LMFDB - Embedded newform 605.6.a.p.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,6,Mod(1,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("605.1");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	605.a (trivial)

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:	yes
Analytic conductor:	$97.0322109869$
Analytic rank:	$1$
Dimension:	$20$
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} - x^{19} - 523 x^{18} + 521 x^{17} + 115018 x^{16} - 115347 x^{15} - 13821739 x^{14} + \cdots - 32708279373824 $ x^20 - x^19 - 523x^18 + 521x^17 + 115018x^16 - 115347x^15 - 13821739x^14 + 14112735x^13 + 987264735x^12 - 1043264932x^11 - 42703408468x^10 + 48021607312x^9 + 1089062915552x^8 - 1362443421632x^7 - 15019635572992x^6 + 22119016261376x^5 + 88321308161536x^4 - 163614980036608x^3 - 51220983567360x^2 + 157475390795776x - 32708279373824
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 11^{8} $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Root			$8.99127$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+8.99127 q^{2} +10.3783 q^{3} +48.8429 q^{4} -25.0000 q^{5} +93.3145 q^{6} +132.461 q^{7} +151.440 q^{8} -135.290 q^{9} +O(q^{10})$	\(q+8.99127 q^{2} +10.3783 q^{3} +48.8429 q^{4} -25.0000 q^{5} +93.3145 q^{6} +132.461 q^{7} +151.440 q^{8} -135.290 q^{9} -224.782 q^{10} +506.909 q^{12} -910.993 q^{13} +1190.99 q^{14} -259.459 q^{15} -201.341 q^{16} -1672.49 q^{17} -1216.43 q^{18} -1461.27 q^{19} -1221.07 q^{20} +1374.73 q^{21} -3856.64 q^{23} +1571.69 q^{24} +625.000 q^{25} -8190.98 q^{26} -3926.02 q^{27} +6469.79 q^{28} +2327.23 q^{29} -2332.86 q^{30} +1119.34 q^{31} -6656.37 q^{32} -15037.8 q^{34} -3311.53 q^{35} -6607.96 q^{36} +4880.76 q^{37} -13138.6 q^{38} -9454.60 q^{39} -3785.99 q^{40} +15684.4 q^{41} +12360.5 q^{42} +13416.2 q^{43} +3382.25 q^{45} -34676.1 q^{46} -8731.60 q^{47} -2089.58 q^{48} +738.944 q^{49} +5619.54 q^{50} -17357.7 q^{51} -44495.6 q^{52} +33426.3 q^{53} -35299.9 q^{54} +20059.8 q^{56} -15165.5 q^{57} +20924.8 q^{58} -6584.54 q^{59} -12672.7 q^{60} +1649.58 q^{61} +10064.3 q^{62} -17920.7 q^{63} -53406.4 q^{64} +22774.8 q^{65} -1157.15 q^{67} -81689.5 q^{68} -40025.6 q^{69} -29774.8 q^{70} -2009.03 q^{71} -20488.2 q^{72} +56087.1 q^{73} +43884.2 q^{74} +6486.47 q^{75} -71372.6 q^{76} -85008.9 q^{78} -100146. q^{79} +5033.52 q^{80} -7870.19 q^{81} +141022. q^{82} +45650.0 q^{83} +67145.7 q^{84} +41812.3 q^{85} +120628. q^{86} +24152.8 q^{87} +54746.8 q^{89} +30410.7 q^{90} -120671. q^{91} -188370. q^{92} +11616.9 q^{93} -78508.2 q^{94} +36531.7 q^{95} -69082.2 q^{96} -92919.0 q^{97} +6644.04 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9}+O(q^{10}) $ 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9} - 25 q^{10} - 253 q^{12} - 769 q^{13} - 1045 q^{14} + 6963 q^{16} + 2989 q^{17} - 3775 q^{18} - 5828 q^{19} - 10175 q^{20} - 3310 q^{21} - 695 q^{23} - 16724 q^{24} + 12500 q^{25} - 7384 q^{26} + 5925 q^{27} + 3508 q^{28} - 11268 q^{29} + 6600 q^{30} - 11465 q^{31} + 9062 q^{32} + 1217 q^{34} + 4175 q^{35} + 112083 q^{36} - 3057 q^{37} - 13510 q^{38} - 13459 q^{39} + 1425 q^{40} + 839 q^{41} - 14772 q^{42} - 43671 q^{43} - 39950 q^{45} - 81471 q^{46} + 32245 q^{47} - 104315 q^{48} + 2959 q^{49} + 625 q^{50} - 69047 q^{51} - 42696 q^{52} + 27981 q^{53} - 61212 q^{54} - 28294 q^{56} - 79425 q^{57} + 37274 q^{58} - 56847 q^{59} + 6325 q^{60} - 85616 q^{61} - 38095 q^{62} - 100055 q^{63} - 18233 q^{64} + 19225 q^{65} - 31091 q^{67} + 83972 q^{68} - 48708 q^{69} + 26125 q^{70} - 106431 q^{71} - 350510 q^{72} - 117959 q^{73} - 154757 q^{74} - 451972 q^{76} + 348898 q^{78} - 215138 q^{79} - 174075 q^{80} + 75516 q^{81} - 127864 q^{82} - 66761 q^{83} - 521275 q^{84} - 74725 q^{85} - 32222 q^{86} + 5311 q^{87} + 270560 q^{89} + 94375 q^{90} - 269192 q^{91} - 461663 q^{92} + 9345 q^{93} - 479494 q^{94} + 145700 q^{95} - 1247523 q^{96} + 45338 q^{97} + 420757 q^{98}+O(q^{100}) \) 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9 - 25 * q^10 - 253 * q^12 - 769 * q^13 - 1045 * q^14 + 6963 * q^16 + 2989 * q^17 - 3775 * q^18 - 5828 * q^19 - 10175 * q^20 - 3310 * q^21 - 695 * q^23 - 16724 * q^24 + 12500 * q^25 - 7384 * q^26 + 5925 * q^27 + 3508 * q^28 - 11268 * q^29 + 6600 * q^30 - 11465 * q^31 + 9062 * q^32 + 1217 * q^34 + 4175 * q^35 + 112083 * q^36 - 3057 * q^37 - 13510 * q^38 - 13459 * q^39 + 1425 * q^40 + 839 * q^41 - 14772 * q^42 - 43671 * q^43 - 39950 * q^45 - 81471 * q^46 + 32245 * q^47 - 104315 * q^48 + 2959 * q^49 + 625 * q^50 - 69047 * q^51 - 42696 * q^52 + 27981 * q^53 - 61212 * q^54 - 28294 * q^56 - 79425 * q^57 + 37274 * q^58 - 56847 * q^59 + 6325 * q^60 - 85616 * q^61 - 38095 * q^62 - 100055 * q^63 - 18233 * q^64 + 19225 * q^65 - 31091 * q^67 + 83972 * q^68 - 48708 * q^69 + 26125 * q^70 - 106431 * q^71 - 350510 * q^72 - 117959 * q^73 - 154757 * q^74 - 451972 * q^76 + 348898 * q^78 - 215138 * q^79 - 174075 * q^80 + 75516 * q^81 - 127864 * q^82 - 66761 * q^83 - 521275 * q^84 - 74725 * q^85 - 32222 * q^86 + 5311 * q^87 + 270560 * q^89 + 94375 * q^90 - 269192 * q^91 - 461663 * q^92 + 9345 * q^93 - 479494 * q^94 + 145700 * q^95 - 1247523 * q^96 + 45338 * q^97 + 420757 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	8.99127	1.58945	0.794724	−	0.606972i	$-0.207616\pi$
$2$	8.99127	1.58945	0.794724	+	0.606972i	$0.207616\pi$
$3$	10.3783	0.665771	0.332886	−	0.942967i	$-0.391978\pi$
$3$	10.3783	0.665771	0.332886	+	0.942967i	$0.391978\pi$
$4$	48.8429	1.52634
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	93.3145	1.05821
$7$	132.461	1.02175	0.510873	−	0.859656i	$-0.329322\pi$
$7$	132.461	1.02175	0.510873	+	0.859656i	$0.329322\pi$
$8$	151.440	0.836593
$9$	−135.290	−0.556749
$10$	−224.782	−0.710822
$11$	0	0
$11$	0	0
$12$	506.909	1.01619
$13$	−910.993	−1.49505	−0.747526	−	0.664232i	$-0.768759\pi$
$13$	−910.993	−1.49505	−0.747526	+	0.664232i	$0.768759\pi$
$14$	1190.99	1.62401
$15$	−259.459	−0.297742
$16$	−201.341	−0.196622
$17$	−1672.49	−1.40360	−0.701798	−	0.712376i	$-0.747619\pi$
$17$	−1672.49	−1.40360	−0.701798	+	0.712376i	$0.747619\pi$
$18$	−1216.43	−0.884922
$19$	−1461.27	−0.928636	−0.464318	−	0.885669i	$-0.653700\pi$
$19$	−1461.27	−0.928636	−0.464318	+	0.885669i	$0.653700\pi$
$20$	−1221.07	−0.682601
$21$	1374.73	0.680250
