^42 - 514 * q^43 - 1246 * q^44 - 970 * q^45 + 3650 * q^46 + 522 * q^47 + 4 * q^48 + 1582 * q^49 + 150 * q^50 - 1080 * q^51 + 569 * q^52 - 681 * q^53 - 321 * q^54 - 90 * q^55 - 3184 * q^56 + 514 * q^57 + 1198 * q^58 - 891 * q^59 + 465 * q^60 + 1110 * q^61 - 1921 * q^62 - 727 * q^63 + 952 * q^64 + 140 * q^65 + 3312 * q^66 - 691 * q^67 - 228 * q^68 + 172 * q^69 - 340 * q^70 + 382 * q^71 - 2678 * q^72 - 797 * q^73 + 404 * q^74 + 250 * q^75 + 462 * q^76 + 2390 * q^77 + 1000 * q^78 - 660 * q^79 - 45 * q^80 - 2454 * q^81 - 1155 * q^82 - 2026 * q^83 + 10756 * q^84 + 720 * q^85 + 858 * q^86 + 312 * q^87 - 98 * q^88 - 2957 * q^89 - 55 * q^90 - 3110 * q^91 + 98 * q^92 + 1500 * q^93 - 6374 * q^94 + 945 * q^95 - 584 * q^96 - 2881 * q^97 + 4062 * q^98 + 2723 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/95\mathbb{Z}\right)^\times$.

$n$	$21$	$77$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.09984	+	1.90498i	0.388852	+	0.673511i	0.992295	−	0.123894i	$-0.0395384\pi$
$2$	1.09984	+	1.90498i	0.388852	+	0.673511i	−0.603443	+	0.797406i	$0.706205\pi$
$3$	−4.37756	−	7.58215i	−0.842462	−	1.45919i	−0.887808	−	0.460215i	$-0.847772\pi$
$3$	−4.37756	−	7.58215i	−0.842462	−	1.45919i	0.0453461	−	0.998971i	$-0.485561\pi$
$4$	1.58071	−	2.73786i	0.197588	−	0.342233i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	9.62922	−	16.6783i	0.655186	−	1.13481i
$7$	−33.5680			−1.81250			−0.906250	−	0.422742i	$-0.861068\pi$
$7$	−33.5680			−1.81250			−0.906250	+	0.422742i	$0.861068\pi$
$8$	24.5515			1.08503
$9$	−24.8260	+	43.0000i	−0.919483	+	1.59259i
$10$	−5.49920	+	9.52489i	−0.173900	+	0.301203i
$11$	−52.8293			−1.44806			−0.724029	−	0.689770i	$-0.757712\pi$
$11$	−52.8293			−1.44806			−0.724029	+	0.689770i	$0.757712\pi$
$12$	−27.6785			−0.665842
$13$	23.5896	−	40.8584i	0.503275	−	0.871699i	−0.496717	−	0.867912i	$-0.665461\pi$
$13$	23.5896	−	40.8584i	0.503275	−	0.871699i	0.999993	−	0.00378625i	$-0.00120520\pi$
$14$	−36.9194	−	63.9463i	−0.704794	−	1.22074i
$15$	21.8878	−	37.9108i	0.376760	−	0.652568i
$16$	14.3571	+	24.8672i	0.224330	+	0.388550i
$17$	−19.3309	−	33.4821i	−0.275790	−	0.477683i	0.694544	−	0.719450i	$-0.255606\pi$
$17$	−19.3309	−	33.4821i	−0.275790	−	0.477683i	−0.970334	+	0.241767i	$0.922273\pi$
$18$	−109.219			−1.43017
$19$	−57.7308	+	59.3814i	−0.697071	+	0.717002i
$19$	−57.7308	+	59.3814i	−0.697071	+	0.717002i
$20$	15.8071			0.176728
$21$	146.946	+	254.518i	1.52696	+	2.64478i
$22$	−58.1037	−	100.639i	−0.563080	−	0.975283i
$23$	94.9663	−	164.486i	0.860950	−	1.49121i	−0.0100635	−	0.999949i	$-0.503203\pi$
$23$	94.9663	−	164.486i	0.860950	−	1.49121i	0.871013	−	0.491259i	$-0.163463\pi$
$24$	−107.476	−	186.153i	−0.914100	−	1.58327i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	103.779			0.782799
$27$	198.322			1.41359
$28$	−53.0611	+	91.9045i	−0.358129	+	0.620297i
$29$	51.2938	−	88.8434i	0.328449	−	0.568890i	−0.653755	−	0.756706i	$-0.726807\pi$
$29$	51.2938	−	88.8434i	0.328449	−	0.568890i	0.982204	+	0.187816i	$0.0601408\pi$
$30$	96.2922			0.586016
$31$	62.8629			0.364210			0.182105	−	0.983279i	$-0.441709\pi$
$31$	62.8629			0.364210			0.182105	+	0.983279i	$0.441709\pi$
$32$	66.6251	−	115.398i	0.368055	−	0.637490i
$33$	231.263	+	400.560i	1.21993	+	2.11299i
$34$	42.5218	−	73.6500i	0.214483	−	0.371496i
$35$	−83.9199	−	145.354i	−0.405287	−	0.701978i
$36$	78.4853	+	135.941i	0.363358	+	0.629354i
$37$	−121.050			−0.537851			−0.268925	−	0.963161i	$-0.586669\pi$
$37$	−121.050			−0.537851			−0.268925	+	0.963161i	$0.586669\pi$
$38$	−176.615	−	44.6659i	−0.753966	−	0.190678i
$39$	−413.060			−1.69596
$40$	61.3788	+	106.311i	0.242621	+	0.420232i
$41$	18.6460	+	32.2958i	0.0710248	+	0.123019i	0.899351	−	0.437228i	$-0.144040\pi$
$41$	18.6460	+	32.2958i	0.0710248	+	0.123019i	−0.828326	+	0.560247i	$0.810706\pi$
$42$	−323.234	+	559.857i	−1.18752	+	2.05685i
$43$	−92.8180	−	160.765i	−0.329177	−	0.570151i	0.653172	−	0.757210i	$-0.273438\pi$
$43$	−92.8180	−	160.765i	−0.329177	−	0.570151i	−0.982349	+	0.187058i	$0.940105\pi$
$44$	−83.5076	+	144.639i	−0.286119	+	0.495573i
$45$	−248.260			−0.822410
$46$	417.791			1.33913
$47$	−142.854	+	247.430i	−0.443348	+	0.767901i	−0.997935	−	0.0642246i	$-0.979543\pi$
$47$	−142.854	+	247.430i	−0.443348	+	0.767901i	0.554588	+	0.832125i	$0.312876\pi$
$48$	125.698	−	217.715i	0.377978	−	0.654677i
$49$	783.809			2.28516
$50$	−54.9920			−0.155541
$51$	−169.245	+	293.140i	−0.464686	+	0.804859i
$52$	−74.5765	−	129.170i	−0.198883	−	0.344475i
$53$	139.396	−	241.441i	0.361274	−	0.625746i	−0.626896	−	0.779103i	$-0.715675\pi$
$53$	139.396	−	241.441i	0.361274	−	0.625746i	0.988171	+	0.153357i	$0.0490084\pi$
$54$	218.122	+	377.798i	0.549678	+	0.952071i
$55$	−132.073	−	228.758i	−0.323795	−	0.560830i
$56$	−824.145			−1.96663
$57$	702.959	+	177.778i	1.63349	+	0.413111i
$58$	225.660			0.510872
$59$	49.5587	+	85.8381i	0.109356	+	0.189410i	0.915509	−	0.402296i	$-0.131788\pi$
$59$	49.5587	+	85.8381i	0.109356	+	0.189410i	−0.806154	+	0.591706i	$0.798455\pi$
$60$	−69.1963	−	119.852i	−0.148887	−	0.257879i
$61$	192.118	−	332.758i	0.403249	−	0.698448i	−0.590867	−	0.806769i	$-0.701214\pi$
$61$	192.118	−	332.758i	0.403249	−	0.698448i	0.994116	+	0.108321i	$0.0345475\pi$
$62$	69.1391	+	119.752i	0.141624	+	0.245300i
$63$	833.360	−	1443.42i	1.66656	−	2.88657i
$64$	522.821			1.02114
$65$	235.896			0.450143
$66$	−508.705	+	881.103i	−0.948747	+	1.64328i
$67$	275.126	−	476.532i	0.501672	−	0.868921i	−0.498327	−	0.866989i	$-0.666052\pi$
$67$	275.126	−	476.532i	0.501672	−	0.868921i	0.999998	−	0.00193131i	$-0.000614756\pi$
$68$	−122.226			−0.217972
$69$	−1662.88			−2.90127
$70$	184.597	−	319.731i	0.315194	−	0.545931i
$71$	−446.673	−	773.660i	−0.746624	−	1.29319i	−0.949432	−	0.313973i	$-0.898340\pi$
$71$	−446.673	−	773.660i	−0.746624	−	1.29319i	0.202808	−	0.979219i	$-0.434993\pi$
$72$	−609.517	+	1055.71i	−0.997670	+	1.72802i
$73$	97.1143	+	168.207i	0.155704	+	0.269687i	0.933315	−	0.359059i	$-0.116902\pi$
$73$	97.1143	+	168.207i	0.155704	+	0.269687i	−0.777611	+	0.628745i	$0.783569\pi$
$74$	−133.135	−	230.597i	−0.209144	−	0.362249i
$75$	218.878			0.336985
$76$	71.3227	+	251.924i	0.107648	+	0.380232i
$77$	1773.37			2.62460
$78$	−454.299	−	786.869i	−0.659478	−	1.14225i
$79$	318.203	+	551.144i	0.453173	+	0.784919i	0.998581	−	0.0532519i	$-0.0169586\pi$
$79$	318.203	+	551.144i	0.453173	+	0.784919i	−0.545408	+	0.838171i	$0.683625\pi$
$80$	−71.7854	+	124.336i	−0.100323	+	0.173765i
$81$	−197.861	−	342.705i	−0.271414	−	0.470104i
$82$	−41.0152	+	71.0405i	−0.0552363	+	0.0956720i
$83$	−465.318			−0.615365			−0.307683	−	0.951489i	$-0.599554\pi$
$83$	−465.318			−0.615365			−0.307683	+	0.951489i	$0.599554\pi$
$84$	929.112			1.20684
$85$	96.6546	−	167.411i	0.123337	−	0.213626i
$86$	204.170	−	353.632i	0.256002	−	0.443409i
$87$	−898.166			−1.10682
$88$	−1297.04			−1.57119
$89$	−617.121	+	1068.88i	−0.734996	+	1.27305i	0.219728	+	0.975561i	$0.429483\pi$
$89$	−617.121	+	1068.88i	−0.734996	+	1.27305i	−0.954725	+	0.297490i	$0.903850\pi$
$90$	−273.047	−	472.930i	−0.319796	−	0.553903i
$91$	−791.855	+	1371.53i	−0.912187	+	1.57995i
$92$	−300.228	−	520.010i	−0.340227	−	0.589291i
$93$	−275.186	−	476.636i	−0.306833	−	0.531450i
$94$	−628.464			−0.689586
$95$	−401.456	−	101.528i	−0.433563	−	0.109648i
$96$	−1166.62			−1.24029
$97$	−355.282	−	615.367i	−0.371891	−	0.644135i	0.617965	−	0.786205i	$-0.287957\pi$
$97$	−355.282	−	615.367i	−0.371891	−	0.644135i	−0.989857	+	0.142071i	$0.954624\pi$
$98$	862.064	+	1493.14i	0.888588	+	1.53908i
$99$	1311.54	−	2271.66i	1.33146	−	2.30616i
$100$	39.5176	+	68.4466i	0.0395176	+	0.0684466i
$101$	−192.743	+	333.840i	−0.189887	+	0.328894i	−0.945212	−	0.326456i	$-0.894146\pi$
$101$	−192.743	+	333.840i	−0.189887	+	0.328894i	0.755325	+	0.655350i	$0.227479\pi$
$102$	−744.567			−0.722776
$103$	−237.487			−0.227187			−0.113594	−	0.993527i	$-0.536236\pi$
$103$	−237.487			−0.227187			−0.113594	+	0.993527i	$0.536236\pi$
$104$	579.161	−	1003.14i	0.546071	−	0.945823i
$105$	−734.729	+	1272.59i	−0.682878	+	1.18278i
$106$	613.254			0.561929
$107$	−150.931			−0.136365			−0.0681826	−	0.997673i	$-0.521720\pi$
$107$	−150.931			−0.136365			−0.0681826	+	0.997673i	$0.521720\pi$
$108$	313.488	−	542.977i	0.279309	−	0.483778i
$109$	−197.545	−	342.158i	−0.173590	−	0.300668i	0.766082	−	0.642743i	$-0.222204\pi$
$109$	−197.545	−	342.158i	−0.173590	−	0.300668i	−0.939673	+	0.342075i	$0.888870\pi$
