# Properties

 Label 234.6.b.b.181.2 Level $234$ Weight $6$ Character 234.181 Analytic conductor $37.530$ Analytic rank $0$ Dimension $2$ Inner twists $2$

# Related objects

Show commands: Magma / PariGP / SageMath

## Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [234,6,Mod(181,234)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(234, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("234.181");

S:= CuspForms(chi, 6);

N := Newforms(S);

 Level: $$N$$ $$=$$ $$234 = 2 \cdot 3^{2} \cdot 13$$ Weight: $$k$$ $$=$$ $$6$$ Character orbit: $$[\chi]$$ $$=$$ 234.b (of order $$2$$, degree $$1$$, 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: $$37.5298138362$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(i)$$ comment: defining polynomial  gp: f.mod \\ as an extension of the character field Defining polynomial: $$x^{2} + 1$$ x^2 + 1 Coefficient ring: $$\Z[a_1, \ldots, a_{5}]$$ Coefficient ring index: $$1$$ Twist minimal: no (minimal twist has level 26) Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

## Embedding invariants

 Embedding label 181.2 Root $$-1.00000i$$ of defining polynomial Character $$\chi$$ $$=$$ 234.181 Dual form 234.6.b.b.181.1

## $q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

 $$f(q)$$ $$=$$ $$q+4.00000i q^{2} -16.0000 q^{4} -51.0000i q^{5} +105.000i q^{7} -64.0000i q^{8} +O(q^{10})$$ $$q+4.00000i q^{2} -16.0000 q^{4} -51.0000i q^{5} +105.000i q^{7} -64.0000i q^{8} +204.000 q^{10} -120.000i q^{11} +(-598.000 + 117.000i) q^{13} -420.000 q^{14} +256.000 q^{16} +1101.00 q^{17} -1170.00i q^{19} +816.000i q^{20} +480.000 q^{22} -1050.00 q^{23} +524.000 q^{25} +(-468.000 - 2392.00i) q^{26} -1680.00i q^{28} +4104.00 q^{29} +9624.00i q^{31} +1024.00i q^{32} +4404.00i q^{34} +5355.00 q^{35} +8709.00i q^{37} +4680.00 q^{38} -3264.00 q^{40} +9480.00i q^{41} +9995.00 q^{43} +1920.00i q^{44} -4200.00i q^{46} +2943.00i q^{47} +5782.00 q^{49} +2096.00i q^{50} +(9568.00 - 1872.00i) q^{52} +750.000 q^{53} -6120.00 q^{55} +6720.00 q^{56} +16416.0i q^{58} +40938.0i q^{59} -57920.0 q^{61} -38496.0 q^{62} -4096.00 q^{64} +(5967.00 + 30498.0i) q^{65} +22812.0i q^{67} -17616.0 q^{68} +21420.0i q^{70} -63741.0i q^{71} +58866.0i q^{73} -34836.0 q^{74} +18720.0i q^{76} +12600.0 q^{77} +63202.0 q^{79} -13056.0i q^{80} -37920.0 q^{82} -55458.0i q^{83} -56151.0i q^{85} +39980.0i q^{86} -7680.00 q^{88} +104778. i q^{89} +(-12285.0 - 62790.0i) q^{91} +16800.0 q^{92} -11772.0 q^{94} -59670.0 q^{95} +160452. i q^{97} +23128.0i q^{98} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2 q - 32 q^{4}+O(q^{10})$$ 2 * q - 32 * q^4 $$2 q - 32 q^{4} + 408 q^{10} - 1196 q^{13} - 840 q^{14} + 512 q^{16} + 2202 q^{17} + 960 q^{22} - 2100 q^{23} + 1048 q^{25} - 936 q^{26} + 8208 q^{29} + 10710 q^{35} + 9360 q^{38} - 6528 q^{40} + 19990 q^{43} + 11564 q^{49} + 19136 q^{52} + 1500 q^{53} - 12240 q^{55} + 13440 q^{56} - 115840 q^{61} - 76992 q^{62} - 8192 q^{64} + 11934 q^{65} - 35232 q^{68} - 69672 q^{74} + 25200 q^{77} + 126404 q^{79} - 75840 q^{82} - 15360 q^{88} - 24570 q^{91} + 33600 q^{92} - 23544 q^{94} - 119340 q^{95}+O(q^{100})$$ 2 * q - 32 * q^4 + 408 * q^10 - 1196 * q^13 - 840 * q^14 + 512 * q^16 + 2202 * q^17 + 960 * q^22 - 2100 * q^23 + 1048 * q^25 - 936 * q^26 + 8208 * q^29 + 10710 * q^35 + 9360 * q^38 - 6528 * q^40 + 19990 * q^43 + 11564 * q^49 + 19136 * q^52 + 1500 * q^53 - 12240 * q^55 + 13440 * q^56 - 115840 * q^61 - 76992 * q^62 - 8192 * q^64 + 11934 * q^65 - 35232 * q^68 - 69672 * q^74 + 25200 * q^77 + 126404 * q^79 - 75840 * q^82 - 15360 * q^88 - 24570 * q^91 + 33600 * q^92 - 23544 * q^94 - 119340 * q^95