$22$	0	0
$23$	−3856.64	−1.52016	−0.760081	−	0.649829i	$-0.774841\pi$
$23$	−3856.64	−1.52016	−0.760081	+	0.649829i	$0.774841\pi$
$24$	1571.69	0.556980
$25$	625.000	0.200000
$26$	−8190.98	−2.37631
$27$	−3926.02	−1.03644
$28$	6469.79	1.55954
$29$	2327.23	0.513859	0.256930	−	0.966430i	$-0.417289\pi$
$29$	2327.23	0.513859	0.256930	+	0.966430i	$0.417289\pi$
$30$	−2332.86	−0.473245
$31$	1119.34	0.209198	0.104599	−	0.994514i	$-0.466644\pi$
$31$	1119.34	0.209198	0.104599	+	0.994514i	$0.466644\pi$
$32$	−6656.37	−1.14911
$33$	0	0
$34$	−15037.8	−2.23094
$35$	−3311.53	−0.456939
$36$	−6607.96	−0.849789
$37$	4880.76	0.586115	0.293058	−	0.956095i	$-0.405327\pi$
$37$	4880.76	0.586115	0.293058	+	0.956095i	$0.405327\pi$
$38$	−13138.6	−1.47602
$39$	−9454.60	−0.995363
$40$	−3785.99	−0.374136
$41$	15684.4	1.45716	0.728579	−	0.684961i	$-0.240181\pi$
$41$	15684.4	1.45716	0.728579	+	0.684961i	$0.240181\pi$
$42$	12360.5	1.08122
$43$	13416.2	1.10652	0.553258	−	0.833010i	$-0.313384\pi$
$43$	13416.2	1.10652	0.553258	+	0.833010i	$0.313384\pi$
$44$	0	0
$45$	3382.25	0.248986
$46$	−34676.1	−2.41622
$47$	−8731.60	−0.576566	−0.288283	−	0.957545i	$-0.593084\pi$
$47$	−8731.60	−0.576566	−0.288283	+	0.957545i	$0.593084\pi$
$48$	−2089.58	−0.130905
$49$	738.944	0.0439664
$50$	5619.54	0.317889
$51$	−17357.7	−0.934474
$52$	−44495.6	−2.28196
$53$	33426.3	1.63455	0.817276	−	0.576246i	$-0.195483\pi$
$53$	33426.3	1.63455	0.817276	+	0.576246i	$0.195483\pi$
$54$	−35299.9	−1.64736
$55$	0	0
$56$	20059.8	0.854786
$57$	−15165.5	−0.618259
$58$	20924.8	0.816752
$59$	−6584.54	−0.246261	−0.123130	−	0.992390i	$-0.539293\pi$
$59$	−6584.54	−0.246261	−0.123130	+	0.992390i	$0.539293\pi$
$60$	−12672.7	−0.454456
$61$	1649.58	0.0567608	0.0283804	−	0.999597i	$-0.490965\pi$
$61$	1649.58	0.0567608	0.0283804	+	0.999597i	$0.490965\pi$
$62$	10064.3	0.332509
$63$	−17920.7	−0.568856
$64$	−53406.4	−1.62983
$65$	22774.8	0.668608
$66$	0	0
$67$	−1157.15	−0.0314921	−0.0157460	−	0.999876i	$-0.505012\pi$
$67$	−1157.15	−0.0314921	−0.0157460	+	0.999876i	$0.505012\pi$
$68$	−81689.5	−2.14237
$69$	−40025.6	−1.01208
$70$	−29774.8	−0.726280
$71$	−2009.03	−0.0472977	−0.0236488	−	0.999720i	$-0.507528\pi$
$71$	−2009.03	−0.0472977	−0.0236488	+	0.999720i	$0.507528\pi$
$72$	−20488.2	−0.465772
$73$	56087.1	1.23184	0.615922	−	0.787807i	$-0.288784\pi$
$73$	56087.1	1.23184	0.615922	+	0.787807i	$0.288784\pi$
$74$	43884.2	0.931599
$75$	6486.47	0.133154
$76$	−71372.6	−1.41742
$77$	0	0
$78$	−85008.9	−1.58208
$79$	−100146.	−1.80537	−0.902684	−	0.430304i	$-0.858406\pi$
$79$	−100146.	−1.80537	−0.902684	+	0.430304i	$0.858406\pi$
$80$	5033.52	0.0879319
$81$	−7870.19	−0.133282
$82$	141022.	2.31608
$83$	45650.0	0.727353	0.363677	−	0.931525i	$-0.381521\pi$
$83$	45650.0	0.727353	0.363677	+	0.931525i	$0.381521\pi$
$84$	67145.7	1.03829
$85$	41812.3	0.627707
$86$	120628.	1.75875
$87$	24152.8	0.342113
$88$	0	0
$89$	54746.8	0.732628	0.366314	−	0.930491i	$-0.380620\pi$
$89$	54746.8	0.732628	0.366314	+	0.930491i	$0.380620\pi$
$90$	30410.7	0.395749
$91$	−120671.	−1.52757
$92$	−188370.	−2.32029
$93$	11616.9	0.139278
$94$	−78508.2	−0.916422
$95$	36531.7	0.415299
$96$	−69082.2	−0.765046
$97$	−92919.0	−1.00271	−0.501355	−	0.865242i	$-0.667165\pi$
$97$	−92919.0	−1.00271	−0.501355	+	0.865242i	$0.667165\pi$
$98$	6644.04	0.0698823
$99$	0	0
$100$	30526.8	0.305268
$101$	−9075.78	−0.0885279	−0.0442640	−	0.999020i	$-0.514094\pi$
$101$	−9075.78	−0.0885279	−0.0442640	+	0.999020i	$0.514094\pi$
$102$	−156068.	−1.48530
$103$	−34779.8	−0.323023	−0.161512	−	0.986871i	$-0.551637\pi$
$103$	−34779.8	−0.323023	−0.161512	+	0.986871i	$0.551637\pi$
$104$	−137960.	−1.25075
$105$	−34368.2	−0.304217
$106$	300545.	2.59803
$107$	−215341.	−1.81830	−0.909152	−	0.416464i	$-0.863269\pi$
$107$	−215341.	−1.81830	−0.909152	+	0.416464i	$0.863269\pi$
$108$	−191759.	−1.58196
$109$	−44496.3	−0.358722	−0.179361	−	0.983783i	$-0.557403\pi$
$109$	−44496.3	−0.358722	−0.179361	+	0.983783i	$0.557403\pi$
$110$	0	0
$111$	50654.2	0.390219
$112$	−26669.8	−0.200898
$113$	−115571.	−0.851440	−0.425720	−	0.904855i	$-0.639979\pi$
$113$	−115571.	−0.851440	−0.425720	+	0.904855i	$0.639979\pi$
$114$	−136357.	−0.982690
$115$	96416.1	0.679837
$116$	113669.	0.784325
$117$	123248.	0.832369
$118$	−59203.4	−0.391419
$119$	−221540.	−1.43412
$120$	−39292.3	−0.249089
$121$	0	0
$122$	14831.8	0.0902183
$123$	162778.	0.970135
$124$	54671.8	0.319307
$125$	−15625.0	−0.0894427
$126$	−161129.	−0.904167
$127$	107499.	0.591420	0.295710	−	0.955278i	$-0.404444\pi$
$127$	107499.	0.591420	0.295710	+	0.955278i	$0.404444\pi$
$128$	−267187.	−1.44142
$129$	139238.	0.736686
$130$	204775.	1.06272
$131$	−137802.	−0.701579	−0.350790	−	0.936454i	$-0.614087\pi$
$131$	−137802.	−0.701579	−0.350790	+	0.936454i	$0.614087\pi$
$132$	0	0
$133$	−193561.	−0.948831
$134$	−10404.2	−0.0500550
$135$	98150.6	0.463509
$136$	−253282.	−1.17424
$137$	−201952.	−0.919276	−0.459638	−	0.888106i	$-0.652021\pi$
$137$	−201952.	−0.919276	−0.459638	+	0.888106i	$0.652021\pi$
$138$	−359881.	−1.60865
$139$	83352.8	0.365917	0.182959	−	0.983121i	$-0.441433\pi$
$139$	83352.8	0.365917	0.182959	+	0.983121i	$0.441433\pi$
$140$	−161745.	−0.697445
$141$	−90619.6	−0.383861
$142$	−18063.7	−0.0751772
$143$	0	0
$144$	27239.4	0.109469
$145$	−58180.7	−0.229805
$146$	504294.	1.95795
$147$	7669.02	0.0292716
$148$	238391.	0.894613
$149$	32322.3	0.119271	0.0596357	−	0.998220i	$-0.481006\pi$
$149$	32322.3	0.119271	0.0596357	+	0.998220i	$0.481006\pi$
$150$	58321.6	0.211642
$151$	−468862.	−1.67341	−0.836705	−	0.547654i	$-0.815521\pi$
$151$	−468862.	−1.67341	−0.836705	+	0.547654i	$0.815521\pi$
$152$	−221293.	−0.776890
$153$	226271.	0.781450
$154$	0	0
$155$	−27983.4	−0.0935561
$156$	−461790.	−1.51926
$157$	399925.	1.29488	0.647440	−	0.762116i	$-0.275840\pi$
$157$	399925.	1.29488	0.647440	+	0.762116i	$0.275840\pi$
$158$	−900440.	−2.86954
$159$	346910.	1.08824
$160$	166409.	0.513899
$161$	−510855.	−1.55322
$162$	−70763.0	−0.211845
$163$	411067.	1.21184	0.605918	−	0.795527i	$-0.292806\pi$
$163$	411067.	1.21184	0.605918	+	0.795527i	$0.292806\pi$
$164$	766070.	2.22412
$165$	0	0
$166$	410451.	1.15609
$167$	−147620.	−0.409594	−0.204797	−	0.978804i	$-0.565653\pi$
$167$	−147620.	−0.409594	−0.204797	+	0.978804i	$0.565653\pi$
$168$	208188.	0.569092