$110$	290.519	−	503.193i	0.251817	−	0.436160i
$111$	529.903	+	917.819i	0.453119	+	0.784825i
$112$	−481.938	−	834.742i	−0.406597	−	0.704247i
$113$	−1310.50			−1.09099			−0.545495	−	0.838114i	$-0.683658\pi$
$113$	−1310.50			−1.09099			−0.545495	+	0.838114i	$0.683658\pi$
$114$	434.478	+	1534.65i	0.356953	+	1.26082i
$115$	949.663			0.770057
$116$	−162.161	−	280.871i	−0.129795	−	0.224812i
$117$	1171.27	+	2028.70i	0.925506	+	1.60302i
$118$	−109.013	+	188.816i	−0.0850464	+	0.147305i
$119$	648.900	+	1123.93i	0.499870	+	0.865801i
$120$	537.379	−	930.767i	0.408798	−	0.708059i
$121$	1459.93			1.09687
$122$	845.196			0.627217
$123$	163.248	−	282.754i	0.119671	−	0.207277i
$124$	99.3678	−	172.110i	0.0719637	−	0.124645i
$125$	−125.000			−0.0894427
$126$	3666.25			2.59219
$127$	−954.294	+	1652.89i	−0.666771	+	1.15488i	0.312031	+	0.950072i	$0.398991\pi$
$127$	−954.294	+	1652.89i	−0.666771	+	1.15488i	−0.978802	+	0.204809i	$0.934343\pi$
$128$	42.0185	+	72.7782i	0.0290152	+	0.0502558i
$129$	−812.632	+	1407.52i	−0.554638	+	0.960661i
$130$	259.448	+	449.377i	0.175039	+	0.303177i
$131$	−620.371	−	1074.51i	−0.413756	−	0.716647i	0.581541	−	0.813517i	$-0.302450\pi$
$131$	−620.371	−	1074.51i	−0.413756	−	0.716647i	−0.995297	+	0.0968702i	$0.969117\pi$
$132$	1462.24			0.964177
$133$	1937.91	−	1993.31i	1.26344	−	1.29957i
$134$	1210.38			0.780304
$135$	495.804	+	858.757i	0.316089	+	0.547482i
$136$	−474.604	−	822.038i	−0.299242	−	0.518303i
$137$	−390.802	+	676.889i	−0.243712	+	0.422121i	−0.961769	−	0.273863i	$-0.911698\pi$
$137$	−390.802	+	676.889i	−0.243712	+	0.422121i	0.718057	+	0.695984i	$0.245032\pi$
$138$	−1828.90	−	3167.75i	−1.12816	−	1.95404i
$139$	−245.493	+	425.206i	−0.149802	+	0.259464i	−0.931154	−	0.364626i	$-0.881197\pi$
$139$	−245.493	+	425.206i	−0.149802	+	0.259464i	0.781352	+	0.624090i	$0.214530\pi$
$140$	−530.611			−0.320320
$141$	2501.40			1.49401
$142$	982.537	−	1701.80i	0.580653	−	1.00572i
$143$	−1246.22	+	2158.52i	−0.728772	+	1.26227i
$144$	−1425.72			−0.825069
$145$	512.938			0.293774
$146$	−213.620	+	370.001i	−0.121091	+	0.209736i
$147$	−3431.17	−	5942.96i	−1.92516	−	3.33447i
$148$	−191.344	+	331.418i	−0.106273	+	0.184070i
$149$	−1150.47	−	1992.67i	−0.632552	−	1.09561i	−0.987028	−	0.160547i	$-0.948674\pi$
$149$	−1150.47	−	1992.67i	−0.632552	−	1.09561i	0.354476	−	0.935065i	$-0.384659\pi$
$150$	240.731	+	416.958i	0.131037	+	0.226963i
$151$	1088.03			0.586376			0.293188	−	0.956055i	$-0.405284\pi$
$151$	1088.03			0.586376			0.293188	+	0.956055i	$0.405284\pi$
$152$	−1417.38	+	1457.90i	−0.756346	+	0.777971i
$153$	1919.64			1.01434
$154$	1950.43	+	3378.24i	1.02058	+	1.76770i
$155$	157.157	+	272.204i	0.0814399	+	0.141058i
$156$	−652.926	+	1130.90i	−0.335102	+	0.580413i
$157$	944.065	+	1635.17i	0.479902	+	0.831215i	0.999734	−	0.0230538i	$-0.00733890\pi$
$157$	944.065	+	1635.17i	0.479902	+	0.831215i	−0.519832	+	0.854268i	$0.674006\pi$
$158$	−699.945	+	1212.34i	−0.352434	+	0.610434i
$159$	−2440.86			−1.21744
$160$	666.251			0.329199
$161$	−3187.83	+	5521.48i	−1.56047	+	2.70282i
$162$	435.231	−	753.842i	0.211080	−	0.365601i
$163$	2939.53			1.41253			0.706263	−	0.707950i	$-0.250380\pi$
$163$	2939.53			1.41253			0.706263	+	0.707950i	$0.250380\pi$
$164$	117.895			0.0561347
$165$	−1156.32	+	2002.80i	−0.545570	+	0.944956i
$166$	−511.776	−	886.421i	−0.239286	−	0.414456i
$167$	484.227	−	838.706i	0.224375	−	0.388629i	−0.731757	−	0.681566i	$-0.761299\pi$
$167$	484.227	−	838.706i	0.224375	−	0.388629i	0.956132	+	0.292937i	$0.0946326\pi$
$168$	3607.74	+	6248.79i	1.65681	+	2.86967i
$169$	−14.4393	−	25.0095i	−0.00657226	−	0.0113835i
$170$	425.218			0.191840
$171$	−1120.17	−	3956.63i	−0.500945	−	1.76942i
$172$	−586.872			−0.260166
$173$	−252.819	−	437.895i	−0.111107	−	0.192443i	0.805110	−	0.593125i	$-0.202106\pi$
$173$	−252.819	−	437.895i	−0.111107	−	0.192443i	−0.916217	+	0.400683i	$0.868773\pi$
$174$	−987.839	−	1710.99i	−0.430390	−	0.745457i
$175$	419.600	−	726.768i	0.181250	−	0.313934i
$176$	−758.475	−	1313.72i	−0.324842	−	0.562643i
$177$	433.892	−	751.523i	0.184256	−	0.319141i
$178$	−2714.94			−1.14322
$179$	1467.79			0.612894			0.306447	−	0.951888i	$-0.400860\pi$
$179$	1467.79			0.612894			0.306447	+	0.951888i	$0.400860\pi$
$180$	−392.427	+	679.703i	−0.162499	+	0.281456i
$181$	223.681	−	387.427i	0.0918569	−	0.159101i	−0.816436	−	0.577436i	$-0.804053\pi$
$181$	223.681	−	387.427i	0.0918569	−	0.159101i	0.908292	+	0.418336i	$0.137386\pi$
$182$	−3483.66			−1.41882
$183$	−3364.03			−1.35889
$184$	2331.57	−	4038.39i	0.934160	−	1.61801i
$185$	−302.625	−	524.162i	−0.120267	−	0.208309i
$186$	605.321	−	1048.45i	0.238625	−	0.413311i
$187$	1021.24	+	1768.84i	0.399360	+	0.691713i
$188$	451.619	+	782.227i	0.175201	+	0.303456i
$189$	−6657.25			−2.56214
$190$	−248.128	−	876.430i	−0.0947427	−	0.334647i
$191$	1763.01			0.667889			0.333944	−	0.942593i	$-0.391620\pi$
$191$	1763.01			0.667889			0.333944	+	0.942593i	$0.391620\pi$
$192$	−2288.68	−	3964.11i	−0.860267	−	1.49003i
$193$	−1630.63	−	2824.34i	−0.608164	−	1.05337i	−0.991543	−	0.129780i	$-0.958573\pi$
$193$	−1630.63	−	2824.34i	−0.608164	−	1.05337i	0.383379	−	0.923591i	$-0.374760\pi$
$194$	781.507	−	1353.61i	0.289221	−	0.500946i
$195$	−1032.65	−	1788.60i	−0.379228	−	0.656843i
$196$	1238.97	−	2145.96i	0.451520	−	0.782056i
$197$	3612.79			1.30660			0.653301	−	0.757098i	$-0.273384\pi$
$197$	3612.79			1.30660			0.653301	+	0.757098i	$0.273384\pi$
$198$	5769.94			2.07097
$199$	2332.57	−	4040.13i	0.830912	−	1.43918i	−0.0664044	−	0.997793i	$-0.521153\pi$
$199$	2332.57	−	4040.13i	0.830912	−	1.43918i	0.897316	−	0.441389i	$-0.145514\pi$
$200$	−306.894	+	531.556i	−0.108503	+	0.187933i
$201$	−4817.52			−1.69056
$202$	−847.944			−0.295352
$203$	−1721.83	+	2982.29i	−0.595314	+	1.03111i
$204$	535.052	+	926.737i	0.183633	+	0.318061i
$205$	−93.2300	+	161.479i	−0.0317633	+	0.0550156i
$206$	−261.198	−	452.407i	−0.0883422	−	0.153013i
$207$	4715.27	+	8167.09i	1.58326	+	2.74228i
$208$	1354.71			0.451598
$209$	3049.88	−	3137.08i	1.00940	−	1.03826i
$210$	−3232.34			−1.06215
$211$	1021.28	+	1768.92i	0.333214	+	0.577143i	0.983140	−	0.182854i	$-0.0585336\pi$
$211$	1021.28	+	1768.92i	0.333214	+	0.577143i	−0.649926	+	0.759997i	$0.725200\pi$
$212$	−440.689	−	763.296i	−0.142767	−	0.247280i
$213$	−3910.67	+	6773.49i	−1.25800	+	2.17893i
$214$	−166.000	−	287.521i	−0.0530258	−	0.0918435i
$215$	464.090	−	803.827i	0.147212	−	0.254979i
$216$	4869.10			1.53380
$217$	−2110.18			−0.660131
$218$	434.535	−	752.637i	0.135002	−	0.233830i
$219$	850.247	−	1472.67i	0.262349	−	0.454401i
$220$	−835.076			−0.255913
$221$	−1824.04			−0.555194
$222$	−1165.62	+	2018.91i	−0.352392	+	0.610361i
$223$	2894.33	+	5013.12i	0.869141	+	1.50540i	0.862876	+	0.505415i	$0.168661\pi$
$223$	2894.33	+	5013.12i	0.869141	+	1.50540i	0.00626455	+	0.999980i	$0.498006\pi$
$224$	−2236.47	+	3873.68i	−0.667100	+	1.15545i
$225$	−620.651	−	1075.00i	−0.183897	−	0.318518i
$226$	−1441.34	−	2496.48i	−0.424233	−	0.734794i
$227$	1033.17			0.302087			0.151043	−	0.988527i	$-0.451737\pi$
$227$	1033.17			0.302087			0.151043	+	0.988527i	$0.451737\pi$
$228$	1597.90	−	1643.59i	0.464139	−	0.477410i
$229$	−5757.42			−1.66140			−0.830701	−	0.556719i	$-0.812060\pi$
$229$	−5757.42			−1.66140			−0.830701	+	0.556719i	$0.812060\pi$
$230$	1044.48	+	1809.09i	0.299438	+	0.518642i
$231$	−7763.04	−	13446.0i	−2.21113	−	3.82979i
$232$	1259.34	−	2181.24i	0.356378	−	0.617265i
$233$	−1720.22	−	2979.51i	−0.483671	−	0.837743i	0.516153	−	0.856497i	$-0.327364\pi$
$233$	−1720.22	−	2979.51i	−0.483671	−	0.837743i	−0.999824	+	0.0187532i	$0.994030\pi$
$234$	−2576.42	+	4462.50i	−0.719770	+	1.24668i
$235$	−1428.54			−0.396542
$236$	313.351			0.0864296
$237$	2785.91	−	4825.33i	0.763562	−	1.32253i
$238$	−1427.37	+	2472.28i	−0.388751	+	0.673337i
$239$	2674.35			0.723806			0.361903	−	0.932216i	$-0.382127\pi$
$239$	2674.35			0.723806			0.361903	+	0.932216i	$0.382127\pi$
$240$	1256.98			0.338074
$241$	−401.622	+	695.630i	−0.107347	+	0.185931i	−0.914695	−	0.404145i	$-0.867569\pi$
$241$	−401.622	+	695.630i	−0.107347	+	0.185931i	0.807347	+	0.590076i	$0.200902\pi$
$242$	1605.69	+	2781.14i	0.426520	+	0.738755i
$243$	945.044	−	1636.86i	0.249484	−	0.432119i
$244$	−607.364	−	1051.99i	−0.159355	−	0.276010i
$245$	1959.52	+	3393.99i	0.510977	+	0.885038i
$246$	718.186			0.186138