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/234\mathbb{Z}\right)^\times$$.

 $$n$$ $$145$$ $$209$$ $$\chi(n)$$ $$-1$$ $$1$$

## 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 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 4.00000i 0.707107i
$$3$$ 0 0
$$4$$ −16.0000 −0.500000
$$5$$ 51.0000i 0.912316i −0.889899 0.456158i $$-0.849225\pi$$
0.889899 0.456158i $$-0.150775\pi$$
$$6$$ 0 0
$$7$$ 105.000i 0.809924i 0.914334 + 0.404962i $$0.132715\pi$$
−0.914334 + 0.404962i $$0.867285\pi$$
$$8$$ 64.0000i 0.353553i
$$9$$ 0 0
$$10$$ 204.000 0.645105
$$11$$ 120.000i 0.299020i −0.988760 0.149510i $$-0.952230\pi$$
0.988760 0.149510i $$-0.0477695\pi$$
$$12$$ 0 0
$$13$$ −598.000 + 117.000i −0.981393 + 0.192012i
$$14$$ −420.000 −0.572703
$$15$$ 0 0
$$16$$ 256.000 0.250000
$$17$$ 1101.00 0.923985 0.461993 0.886884i $$-0.347135\pi$$
0.461993 + 0.886884i $$0.347135\pi$$
$$18$$ 0 0
$$19$$ 1170.00i 0.743536i −0.928326 0.371768i $$-0.878752\pi$$
0.928326 0.371768i $$-0.121248\pi$$
$$20$$ 816.000i 0.456158i
$$21$$ 0 0
$$22$$ 480.000 0.211439
$$23$$ −1050.00 −0.413875 −0.206938 0.978354i $$-0.566350\pi$$
−0.206938 + 0.978354i $$0.566350\pi$$
$$24$$ 0 0
$$25$$ 524.000 0.167680
$$26$$ −468.000 2392.00i −0.135773 0.693949i
$$27$$ 0 0
$$28$$ 1680.00i 0.404962i
$$29$$ 4104.00 0.906176 0.453088 0.891466i $$-0.350322\pi$$
0.453088 + 0.891466i $$0.350322\pi$$
$$30$$ 0 0
$$31$$ 9624.00i 1.79867i 0.437261 + 0.899335i $$0.355949\pi$$
−0.437261 + 0.899335i $$0.644051\pi$$
$$32$$ 1024.00i 0.176777i
$$33$$ 0 0
$$34$$ 4404.00i 0.653356i
$$35$$ 5355.00 0.738906
$$36$$ 0 0
$$37$$ 8709.00i 1.04584i 0.852383 + 0.522918i $$0.175157\pi$$
−0.852383 + 0.522918i $$0.824843\pi$$
$$38$$ 4680.00 0.525759
$$39$$ 0 0
$$40$$ −3264.00 −0.322552
$$41$$ 9480.00i 0.880742i 0.897816 + 0.440371i $$0.145153\pi$$
−0.897816 + 0.440371i $$0.854847\pi$$
$$42$$ 0 0
$$43$$ 9995.00 0.824350 0.412175 0.911105i $$-0.364769\pi$$
0.412175 + 0.911105i $$0.364769\pi$$
$$44$$ 1920.00i 0.149510i
$$45$$ 0 0
$$46$$ 4200.00i 0.292654i
$$47$$ 2943.00i 0.194333i 0.995268 + 0.0971663i $$0.0309779\pi$$
−0.995268 + 0.0971663i $$0.969022\pi$$
$$48$$ 0 0
$$49$$ 5782.00 0.344023
$$50$$ 2096.00i 0.118568i
$$51$$ 0 0
$$52$$ 9568.00 1872.00i 0.490696 0.0960058i