$169$	458615.	1.23518
$170$	375946.	0.997707
$171$	197695.	0.517017
$172$	655286.	1.68892
$173$	672333.	1.70793	0.853964	−	0.520332i	$-0.174192\pi$
$173$	672333.	1.70793	0.853964	+	0.520332i	$0.174192\pi$
$174$	217164.	0.543770
$175$	82788.2	0.204349
$176$	0	0
$177$	−68336.6	−0.163953
$178$	492243.	1.16447
$179$	−145186.	−0.338682	−0.169341	−	0.985557i	$-0.554164\pi$
$179$	−145186.	−0.338682	−0.169341	+	0.985557i	$0.554164\pi$
$180$	165199.	0.380037
$181$	−979.785	−0.00222297	−0.00111149	−	0.999999i	$-0.500354\pi$
$181$	−979.785	−0.00222297	−0.00111149	+	0.999999i	$0.500354\pi$
$182$	−1.08499e6	−2.42798
$183$	17119.9	0.0377897
$184$	−584048.	−1.27176
$185$	−122019.	−0.262119
$186$	104450.	0.221375
$187$	0	0
$188$	−426477.	−0.880037
$189$	−520045.	−1.05898
$190$	328466.	0.660095
$191$	771574.	1.53036	0.765181	−	0.643815i	$-0.222649\pi$
$191$	771574.	1.53036	0.765181	+	0.643815i	$0.222649\pi$
$192$	−554270.	−1.08510
$193$	−854770.	−1.65180	−0.825898	−	0.563820i	$-0.809331\pi$
$193$	−854770.	−1.65180	−0.825898	+	0.563820i	$0.809331\pi$
$194$	−835460.	−1.59375
$195$	236365.	0.445140
$196$	36092.2	0.0671078
$197$	−626726.	−1.15057	−0.575284	−	0.817954i	$-0.695108\pi$
$197$	−626726.	−1.15057	−0.575284	+	0.817954i	$0.695108\pi$
$198$	0	0
$199$	409145.	0.732393	0.366197	−	0.930538i	$-0.380660\pi$
$199$	409145.	0.732393	0.366197	+	0.930538i	$0.380660\pi$
$200$	94649.7	0.167319
$201$	−12009.3	−0.0209665
$202$	−81602.8	−0.140710
$203$	308267.	0.525034
$204$	−847802.	−1.42633
$205$	−392109.	−0.651661
$206$	−312714.	−0.513428
$207$	521765.	0.846348
$208$	183420.	0.293960
$209$	0	0
$210$	−309014.	−0.483537
$211$	−952793.	−1.47330	−0.736652	−	0.676272i	$-0.763594\pi$
$211$	−952793.	−1.47330	−0.736652	+	0.676272i	$0.763594\pi$
$212$	1.63264e6	2.49489
$213$	−20850.4	−0.0314894
$214$	−1.93619e6	−2.89010
$215$	−335404.	−0.494849
$216$	−594555.	−0.867077
$217$	148269.	0.213747
$218$	−400078.	−0.570169
$219$	582091.	0.820126
$220$	0	0
$221$	1.52363e6	2.09845
$222$	455446.	0.620232
$223$	545447.	0.734497	0.367249	−	0.930123i	$-0.380300\pi$
$223$	545447.	0.734497	0.367249	+	0.930123i	$0.380300\pi$
$224$	−881711.	−1.17410
$225$	−84556.2	−0.111350
$226$	−1.03913e6	−1.35332
$227$	−236250.	−0.304303	−0.152152	−	0.988357i	$-0.548620\pi$
$227$	−236250.	−0.304303	−0.152152	+	0.988357i	$0.548620\pi$
$228$	−740729.	−0.943675
$229$	−1.20624e6	−1.52001	−0.760003	−	0.649919i	$-0.774803\pi$
$229$	−1.20624e6	−1.52001	−0.760003	+	0.649919i	$0.774803\pi$
$230$	866903.	1.08056
$231$	0	0
$232$	352435.	0.429891
$233$	1.43949e6	1.73708	0.868539	−	0.495621i	$-0.165059\pi$
$233$	1.43949e6	1.73708	0.868539	+	0.495621i	$0.165059\pi$
$234$	1.10816e6	1.32301
$235$	218290.	0.257848
$236$	−321608.	−0.375878
$237$	−1.03935e6	−1.20196
$238$	−1.99193e6	−2.27946
$239$	−464046.	−0.525492	−0.262746	−	0.964865i	$-0.584628\pi$
$239$	−464046.	−0.525492	−0.262746	+	0.964865i	$0.584628\pi$
$240$	52239.6	0.0585426
$241$	−590005.	−0.654355	−0.327177	−	0.944963i	$-0.606097\pi$
$241$	−590005.	−0.654355	−0.327177	+	0.944963i	$0.606097\pi$
$242$	0	0
$243$	872344.	0.947703
$244$	80570.3	0.0866364
$245$	−18473.6	−0.0196624
$246$	1.46358e6	1.54198
$247$	1.33120e6	1.38836
$248$	169512.	0.175013
$249$	473771.	0.484251
$250$	−140489.	−0.142164
$251$	800887.	0.802392	0.401196	−	0.915992i	$-0.368595\pi$
$251$	800887.	0.802392	0.401196	+	0.915992i	$0.368595\pi$
$252$	−875297.	−0.868269
$253$	0	0
$254$	966555.	0.940032
$255$	433943.	0.417909
$256$	−693348.	−0.661228
$257$	−1.32233e6	−1.24884	−0.624421	−	0.781088i	$-0.714665\pi$
$257$	−1.32233e6	−1.24884	−0.624421	+	0.781088i	$0.714665\pi$
$258$	1.25192e6	1.17092
$259$	646511.	0.598861
$260$	1.11239e6	1.02052
$261$	−314851.	−0.286090
$262$	−1.23901e6	−1.11512
$263$	127563.	0.113720	0.0568599	−	0.998382i	$-0.481891\pi$
$263$	127563.	0.113720	0.0568599	+	0.998382i	$0.481891\pi$
$264$	0	0
$265$	−835658.	−0.730994
$266$	−1.74036e6	−1.50812
$267$	568181.	0.487763
$268$	−56518.4	−0.0480677
$269$	−23798.0	−0.0200521	−0.0100260	−	0.999950i	$-0.503191\pi$
$269$	−23798.0	−0.0200521	−0.0100260	+	0.999950i	$0.503191\pi$
$270$	882499.	0.736724
$271$	−154473.	−0.127770	−0.0638850	−	0.997957i	$-0.520349\pi$
$271$	−154473.	−0.127770	−0.0638850	+	0.997957i	$0.520349\pi$
$272$	336741.	0.275977
$273$	−1.25237e6	−1.01701
$274$	−1.81580e6	−1.46114
$275$	0	0
$276$	−1.95497e6	−1.54478
$277$	−593171.	−0.464494	−0.232247	−	0.972657i	$-0.574608\pi$
$277$	−593171.	−0.464494	−0.232247	+	0.972657i	$0.574608\pi$
$278$	749447.	0.581606
$279$	−151435.	−0.116471
$280$	−501496.	−0.382272
$281$	−1.11077e6	−0.839186	−0.419593	−	0.907712i	$-0.637827\pi$
$281$	−1.11077e6	−0.839186	−0.419593	+	0.907712i	$0.637827\pi$
$282$	−814785.	−0.610127
$283$	122129.	0.0906467	0.0453234	−	0.998972i	$-0.485568\pi$
$283$	122129.	0.0906467	0.0453234	+	0.998972i	$0.485568\pi$
$284$	−98126.8	−0.0721925
$285$	379138.	0.276494
$286$	0	0
$287$	2.07757e6	1.48885
$288$	900540.	0.639767
$289$	1.37738e6	0.970080
$290$	−523119.	−0.365263
$291$	−964346.	−0.667576
$292$	2.73946e6	1.88021
$293$	2.35648e6	1.60360	0.801798	−	0.597595i	$-0.203877\pi$
$293$	2.35648e6	1.60360	0.801798	+	0.597595i	$0.203877\pi$
$294$	68954.2	0.0465256
$295$	164613.	0.110131
$296$	739140.	0.490340
$297$	0	0
$298$	290618.	0.189575
$299$	3.51337e6	2.27272
$300$	316818.	0.203239
$301$	1.77712e6	1.13058
$302$	−4.21566e6	−2.65980
$303$	−94191.6	−0.0589394
$304$	294212.	0.182590
$305$	−41239.5	−0.0253842
$306$	2.03447e6	1.24207
$307$	−2.49668e6	−1.51188	−0.755941	−	0.654640i	$-0.772820\pi$
$307$	−2.49668e6	−1.51188	−0.755941	+	0.654640i	$0.772820\pi$
$308$	0	0
$309$	−360957.	−0.215060
$310$	−251607.	−0.148702
$311$	−2.71103e6	−1.58940	−0.794701	−	0.607001i	$-0.792373\pi$
$311$	−2.71103e6	−1.58940	−0.794701	+	0.607001i	$0.792373\pi$
$312$	−1.43180e6	−0.832714
$313$	2.42705e6	1.40029	0.700145	−	0.714001i	$-0.253119\pi$
$313$	2.42705e6	1.40029	0.700145	+	0.714001i	$0.253119\pi$
$314$	3.59584e6	2.05814
$315$	448016.	0.254400
$316$	−4.89142e6	−2.75561
$317$	−1.33834e6	−0.748029	−0.374015	−	0.927423i	$-0.622019\pi$
$317$	−1.33834e6	−0.748029	−0.374015	+	0.927423i	$0.622019\pi$
$318$	3.11916e6	1.72970
$319$	0	0
$320$	1.33516e6	0.728883
$321$	−2.23488e6	−1.21058
$322$	−4.59324e6	−2.46876
$323$	2.44396e6	1.30343