$247$	1064.38	+	3759.57i	0.274190	+	0.968485i
$248$	1543.38			0.395181
$249$	2036.96	+	3528.12i	0.518422	+	0.897933i
$250$	−137.480	−	238.122i	−0.0347800	−	0.0602407i
$251$	1659.00	−	2873.48i	0.417192	−	0.722598i	−0.578463	−	0.815708i	$-0.696347\pi$
$251$	1659.00	−	2873.48i	0.417192	−	0.722598i	0.995656	+	0.0931099i	$0.0296808\pi$
$252$	−2634.59	−	4563.25i	−0.658586	−	1.14071i
$253$	−5017.00	+	8689.70i	−1.24670	+	2.15936i
$254$	−4198.28			−1.03710
$255$	−1692.45			−0.415628
$256$	1998.86	−	3462.12i	0.488002	−	0.845245i
$257$	2277.91	−	3945.46i	0.552888	−	0.957629i	−0.445177	−	0.895443i	$-0.646859\pi$
$257$	2277.91	−	3945.46i	0.552888	−	0.957629i	0.998065	−	0.0621867i	$-0.0198074\pi$
$258$	−3575.06			−0.862688
$259$	4063.40			0.974855
$260$	372.882	−	645.851i	0.0889430	−	0.154054i
$261$	2546.84	+	4411.26i	0.604006	+	1.04617i
$262$	1364.62	−	2363.59i	0.321780	−	0.557339i
$263$	−1869.96	−	3238.87i	−0.438429	−	0.759382i	0.559139	−	0.829074i	$-0.311132\pi$
$263$	−1869.96	−	3238.87i	−0.438429	−	0.759382i	−0.997569	+	0.0696919i	$0.977798\pi$
$264$	5677.87	+	9834.35i	1.32367	+	2.29266i
$265$	1393.96			0.323134
$266$	5928.61	+	1499.34i	1.36656	+	0.345604i
$267$	10805.9			2.47682
$268$	−869.787	−	1506.52i	−0.198249	−	0.343377i
$269$	1075.30	+	1862.47i	0.243726	+	0.422145i	0.961773	−	0.273850i	$-0.0882971\pi$
$269$	1075.30	+	1862.47i	0.243726	+	0.422145i	−0.718047	+	0.695995i	$0.754964\pi$
$270$	−1090.61	+	1888.99i	−0.245824	+	0.425779i
$271$	−664.544	−	1151.02i	−0.148960	−	0.258006i	0.781883	−	0.623425i	$-0.214259\pi$
$271$	−664.544	−	1151.02i	−0.148960	−	0.258006i	−0.930843	+	0.365418i	$0.880926\pi$
$272$	555.072	−	961.412i	0.123736	−	0.214317i
$273$	13865.6			3.07393
$274$	−1719.28			−0.379071
$275$	660.366	−	1143.79i	0.144806	−	0.250811i
$276$	−2628.53	+	4552.74i	−0.573256	+	0.992909i
$277$	−1576.45			−0.341948			−0.170974	−	0.985276i	$-0.554691\pi$
$277$	−1576.45			−0.341948			−0.170974	+	0.985276i	$0.554691\pi$
$278$	−1080.01			−0.233003
$279$	−1560.64	+	2703.10i	−0.334885	+	0.580038i
$280$	−2060.36	−	3568.65i	−0.439751	−	0.761671i
$281$	1690.19	−	2927.50i	0.358821	−	0.621495i	−0.628944	−	0.777451i	$-0.716512\pi$
$281$	1690.19	−	2927.50i	0.358821	−	0.621495i	0.987764	+	0.155956i	$0.0498457\pi$
$282$	2751.14	+	4765.11i	0.580950	+	1.00623i
$283$	−1207.16	−	2090.86i	−0.253563	−	0.439184i	0.710941	−	0.703251i	$-0.248269\pi$
$283$	−1207.16	−	2090.86i	−0.253563	−	0.439184i	−0.964504	+	0.264068i	$0.914936\pi$
$284$	−2824.23			−0.590097
$285$	987.595	+	3488.35i	0.205263	+	0.725024i
$286$	−5482.58			−1.13354
$287$	−625.909	−	1084.11i	−0.128732	−	0.222971i
$288$	3308.07	+	5729.75i	0.676841	+	1.17232i
$289$	1709.13	−	2960.30i	0.347879	−	0.602545i
$290$	564.149	+	977.135i	0.114234	+	0.197860i
$291$	−3110.54	+	5387.61i	−0.626608	+	1.08532i
$292$	614.037			0.123061
$293$	−7587.26			−1.51281			−0.756403	−	0.654106i	$-0.773045\pi$
$293$	−7587.26			−1.51281			−0.756403	+	0.654106i	$0.773045\pi$
$294$	7547.47	−	13072.6i	1.49720	−	2.59323i
$295$	−247.793	+	429.191i	−0.0489054	+	0.0847066i
$296$	−2971.96			−0.583587
$297$	−10477.2			−2.04696
$298$	2530.67	−	4383.24i	0.491938	−	0.852062i
$299$	−4480.44	−	7760.34i	−0.866590	−	1.50098i
$300$	345.982	−	599.258i	0.0665842	−	0.115327i
$301$	3115.71	+	5396.57i	0.596633	+	1.03340i
$302$	1196.66	+	2072.68i	0.228014	+	0.394931i
$303$	3374.97			0.639891
$304$	−2305.50	−	583.060i	−0.434965	−	0.110003i
$305$	1921.18			0.360677
$306$	2111.30	+	3656.87i	0.394427	+	0.683168i
$307$	−890.420	−	1542.25i	−0.165534	−	0.286714i	0.771311	−	0.636459i	$-0.219601\pi$
$307$	−890.420	−	1542.25i	−0.165534	−	0.286714i	−0.936845	+	0.349745i	$0.886268\pi$
$308$	2803.18	−	4855.25i	0.518591	−	0.898226i
$309$	1039.61	+	1800.66i	0.191396	+	0.331508i
$310$	−345.696	+	598.762i	−0.0633361	+	0.109701i
$311$	−2594.78			−0.473108			−0.236554	−	0.971618i	$-0.576018\pi$
$311$	−2594.78			−0.473108			−0.236554	+	0.971618i	$0.576018\pi$
$312$	−10141.2			−1.84018
$313$	−788.294	+	1365.36i	−0.142355	+	0.246565i	−0.928383	−	0.371625i	$-0.878801\pi$
$313$	−788.294	+	1365.36i	−0.142355	+	0.246565i	0.786028	+	0.618191i	$0.212134\pi$
$314$	−2076.64	+	3596.85i	−0.373222	+	0.646439i
$315$	8333.60			1.49062
$316$	2011.94			0.358167
$317$	−2136.44	+	3700.42i	−0.378531	+	0.655634i	−0.990849	−	0.134977i	$-0.956904\pi$
$317$	−2136.44	+	3700.42i	−0.378531	+	0.655634i	0.612318	+	0.790612i	$0.290237\pi$
$318$	−2684.56	−	4649.79i	−0.473404	−	0.819959i
$319$	−2709.81	+	4693.54i	−0.475613	+	0.823785i
$320$	1307.05	+	2263.88i	0.228333	+	0.395484i
$321$	660.710	+	1144.38i	0.114882	+	0.198982i
$322$	−14024.4			−2.42717
$323$	3104.21	+	785.054i	0.534745	+	0.135237i
$324$	−1251.04			−0.214513
$325$	589.740	+	1021.46i	0.100655	+	0.174340i
$326$	3233.01	+	5599.74i	0.549263	+	0.951352i
$327$	−1729.53	+	2995.63i	−0.292487	+	0.506602i
$328$	457.788	+	792.912i	0.0770643	+	0.133479i
$329$	4795.31	−	8305.71i	0.803568	−	1.39182i
$330$	−5087.05			−0.848585
$331$	10622.8			1.76399			0.881996	−	0.471258i	$-0.156200\pi$
$331$	10622.8			1.76399			0.881996	+	0.471258i	$0.156200\pi$
$332$	−735.532	+	1273.98i	−0.121589	+	0.210598i
$333$	3005.19	−	5205.14i	0.494545	−	0.856577i
$334$	2130.29			0.348995
$335$	2751.26			0.448709
$336$	−4219.43	+	7308.26i	−0.685085	+	1.18660i
$337$	−2194.73	−	3801.38i	−0.354761	−	0.614464i	0.632316	−	0.774711i	$-0.282104\pi$
$337$	−2194.73	−	3801.38i	−0.354761	−	0.614464i	−0.987077	+	0.160246i	$0.948771\pi$
$338$	31.7617	−	55.0130i	0.00511128	−	0.00885299i
$339$	5736.80	+	9936.44i	0.919116	+	1.59196i
$340$	−305.565	−	529.254i	−0.0487400	−	0.0844201i
$341$	−3321.00			−0.527397
$342$	6305.28	−	6485.56i	0.996931	−	1.02543i
$343$	−14797.1			−2.32935
$344$	−2278.82	−	3947.04i	−0.357168	−	0.618634i
$345$	−4157.21	−	7200.49i	−0.648743	−	1.12366i
$346$	556.120	−	963.229i	0.0864082	−	0.149663i
$347$	−680.517	−	1178.69i	−0.105280	−	0.182350i	0.808573	−	0.588396i	$-0.200240\pi$
$347$	−680.517	−	1178.69i	−0.105280	−	0.182350i	−0.913852	+	0.406046i	$0.866907\pi$
$348$	−1419.74	+	2459.06i	−0.218695	+	0.378791i
$349$	5738.02			0.880084			0.440042	−	0.897977i	$-0.354964\pi$
$349$	5738.02			0.880084			0.440042	+	0.897977i	$0.354964\pi$
$350$	1845.97			0.281918
$351$	4678.33	−	8103.10i	0.711426	−	1.23223i
$352$	−3519.76	+	6096.40i	−0.532965	+	0.923123i
$353$	−7246.04			−1.09254			−0.546272	−	0.837608i	$-0.683953\pi$
$353$	−7246.04			−1.09254			−0.546272	+	0.837608i	$0.683953\pi$
$354$	1908.85			0.286593
$355$	2233.36	−	3868.30i	0.333901	−	0.578333i
$356$	1950.97	+	3379.19i	0.290453	+	0.503080i
$357$	5681.20	−	9840.12i	0.842243	−	1.45881i
$358$	1614.34	+	2796.11i	0.238325	+	0.412791i
$359$	−2417.54	−	4187.31i	−0.355412	−	0.615592i	0.631776	−	0.775151i	$-0.282326\pi$
$359$	−2417.54	−	4187.31i	−0.355412	−	0.615592i	−0.987188	+	0.159559i	$0.948993\pi$
$360$	−6095.17			−0.892344
$361$	−193.306	−	6856.28i	−0.0281828	−	0.999603i
$362$	984.054			0.142875
$363$	−6390.95	−	11069.4i	−0.924071	−	1.60054i
$364$	2503.38	+	4335.98i	0.360475	+	0.624361i
$365$	−485.571	+	841.034i	−0.0696328	+	0.120608i
$366$	−3699.89	−	6408.40i	−0.528406	−	0.915226i
$367$	−6158.49	+	10666.8i	−0.875941	+	1.51718i	−0.0201850	+	0.999796i	$0.506426\pi$
$367$	−6158.49	+	10666.8i	−0.875941	+	1.51718i	−0.855756	+	0.517379i	$0.826908\pi$
$368$	5453.76			0.772546
$369$	−1851.63			−0.261224
$370$	665.677	−	1152.99i	0.0935322	−	0.162003i
$371$	−4679.25	+	8104.70i	−0.654810	+	1.13416i
$372$	−1739.95			−0.242506
$373$	7876.55			1.09338			0.546692	−	0.837334i	$-0.315887\pi$
$373$	7876.55			1.09338			0.546692	+	0.837334i	$0.315887\pi$
$374$	−2246.40	+	3890.88i	−0.310584	+	0.537948i
$375$	547.195	+	947.769i	0.0753520	+	0.130514i
$376$	−3507.27	+	6074.78i	−0.481047	+	0.833199i
$377$	−2420.00	−	4191.56i	−0.330600	−	0.572617i
$378$	−7321.91	−	12681.9i	−0.996292	−	1.72563i
$379$	−2533.59			−0.343382			−0.171691	−	0.985151i	$-0.554923\pi$
$379$	−2533.59			−0.343382			−0.171691	+	0.985151i	$0.554923\pi$
$380$	−912.554	+	938.646i	−0.123192	+	0.126714i
$381$	16709.9			2.24692
$382$	1939.03	+	3358.49i	0.259710	+	0.449831i
$383$	−3190.88	−	5526.77i	−0.425708	−	0.737349i	0.570778	−	0.821105i	$-0.306642\pi$
$383$	−3190.88	−	5526.77i	−0.425708	−	0.737349i	−0.996486	+	0.0837558i	$0.973308\pi$
$384$	367.877	−	637.181i	0.0488884	−	0.0846772i
$385$	4433.43	+	7678.93i	0.586879	+	1.01650i