$$53$$ 750.000 0.0366751 0.0183376 0.999832i $$-0.494163\pi$$
0.0183376 + 0.999832i $$0.494163\pi$$
$$54$$ 0 0
$$55$$ −6120.00 −0.272800
$$56$$ 6720.00 0.286351
$$57$$ 0 0
$$58$$ 16416.0i 0.640763i
$$59$$ 40938.0i 1.53108i 0.643391 + 0.765538i $$0.277527\pi$$
−0.643391 + 0.765538i $$0.722473\pi$$
$$60$$ 0 0
$$61$$ −57920.0 −1.99298 −0.996492 0.0836839i $$-0.973331\pi$$
−0.996492 + 0.0836839i $$0.973331\pi$$
$$62$$ −38496.0 −1.27185
$$63$$ 0 0
$$64$$ −4096.00 −0.125000
$$65$$ 5967.00 + 30498.0i 0.175175 + 0.895340i
$$66$$ 0 0
$$67$$ 22812.0i 0.620835i 0.950600 + 0.310418i $$0.100469\pi$$
−0.950600 + 0.310418i $$0.899531\pi$$
$$68$$ −17616.0 −0.461993
$$69$$ 0 0
$$70$$ 21420.0i 0.522486i
$$71$$ 63741.0i 1.50063i −0.661082 0.750314i $$-0.729902\pi$$
0.661082 0.750314i $$-0.270098\pi$$
$$72$$ 0 0
$$73$$ 58866.0i 1.29288i 0.762966 + 0.646439i $$0.223742\pi$$
−0.762966 + 0.646439i $$0.776258\pi$$
$$74$$ −34836.0 −0.739518
$$75$$ 0 0
$$76$$ 18720.0i 0.371768i
$$77$$ 12600.0 0.242183
$$78$$ 0 0
$$79$$ 63202.0 1.13937 0.569683 0.821865i $$-0.307066\pi$$
0.569683 + 0.821865i $$0.307066\pi$$
$$80$$ 13056.0i 0.228079i
$$81$$ 0 0
$$82$$ −37920.0 −0.622779
$$83$$ 55458.0i 0.883627i −0.897107 0.441813i $$-0.854335\pi$$
0.897107 0.441813i $$-0.145665\pi$$
$$84$$ 0 0
$$85$$ 56151.0i 0.842966i
$$86$$ 39980.0i 0.582903i
$$87$$ 0 0
$$88$$ −7680.00 −0.105719
$$89$$ 104778.i 1.40215i 0.713087 + 0.701076i $$0.247297\pi$$
−0.713087 + 0.701076i $$0.752703\pi$$
$$90$$ 0 0
$$91$$ −12285.0 62790.0i −0.155515 0.794853i
$$92$$ 16800.0 0.206938
$$93$$ 0 0
$$94$$ −11772.0 −0.137414
$$95$$ −59670.0 −0.678339
$$96$$ 0 0
$$97$$ 160452.i 1.73147i 0.500500 + 0.865737i $$0.333150\pi$$
−0.500500 + 0.865737i $$0.666850\pi$$
$$98$$ 23128.0i 0.243261i
$$99$$ 0 0
$$100$$ −8384.00 −0.0838400
$$101$$ 113124. 1.10345 0.551723 0.834027i $$-0.313970\pi$$
0.551723 + 0.834027i $$0.313970\pi$$
$$102$$ 0 0
$$103$$ 25046.0 0.232619 0.116310 0.993213i $$-0.462894\pi$$
0.116310 + 0.993213i $$0.462894\pi$$
$$104$$ 7488.00 + 38272.0i 0.0678864 + 0.346975i
$$105$$ 0 0
$$106$$ 3000.00i 0.0259332i
$$107$$ −24924.0 −0.210455 −0.105227 0.994448i $$-0.533557\pi$$
−0.105227 + 0.994448i $$0.533557\pi$$
$$108$$ 0 0
$$109$$ 144831.i 1.16760i 0.811896 + 0.583802i $$0.198435\pi$$