$324$	−384403.	−0.203435
$325$	−569370.	−0.299011
$326$	3.69602e6	1.92615
$327$	−461798.	−0.238826
$328$	2.37523e6	1.21905
$329$	−1.15660e6	−0.589105
$330$	0	0
$331$	3.12566e6	1.56810	0.784048	−	0.620701i	$-0.213152\pi$
$331$	3.12566e6	1.56810	0.784048	+	0.620701i	$0.213152\pi$
$332$	2.22968e6	1.11019
$333$	−660317.	−0.326319
$334$	−1.32729e6	−0.651029
$335$	28928.6	0.0140837
$336$	−276789.	−0.133752
$337$	−1.47590e6	−0.707917	−0.353958	−	0.935261i	$-0.615165\pi$
$337$	−1.47590e6	−0.707917	−0.353958	+	0.935261i	$0.615165\pi$
$338$	4.12353e6	1.96326
$339$	−1.19944e6	−0.566864
$340$	2.04224e6	0.958096
$341$	0	0
$342$	1.77753e6	0.821771
$343$	−2.12839e6	−0.976824
$344$	2.03174e6	0.925703
$345$	1.00064e6	0.452616
$346$	6.04513e6	2.71466
$347$	−1.74865e6	−0.779615	−0.389807	−	0.920896i	$-0.627458\pi$
$347$	−1.74865e6	−0.779615	−0.389807	+	0.920896i	$0.627458\pi$
$348$	1.17969e6	0.522181
$349$	−907753.	−0.398937	−0.199468	−	0.979904i	$-0.563922\pi$
$349$	−907753.	−0.398937	−0.199468	+	0.979904i	$0.563922\pi$
$350$	744371.	0.324802
$351$	3.57658e6	1.54953
$352$	0	0
$353$	−3.61050e6	−1.54216	−0.771081	−	0.636737i	$-0.780284\pi$
$353$	−3.61050e6	−1.54216	−0.771081	+	0.636737i	$0.780284\pi$
$354$	−614433.	−0.260595
$355$	50225.7	0.0211522
$356$	2.67400e6	1.11824
$357$	−2.29922e6	−0.954795
$358$	−1.30541e6	−0.538318
$359$	−365948.	−0.149859	−0.0749295	−	0.997189i	$-0.523873\pi$
$359$	−365948.	−0.149859	−0.0749295	+	0.997189i	$0.523873\pi$
$360$	512206.	0.208300
$361$	−340799.	−0.137636
$362$	−8809.52	−0.00353330
$363$	0	0
$364$	−5.89393e6	−2.33159
$365$	−1.40218e6	−0.550897
$366$	153930.	0.0600648
$367$	−1.60619e6	−0.622488	−0.311244	−	0.950330i	$-0.600746\pi$
$367$	−1.60619e6	−0.622488	−0.311244	+	0.950330i	$0.600746\pi$
$368$	776499.	0.298897
$369$	−2.12193e6	−0.811271
$370$	−1.09711e6	−0.416624
$371$	4.42769e6	1.67010
$372$	567402.	0.212586
$373$	−4.02801e6	−1.49906	−0.749528	−	0.661972i	$-0.769720\pi$
$373$	−4.02801e6	−1.49906	−0.749528	+	0.661972i	$0.769720\pi$
$374$	0	0
$375$	−162162.	−0.0595484
$376$	−1.32231e6	−0.482351
$377$	−2.12009e6	−0.768247
$378$	−4.67587e6	−1.68319
$379$	−1.36780e6	−0.489132	−0.244566	−	0.969633i	$-0.578645\pi$
$379$	−1.36780e6	−0.489132	−0.244566	+	0.969633i	$0.578645\pi$
$380$	1.78431e6	0.633888
$381$	1.11567e6	0.393751
$382$	6.93743e6	2.43243
$383$	−1.37780e6	−0.479943	−0.239971	−	0.970780i	$-0.577138\pi$
$383$	−1.37780e6	−0.479943	−0.239971	+	0.970780i	$0.577138\pi$
$384$	−2.77296e6	−0.959656
$385$	0	0
$386$	−7.68547e6	−2.62544
$387$	−1.81507e6	−0.616051
$388$	−4.53844e6	−1.53048
$389$	1.35226e6	0.453091	0.226546	−	0.974001i	$-0.427257\pi$
$389$	1.35226e6	0.453091	0.226546	+	0.974001i	$0.427257\pi$
$390$	2.12522e6	0.707526
$391$	6.45021e6	2.13369
$392$	111905.	0.0367820
$393$	−1.43015e6	−0.467091
$394$	−5.63506e6	−1.82877
$395$	2.50365e6	0.807385
$396$	0	0
$397$	−606260.	−0.193056	−0.0965279	−	0.995330i	$-0.530774\pi$
$397$	−606260.	−0.193056	−0.0965279	+	0.995330i	$0.530774\pi$
$398$	3.67873e6	1.16410
$399$	−2.00884e6	−0.631704
$400$	−125838.	−0.0393244
$401$	3.74878e6	1.16420	0.582101	−	0.813116i	$-0.302231\pi$
$401$	3.74878e6	1.16420	0.582101	+	0.813116i	$0.302231\pi$
$402$	−107979.	−0.0333252
$403$	−1.01971e6	−0.312762
$404$	−443288.	−0.135124
$405$	196755.	0.0596057
$406$	2.77172e6	0.834514
$407$	0	0
$408$	−2.62864e6	−0.781774
$409$	−2.45522e6	−0.725741	−0.362870	−	0.931840i	$-0.618203\pi$
$409$	−2.45522e6	−0.725741	−0.362870	+	0.931840i	$0.618203\pi$
$410$	−3.52556e6	−1.03578
$411$	−2.09592e6	−0.612028
$412$	−1.69875e6	−0.493044
$413$	−872195.	−0.251616
$414$	4.69133e6	1.34523
$415$	−1.14125e6	−0.325282
$416$	6.06391e6	1.71798
$417$	865064.	0.243617
$418$	0	0
$419$	5.76795e6	1.60504	0.802521	−	0.596625i	$-0.203492\pi$
$419$	5.76795e6	1.60504	0.802521	+	0.596625i	$0.203492\pi$
$420$	−1.67864e6	−0.464339
$421$	816693.	0.224571	0.112285	−	0.993676i	$-0.464183\pi$
$421$	816693.	0.224571	0.112285	+	0.993676i	$0.464183\pi$
$422$	−8.56682e6	−2.34174
$423$	1.18130e6	0.321002
$424$	5.06207e6	1.36746
$425$	−1.04531e6	−0.280719
$426$	−187471.	−0.0500508
$427$	218505.	0.0579952
$428$	−1.05179e7	−2.77536
$429$	0	0
$430$	−3.01571e6	−0.786536
$431$	−7.66302e6	−1.98704	−0.993521	−	0.113649i	$-0.963746\pi$
$431$	−7.66302e6	−1.98704	−0.993521	+	0.113649i	$0.963746\pi$
$432$	790468.	0.203786
$433$	−78179.3	−0.0200388	−0.0100194	−	0.999950i	$-0.503189\pi$
$433$	−78179.3	−0.0200388	−0.0100194	+	0.999950i	$0.503189\pi$
$434$	1.33312e6	0.339740
$435$	−603820.	−0.152997
$436$	−2.17333e6	−0.547532
$437$	5.63558e6	1.41168
$438$	5.23374e6	1.30355
$439$	−4.33391e6	−1.07329	−0.536647	−	0.843807i	$-0.680309\pi$
$439$	−4.33391e6	−1.07329	−0.536647	+	0.843807i	$0.680309\pi$
$440$	0	0
$441$	−99971.7	−0.0244783
$442$	1.36994e7	3.33537
$443$	−1.99539e6	−0.483080	−0.241540	−	0.970391i	$-0.577652\pi$
$443$	−1.99539e6	−0.483080	−0.241540	+	0.970391i	$0.577652\pi$
$444$	2.47410e6	0.595607
$445$	−1.36867e6	−0.327641
$446$	4.90426e6	1.16744
$447$	335452.	0.0794074
$448$	−7.07426e6	−1.66528
$449$	7.90177e6	1.84973	0.924865	−	0.380295i	$-0.124178\pi$
$449$	7.90177e6	1.84973	0.924865	+	0.380295i	$0.124178\pi$
$450$	−760268.	−0.176984
$451$	0	0
$452$	−5.64484e6	−1.29959
$453$	−4.86601e6	−1.11411
$454$	−2.12419e6	−0.483674
$455$	3.01678e6	0.683148
$456$	−2.29666e6	−0.517231
$457$	−259031.	−0.0580178	−0.0290089	−	0.999579i	$-0.509235\pi$
$457$	−259031.	−0.0580178	−0.0290089	+	0.999579i	$0.509235\pi$
$458$	−1.08456e7	−2.41597
$459$	6.56625e6	1.45474
$460$	4.70924e6	1.03766
$461$	3.85388e6	0.844589	0.422295	−	0.906459i	$-0.361225\pi$
$461$	3.85388e6	0.844589	0.422295	+	0.906459i	$0.361225\pi$
$462$	0	0
$463$	−1.40618e6	−0.304852	−0.152426	−	0.988315i	$-0.548709\pi$
$463$	−1.40618e6	−0.304852	−0.152426	+	0.988315i	$0.548709\pi$
$464$	−468566.	−0.101036
$465$	−290422.	−0.0622869
$466$	1.29429e7	2.76099
$467$	−2.98971e6	−0.634362	−0.317181	−	0.948365i	$-0.602736\pi$
$467$	−2.98971e6	−0.634362	−0.317181	+	0.948365i	$0.602736\pi$
$468$	6.01980e6	1.27048
$469$	−153277.	−0.0321769
$470$	1.96270e6	0.409836
$471$	4.15056e6	0.862094
$472$	−997160.	−0.206020
$473$	0	0
$474$	−9.34507e6	−1.91046
$475$	−913292.	−0.185727
$476$	−1.08207e7	−2.18896
$477$	−4.52224e6	−0.910035
$478$	−4.17236e6	−0.835242