$386$	3586.87	−	6212.65i	0.472972	−	0.819211i
$387$	9217.21			1.21069
$388$	−2246.39			−0.293925
$389$	7359.94	−	12747.8i	0.959290	−	1.66154i	0.235059	−	0.971981i	$-0.424472\pi$
$389$	7359.94	−	12747.8i	0.959290	−	1.66154i	0.724231	−	0.689557i	$-0.242195\pi$
$390$	2271.50	−	3934.35i	0.294927	−	0.510829i
$391$	−7343.15			−0.949767
$392$	19243.7			2.47947
$393$	−5431.42	+	9407.50i	−0.697148	+	1.20750i
$394$	3973.49	+	6882.28i	0.508075	+	0.880011i
$395$	−1591.02	+	2755.72i	−0.202665	+	0.351026i
$396$	−4146.32	−	7181.64i	−0.526163	−	0.911341i
$397$	−4044.15	−	7004.67i	−0.511259	−	0.885527i	−0.999915	−	0.0130502i	$-0.995846\pi$
$397$	−4044.15	−	7004.67i	−0.511259	−	0.885527i	0.488656	−	0.872477i	$-0.337487\pi$
$398$	10261.8			1.29241
$399$	−23596.9	−	5967.66i	−2.96071	−	0.748763i
$400$	−717.854			−0.0897318
$401$	1567.31	+	2714.66i	0.195182	+	0.338064i	0.946960	−	0.321351i	$-0.104137\pi$
$401$	1567.31	+	2714.66i	0.195182	+	0.338064i	−0.751778	+	0.659416i	$0.770804\pi$
$402$	−5298.50	−	9177.27i	−0.657376	−	1.13861i
$403$	1482.91	−	2568.48i	0.183298	−	0.317481i
$404$	609.339	+	1055.41i	0.0750390	+	0.129971i
$405$	989.305	−	1713.53i	0.121380	−	0.210237i
$406$	−7574.94			−0.925955
$407$	6394.98			0.778839
$408$	−4155.21	+	7197.04i	−0.504200	+	0.873300i
$409$	−7719.88	+	13371.2i	−0.933309	+	1.61654i	−0.155688	+	0.987806i	$0.549759\pi$
$409$	−7719.88	+	13371.2i	−0.933309	+	1.61654i	−0.777621	+	0.628733i	$0.783574\pi$
$410$	−410.152			−0.0494048
$411$	6843.04			0.821271
$412$	−375.397	+	650.207i	−0.0448895	+	0.0777509i
$413$	−1663.58	−	2881.41i	−0.198207	−	0.343305i
$414$	−10372.1	+	17965.0i	−1.23131	+	2.13268i
$415$	−1163.30	−	2014.89i	−0.137600	−	0.238330i
$416$	−3143.32	−	5444.39i	−0.370466	−	0.641666i
$417$	4298.63			0.504808
$418$	9330.44	+	2359.67i	1.09179	+	0.276113i
$419$	−767.138			−0.0894442			−0.0447221	−	0.998999i	$-0.514240\pi$
$419$	−767.138			−0.0894442			−0.0447221	+	0.998999i	$0.514240\pi$
$420$	2322.78	+	4023.17i	0.269857	+	0.467407i
$421$	7115.75	+	12324.8i	0.823754	+	1.42678i	0.902868	+	0.429918i	$0.141457\pi$
$421$	7115.75	+	12324.8i	0.823754	+	1.42678i	−0.0791144	+	0.996866i	$0.525209\pi$
$422$	−2246.50	+	3891.05i	−0.259142	+	0.448847i
$423$	−7092.98	−	12285.4i	−0.815301	−	1.41214i
$424$	3422.39	−	5927.75i	0.391995	−	0.678956i
$425$	966.546			0.110316
$426$	−17204.5			−1.95671
$427$	−6449.01	+	11170.0i	−0.730889	+	1.26594i
$428$	−238.578	+	413.229i	−0.0269441	+	0.0466686i
$429$	21821.6			2.45585
$430$	2041.70			0.228975
$431$	2211.29	−	3830.07i	0.247132	−	0.428046i	−0.715597	−	0.698514i	$-0.753845\pi$
$431$	2211.29	−	3830.07i	0.247132	−	0.428046i	0.962729	+	0.270468i	$0.0871784\pi$
$432$	2847.32	+	4931.70i	0.317111	+	0.549252i
$433$	5356.73	−	9278.13i	0.594522	−	1.02974i	−0.399092	−	0.916911i	$-0.630675\pi$
$433$	5356.73	−	9278.13i	0.594522	−	1.02974i	0.993614	−	0.112831i	$-0.0359919\pi$
$434$	−2320.86	−	4019.85i	−0.256693	−	0.444606i
$435$	−2245.42	−	3889.17i	−0.247493	−	0.428670i
$436$	−1249.04			−0.137198
$437$	4284.96	+	15135.2i	0.469056	+	1.65678i
$438$	3740.54			0.408059
$439$	3397.02	+	5883.81i	0.369318	+	0.639678i	0.989459	−	0.144812i	$-0.0462579\pi$
$439$	3397.02	+	5883.81i	0.369318	+	0.639678i	−0.620141	+	0.784491i	$0.712925\pi$
$440$	−3242.60	−	5616.35i	−0.351329	−	0.608520i
$441$	−19458.9	+	33703.7i	−2.10116	+	3.63932i
$442$	−2006.15	−	3474.75i	−0.215888	−	0.373930i
$443$	1014.91	−	1757.87i	0.108848	−	0.188531i	−0.806456	−	0.591295i	$-0.798617\pi$
$443$	1014.91	−	1757.87i	0.108848	−	0.188531i	0.915304	+	0.402764i	$0.131950\pi$
$444$	3350.48			0.358124
$445$	−6171.21			−0.657401
$446$	−6366.59	+	11027.3i	−0.675934	+	1.17075i
$447$	−10072.5	+	17446.1i	−1.06580	+	1.84602i
$448$	−17550.0			−1.85081
$449$	7113.41			0.747667			0.373834	−	0.927496i	$-0.378043\pi$
$449$	7113.41			0.747667			0.373834	+	0.927496i	$0.378043\pi$
$450$	1365.23	−	2364.65i	0.143017	−	0.247713i
$451$	−985.055	−	1706.17i	−0.102848	−	0.178138i
$452$	−2071.52	+	3587.98i	−0.215567	+	0.373372i
$453$	−4762.93	−	8249.63i	−0.494000	−	0.855632i
$454$	1136.32	+	1968.16i	0.117467	+	0.203459i
$455$	−7918.55			−0.815885
$456$	17258.7	+	4364.73i	1.77240	+	0.448239i
$457$	−10681.0			−1.09330			−0.546650	−	0.837361i	$-0.684097\pi$
$457$	−10681.0			−1.09330			−0.546650	+	0.837361i	$0.684097\pi$
$458$	−6332.24	−	10967.8i	−0.646039	−	1.11897i
$459$	−3833.74	−	6640.23i	−0.389855	−	0.675249i
$460$	1501.14	−	2600.05i	0.152154	−	0.263539i
$461$	−1701.77	−	2947.55i	−0.171929	−	0.297790i	0.767165	−	0.641449i	$-0.221667\pi$
$461$	−1701.77	−	2947.55i	−0.171929	−	0.297790i	−0.939094	+	0.343660i	$0.888333\pi$
$462$	17076.2	−	29576.8i	1.71960	−	2.97844i
$463$	16242.7			1.63038			0.815188	−	0.579196i	$-0.196633\pi$
$463$	16242.7			1.63038			0.815188	+	0.579196i	$0.196633\pi$
$464$	2945.72			0.294723
$465$	1375.93	−	2383.18i	0.137220	−	0.237672i
$466$	3783.93	−	6553.97i	0.376153	−	0.651516i
$467$	13443.3			1.33208			0.666040	−	0.745916i	$-0.267988\pi$
$467$	13443.3			1.33208			0.666040	+	0.745916i	$0.267988\pi$
$468$	7405.75			0.731477
$469$	−9235.43	+	15996.2i	−0.909280	+	1.57492i
$470$	−1571.16	−	2721.33i	−0.154196	−	0.267076i
$471$	8265.40	−	14316.1i	0.808598	−	1.40053i
$472$	1216.74	+	2107.46i	0.118655	+	0.205516i
$473$	4903.51	+	8493.13i	0.476667	+	0.825612i
$474$	12256.2			1.18765
$475$	−564.010	−	1992.18i	−0.0544812	−	0.192436i
$476$	4102.88			0.395074
$477$	6921.31	+	11988.1i	0.664371	+	1.15072i
$478$	2941.36	+	5094.59i	0.281453	+	0.487492i
$479$	−1386.57	+	2401.61i	−0.132263	+	0.229087i	−0.924549	−	0.381064i	$-0.875558\pi$
$479$	−1386.57	+	2401.61i	−0.132263	+	0.229087i	0.792285	+	0.610151i	$0.208891\pi$
$480$	−2916.55	−	5051.62i	−0.277337	−	0.480362i
$481$	−2855.52	+	4945.91i	−0.270687	+	0.468844i
$482$	−1766.88			−0.166969
$483$	55819.6			5.25855
$484$	2307.73	−	3997.10i	0.216729	−	0.375385i
$485$	1776.41	−	3076.84i	0.166315	−	0.288066i
$486$	4157.59			0.388049
$487$	−15018.1			−1.39740			−0.698700	−	0.715415i	$-0.746238\pi$
$487$	−15018.1			−1.39740			−0.698700	+	0.715415i	$0.746238\pi$
$488$	4716.79	−	8169.72i	0.437539	−	0.757840i
$489$	−12868.0	−	22288.0i	−1.19000	−	2.06114i
$490$	−4310.32	+	7465.69i	−0.397389	+	0.688297i
$491$	−5124.95	−	8876.67i	−0.471050	−	0.815883i	0.528402	−	0.848995i	$-0.322792\pi$
$491$	−5124.95	−	8876.67i	−0.471050	−	0.815883i	−0.999452	+	0.0331120i	$0.989458\pi$
$492$	−516.094	−	893.901i	−0.0472913	−	0.0819109i
$493$	−3966.22			−0.362332
$494$	−5991.25	+	6162.55i	−0.545667	+	0.561268i
$495$	13115.4			1.19090
$496$	902.529	+	1563.23i	0.0817031	+	0.141514i
$497$	14993.9	+	25970.2i	1.35326	+	2.34391i
$498$	−4480.66	+	7760.72i	−0.403179	+	0.698326i
$499$	−235.153	−	407.297i	−0.0210960	−	0.0365393i	0.855285	−	0.518158i	$-0.173382\pi$
$499$	−235.153	−	407.297i	−0.0210960	−	0.0365393i	−0.876381	+	0.481619i	$0.840049\pi$
$500$	−197.588	+	342.233i	−0.0176728	+	0.0306102i
$501$	−8478.93			−0.756109
$502$	7298.55			0.648904
$503$	−1979.91	+	3429.31i	−0.175507	+	0.303987i	−0.940337	−	0.340246i	$-0.889490\pi$
$503$	−1979.91	+	3429.31i	−0.175507	+	0.303987i	0.764830	+	0.644232i	$0.222823\pi$
$504$	20460.3	−	35438.2i	1.80828	−	3.13203i
$505$	−1927.43			−0.169840
$506$	−22071.6			−1.93913
$507$	−126.417	+	218.961i	−0.0110738	+	0.0191803i
$508$	3016.92	+	5225.45i	0.263492	+	0.456382i
$509$	−1863.91	+	3228.38i	−0.162311	+	0.281131i	−0.935697	−	0.352805i	$-0.885228\pi$
$509$	−1863.91	+	3228.38i	−0.162311	+	0.281131i	0.773386	+	0.633935i	$0.218561\pi$
$510$	−1861.42	−	3224.07i	−0.161618	−	0.279930i
$511$	−3259.93	−	5646.36i	−0.282213	−	0.488807i
$512$	9465.99			0.817073
$513$	−11449.3	+	11776.6i	−0.985375	+	1.01355i
$514$	10021.3			0.859966
$515$	−593.717	−	1028.35i	−0.0508006	−	0.0879892i
$516$	2569.07	+	4449.75i	0.219180	+	0.379631i
$517$	7546.85	−	13071.5i	0.641993	−	1.11196i
$518$	4469.09	+	7740.69i	0.379074	+	0.656576i
$519$	−2213.46	+	3833.82i	−0.187206	+	0.324251i
$520$	5791.61			0.488421
$521$	895.157			0.0752736			0.0376368	−	0.999291i	$-0.488017\pi$
$521$	895.157			0.0752736			0.0376368	+	0.999291i	$0.488017\pi$
$522$	−5602.24	+	9703.36i	−0.469738	+	0.813610i
$523$	−4418.42	+	7652.92i	−0.369415	+	0.639845i	−0.989474	−	0.144710i	$-0.953775\pi$
$523$	−4418.42	+	7652.92i	−0.369415	+	0.639845i	0.620059	+	0.784555i	$0.287108\pi$
$524$	−3922.50			−0.327014
$525$	−7347.29			−0.610785
$526$	4113.32	−	7124.48i	0.340968	−	0.590574i