−0.811896 + 0.583802i $$0.801565\pi$$
$$110$$ 24480.0i 0.192899i
$$111$$ 0 0
$$112$$ 26880.0i 0.202481i
$$113$$ −100266. −0.738682 −0.369341 0.929294i $$-0.620417\pi$$
−0.369341 + 0.929294i $$0.620417\pi$$
$$114$$ 0 0
$$115$$ 53550.0i 0.377585i
$$116$$ −65664.0 −0.453088
$$117$$ 0 0
$$118$$ −163752. −1.08263
$$119$$ 115605.i 0.748358i
$$120$$ 0 0
$$121$$ 146651. 0.910587
$$122$$ 231680.i 1.40925i
$$123$$ 0 0
$$124$$ 153984.i 0.899335i
$$125$$ 186099.i 1.06529i
$$126$$ 0 0
$$127$$ −202754. −1.11548 −0.557738 0.830017i $$-0.688331\pi$$
−0.557738 + 0.830017i $$0.688331\pi$$
$$128$$ 16384.0i 0.0883883i
$$129$$ 0 0
$$130$$ −121992. + 23868.0i −0.633101 + 0.123868i
$$131$$ 303855. 1.54699 0.773496 0.633801i $$-0.218506\pi$$
0.773496 + 0.633801i $$0.218506\pi$$
$$132$$ 0 0
$$133$$ 122850. 0.602207
$$134$$ −91248.0 −0.438997
$$135$$ 0 0
$$136$$ 70464.0i 0.326678i
$$137$$ 63738.0i 0.290133i 0.989422 + 0.145066i $$0.0463396\pi$$
−0.989422 + 0.145066i $$0.953660\pi$$
$$138$$ 0 0
$$139$$ 13841.0 0.0607618 0.0303809 0.999538i $$-0.490328\pi$$
0.0303809 + 0.999538i $$0.490328\pi$$
$$140$$ −85680.0 −0.369453
$$141$$ 0 0
$$142$$ 254964. 1.06110
$$143$$ 14040.0 + 71760.0i 0.0574152 + 0.293456i
$$144$$ 0 0
$$145$$ 209304.i 0.826718i
$$146$$ −235464. −0.914202
$$147$$ 0 0
$$148$$ 139344.i 0.522918i
$$149$$ 276426.i 1.02003i 0.860165 + 0.510015i $$0.170360\pi$$
−0.860165 + 0.510015i $$0.829640\pi$$
$$150$$ 0 0
$$151$$ 321333.i 1.14687i −0.819252 0.573433i $$-0.805611\pi$$
0.819252 0.573433i $$-0.194389\pi$$
$$152$$ −74880.0 −0.262880
$$153$$ 0 0
$$154$$ 50400.0i 0.171249i
$$155$$ 490824. 1.64095
$$156$$ 0 0
$$157$$ 339506. 1.09925 0.549627 0.835410i $$-0.314770\pi$$
0.549627 + 0.835410i $$0.314770\pi$$
$$158$$ 252808.i 0.805653i
$$159$$ 0 0
$$160$$ 52224.0 0.161276
$$161$$ 110250.i 0.335208i
$$162$$ 0 0
$$163$$ 395718.i 1.16659i −0.812262 0.583293i $$-0.801764\pi$$
0.812262 0.583293i $$-0.198236\pi$$
$$164$$ 151680.i 0.440371i
$$165$$ 0 0
$$166$$ 221832. 0.624819
$$167$$ 426708.i 1.18397i −0.805950 0.591984i $$-0.798345\pi$$
0.805950 0.591984i $$-0.201655\pi$$
$$168$$ 0 0
$$169$$ 343915. 139932.i 0.926263 0.376878i
$$170$$ 224604. 0.596067
$$171$$ 0 0
$$172$$ −159920. −0.412175
$$173$$ −16026.0 −0.0407108 −0.0203554 0.999793i $$-0.506480\pi$$