$479$	−4.34921e6	−0.866108	−0.433054	−	0.901368i	$-0.642564\pi$
$479$	−4.34921e6	−0.866108	−0.433054	+	0.901368i	$0.642564\pi$
$480$	1.72705e6	0.342139
$481$	−4.44634e6	−0.876273
$482$	−5.30490e6	−1.04006
$483$	−5.30183e6	−1.03409
$484$	0	0
$485$	2.32298e6	0.448426
$486$	7.84348e6	1.50632
$487$	4.06196e6	0.776093	0.388046	−	0.921640i	$-0.373150\pi$
$487$	4.06196e6	0.776093	0.388046	+	0.921640i	$0.373150\pi$
$488$	249811.	0.0474857
$489$	4.26620e6	0.806805
$490$	−166101.	−0.0312523
$491$	1.28492e6	0.240532	0.120266	−	0.992742i	$-0.461625\pi$
$491$	1.28492e6	0.240532	0.120266	+	0.992742i	$0.461625\pi$
$492$	7.95054e6	1.48076
$493$	−3.89228e6	−0.721251
$494$	1.19692e7	2.20672
$495$	0	0
$496$	−225368.	−0.0411328
$497$	−266118.	−0.0483263
$498$	4.25981e6	0.769691
$499$	3.80061e6	0.683286	0.341643	−	0.939830i	$-0.389017\pi$
$499$	3.80061e6	0.683286	0.341643	+	0.939830i	$0.389017\pi$
$500$	−763171.	−0.136520
$501$	−1.53205e6	−0.272696
$502$	7.20099e6	1.27536
$503$	3.98713e6	0.702653	0.351326	−	0.936253i	$-0.385731\pi$
$503$	3.98713e6	0.702653	0.351326	+	0.936253i	$0.385731\pi$
$504$	−2.71389e6	−0.475901
$505$	226894.	0.0395909
$506$	0	0
$507$	4.75966e6	0.822349
$508$	5.25058e6	0.902710
$509$	457608.	0.0782887	0.0391443	−	0.999234i	$-0.487537\pi$
$509$	457608.	0.0782887	0.0391443	+	0.999234i	$0.487537\pi$
$510$	3.90170e6	0.664245
$511$	7.42935e6	1.25863
$512$	2.31591e6	0.390433
$513$	5.73697e6	0.962474
$514$	−1.18894e7	−1.98497
$515$	869494.	0.144460
$516$	6.80078e6	1.12444
$517$	0	0
$518$	5.81295e6	0.951859
$519$	6.97771e6	1.13709
$520$	3.44901e6	0.559353
$521$	8.97583e6	1.44871	0.724353	−	0.689429i	$-0.242139\pi$
$521$	8.97583e6	1.44871	0.724353	+	0.689429i	$0.242139\pi$
$522$	−2.83091e6	−0.454726
$523$	−1.21253e6	−0.193837	−0.0969186	−	0.995292i	$-0.530899\pi$
$523$	−1.21253e6	−0.193837	−0.0969186	+	0.995292i	$0.530899\pi$
$524$	−6.73065e6	−1.07085
$525$	859205.	0.136050
$526$	1.14695e6	0.180752
$527$	−1.87208e6	−0.293629
$528$	0	0
$529$	8.43735e6	1.31089
$530$	−7.51363e6	−1.16188
$531$	890822.	0.137105
$532$	−9.45409e6	−1.44824
$533$	−1.42883e7	−2.17853
$534$	5.10867e6	0.775273
$535$	5.38352e6	0.813171
$536$	−175238.	−0.0263460
$537$	−1.50679e6	−0.225485
$538$	−213974.	−0.0318717
$539$	0	0
$540$	4.79396e6	0.707474
$541$	3.95450e6	0.580896	0.290448	−	0.956891i	$-0.406196\pi$
$541$	3.95450e6	0.580896	0.290448	+	0.956891i	$0.406196\pi$
$542$	−1.38891e6	−0.203084
$543$	−10168.6	−0.00147999
$544$	1.11327e7	1.61289
$545$	1.11241e6	0.160425
$546$	−1.12604e7	−1.61648
$547$	2.17830e6	0.311279	0.155639	−	0.987814i	$-0.450256\pi$
$547$	2.17830e6	0.311279	0.155639	+	0.987814i	$0.450256\pi$
$548$	−9.86391e6	−1.40313
$549$	−223171.	−0.0316015
$550$	0	0
$551$	−3.40070e6	−0.477188
$552$	−6.06145e6	−0.846699
$553$	−1.32654e7	−1.84463
$554$	−5.33336e6	−0.738289
$555$	−1.26636e6	−0.174511
$556$	4.07119e6	0.558515
$557$	7.63801e6	1.04314	0.521569	−	0.853209i	$-0.325347\pi$
$557$	7.63801e6	1.04314	0.521569	+	0.853209i	$0.325347\pi$
$558$	−1.36159e6	−0.185124
$559$	−1.22220e7	−1.65430
$560$	666745.	0.0898442
$561$	0	0
$562$	−9.98723e6	−1.33384
$563$	−6.33875e6	−0.842816	−0.421408	−	0.906871i	$-0.638464\pi$
$563$	−6.33875e6	−0.842816	−0.421408	+	0.906871i	$0.638464\pi$
$564$	−4.42613e6	−0.585904
$565$	2.88928e6	0.380775
$566$	1.09809e6	0.144078
$567$	−1.04249e6	−0.136181
$568$	−304246.	−0.0395689
$569$	7.14139e6	0.924702	0.462351	−	0.886697i	$-0.347006\pi$
$569$	7.14139e6	0.924702	0.462351	+	0.886697i	$0.347006\pi$
$570$	3.40893e6	0.439472
$571$	−4.75335e6	−0.610112	−0.305056	−	0.952334i	$-0.598675\pi$
$571$	−4.75335e6	−0.610112	−0.305056	+	0.952334i	$0.598675\pi$
$572$	0	0
$573$	8.00766e6	1.01887
$574$	1.86800e7	2.36644
$575$	−2.41040e6	−0.304032
$576$	7.22534e6	0.907407
$577$	7.26734e6	0.908732	0.454366	−	0.890815i	$-0.349866\pi$
$577$	7.26734e6	0.908732	0.454366	+	0.890815i	$0.349866\pi$
$578$	1.23844e7	1.54189
$579$	−8.87110e6	−1.09972
$580$	−2.84172e6	−0.350761
$581$	6.04685e6	0.743171
$582$	−8.67070e6	−1.06108
$583$	0	0
$584$	8.49380e6	1.03055
$585$	−3.08120e6	−0.372247
$586$	2.11878e7	2.54883
$587$	1.25346e7	1.50147	0.750735	−	0.660603i	$-0.229699\pi$
$587$	1.25346e7	1.50147	0.750735	+	0.660603i	$0.229699\pi$
$588$	374577.	0.0446785
$589$	−1.63565e6	−0.194268
$590$	1.48008e6	0.175048
$591$	−6.50438e6	−0.766015
$592$	−982696.	−0.115243
$593$	1.41287e7	1.64993	0.824966	−	0.565182i	$-0.191194\pi$
$593$	1.41287e7	1.64993	0.824966	+	0.565182i	$0.191194\pi$
$594$	0	0
$595$	5.53851e6	0.641358
$596$	1.57871e6	0.182049
$597$	4.24625e6	0.487606
$598$	3.15897e7	3.61237
$599$	−1.40972e7	−1.60533	−0.802665	−	0.596430i	$-0.796585\pi$
$599$	−1.40972e7	−1.60533	−0.802665	+	0.596430i	$0.796585\pi$
$600$	982307.	0.111396
$601$	−1.99365e6	−0.225145	−0.112572	−	0.993644i	$-0.535909\pi$
$601$	−1.99365e6	−0.225145	−0.112572	+	0.993644i	$0.535909\pi$
$602$	1.59786e7	1.79700
$603$	156550.	0.0175332
$604$	−2.29006e7	−2.55420
$605$	0	0
$606$	−846902.	−0.0936810
$607$	1.52539e7	1.68039	0.840194	−	0.542286i	$-0.182441\pi$
$607$	1.52539e7	1.68039	0.840194	+	0.542286i	$0.182441\pi$
$608$	9.72674e6	1.06711
$609$	3.19931e6	0.349553
$610$	−370795.	−0.0403469
$611$	7.95443e6	0.861997
$612$	1.10518e7	1.19276
$613$	−1.40234e7	−1.50730	−0.753652	−	0.657273i	$-0.771710\pi$
$613$	−1.40234e7	−1.50730	−0.753652	+	0.657273i	$0.771710\pi$
$614$	−2.24484e7	−2.40306
$615$	−4.06944e6	−0.433857
$616$	0	0
$617$	1.49282e7	1.57868	0.789338	−	0.613958i	$-0.210424\pi$
$617$	1.49282e7	1.57868	0.789338	+	0.613958i	$0.210424\pi$
$618$	−3.24546e6	−0.341826
$619$	2.70782e6	0.284049	0.142024	−	0.989863i	$-0.454639\pi$
$619$	2.70782e6	0.284049	0.142024	+	0.989863i	$0.454639\pi$
$620$	−1.36679e6	−0.142799
$621$	1.51413e7	1.57555
$622$	−2.43756e7	−2.52627
$623$	7.25182e6	0.748561
$624$	1.90360e6	0.195710
$625$	390625.	0.0400000
$626$	2.18223e7	2.22569
$627$	0	0
$628$	1.95335e7	1.97643
$629$	−8.16304e6	−0.822669
$630$	4.02824e6	0.404356
$631$	−2.63522e6	−0.263478	−0.131739	−	0.991284i	$-0.542056\pi$
$631$	−2.63522e6	−0.263478	−0.131739	+	0.991284i	$0.542056\pi$
$632$	−1.51661e7	−1.51036
$633$	−9.88842e6	−0.980884
$634$	−1.20334e7	−1.18895
$635$	−2.68748e6	−0.264491
$636$	1.69441e7	1.66102
$637$	−673173.	−0.0657321
$638$	0	0
$639$	271801.	0.0263329
$640$	6.67968e6	0.644622