$527$	−1215.20	−	2104.79i	−0.100446	−	0.173977i
$528$	−6640.54	+	11501.7i	−0.547334	+	0.948010i
$529$	−11953.7	−	20704.4i	−0.982469	−	1.70169i
$530$	1533.14	+	2655.47i	0.125651	+	0.217634i
$531$	−4921.38			−0.402203
$532$	−2394.16	−	8456.57i	−0.195113	−	0.689170i
$533$	1759.41			0.142980
$534$	11884.8	+	20585.1i	0.963118	+	1.66817i
$535$	−377.328	−	653.551i	−0.0304922	−	0.0528140i
$536$	6754.76	−	11699.6i	0.544331	−	0.942809i
$537$	−6425.35	−	11129.0i	−0.516340	−	0.894327i
$538$	−2365.31	+	4096.84i	−0.189546	+	0.328304i
$539$	−41408.1			−3.30904
$540$	3134.88			0.249822
$541$	605.044	−	1047.97i	0.0480830	−	0.0832822i	−0.840982	−	0.541063i	$-0.818022\pi$
$541$	605.044	−	1047.97i	0.0480830	−	0.0832822i	0.889065	+	0.457781i	$0.151355\pi$
$542$	1461.78	−	2531.88i	0.115847	−	0.200653i
$543$	−3916.71			−0.309543
$544$	−5151.70			−0.406024
$545$	987.724	−	1710.79i	0.0776320	−	0.134463i
$546$	15249.9	+	26413.6i	1.19530	+	2.07033i
$547$	3265.72	−	5656.40i	0.255269	−	0.442139i	−0.709700	−	0.704505i	$-0.751169\pi$
$547$	3265.72	−	5656.40i	0.255269	−	0.442139i	0.964969	+	0.262366i	$0.0845026\pi$
$548$	1235.49	+	2139.93i	0.0963091	+	0.166812i
$549$	9539.06	+	16522.1i	0.741561	+	1.28442i
$550$	2905.19			0.225232
$551$	2314.42	+	8174.90i	0.178943	+	0.632055i
$552$	−40826.3			−3.14798
$553$	−10681.4	−	18500.8i	−0.821376	−	1.42267i
$554$	−1733.84	−	3003.10i	−0.132967	−	0.230306i
$555$	−2649.52	+	4589.10i	−0.202641	+	0.350984i
$556$	776.104	+	1344.25i	0.0591981	+	0.102534i
$557$	7949.35	−	13768.7i	0.604712	−	1.04739i	−0.387384	−	0.921918i	$-0.626621\pi$
$557$	7949.35	−	13768.7i	0.604712	−	1.04739i	0.992097	−	0.125474i	$-0.0400453\pi$
$558$	−6865.80			−0.520883
$559$	−8758.16			−0.662667
$560$	2409.69	−	4173.71i	0.181836	−	0.314949i
$561$	8941.07	−	15486.4i	0.672892	−	1.16548i
$562$	7435.77			0.558112
$563$	−21833.4			−1.63440			−0.817202	−	0.576352i	$-0.804476\pi$
$563$	−21833.4			−1.63440			−0.817202	+	0.576352i	$0.804476\pi$
$564$	3953.98	−	6848.49i	0.295199	−	0.511300i
$565$	−3276.26	−	5674.65i	−0.243953	−	0.422538i
$566$	2655.37	−	4599.23i	0.197197	−	0.341555i
$567$	6641.80	+	11503.9i	0.491939	+	0.852063i
$568$	−10966.5	−	18994.5i	−0.810113	−	1.40316i
$569$	−12370.9			−0.911448			−0.455724	−	0.890121i	$-0.650620\pi$
$569$	−12370.9			−0.911448			−0.455724	+	0.890121i	$0.650620\pi$
$570$	−5559.03	+	5717.97i	−0.408495	+	0.420174i
$571$	15169.6			1.11178			0.555892	−	0.831254i	$-0.312377\pi$
$571$	15169.6			1.11178			0.555892	+	0.831254i	$0.312377\pi$
$572$	3939.82	+	6823.97i	0.287993	+	0.498819i
$573$	−7717.67	−	13367.4i	−0.562671	−	0.974574i
$574$	1376.80	−	2384.68i	0.100116	−	0.173406i
$575$	2374.16	+	4112.16i	0.172190	+	0.298242i
$576$	−12979.6	+	22481.3i	−0.938916	+	1.62625i
$577$	18083.0			1.30469			0.652343	−	0.757924i	$-0.273786\pi$
$577$	18083.0			1.30469			0.652343	+	0.757924i	$0.273786\pi$
$578$	7519.08			0.541094
$579$	−14276.4	+	24727.4i	−1.02471	+	1.77485i
$580$	810.804	−	1404.35i	0.0580462	−	0.100539i
$581$	15619.8			1.11535
$582$	−13684.4			−0.974632
$583$	−7364.21	+	12755.2i	−0.523146	+	0.906116i
$584$	2384.30	+	4129.74i	0.168944	+	0.292619i
$585$	−5856.36	+	10143.5i	−0.413899	+	0.716894i
$586$	−8344.77	−	14453.6i	−0.588258	−	1.01889i
$587$	−8771.98	−	15193.5i	−0.616794	−	1.06832i	−0.990067	−	0.140597i	$-0.955098\pi$
$587$	−8771.98	−	15193.5i	−0.616794	−	1.06832i	0.373272	−	0.927722i	$-0.378236\pi$
$588$	−21694.7			−1.52155
$589$	−3629.13	+	3732.89i	−0.253881	+	0.261139i
$590$	−1090.13			−0.0760678
$591$	−15815.2	−	27392.7i	−1.10076	−	1.90657i
$592$	−1737.92	−	3010.17i	−0.120656	−	0.208982i
$593$	−1422.39	+	2463.65i	−0.0985000	+	0.170607i	−0.911064	−	0.412265i	$-0.864738\pi$
$593$	−1422.39	+	2463.65i	−0.0985000	+	0.170607i	0.812564	+	0.582872i	$0.198071\pi$
$594$	−11523.2	−	19958.8i	−0.795966	−	1.37865i
$595$	−3244.50	+	5619.64i	−0.223549	+	0.387198i
$596$	−7274.22			−0.499939
$597$	−40843.8			−2.80004
$598$	9855.52	−	17070.3i	0.673950	−	1.16732i
$599$	−1217.27	+	2108.38i	−0.0830324	+	0.143816i	−0.904551	−	0.426365i	$-0.859794\pi$
$599$	−1217.27	+	2108.38i	−0.0830324	+	0.143816i	0.821519	+	0.570182i	$0.193127\pi$
$600$	5373.79			0.365640
$601$	−2976.95			−0.202051			−0.101025	−	0.994884i	$-0.532212\pi$
$601$	−2976.95			−0.202051			−0.101025	+	0.994884i	$0.532212\pi$
$602$	−6853.57	+	11870.7i	−0.464004	+	0.803679i
$603$	13660.6	+	23660.8i	0.922557	+	1.59792i
$604$	1719.86	−	2978.88i	0.115861	−	0.200677i
$605$	3649.84	+	6321.70i	0.245268	+	0.424816i
$606$	3711.92	+	6429.24i	0.248823	+	0.430974i
$607$	−10120.6			−0.676739			−0.338370	−	0.941013i	$-0.609875\pi$
$607$	−10120.6			−0.676739			−0.338370	+	0.941013i	$0.609875\pi$
$608$	3006.18	+	10618.3i	0.200521	+	0.708272i
$609$	30149.6			2.00612
$610$	2112.99	+	3659.81i	0.140250	+	0.242920i
$611$	6739.72	+	11673.5i	0.446252	+	0.772931i
$612$	3034.39	−	5255.71i	0.200421	−	0.347140i
$613$	12304.4	+	21311.8i	0.810717	+	1.40420i	0.912363	+	0.409382i	$0.134256\pi$
$613$	12304.4	+	21311.8i	0.810717	+	1.40420i	−0.101646	+	0.994821i	$0.532411\pi$
$614$	1958.64	−	3392.46i	0.128737	−	0.222978i
$615$	1632.48			0.107037
$616$	43539.0			2.84779
$617$	13331.8	−	23091.4i	0.869886	−	1.50669i	0.00777269	−	0.999970i	$-0.497526\pi$
$617$	13331.8	−	23091.4i	0.869886	−	1.50669i	0.862113	−	0.506716i	$-0.169141\pi$
$618$	−2286.81	+	3960.88i	−0.148850	+	0.257815i
$619$	17935.1			1.16458			0.582288	−	0.812983i	$-0.302158\pi$
$619$	17935.1			1.16458			0.582288	+	0.812983i	$0.302158\pi$
$620$	993.678			0.0643662
$621$	18833.9	−	32621.2i	1.21703	−	2.10796i
$622$	−2853.84	−	4943.00i	−0.183969	−	0.318644i
$623$	20715.5	−	35880.3i	1.33218	−	2.30741i
$624$	−5930.33	−	10271.6i	−0.380454	−	0.658966i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−3467.99			−0.221419
$627$	−37136.8	−	9391.90i	−2.36539	−	0.598208i
$628$	5969.16			0.379292
$629$	2340.01	+	4053.01i	0.148334	+	0.256922i
$630$	9165.62	+	15875.3i	0.579630	+	1.00395i
$631$	−11866.4	+	20553.3i	−0.748646	+	1.29669i	0.199826	+	0.979831i	$0.435962\pi$
$631$	−11866.4	+	20553.3i	−0.748646	+	1.29669i	−0.948472	+	0.316861i	$0.897371\pi$
$632$	7812.38	+	13531.4i	0.491708	+	0.851664i
$633$	8941.46	−	15487.1i	0.561440	−	0.972442i
$634$	−9398.95			−0.588770
$635$	−9542.94			−0.596378
$636$	−3858.28	+	6682.74i	−0.240552	+	0.416648i
$637$	18489.7	−	32025.2i	1.15006	−	1.99197i
$638$	−11921.4			−0.739772
$639$	44356.5			2.74603
$640$	−210.093	+	363.891i	−0.0129760	+	0.0224751i
$641$	−9004.39	−	15596.1i	−0.554840	−	0.961010i	−0.997916	−	0.0645264i	$-0.979446\pi$
$641$	−9004.39	−	15596.1i	−0.554840	−	0.961010i	0.443076	−	0.896484i	$-0.353887\pi$
$642$	−1453.35	+	2517.28i	−0.0893445	+	0.154749i
$643$	8763.10	+	15178.1i	0.537454	+	0.930897i	0.999040	+	0.0438022i	$0.0139471\pi$
$643$	8763.10	+	15178.1i	0.537454	+	0.930897i	−0.461586	+	0.887095i	$0.652720\pi$
$644$	10078.0	+	17455.7i	0.616662	+	1.06809i
$645$	−8126.32			−0.496083
$646$	1918.62	+	6776.88i	0.116853	+	0.412744i
$647$	−19408.8			−1.17935			−0.589673	−	0.807642i	$-0.700743\pi$
$647$	−19408.8			−1.17935			−0.589673	+	0.807642i	$0.700743\pi$
$648$	−4857.79	−	8413.94i	−0.294494	−	0.510078i
$649$	−2618.15	−	4534.77i	−0.158353	−	0.274276i
$650$	−1297.24	+	2246.88i	−0.0782799	+	0.135585i
$651$	9237.44	+	15999.7i	0.556135	+	0.963254i
$652$	4646.53	−	8048.02i	0.279098	−	0.483413i
$653$	−21561.7			−1.29215			−0.646075	−	0.763274i	$-0.723591\pi$
$653$	−21561.7			−1.29215			−0.646075	+	0.763274i	$0.723591\pi$
$654$	−7608.81			−0.454936
$655$	3101.86	−	5372.57i	0.185038	−	0.320494i
$656$	−535.405	+	927.348i	−0.0318659	+	0.0551934i
$657$	−9643.85			−0.572667
$658$	21096.3			1.24988
$659$	−4081.97	+	7070.18i	−0.241291	+	0.417929i	−0.961082	−	0.276262i	$-0.910904\pi$
$659$	−4081.97	+	7070.18i	−0.241291	+	0.417929i	0.719791	+	0.694191i	$0.244238\pi$
$660$	3655.59	+	6331.67i	0.215597	+	0.373424i
$661$	8599.69	−	14895.1i	0.506035	−	0.876478i	−0.493941	−	0.869496i	$-0.664444\pi$
$661$	8599.69	−	14895.1i	0.506035	−	0.876478i	0.999976	−	0.00698260i	$-0.00222265\pi$
$662$	11683.4	+	20236.2i	0.685931	+	1.18807i
$663$	7984.82	+	13830.1i	0.467730	+	0.810132i
$664$	−11424.3			−0.667693
$665$	13476.1	+	3408.10i	0.785834	+	0.198737i
$666$	13220.9			0.769219
$667$	−9742.36	−	16874.3i	−0.565556	−	0.979571i
$668$	−1530.84	−	2651.50i	−0.0886678	−	0.153577i