$641$	−6.56723e6	−0.631302	−0.315651	−	0.948875i	$-0.602223\pi$
$641$	−6.56723e6	−0.631302	−0.315651	+	0.948875i	$0.602223\pi$
$642$	−2.00944e7	−1.92415
$643$	−2.93019e6	−0.279491	−0.139746	−	0.990187i	$-0.544628\pi$
$643$	−2.93019e6	−0.279491	−0.139746	+	0.990187i	$0.544628\pi$
$644$	−2.49517e7	−2.37075
$645$	−3.48094e6	−0.329456
$646$	2.19743e7	2.07173
$647$	−3.40185e6	−0.319488	−0.159744	−	0.987158i	$-0.551067\pi$
$647$	−3.40185e6	−0.319488	−0.159744	+	0.987158i	$0.551067\pi$
$648$	−1.19186e6	−0.111503
$649$	0	0
$650$	−5.11936e6	−0.475261
$651$	1.53878e6	0.142307
$652$	2.00777e7	1.84968
$653$	−1.60696e6	−0.147476	−0.0737380	−	0.997278i	$-0.523493\pi$
$653$	−1.60696e6	−0.147476	−0.0737380	+	0.997278i	$0.523493\pi$
$654$	−4.15215e6	−0.379602
$655$	3.44504e6	0.313756
$656$	−3.15790e6	−0.286509
$657$	−7.58801e6	−0.685827
$658$	−1.03993e7	−0.936351
$659$	138370.	0.0124116	0.00620580	−	0.999981i	$-0.498025\pi$
$659$	138370.	0.0124116	0.00620580	+	0.999981i	$0.498025\pi$
$660$	0	0
$661$	7.13645e6	0.635300	0.317650	−	0.948208i	$-0.397106\pi$
$661$	7.13645e6	0.635300	0.317650	+	0.948208i	$0.397106\pi$
$662$	2.81037e7	2.49240
$663$	1.58127e7	1.39709
$664$	6.91321e6	0.608499
$665$	4.83902e6	0.424330
$666$	−5.93709e6	−0.518667
$667$	−8.97529e6	−0.781149
$668$	−7.21020e6	−0.625181
$669$	5.66083e6	0.489007
$670$	260105.	0.0223853
$671$	0	0
$672$	−9.15070e6	−0.781684
$673$	−6.51506e6	−0.554473	−0.277237	−	0.960802i	$-0.589419\pi$
$673$	−6.51506e6	−0.554473	−0.277237	+	0.960802i	$0.589419\pi$
$674$	−1.32702e7	−1.12520
$675$	−2.45377e6	−0.207288
$676$	2.24001e7	1.88531
$677$	−5.06967e6	−0.425117	−0.212558	−	0.977148i	$-0.568180\pi$
$677$	−5.06967e6	−0.425117	−0.212558	+	0.977148i	$0.568180\pi$
$678$	−1.07845e7	−0.901000
$679$	−1.23082e7	−1.02452
$680$	6.33204e6	0.525135
$681$	−2.45188e6	−0.202597
$682$	0	0
$683$	−2.73904e6	−0.224670	−0.112335	−	0.993670i	$-0.535833\pi$
$683$	−2.73904e6	−0.224670	−0.112335	+	0.993670i	$0.535833\pi$
$684$	9.65599e6	0.789144
$685$	5.04879e6	0.411113
$686$	−1.91370e7	−1.55261
$687$	−1.25188e7	−1.01198
$688$	−2.70122e6	−0.217565
$689$	−3.04511e7	−2.44374
$690$	8.99702e6	0.719409
$691$	2.03617e7	1.62226	0.811128	−	0.584869i	$-0.198854\pi$
$691$	2.03617e7	1.62226	0.811128	+	0.584869i	$0.198854\pi$
$692$	3.28387e7	2.60688
$693$	0	0
$694$	−1.57226e7	−1.23916
$695$	−2.08382e6	−0.163643
$696$	3.65769e6	0.286209
$697$	−2.62320e7	−2.04526
$698$	−8.16185e6	−0.634089
$699$	1.49395e7	1.15650
$700$	4.04362e6	0.311907
$701$	−9.68582e6	−0.744460	−0.372230	−	0.928141i	$-0.621407\pi$
$701$	−9.68582e6	−0.744460	−0.372230	+	0.928141i	$0.621407\pi$
$702$	3.21580e7	2.46290
$703$	−7.13209e6	−0.544288
$704$	0	0
$705$	2.26549e6	0.171668
$706$	−3.24629e7	−2.45119
$707$	−1.20219e6	−0.0904531
$708$	−3.33776e6	−0.250249
$709$	−2.40408e7	−1.79611	−0.898057	−	0.439879i	$-0.855021\pi$
$709$	−2.40408e7	−1.79611	−0.898057	+	0.439879i	$0.855021\pi$
$710$	451593.	0.0336203
$711$	1.35487e7	1.00514
$712$	8.29083e6	0.612912
$713$	−4.31689e6	−0.318014
$714$	−2.06729e7	−1.51760
$715$	0	0
$716$	−7.09132e6	−0.516945
$717$	−4.81603e6	−0.349858
$718$	−3.29034e6	−0.238193
$719$	3.08496e6	0.222550	0.111275	−	0.993790i	$-0.464507\pi$
$719$	3.08496e6	0.222550	0.111275	+	0.993790i	$0.464507\pi$
$720$	−680984.	−0.0489560
$721$	−4.60697e6	−0.330048
$722$	−3.06422e6	−0.218764
$723$	−6.12328e6	−0.435651
$724$	−47855.6	−0.00339302
$725$	1.45452e6	0.102772
$726$	0	0
$727$	−1.88804e7	−1.32488	−0.662438	−	0.749117i	$-0.730478\pi$
$727$	−1.88804e7	−1.32488	−0.662438	+	0.749117i	$0.730478\pi$
$728$	−1.82744e7	−1.27795
$729$	1.09659e7	0.764236
$730$	−1.26073e7	−0.875622
$731$	−2.24385e7	−1.55310
$732$	836187.	0.0576800
$733$	1.38469e7	0.951905	0.475952	−	0.879471i	$-0.342103\pi$
$733$	1.38469e7	0.951905	0.475952	+	0.879471i	$0.342103\pi$
$734$	−1.44417e7	−0.989411
$735$	−191725.	−0.0130907
$736$	2.56713e7	1.74684
$737$	0	0
$738$	−1.90789e7	−1.28947
$739$	−1.85405e7	−1.24885	−0.624424	−	0.781086i	$-0.714666\pi$
$739$	−1.85405e7	−1.24885	−0.624424	+	0.781086i	$0.714666\pi$
$740$	−5.95977e6	−0.400083
$741$	1.38157e7	0.924330
$742$	3.98105e7	2.65453
$743$	8.67757e6	0.576669	0.288334	−	0.957530i	$-0.406899\pi$
$743$	8.67757e6	0.576669	0.288334	+	0.957530i	$0.406899\pi$
$744$	1.75925e6	0.116519
$745$	−808057.	−0.0533398
$746$	−3.62169e7	−2.38267
$747$	−6.17598e6	−0.404953
$748$	0	0
$749$	−2.85243e7	−1.85785
$750$	−1.45804e6	−0.0946490
$751$	1.07937e7	0.698345	0.349172	−	0.937059i	$-0.386463\pi$
$751$	1.07937e7	0.698345	0.349172	+	0.937059i	$0.386463\pi$
$752$	1.75803e6	0.113365
$753$	8.31188e6	0.534210
$754$	−1.90623e7	−1.22109
$755$	1.17215e7	0.748372
$756$	−2.54006e7	−1.61636
$757$	−653864.	−0.0414713	−0.0207357	−	0.999785i	$-0.506601\pi$
$757$	−653864.	−0.0414713	−0.0207357	+	0.999785i	$0.506601\pi$
$758$	−1.22983e7	−0.777449
$759$	0	0
$760$	5.53234e6	0.347436
$761$	5.53759e6	0.346624	0.173312	−	0.984867i	$-0.444553\pi$
$761$	5.53759e6	0.346624	0.173312	+	0.984867i	$0.444553\pi$
$762$	1.00312e7	0.625846
$763$	−5.89403e6	−0.366523
$764$	3.76859e7	2.33586
$765$	−5.65679e6	−0.349475
$766$	−1.23882e7	−0.762843
$767$	5.99847e6	0.368173
$768$	−7.19580e6	−0.440226
$769$	−6.85146e6	−0.417799	−0.208899	−	0.977937i	$-0.566988\pi$
$769$	−6.85146e6	−0.417799	−0.208899	+	0.977937i	$0.566988\pi$
$770$	0	0
$771$	−1.37236e7	−0.831444
$772$	−4.17495e7	−2.52120
$773$	−2.38295e7	−1.43439	−0.717194	−	0.696874i	$-0.754574\pi$
$773$	−2.38295e7	−1.43439	−0.717194	+	0.696874i	$0.754574\pi$
$774$	−1.63198e7	−0.979181
$775$	699586.	0.0418395
$776$	−1.40716e7	−0.838860
$777$	6.70971e6	0.398705
$778$	1.21585e7	0.720165
$779$	−2.29190e7	−1.35317
$780$	1.15448e7	0.679436
$781$	0	0
$782$	5.79956e7	3.39139
$783$	−9.13676e6	−0.532584
$784$	−148779.	−0.00864476
$785$	−9.99813e6	−0.579088
$786$	−1.28589e7	−0.742417
$787$	1.34821e7	0.775928	0.387964	−	0.921675i	$-0.373178\pi$
$787$	1.34821e7	0.775928	0.387964	+	0.921675i	$0.373178\pi$
$788$	−3.06111e7	−1.75616
$789$	1.32389e6	0.0757113
$790$	2.25110e7	1.28330
$791$	−1.53087e7	−0.869956
$792$	0	0
$793$	−1.50275e6	−0.0848604
$794$	−5.45105e6	−0.306852
$795$	−8.67275e6	−0.486675
$796$	1.99838e7	1.11788
$797$	−1.71309e7	−0.955288	−0.477644	−	0.878553i	$-0.658509\pi$
$797$	−1.71309e7	−0.955288	−0.477644	+	0.878553i	$0.658509\pi$