$669$	25340.2	−	43890.4i	1.46444	−	2.53648i
$670$	3025.95	+	5241.09i	0.174481	+	0.302210i
$671$	−10149.5	+	17579.4i	−0.583928	+	1.01139i
$672$	39161.1			2.24802
$673$	−26519.7			−1.51896			−0.759478	−	0.650533i	$-0.774546\pi$
$673$	−26519.7			−1.51896			−0.759478	+	0.650533i	$0.774546\pi$
$674$	4827.70	−	8361.82i	0.275899	−	0.477871i
$675$	−2479.02	+	4293.79i	−0.141359	+	0.244841i
$676$	−91.2969			−0.00519441
$677$	16854.5			0.956824			0.478412	−	0.878135i	$-0.341213\pi$
$677$	16854.5			0.956824			0.478412	+	0.878135i	$0.341213\pi$
$678$	−12619.1	+	21857.0i	−0.714800	+	1.23807i
$679$	11926.1	+	20656.6i	0.674053	+	1.16749i
$680$	2373.02	−	4110.19i	0.133825	−	0.231792i
$681$	−4522.75	−	7833.63i	−0.254496	−	0.440801i
$682$	−3652.57	−	6326.44i	−0.205079	−	0.355208i
$683$	22859.4			1.28066			0.640330	−	0.768100i	$-0.278798\pi$
$683$	22859.4			1.28066			0.640330	+	0.768100i	$0.278798\pi$
$684$	−12603.4	−	3187.39i	−0.704535	−	0.178177i
$685$	−3908.02			−0.217982
$686$	−16274.4	−	28188.1i	−0.905772	−	1.56884i
$687$	25203.4	+	43653.6i	1.39967	+	2.42429i
$688$	2665.19	−	4616.25i	0.147688	−	0.255804i
$689$	−6576.61	−	11391.0i	−0.363641	−	0.629845i
$690$	9144.52	−	15838.8i	0.504530	−	0.873872i
$691$	−3489.61			−0.192114			−0.0960572	−	0.995376i	$-0.530623\pi$
$691$	−3489.61			−0.192114			−0.0960572	+	0.995376i	$0.530623\pi$
$692$	−1598.53			−0.0878135
$693$	−44025.8	+	76254.9i	−2.41328	+	4.17992i
$694$	1496.92	−	2592.74i	0.0818764	−	0.141814i
$695$	−2454.93			−0.133987
$696$	−22051.3			−1.20094
$697$	720.889	−	1248.62i	0.0391759	−	0.0678547i
$698$	6310.90	+	10930.8i	0.342222	+	0.592747i
$699$	−15060.7	+	26086.0i	−0.814949	+	1.41153i
$700$	−1326.53	−	2297.61i	−0.0716258	−	0.124059i
$701$	−488.502	−	846.110i	−0.0263202	−	0.0455879i	0.852565	−	0.522621i	$-0.175046\pi$
$701$	−488.502	−	846.110i	−0.0263202	−	0.0455879i	−0.878885	+	0.477033i	$0.841712\pi$
$702$	20581.6			1.10656
$703$	6988.31	−	7188.12i	0.374921	−	0.385640i
$704$	−27620.3			−1.47866
$705$	6253.50	+	10831.4i	0.334072	+	0.578629i
$706$	−7969.48	−	13803.6i	−0.424838	−	0.735841i
$707$	6469.98	−	11206.3i	0.344171	−	0.596121i
$708$	−1371.71	−	2375.87i	−0.0728136	−	0.126117i
$709$	−2196.86	+	3805.07i	−0.116368	+	0.201555i	−0.918326	−	0.395826i	$-0.870458\pi$
$709$	−2196.86	+	3805.07i	−0.116368	+	0.201555i	0.801958	+	0.597380i	$0.203792\pi$
$710$	9825.37			0.519352
$711$	−31598.9			−1.66674
$712$	−15151.3	+	26242.7i	−0.797496	+	1.38130i
$713$	5969.86	−	10340.1i	0.313567	−	0.543113i
$714$	24993.6			1.31003
$715$	−12462.2			−0.651833
$716$	2320.15	−	4018.62i	0.121101	−	0.209752i
$717$	−11707.1	−	20277.4i	−0.609779	−	1.05617i
$718$	5317.82	−	9210.73i	0.276406	−	0.478749i
$719$	16137.8	+	27951.5i	0.837050	+	1.44981i	0.892350	+	0.451344i	$0.149055\pi$
$719$	16137.8	+	27951.5i	0.837050	+	1.44981i	−0.0552997	+	0.998470i	$0.517611\pi$
$720$	−3564.30	−	6173.54i	−0.184491	−	0.319548i
$721$	7971.96			0.411777
$722$	12848.4	−	7909.05i	0.662285	−	0.407679i
$723$	7032.49			0.361745
$724$	−707.148	−	1224.82i	−0.0362997	−	0.0628729i
$725$	1282.34	+	2221.09i	0.0656898	+	0.113778i
$726$	14058.0	−	24349.2i	0.718654	−	1.24474i
$727$	6895.02	+	11942.5i	0.351750	+	0.609248i	0.986556	−	0.163423i	$-0.0522535\pi$
$727$	6895.02	+	11942.5i	0.351750	+	0.609248i	−0.634806	+	0.772671i	$0.718920\pi$
$728$	−19441.3	+	33673.2i	−0.989754	+	1.71430i
$729$	−27232.4			−1.38355
$730$	−2136.20			−0.108307
$731$	−3588.52	+	6215.49i	−0.181568	+	0.314485i
$732$	−5317.54	+	9210.26i	−0.268500	+	0.465056i
$733$	31204.5			1.57240			0.786198	−	0.617975i	$-0.212047\pi$
$733$	31204.5			1.57240			0.786198	+	0.617975i	$0.212047\pi$
$734$	−27093.4			−1.36245
$735$	17155.8	−	29714.8i	0.860956	−	1.49122i
$736$	−12654.3	−	21917.9i	−0.633754	−	1.09769i
$737$	−14534.7	+	25174.9i	−0.726449	+	1.25825i
$738$	−2036.49	−	3527.31i	−0.101578	−	0.175938i
$739$	−1349.20	−	2336.88i	−0.0671598	−	0.116324i	0.830490	−	0.557033i	$-0.188060\pi$
$739$	−1349.20	−	2336.88i	−0.0671598	−	0.116324i	−0.897650	+	0.440709i	$0.854727\pi$
$740$	−1913.44			−0.0950535
$741$	23846.3	−	24528.1i	1.18221	−	1.21601i
$742$	−20585.7			−1.01850
$743$	10259.2	+	17769.4i	0.506558	+	0.877384i	0.999971	+	0.00758908i	$0.00241570\pi$
$743$	10259.2	+	17769.4i	0.506558	+	0.877384i	−0.493413	+	0.869795i	$0.664251\pi$
$744$	−6756.24	−	11702.1i	−0.332924	−	0.576642i
$745$	5752.35	−	9963.37i	0.282886	−	0.489972i
$746$	8662.94	+	15004.7i	0.425165	+	0.736407i
$747$	11552.0	−	20008.7i	0.565818	−	0.980025i
$748$	6457.12			0.315636
$749$	5066.45			0.247162
$750$	−1203.65	+	2084.79i	−0.0586016	+	0.101501i
$751$	−3646.10	+	6315.24i	−0.177161	+	0.306853i	−0.940907	−	0.338665i	$-0.890025\pi$
$751$	−3646.10	+	6315.24i	−0.177161	+	0.306853i	0.763746	+	0.645517i	$0.223358\pi$
$752$	−8203.85			−0.397824
$753$	−29049.5			−1.40587
$754$	5323.22	−	9220.09i	0.257109	−	0.445326i
$755$	2720.08	+	4711.32i	0.131118	+	0.227103i
$756$	−10523.2	+	18226.6i	−0.506248	+	0.876847i
$757$	5277.93	+	9141.64i	0.253408	+	0.438915i	0.964462	−	0.264222i	$-0.0851153\pi$
$757$	5277.93	+	9141.64i	0.253408	+	0.438915i	−0.711054	+	0.703137i	$0.751782\pi$
$758$	−2786.55	−	4826.44i	−0.133525	−	0.231272i
$759$	87848.9			4.20120
$760$	−9856.36	−	2492.67i	−0.470431	−	0.118972i
$761$	−9699.72			−0.462043			−0.231021	−	0.972949i	$-0.574207\pi$
$761$	−9699.72			−0.462043			−0.231021	+	0.972949i	$0.574207\pi$
$762$	18378.2	+	31832.0i	0.873717	+	1.51332i
$763$	6631.18	+	11485.5i	0.314633	+	0.544960i
$764$	2786.80	−	4826.87i	0.131967	−	0.228573i
$765$	4799.10	+	8312.29i	0.226813	+	0.392852i
$766$	7018.91	−	12157.1i	0.331075	−	0.573439i
$767$	4676.28			0.220144
$768$	−35000.5			−1.64449
$769$	−13647.8	+	23638.8i	−0.639992	+	1.10850i	0.345442	+	0.938440i	$0.387729\pi$
$769$	−13647.8	+	23638.8i	−0.639992	+	1.10850i	−0.985434	+	0.170059i	$0.945604\pi$
$770$	−9752.13	+	16891.2i	−0.456418	+	0.790540i
$771$	−39886.7			−1.86315
$772$	−10310.2			−0.480664
$773$	11898.4	−	20608.7i	0.553631	−	0.958916i	−0.444378	−	0.895839i	$-0.646575\pi$
$773$	11898.4	−	20608.7i	0.553631	−	0.958916i	0.998009	−	0.0630769i	$-0.0200913\pi$
$774$	10137.5	+	17558.6i	0.470779	+	0.815414i
$775$	−785.787	+	1361.02i	−0.0364210	+	0.0630831i
$776$	−8722.72	−	15108.2i	−0.403515	−	0.698908i
$777$	−17787.8	−	30809.3i	−0.821278	−	1.42249i
$778$	32379.0			1.49209
$779$	−2994.22	−	757.238i	−0.137714	−	0.0348278i
$780$	−6529.26			−0.299724
$781$	23597.4	+	40871.9i	1.08115	+	1.87262i
$782$	−8076.28	−	13988.5i	−0.369319	−	0.639679i
$783$	10172.7	−	17619.6i	0.464293	−	0.804179i
$784$	11253.2	+	19491.1i	0.512628	+	0.887898i
$785$	−4720.33	+	8175.84i	−0.214619	+	0.371730i
$786$	−23894.8			−1.08435
$787$	38347.5			1.73690			0.868451	−	0.495775i	$-0.165116\pi$
$787$	38347.5			1.73690			0.868451	+	0.495775i	$0.165116\pi$
$788$	5710.76	−	9891.32i	0.258169	−	0.447162i
$789$	−16371.8	+	28356.7i	−0.738720	+	1.27950i
$790$	−6999.45			−0.315227
$791$	43990.9			1.97742
$792$	32200.4	−	55772.6i	1.44468	−	2.50227i
$793$	−9063.98	−	15699.3i	−0.405891	−	0.703023i
$794$	8895.83	−	15408.0i	0.397608	−	0.688678i
$795$	−6102.15	−	10569.2i	−0.272228	−	0.471512i
$796$	−7374.21	−	12772.5i	−0.328357	−	0.568731i
$797$	10845.2			0.482006			0.241003	−	0.970524i	$-0.422524\pi$
$797$	10845.2			0.482006			0.241003	+	0.970524i	$0.422524\pi$
$798$	−14584.6	−	51515.1i	−0.646977	−	2.28523i
$799$	11046.0			0.489084
$800$	1665.63	+	2884.95i	0.0736110	+	0.127498i
$801$	−30641.3	−	53072.3i	−1.35163	−	2.34110i
$802$	−3447.58	+	5971.39i	−0.151793	+	0.262914i
$803$	−5130.48	−	8886.25i	−0.225468	−	0.390522i
$804$	−7615.09	+	13189.7i	−0.334034	+	0.578564i
$805$	−31878.3			−1.39573
$806$	6523.86			0.285103
$807$	9414.37	−	16306.2i	0.410659	−	0.711282i
$808$	−4732.13	+	8196.28i	−0.206034	+	0.356862i
$809$	−25939.8			−1.12731			−0.563656	−	0.826009i	$-0.690606\pi$
$809$	−25939.8			−1.12731			−0.563656	+	0.826009i	$0.690606\pi$
$810$	4352.31			0.188796
$811$	−12557.6	+	21750.4i	−0.543720	+	0.941750i	0.454966	+	0.890509i	$0.349651\pi$
$811$	−12557.6	+	21750.4i	−0.543720	+	0.941750i	−0.998686	+	0.0512418i	$0.983682\pi$
$812$	5443.41	+	9428.26i	0.235254	+	0.407472i
$813$	−5818.16	+	10077.3i	−0.250986	+	0.434721i
$814$	7033.45	+	12182.3i	0.302853	+	0.524557i
$815$	7348.82	+	12728.5i	0.315850	+	0.547069i
$816$	−9719.43			−0.416971
$817$	14904.9	+	3769.46i	0.638259	+	0.161416i
$818$	−33962.5			−1.45168
$819$	−39317.3	−	68099.5i	−1.67748	−	2.90548i
$820$	294.739	+	510.502i	0.0125521	+	0.0217409i
$821$	843.782	−	1461.47i	0.0358687	−	0.0621264i	−0.847534	−	0.530741i	$-0.821914\pi$
$821$	843.782	−	1461.47i	0.0358687	−	0.0621264i	0.883402	+	0.468615i	$0.155247\pi$
$822$	7526.25	+	13035.8i	0.319353	+	0.553135i
$823$	−5845.12	+	10124.0i	−0.247567	+	0.428799i	−0.962850	−	0.270036i	$-0.912965\pi$
$823$	−5845.12	+	10124.0i	−0.247567	+	0.428799i	0.715283	+	0.698835i	$0.246298\pi$
$824$	−5830.67			−0.246506
$825$	−11563.2			−0.487973
$826$	3659.35	−	6338.18i	0.154147	−	0.266990i
$827$	−23331.4	+	40411.2i	−0.981032	+	1.69920i	−0.322643	+	0.946521i	$0.604571\pi$
$827$	−23331.4	+	40411.2i	−0.981032	+	1.69920i	−0.658390	+	0.752677i	$0.728762\pi$
$828$	29813.8			1.25133
$829$	38751.9			1.62353			0.811767	−	0.583982i	$-0.198506\pi$
$829$	38751.9			1.62353			0.811767	+	0.583982i	$0.198506\pi$
$830$	2558.88	−	4432.11i	0.107012	−	0.185350i
$831$	6901.00	+	11952.9i	0.288078	+	0.498966i
$832$	12333.1	−	21361.6i	0.513912	−	0.890122i
$833$	−15151.8	−	26243.6i	−0.630225	−	1.09158i
$834$	4727.81	+	8188.80i	0.196296	+	0.339994i
$835$	4842.27			0.200687
$836$	−3767.93	−	13308.9i	−0.155881	−	0.550598i
$837$	12467.1			0.514845
$838$	−843.728	−	1461.38i	−0.0347806	−	0.0602417i
$839$	−11551.6	−	20008.0i	−0.475336	−	0.823306i	0.524265	−	0.851555i	$-0.324340\pi$
$839$	−11551.6	−	20008.0i	−0.475336	−	0.823306i	−0.999601	+	0.0282492i	$0.991007\pi$
$840$	−18038.7	+	31244.0i	−0.740946	+	1.28336i
$841$	6932.40	+	12007.3i	0.284243	+	0.492323i
$842$	−15652.4	+	27110.7i	−0.640637	+	1.10961i
$843$	−29595.7			−1.20917
$844$	6457.40			0.263357
$845$	72.1963	−	125.048i	0.00293921	−	0.00509085i
$846$	15602.3	−	27023.9i	0.634063	−	1.09823i
$847$	−49007.0			−1.98808
$848$	8005.30			0.324178
$849$	−10568.8	+	18305.8i	−0.427234	+	0.739990i
$850$	1063.05	+	1841.25i	0.0428967	+	0.0742992i
$851$	−11495.7	+	19911.1i	−0.463063	+	0.802048i
$852$	12363.3	+	21413.8i	0.497134	+	0.861061i
$853$	17640.0	+	30553.3i	0.708066	+	1.22641i	0.965574	+	0.260130i	$0.0837655\pi$
$853$	17640.0	+	30553.3i	0.708066	+	1.22641i	−0.257507	+	0.966276i	$0.582901\pi$
$854$	−28371.5			−1.13683
$855$	14332.3	−	14742.1i	0.573279	−	0.589670i
$856$	−3705.59			−0.147961
$857$	696.225	+	1205.90i	0.0277510	+	0.0480661i	0.879567	−	0.475774i	$-0.157832\pi$
$857$	696.225	+	1205.90i	0.0277510	+	0.0480661i	−0.851816	+	0.523841i	$0.824499\pi$
$858$	24000.3	+	41569.8i	0.954962	+	1.65404i
$859$	20190.4	−	34970.8i	0.801964	−	1.38904i	−0.116358	−	0.993207i	$-0.537122\pi$
$859$	20190.4	−	34970.8i	0.801964	−	1.38904i	0.918322	−	0.395835i	$-0.129545\pi$
$860$	−1467.18	−	2541.23i	−0.0581749	−	0.100762i
$861$	−5479.90	+	9491.47i	−0.216904	+	0.375689i
$862$	9728.25			0.384392
$863$	−23185.3			−0.914527			−0.457263	−	0.889331i	$-0.651170\pi$
$863$	−23185.3			−0.914527			−0.457263	+	0.889331i	$0.651170\pi$
$864$	13213.2	−	22885.9i	0.520280	−	0.901151i
$865$	1264.09	−	2189.48i	0.0496884	−	0.0860629i
$866$	23566.2			0.924724
$867$	−29927.3			−1.17230
$868$	−3335.58	+	5777.39i	−0.130434	+	0.225919i
$869$	−16810.5	−	29116.6i	−0.656221	−	1.13661i
$870$	4939.19	−	8554.93i	0.192476	−	0.333379i
$871$	−12980.2	−	22482.4i	−0.504958	−	0.874613i
$872$	−4850.03	−	8400.49i	−0.188352	−	0.326235i
$873$	35281.0			1.36779
$874$	−24119.4	+	24809.0i	−0.933468	+	0.960157i
$875$	4196.00			0.162115
$876$	−2687.98	−	4655.72i	−0.103674	−	0.179569i
$877$	−19168.1	−	33200.1i	−0.738038	−	1.27832i	−0.953378	−	0.301780i	$-0.902419\pi$
$877$	−19168.1	−	33200.1i	−0.738038	−	1.27832i	0.215339	−	0.976539i	$-0.430914\pi$
$878$	−7472.35	+	12942.5i	−0.287220	+	0.497480i
$879$	33213.7	+	57527.8i	1.27448	+	2.20747i
$880$	3792.37	−	6568.59i	0.145274	−	0.251622i
$881$	39178.2			1.49824			0.749120	−	0.662435i	$-0.230477\pi$
$881$	39178.2			1.49824			0.749120	+	0.662435i	$0.230477\pi$
$882$	−85606.5			−3.26817
$883$	13737.3	−	23793.8i	0.523554	−	0.906822i	−0.476070	−	0.879407i	$-0.657939\pi$
$883$	13737.3	−	23793.8i	0.523554	−	0.906822i	0.999624	−	0.0274144i	$-0.00872738\pi$
$884$	−2883.26	+	4993.96i	−0.109700	+	0.190006i
$885$	4338.92			0.164804
$886$	4464.95			0.169304
$887$	25920.2	−	44895.0i	0.981188	−	1.69947i	0.323405	−	0.946261i	$-0.395173\pi$
$887$	25920.2	−	44895.0i	0.981188	−	1.69947i	0.657784	−	0.753207i	$-0.271494\pi$
$888$	13009.9	+	22533.9i	0.491649	+	0.851562i
$889$	32033.7	−	55484.0i	1.20852	−	2.09322i
$890$	−6787.34	−	11756.0i	−0.255632	−	0.442767i
$891$	10452.9	+	18104.9i	0.393024	+	0.680737i
$892$	18300.3			0.686928
$893$	−6445.67	−	22767.2i	−0.241541	−	0.853163i
$894$	−44312.5			−1.65776
$895$	3669.48	+	6355.73i	0.137047	+	0.237373i
$896$	−1410.48	−	2443.02i	−0.0525901	−	0.0910887i
$897$	−39226.7	+	67942.7i	−1.46014	+	2.52903i
$898$	7823.61	+	13550.9i	0.290732	+	0.503562i
$899$	3224.48	−	5584.96i	0.119624	−	0.207196i
$900$	−3924.27			−0.145343
$901$	−10778.6			−0.398544
$902$	2166.81	−	3753.02i	0.0799853	−	0.138539i
$903$	27278.4	−	47247.6i	1.00528	−	1.74120i
$904$	−32174.9			−1.18376
$905$	2236.81			0.0821593
$906$	10476.9	−	18146.5i	0.384185	−	0.665429i
$907$	−9593.37	−	16616.2i	−0.351205	−	0.608304i	0.635256	−	0.772302i	$-0.280895\pi$
$907$	−9593.37	−	16616.2i	−0.351205	−	0.608304i	−0.986461	+	0.163997i	$0.947561\pi$
$908$	1633.13	−	2828.67i	0.0596888	−	0.103384i
$909$	−9570.07	−	16575.9i	−0.349196	−	0.604825i
$910$	−8709.14	−	15084.7i	−0.317258	−	0.549508i
$911$	15917.9			0.578906			0.289453	−	0.957192i	$-0.406527\pi$
$911$	15917.9			0.578906			0.289453	+	0.957192i	$0.406527\pi$
$912$	5671.60	+	20033.0i	0.205927	+	0.727368i
$913$	24582.4			0.891085
$914$	−11747.4	−	20347.2i	−0.425132	−	0.736350i
$915$	−8410.08	−	14566.7i	−0.303856	−	0.526295i
$916$	−9100.79	+	15763.0i	−0.328273	+	0.568586i
$917$	20824.6	+	36069.3i	0.749934	+	1.29892i
$918$	8432.99	−	14606.4i	0.303192	−	0.525144i
$919$	−980.295			−0.0351871			−0.0175936	−	0.999845i	$-0.505600\pi$
$919$	−980.295			−0.0351871			−0.0175936	+	0.999845i	$0.505600\pi$
$920$	23315.7			0.835538
$921$	−7795.73	+	13502.6i	−0.278912	+	0.483090i
$922$	3743.34	−	6483.66i	0.133710	−	0.231592i
$923$	−42147.4			−1.50303
$924$	−49084.3			−1.74757
$925$	1513.12	−	2620.81i	0.0537851	−	0.0931585i
$926$	17864.4	+	30942.1i	0.633975	+	1.09808i
$927$	5895.86	−	10211.9i	0.208895	−	0.361816i
$928$	−6834.91	−	11838.4i	−0.241775	−	0.418766i
$929$	22729.3	+	39368.3i	0.802718	+	1.39035i	0.917821	+	0.396995i	$0.129947\pi$
$929$	22729.3	+	39368.3i	0.802718	+	1.39035i	−0.115103	+	0.993354i	$0.536720\pi$
$930$	6053.21			0.213433
$931$	−45249.9	+	46543.7i	−1.59292	+	1.63846i
$932$	−10876.7			−0.382271
$933$	11358.8	+	19674.0i	0.398575	+	0.690352i
$934$	14785.5	+	25609.2i	0.517982	+	0.897171i
$935$	−5106.20	+	8844.19i	−0.178599	+	0.309343i
$936$	28756.5	+	49807.8i	1.00421	+	1.73934i
$937$	18517.2	−	32072.7i	0.645604	−	1.11822i	−0.338558	−	0.940946i	$-0.609939\pi$
$937$	18517.2	−	32072.7i	0.645604	−	1.11822i	0.984162	−	0.177273i	$-0.0567276\pi$
$938$	−40629.9			−1.41430
$939$	13803.2			0.479713
$940$	−2258.10	+	3911.14i	−0.0783521	+	0.135710i
$941$	−13043.1	+	22591.2i	−0.451851	+	0.782629i	−0.998501	−	0.0547324i	$-0.982569\pi$
$941$	−13043.1	+	22591.2i	−0.451851	+	0.782629i	0.546650	+	0.837361i	$0.315903\pi$
$942$	36362.5			1.25770
$943$	7082.97			0.244595
$944$	−1423.04	+	2464.77i	−0.0490634	+	0.0849804i
$945$	−16643.1	−	28826.7i	−0.572911	−	0.992311i
$946$	−10786.1	+	18682.2i	−0.370706	+	0.642082i
$947$	−21419.6	−	37099.9i	−0.734999	−	1.27306i	−0.954724	−	0.297494i	$-0.903849\pi$
$947$	−21419.6	−	37099.9i	−0.734999	−	1.27306i	0.219725	−	0.975562i	$-0.429484\pi$
$948$	−8807.40	−	15254.9i	−0.301742	−	0.522632i
$949$	9163.55			0.313447
$950$	3174.73	−	3265.50i	0.108423	−	0.111523i
$951$	37409.5			1.27559
$952$	15931.5	+	27594.1i	0.542376	+	0.939424i
$953$	24043.7	+	41644.9i	0.817262	+	1.41554i	0.907692	+	0.419637i	$0.137843\pi$
$953$	24043.7	+	41644.9i	0.817262	+	1.41554i	−0.0904297	+	0.995903i	$0.528824\pi$
$954$	−15224.7	+	26369.9i	−0.516684	+	0.894923i
$955$	4407.52	+	7634.05i	0.149344	+	0.258672i
$956$	4227.37	−	7322.02i	0.143016	−	0.247710i
$957$	47449.5			1.60274
$958$	−6100.03			−0.205723
$959$	13118.4	−	22721.8i	0.441727	−	0.765094i
$960$	11443.4	−	19820.6i	0.384723	−	0.666360i
$961$	−25839.3			−0.867351
$962$	−12562.5			−0.421029
$963$	3747.02	−	6490.03i	0.125385	−	0.217174i