$798$	−1.80621e7	−1.00406
$799$	1.46035e7	0.809266
$800$	−4.16023e6	−0.229823
$801$	−7.40669e6	−0.407890
$802$	3.37063e7	1.85044
$803$	0	0
$804$	−586568.	−0.0320021
$805$	1.27714e7	0.694621
$806$	−9.16848e6	−0.497118
$807$	−246984.	−0.0133501
$808$	−1.37443e6	−0.0740619
$809$	5.85791e6	0.314681	0.157341	−	0.987544i	$-0.449708\pi$
$809$	5.85791e6	0.314681	0.157341	+	0.987544i	$0.449708\pi$
$810$	1.76908e6	0.0947401
$811$	1.39161e7	0.742960	0.371480	−	0.928441i	$-0.378850\pi$
$811$	1.39161e7	0.742960	0.371480	+	0.928441i	$0.378850\pi$
$812$	1.50567e7	0.801382
$813$	−1.60317e6	−0.0850656
$814$	0	0
$815$	−1.02767e7	−0.541949
$816$	3.49481e6	0.183738
$817$	−1.96046e7	−1.02755
$818$	−2.20755e7	−1.15353
$819$	1.63256e7	0.850470
$820$	−1.91517e7	−0.994658
$821$	2.43049e7	1.25845	0.629226	−	0.777222i	$-0.283372\pi$
$821$	2.43049e7	1.25845	0.629226	+	0.777222i	$0.283372\pi$
$822$	−1.88450e7	−0.972785
$823$	1.90725e7	0.981539	0.490769	−	0.871290i	$-0.336716\pi$
$823$	1.90725e7	0.981539	0.490769	+	0.871290i	$0.336716\pi$
$824$	−5.26703e6	−0.270239
$825$	0	0
$826$	−7.84215e6	−0.399931
$827$	−1.85739e7	−0.944363	−0.472182	−	0.881501i	$-0.656533\pi$
$827$	−1.85739e7	−0.944363	−0.472182	+	0.881501i	$0.656533\pi$
$828$	2.54845e7	1.29182
$829$	−2.71879e7	−1.37401	−0.687004	−	0.726654i	$-0.741074\pi$
$829$	−2.71879e7	−1.37401	−0.687004	+	0.726654i	$0.741074\pi$
$830$	−1.02613e7	−0.517019
$831$	−6.15614e6	−0.309247
$832$	4.86528e7	2.43669
$833$	−1.23588e6	−0.0617111
$834$	7.77802e6	0.387217
$835$	3.69050e6	0.183176
$836$	0	0
$837$	−4.39455e6	−0.216821
$838$	5.18612e7	2.55113
$839$	−818733.	−0.0401548	−0.0200774	−	0.999798i	$-0.506391\pi$
$839$	−818733.	−0.0401548	−0.0200774	+	0.999798i	$0.506391\pi$
$840$	−5.20470e6	−0.254506
$841$	−1.50952e7	−0.735949
$842$	7.34311e6	0.356944
$843$	−1.15280e7	−0.558706
$844$	−4.65372e7	−2.24877
$845$	−1.14654e7	−0.552391
$846$	1.06214e7	0.510216
$847$	0	0
$848$	−6.73008e6	−0.321389
$849$	1.26750e6	0.0603500
$850$	−9.39865e6	−0.446188
$851$	−1.88233e7	−0.890990
$852$	−1.01839e6	−0.0480637
$853$	3.57740e6	0.168343	0.0841714	−	0.996451i	$-0.473176\pi$
$853$	3.57740e6	0.168343	0.0841714	+	0.996451i	$0.473176\pi$
$854$	1.96464e6	0.0921803
$855$	−4.94237e6	−0.231217
$856$	−3.26111e7	−1.52118
$857$	−3.78683e7	−1.76126	−0.880632	−	0.473802i	$-0.842881\pi$
$857$	−3.78683e7	−1.76126	−0.880632	+	0.473802i	$0.842881\pi$
$858$	0	0
$859$	5.83521e6	0.269819	0.134910	−	0.990858i	$-0.456926\pi$
$859$	5.83521e6	0.269819	0.134910	+	0.990858i	$0.456926\pi$
$860$	−1.63821e7	−0.755309
$861$	2.15617e7	0.991232
$862$	−6.89003e7	−3.15830
$863$	1.34079e7	0.612822	0.306411	−	0.951899i	$-0.400872\pi$
$863$	1.34079e7	0.612822	0.306411	+	0.951899i	$0.400872\pi$
$864$	2.61331e7	1.19098
$865$	−1.68083e7	−0.763808
$866$	−702931.	−0.0318506
$867$	1.42949e7	0.645852
$868$	7.24188e6	0.326251
$869$	0	0
$870$	−5.42911e6	−0.243181
$871$	1.05415e6	0.0470823
$872$	−6.73849e6	−0.300104
$873$	1.25710e7	0.558257
$874$	5.06710e7	2.24379
$875$	−2.06970e6	−0.0913878
$876$	2.84310e7	1.25179
$877$	6.67202e6	0.292926	0.146463	−	0.989216i	$-0.453211\pi$
$877$	6.67202e6	0.292926	0.146463	+	0.989216i	$0.453211\pi$
$878$	−3.89673e7	−1.70594
$879$	2.44564e7	1.06763
$880$	0	0
$881$	4.19033e7	1.81890	0.909448	−	0.415817i	$-0.136504\pi$
$881$	4.19033e7	1.81890	0.909448	+	0.415817i	$0.136504\pi$
$882$	−898872.	−0.0389069
$883$	1.02579e7	0.442748	0.221374	−	0.975189i	$-0.428946\pi$
$883$	1.02579e7	0.442748	0.221374	+	0.975189i	$0.428946\pi$
$884$	7.44185e7	3.20295
$885$	1.70842e6	0.0733222
$886$	−1.79411e7	−0.767830
$887$	1.79543e7	0.766230	0.383115	−	0.923701i	$-0.374851\pi$
$887$	1.79543e7	0.766230	0.383115	+	0.923701i	$0.374851\pi$
$888$	7.67105e6	0.326454
$889$	1.42395e7	0.604282
$890$	−1.23061e7	−0.520769
$891$	0	0
$892$	2.66412e7	1.12109
$893$	1.27592e7	0.535420
$894$	3.01614e6	0.126214
$895$	3.62965e6	0.151463
$896$	−3.53919e7	−1.47277
$897$	3.64630e7	1.51311
$898$	7.10469e7	2.94005
$899$	2.60496e6	0.107498
$900$	−4.12997e6	−0.169958
$901$	−5.59053e7	−2.29425
$902$	0	0
$903$	1.84436e7	0.752707
$904$	−1.75021e7	−0.712308
$905$	24494.6	0.000994145 0
$906$	−4.37516e7	−1.77082
$907$	−4.32547e7	−1.74588	−0.872940	−	0.487827i	$-0.837790\pi$
$907$	−4.32547e7	−1.74588	−0.872940	+	0.487827i	$0.837790\pi$
$908$	−1.15391e7	−0.464471
$909$	1.22786e6	0.0492878
$910$	2.71247e7	1.08583
$911$	−3.10453e7	−1.23937	−0.619683	−	0.784853i	$-0.712739\pi$
$911$	−3.10453e7	−1.23937	−0.619683	+	0.784853i	$0.712739\pi$
$912$	3.05344e6	0.121563
$913$	0	0
$914$	−2.32902e6	−0.0922163
$915$	−427998.	−0.0169001
$916$	−5.89164e7	−2.32005
$917$	−1.82534e7	−0.716836
$918$	5.90389e7	2.31223
$919$	−2.15139e7	−0.840293	−0.420147	−	0.907456i	$-0.638021\pi$
$919$	−2.15139e7	−0.840293	−0.420147	+	0.907456i	$0.638021\pi$
$920$	1.46012e7	0.568747
$921$	−2.59115e7	−1.00657
$922$	3.46512e7	1.34243
$923$	1.83021e6	0.0707126
$924$	0	0
$925$	3.05047e6	0.117223
$926$	−1.26434e7	−0.484546
$927$	4.70535e6	0.179843
$928$	−1.54909e7	−0.590482
$929$	−4.09585e7	−1.55706	−0.778530	−	0.627608i	$-0.784034\pi$
$929$	−4.09585e7	−1.55706	−0.778530	+	0.627608i	$0.784034\pi$
$930$	−2.61126e6	−0.0990018
$931$	−1.07979e6	−0.0408288
$932$	7.03090e7	2.65138
$933$	−2.81360e7	−1.05818
$934$	−2.68813e7	−1.00828
$935$	0	0
$936$	1.86646e7	0.696354
$937$	−3.35318e7	−1.24769	−0.623847	−	0.781547i	$-0.714431\pi$
$937$	−3.35318e7	−1.24769	−0.623847	+	0.781547i	$0.714431\pi$
$938$	−1.37815e6	−0.0511435
$939$	2.51888e7	0.932272
$940$	1.06619e7	0.393565
$941$	1.87190e7	0.689143	0.344571	−	0.938760i	$-0.388024\pi$
$941$	1.87190e7	0.689143	0.344571	+	0.938760i	$0.388024\pi$
$942$	3.73188e7	1.37025
$943$	−6.04889e7	−2.21512
$944$	1.32574e6	0.0484202
$945$	1.30011e7	0.473589
$946$	0	0
$947$	2.35678e7	0.853972	0.426986	−	0.904258i	$-0.359575\pi$
$947$	2.35678e7	0.853972	0.426986	+	0.904258i	$0.359575\pi$
$948$	−5.07649e7	−1.83461
$949$	−5.10949e7	−1.84167
$950$	−8.21165e6	−0.295204
$951$	−1.38898e7	−0.498016
$952$	−3.35499e7	−1.19977
$953$	−4.31667e7	−1.53963	−0.769815	−	0.638267i	$-0.779651\pi$
$953$	−4.31667e7	−1.53963	−0.769815	+	0.638267i	$0.779651\pi$
$954$	−4.06607e7	−1.44645
$955$	−1.92894e7	−0.684399
$956$	−2.26654e7	−0.802081
$957$	0	0
$958$	−3.91050e7	−1.37663
$959$	−2.67507e7	−0.939267