$964$	1269.69	+	2199.17i	0.0424212	+	0.0734757i
$965$	8153.17	−	14121.7i	0.271979	−	0.471082i
$966$	61392.6	+	106335.i	2.04480	+	3.54169i
$967$	29688.3	+	51421.6i	0.987291	+	1.71004i	0.631277	+	0.775558i	$0.282531\pi$
$967$	29688.3	+	51421.6i	0.987291	+	1.71004i	0.356014	+	0.934481i	$0.384135\pi$
$968$	35843.6			1.19014
$969$	−7636.45	−	26973.2i	−0.253166	−	0.894225i
$970$	7815.07			0.258687
$971$	18380.4	+	31835.8i	0.607473	+	1.05217i	0.991655	+	0.128916i	$0.0411499\pi$
$971$	18380.4	+	31835.8i	0.607473	+	1.05217i	−0.384183	+	0.923257i	$0.625517\pi$
$972$	−2987.67	−	5174.80i	−0.0985901	−	0.170763i
$973$	8240.69	−	14273.3i	0.271515	−	0.470278i
$974$	−16517.5	−	28609.1i	−0.543382	−	0.941165i
$975$	5163.24	−	8943.00i	0.169596	−	0.293749i
$976$	11033.0			0.361843
$977$	−18904.8			−0.619056			−0.309528	−	0.950890i	$-0.600171\pi$
$977$	−18904.8			−0.619056			−0.309528	+	0.950890i	$0.600171\pi$
$978$	28305.4	−	49026.3i	0.925466	−	1.60295i
$979$	32602.1	−	56468.4i	1.06432	−	1.84345i
$980$	12389.7			0.403852
$981$	19617.0			0.638454
$982$	11273.2	−	19525.8i	0.366337	−	0.634515i
$983$	10770.5	+	18655.0i	0.349466	+	0.605292i	0.986155	−	0.165828i	$-0.0530298\pi$
$983$	10770.5	+	18655.0i	0.349466	+	0.605292i	−0.636689	+	0.771121i	$0.719696\pi$
$984$	4007.99	−	6942.04i	0.129847	−	0.224902i
$985$	9031.97	+	15643.8i	0.292165	+	0.506045i
$986$	−4362.21	−	7555.57i	−0.140894	−	0.244035i
$987$	−83966.9			−2.70790
$988$	11975.7	+	3028.65i	0.385624	+	0.0975244i
$989$	−35258.3			−1.13362
$990$	14424.9	+	24984.6i	0.463083	+	0.802083i
$991$	−23250.3	−	40270.7i	−0.745277	−	1.29086i	−0.950065	−	0.312051i	$-0.898984\pi$
$991$	−23250.3	−	40270.7i	−0.745277	−	1.29086i	0.204788	−	0.978806i	$-0.434349\pi$
$992$	4188.25	−	7254.26i	0.134049	−	0.232180i
$993$	−46501.9	−	80543.6i	−1.48609	−	2.57399i
$994$	−32981.8	+	57126.1i	−1.05243	+	1.82287i
$995$	23325.7			0.743190
$996$	12879.3			0.409736
$997$	−27345.1	+	47363.2i	−0.868635	+	1.50452i	−0.00524355	+	0.999986i	$0.501669\pi$
$997$	−27345.1	+	47363.2i	−0.868635	+	1.50452i	−0.863392	+	0.504534i	$0.831664\pi$
$998$	517.261	−	895.922i	0.0164064	−	0.0284168i
$999$	−24006.8			−0.760302

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	95.4.e.c.26.7	yes	20
19.7	even	3		1805.4.a.r.1.4		10
19.11	even	3	inner	95.4.e.c.11.7	✓	20
19.12	odd	6		1805.4.a.p.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.4.e.c.11.7	✓	20	19.11	even	3	inner
95.4.e.c.26.7	yes	20	1.1	even	1	trivial
1805.4.a.p.1.7		10	19.12	odd	6
1805.4.a.r.1.4		10	19.7	even	3

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:	\( N \)	\(=\)	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	95.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.09984 + 1.90498i) q^{2} +(-4.37756 - 7.58215i) q^{3} +(1.58071 - 2.73786i) q^{4} +(2.50000 + 4.33013i) q^{5} +(9.62922 - 16.6783i) q^{6} -33.5680 q^{7} +24.5515 q^{8} +(-24.8260 + 43.0000i) q^{9} +O(q^{10})\)	\(q+(1.09984 + 1.90498i) q^{2} +(-4.37756 - 7.58215i) q^{3} +(1.58071 - 2.73786i) q^{4} +(2.50000 + 4.33013i) q^{5} +(9.62922 - 16.6783i) q^{6} -33.5680 q^{7} +24.5515 q^{8} +(-24.8260 + 43.0000i) q^{9} +(-5.49920 + 9.52489i) q^{10} -52.8293 q^{11} -27.6785 q^{12} +(23.5896 - 40.8584i) q^{13} +(-36.9194 - 63.9463i) q^{14} +(21.8878 - 37.9108i) q^{15} +(14.3571 + 24.8672i) q^{16} +(-19.3309 - 33.4821i) q^{17} -109.219 q^{18} +(-57.7308 + 59.3814i) q^{19} +15.8071 q^{20} +(146.946 + 254.518i) q^{21} +(-58.1037 - 100.639i) q^{22} +(94.9663 - 164.486i) q^{23} +(-107.476 - 186.153i) q^{24} +(-12.5000 + 21.6506i) q^{25} +103.779 q^{26} +198.322 q^{27} +(-53.0611 + 91.9045i) q^{28} +(51.2938 - 88.8434i) q^{29} +96.2922 q^{30} +62.8629 q^{31} +(66.6251 - 115.398i) q^{32} +(231.263 + 400.560i) q^{33} +(42.5218 - 73.6500i) q^{34} +(-83.9199 - 145.354i) q^{35} +(78.4853 + 135.941i) q^{36} -121.050 q^{37} +(-176.615 - 44.6659i) q^{38} -413.060 q^{39} +(61.3788 + 106.311i) q^{40} +(18.6460 + 32.2958i) q^{41} +(-323.234 + 559.857i) q^{42} +(-92.8180 - 160.765i) q^{43} +(-83.5076 + 144.639i) q^{44} -248.260 q^{45} +417.791 q^{46} +(-142.854 + 247.430i) q^{47} +(125.698 - 217.715i) q^{48} +783.809 q^{49} -54.9920 q^{50} +(-169.245 + 293.140i) q^{51} +(-74.5765 - 129.170i) q^{52} +(139.396 - 241.441i) q^{53} +(218.122 + 377.798i) q^{54} +(-132.073 - 228.758i) q^{55} -824.145 q^{56} +(702.959 + 177.778i) q^{57} +225.660 q^{58} +(49.5587 + 85.8381i) q^{59} +(-69.1963 - 119.852i) q^{60} +(192.118 - 332.758i) q^{61} +(69.1391 + 119.752i) q^{62} +(833.360 - 1443.42i) q^{63} +522.821 q^{64} +235.896 q^{65} +(-508.705 + 881.103i) q^{66} +(275.126 - 476.532i) q^{67} -122.226 q^{68} -1662.88 q^{69} +(184.597 - 319.731i) q^{70} +(-446.673 - 773.660i) q^{71} +(-609.517 + 1055.71i) q^{72} +(97.1143 + 168.207i) q^{73} +(-133.135 - 230.597i) q^{74} +218.878 q^{75} +(71.3227 + 251.924i) q^{76} +1773.37 q^{77} +(-454.299 - 786.869i) q^{78} +(318.203 + 551.144i) q^{79} +(-71.7854 + 124.336i) q^{80} +(-197.861 - 342.705i) q^{81} +(-41.0152 + 71.0405i) q^{82} -465.318 q^{83} +929.112 q^{84} +(96.6546 - 167.411i) q^{85} +(204.170 - 353.632i) q^{86} -898.166 q^{87} -1297.04 q^{88} +(-617.121 + 1068.88i) q^{89} +(-273.047 - 472.930i) q^{90} +(-791.855 + 1371.53i) q^{91} +(-300.228 - 520.010i) q^{92} +(-275.186 - 476.636i) q^{93} -628.464 q^{94} +(-401.456 - 101.528i) q^{95} -1166.62 q^{96} +(-355.282 - 615.367i) q^{97} +(862.064 + 1493.14i) q^{98} +(1311.54 - 2271.66i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 3 q^{2} - 5 q^{3} - 43 q^{4} + 50 q^{5} + 9 q^{6} + 6 q^{7} + 96 q^{8} - 97 q^{9}+O(q^{10}) \) 20 * q - 3 * q^2 - 5 * q^3 - 43 * q^4 + 50 * q^5 + 9 * q^6 + 6 * q^7 + 96 * q^8 - 97 * q^9	\( 20 q - 3 q^{2} - 5 q^{3} - 43 q^{4} + 50 q^{5} + 9 q^{6} + 6 q^{7} + 96 q^{8} - 97 q^{9} + 15 q^{10} - 36 q^{11} + 186 q^{12} + 14 q^{13} + 68 q^{14} + 25 q^{15} + 9 q^{16} - 144 q^{17} - 22 q^{18} + 96 q^{19} - 430 q^{20} + 46 q^{21} - 136 q^{22} + 321 q^{23} - 416 q^{24} - 250 q^{25} - 46 q^{26} + 1006 q^{27} + 130 q^{28} - 178 q^{29} + 90 q^{30} + 604 q^{31} - 202 q^{32} + 1099 q^{33} - 751 q^{34} + 15 q^{35} - 526 q^{36} - 774 q^{37} - 12 q^{38} - 1216 q^{39} + 240 q^{40} - 388 q^{41} + 143 q^{42} - 514 q^{43} - 1246 q^{44} - 970 q^{45} + 3650 q^{46} + 522 q^{47} + 4 q^{48} + 1582 q^{49} + 150 q^{50} - 1080 q^{51} + 569 q^{52} - 681 q^{53} - 321 q^{54} - 90 q^{55} - 3184 q^{56} + 514 q^{57} + 1198 q^{58} - 891 q^{59} + 465 q^{60} + 1110 q^{61} - 1921 q^{62} - 727 q^{63} + 952 q^{64} + 140 q^{65} + 3312 q^{66} - 691 q^{67} - 228 q^{68} + 172 q^{69} - 340 q^{70} + 382 q^{71} - 2678 q^{72} - 797 q^{73} + 404 q^{74} + 250 q^{75} + 462 q^{76} + 2390 q^{77} + 1000 q^{78} - 660 q^{79} - 45 q^{80} - 2454 q^{81} - 1155 q^{82} - 2026 q^{83} + 10756 q^{84} + 720 q^{85} + 858 q^{86} + 312 q^{87} - 98 q^{88} - 2957 q^{89} - 55 q^{90} - 3110 q^{91} + 98 q^{92} + 1500 q^{93} - 6374 q^{94} + 945 q^{95} - 584 q^{96} - 2881 q^{97} + 4062 q^{98} + 2723 q^{99}+O(q^{100}) \) 20 * q - 3 * q^2 - 5 * q^3 - 43 * q^4 + 50 * q^5 + 9 * q^6 + 6 * q^7 + 96 * q^8 - 97 * q^9 + 15 * q^10 - 36 * q^11 + 186 * q^12 + 14 * q^13 + 68 * q^14 + 25 * q^15 + 9 * q^16 - 144 * q^17 - 22 * q^18 + 96 * q^19 - 430 * q^20 + 46 * q^21 - 136 * q^22 + 321 * q^23 - 416 * q^24 - 250 * q^25 - 46 * q^26 + 1006 * q^27 + 130 * q^28 - 178 * q^29 + 90 * q^30 + 604 * q^31 - 202 * q^32 + 1099 * q^33 - 751 * q^34 + 15 * q^35 - 526 * q^36 - 774 * q^37 - 12 * q^38 - 1216 * q^39 + 240 * q^40 - 388 * q^41 + 143 * q^42 - 514 * q^43 - 1246 * q^44 - 970 * q^45 + 3650 * q^46 + 522 * q^47 + 4 * q^48 + 1582 * q^49 + 150 * q^50 - 1080 * q^51 + 569 * q^52 - 681 * q^53 - 321 * q^54 - 90 * q^55 - 3184 * q^56 + 514 * q^57 + 1198 * q^58 - 891 * q^59 + 465 * q^60 + 1110 * q^61 - 1921 * q^62 - 727 * q^63 + 952 * q^64 + 140 * q^65 + 3312 * q^66 - 691 * q^67 - 228 * q^68 + 172 * q^69 - 340 * q^70 + 382 * q^71 - 2678 * q^72 - 797 * q^73 + 404 * q^74 + 250 * q^75 + 462 * q^76 + 2390 * q^77 + 1000 * q^78 - 660 * q^79 - 45 * q^80 - 2454 * q^81 - 1155 * q^82 - 2026 * q^83 + 10756 * q^84 + 720 * q^85 + 858 * q^86 + 312 * q^87 - 98 * q^88 - 2957 * q^89 - 55 * q^90 - 3110 * q^91 + 98 * q^92 + 1500 * q^93 - 6374 * q^94 + 945 * q^95 - 584 * q^96 - 2881 * q^97 + 4062 * q^98 + 2723 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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