$960$	1.38567e7	0.485270
$961$	−2.73762e7	−0.956236
$962$	−3.99782e7	−1.39279
$963$	2.91334e7	1.01234
$964$	−2.88176e7	−0.998769
$965$	2.13693e7	0.738705
$966$	−4.76702e7	−1.64363
$967$	4.30138e7	1.47925	0.739626	−	0.673018i	$-0.235003\pi$
$967$	4.30138e7	1.47925	0.739626	+	0.673018i	$0.235003\pi$
$968$	0	0
$969$	2.53642e7	0.867786
$970$	2.08865e7	0.712749
$971$	−3.03302e7	−1.03235	−0.516175	−	0.856483i	$-0.672645\pi$
$971$	−3.03302e7	−1.03235	−0.516175	+	0.856483i	$0.672645\pi$
$972$	4.26079e7	1.44652
$973$	1.10410e7	0.373875
$974$	3.65222e7	1.23356
$975$	−5.90912e6	−0.199073
$976$	−332127.	−0.0111604
$977$	2.99049e7	1.00232	0.501159	−	0.865355i	$-0.332907\pi$
$977$	2.99049e7	1.00232	0.501159	+	0.865355i	$0.332907\pi$
$978$	3.83585e7	1.28237
$979$	0	0
$980$	−902305.	−0.0300115
$981$	6.01990e6	0.199718
$982$	1.15531e7	0.382314
$983$	−2.44870e7	−0.808262	−0.404131	−	0.914701i	$-0.632426\pi$
$983$	−2.44870e7	−0.808262	−0.404131	+	0.914701i	$0.632426\pi$
$984$	2.46510e7	0.811608
$985$	1.56682e7	0.514550
$986$	−3.49965e7	−1.14639
$987$	−1.20036e7	−0.392209
$988$	6.50199e7	2.11911
$989$	−5.17414e7	−1.68208
$990$	0	0
$991$	−8.05456e6	−0.260530	−0.130265	−	0.991479i	$-0.541583\pi$
$991$	−8.05456e6	−0.260530	−0.130265	+	0.991479i	$0.541583\pi$
$992$	−7.45073e6	−0.240392
$993$	3.24392e7	1.04399
$994$	−2.39274e6	−0.0768121
$995$	−1.02286e7	−0.327536
$996$	2.31404e7	0.739133
$997$	−1.05243e7	−0.335316	−0.167658	−	0.985845i	$-0.553620\pi$
$997$	−1.05243e7	−0.335316	−0.167658	+	0.985845i	$0.553620\pi$
$998$	3.41724e7	1.08605
$999$	−1.91620e7	−0.607473

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.6.a.p.1.18		20
11.3	even	5		55.6.g.b.31.9	yes	40
11.4	even	5		55.6.g.b.16.9	✓	40
11.10	odd	2		605.6.a.o.1.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.6.g.b.16.9	✓	40	11.4	even	5
55.6.g.b.31.9	yes	40	11.3	even	5
605.6.a.o.1.3		20	11.10	odd	2
605.6.a.p.1.18		20	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q+8.99127 q^{2} +10.3783 q^{3} +48.8429 q^{4} -25.0000 q^{5} +93.3145 q^{6} +132.461 q^{7} +151.440 q^{8} -135.290 q^{9} +O(q^{10})\)	\(q+8.99127 q^{2} +10.3783 q^{3} +48.8429 q^{4} -25.0000 q^{5} +93.3145 q^{6} +132.461 q^{7} +151.440 q^{8} -135.290 q^{9} -224.782 q^{10} +506.909 q^{12} -910.993 q^{13} +1190.99 q^{14} -259.459 q^{15} -201.341 q^{16} -1672.49 q^{17} -1216.43 q^{18} -1461.27 q^{19} -1221.07 q^{20} +1374.73 q^{21} -3856.64 q^{23} +1571.69 q^{24} +625.000 q^{25} -8190.98 q^{26} -3926.02 q^{27} +6469.79 q^{28} +2327.23 q^{29} -2332.86 q^{30} +1119.34 q^{31} -6656.37 q^{32} -15037.8 q^{34} -3311.53 q^{35} -6607.96 q^{36} +4880.76 q^{37} -13138.6 q^{38} -9454.60 q^{39} -3785.99 q^{40} +15684.4 q^{41} +12360.5 q^{42} +13416.2 q^{43} +3382.25 q^{45} -34676.1 q^{46} -8731.60 q^{47} -2089.58 q^{48} +738.944 q^{49} +5619.54 q^{50} -17357.7 q^{51} -44495.6 q^{52} +33426.3 q^{53} -35299.9 q^{54} +20059.8 q^{56} -15165.5 q^{57} +20924.8 q^{58} -6584.54 q^{59} -12672.7 q^{60} +1649.58 q^{61} +10064.3 q^{62} -17920.7 q^{63} -53406.4 q^{64} +22774.8 q^{65} -1157.15 q^{67} -81689.5 q^{68} -40025.6 q^{69} -29774.8 q^{70} -2009.03 q^{71} -20488.2 q^{72} +56087.1 q^{73} +43884.2 q^{74} +6486.47 q^{75} -71372.6 q^{76} -85008.9 q^{78} -100146. q^{79} +5033.52 q^{80} -7870.19 q^{81} +141022. q^{82} +45650.0 q^{83} +67145.7 q^{84} +41812.3 q^{85} +120628. q^{86} +24152.8 q^{87} +54746.8 q^{89} +30410.7 q^{90} -120671. q^{91} -188370. q^{92} +11616.9 q^{93} -78508.2 q^{94} +36531.7 q^{95} -69082.2 q^{96} -92919.0 q^{97} +6644.04 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9}+O(q^{10}) \) 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9	\( 20 q + q^{2} + 407 q^{4} - 500 q^{5} - 264 q^{6} - 167 q^{7} - 57 q^{8} + 1598 q^{9} - 25 q^{10} - 253 q^{12} - 769 q^{13} - 1045 q^{14} + 6963 q^{16} + 2989 q^{17} - 3775 q^{18} - 5828 q^{19} - 10175 q^{20} - 3310 q^{21} - 695 q^{23} - 16724 q^{24} + 12500 q^{25} - 7384 q^{26} + 5925 q^{27} + 3508 q^{28} - 11268 q^{29} + 6600 q^{30} - 11465 q^{31} + 9062 q^{32} + 1217 q^{34} + 4175 q^{35} + 112083 q^{36} - 3057 q^{37} - 13510 q^{38} - 13459 q^{39} + 1425 q^{40} + 839 q^{41} - 14772 q^{42} - 43671 q^{43} - 39950 q^{45} - 81471 q^{46} + 32245 q^{47} - 104315 q^{48} + 2959 q^{49} + 625 q^{50} - 69047 q^{51} - 42696 q^{52} + 27981 q^{53} - 61212 q^{54} - 28294 q^{56} - 79425 q^{57} + 37274 q^{58} - 56847 q^{59} + 6325 q^{60} - 85616 q^{61} - 38095 q^{62} - 100055 q^{63} - 18233 q^{64} + 19225 q^{65} - 31091 q^{67} + 83972 q^{68} - 48708 q^{69} + 26125 q^{70} - 106431 q^{71} - 350510 q^{72} - 117959 q^{73} - 154757 q^{74} - 451972 q^{76} + 348898 q^{78} - 215138 q^{79} - 174075 q^{80} + 75516 q^{81} - 127864 q^{82} - 66761 q^{83} - 521275 q^{84} - 74725 q^{85} - 32222 q^{86} + 5311 q^{87} + 270560 q^{89} + 94375 q^{90} - 269192 q^{91} - 461663 q^{92} + 9345 q^{93} - 479494 q^{94} + 145700 q^{95} - 1247523 q^{96} + 45338 q^{97} + 420757 q^{98}+O(q^{100}) \) 20 * q + q^2 + 407 * q^4 - 500 * q^5 - 264 * q^6 - 167 * q^7 - 57 * q^8 + 1598 * q^9 - 25 * q^10 - 253 * q^12 - 769 * q^13 - 1045 * q^14 + 6963 * q^16 + 2989 * q^17 - 3775 * q^18 - 5828 * q^19 - 10175 * q^20 - 3310 * q^21 - 695 * q^23 - 16724 * q^24 + 12500 * q^25 - 7384 * q^26 + 5925 * q^27 + 3508 * q^28 - 11268 * q^29 + 6600 * q^30 - 11465 * q^31 + 9062 * q^32 + 1217 * q^34 + 4175 * q^35 + 112083 * q^36 - 3057 * q^37 - 13510 * q^38 - 13459 * q^39 + 1425 * q^40 + 839 * q^41 - 14772 * q^42 - 43671 * q^43 - 39950 * q^45 - 81471 * q^46 + 32245 * q^47 - 104315 * q^48 + 2959 * q^49 + 625 * q^50 - 69047 * q^51 - 42696 * q^52 + 27981 * q^53 - 61212 * q^54 - 28294 * q^56 - 79425 * q^57 + 37274 * q^58 - 56847 * q^59 + 6325 * q^60 - 85616 * q^61 - 38095 * q^62 - 100055 * q^63 - 18233 * q^64 + 19225 * q^65 - 31091 * q^67 + 83972 * q^68 - 48708 * q^69 + 26125 * q^70 - 106431 * q^71 - 350510 * q^72 - 117959 * q^73 - 154757 * q^74 - 451972 * q^76 + 348898 * q^78 - 215138 * q^79 - 174075 * q^80 + 75516 * q^81 - 127864 * q^82 - 66761 * q^83 - 521275 * q^84 - 74725 * q^85 - 32222 * q^86 + 5311 * q^87 + 270560 * q^89 + 94375 * q^90 - 269192 * q^91 - 461663 * q^92 + 9345 * q^93 - 479494 * q^94 + 145700 * q^95 - 1247523 * q^96 + 45338 * q^97 + 420757 * q^98

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