−0.0203554 + 0.999793i $$0.506480\pi$$
$$174$$ 0 0
$$175$$ 55020.0i 0.135808i
$$176$$ 30720.0i 0.0747549i
$$177$$ 0 0
$$178$$ −419112. −0.991471
$$179$$ 690045. 1.60970 0.804850 0.593479i $$-0.202246\pi$$
0.804850 + 0.593479i $$0.202246\pi$$
$$180$$ 0 0
$$181$$ −96478.0 −0.218893 −0.109446 0.993993i $$-0.534908\pi$$
−0.109446 + 0.993993i $$0.534908\pi$$
$$182$$ 251160. 49140.0i 0.562046 0.109966i
$$183$$ 0 0
$$184$$ 67200.0i 0.146327i
$$185$$ 444159. 0.954134
$$186$$ 0 0
$$187$$ 132120.i 0.276290i
$$188$$ 47088.0i 0.0971663i
$$189$$ 0 0
$$190$$ 238680.i 0.479658i
$$191$$ −708180. −1.40462 −0.702312 0.711869i $$-0.747849\pi$$
−0.702312 + 0.711869i $$0.747849\pi$$
$$192$$ 0 0
$$193$$ 347862.i 0.672224i −0.941822 0.336112i $$-0.890888\pi$$
0.941822 0.336112i $$-0.109112\pi$$
$$194$$ −641808. −1.22434
$$195$$ 0 0
$$196$$ −92512.0 −0.172012
$$197$$ 899589.i 1.65150i −0.564036 0.825750i $$-0.690752\pi$$
0.564036 0.825750i $$-0.309248\pi$$
$$198$$ 0 0
$$199$$ 143116. 0.256186 0.128093 0.991762i $$-0.459114\pi$$
0.128093 + 0.991762i $$0.459114\pi$$
$$200$$ 33536.0i 0.0592838i
$$201$$ 0 0
$$202$$ 452496.i 0.780255i
$$203$$ 430920.i 0.733933i
$$204$$ 0 0
$$205$$ 483480. 0.803515
$$206$$ 100184.i 0.164487i
$$207$$ 0 0
$$208$$ −153088. + 29952.0i −0.245348 + 0.0480029i
$$209$$ −140400. −0.222332
$$210$$ 0 0
$$211$$ −339731. −0.525326 −0.262663 0.964888i $$-0.584601\pi$$
−0.262663 + 0.964888i $$0.584601\pi$$
$$212$$ −12000.0 −0.0183376
$$213$$ 0 0
$$214$$ 99696.0i 0.148814i
$$215$$ 509745.i 0.752068i
$$216$$ 0 0
$$217$$ −1.01052e6 −1.45679
$$218$$ −579324. −0.825620
$$219$$ 0 0
$$220$$ 97920.0 0.136400
$$221$$ −658398. + 128817.i −0.906792 + 0.177416i
$$222$$ 0 0
$$223$$ 623757.i 0.839950i 0.907536 + 0.419975i $$0.137961\pi$$
−0.907536 + 0.419975i $$0.862039\pi$$
$$224$$ −107520. −0.143176
$$225$$ 0 0
$$226$$ 401064.i 0.522327i
$$227$$ 177612.i 0.228775i 0.993436 + 0.114387i $$0.0364905\pi$$
−0.993436 + 0.114387i $$0.963510\pi$$
$$228$$ 0 0
$$229$$ 1.18705e6i 1.49582i −0.663799 0.747911i $$-0.731057\pi$$
0.663799 0.747911i $$-0.268943\pi$$
$$230$$ −214200. −0.266993
$$231$$ 0 0
$$232$$ 262656.i 0.320381i
$$233$$ 112317. 0.135536 0.0677682 0.997701i $$-0.478412\pi$$
0.0677682 + 0.997701i $$0.478412\pi$$
$$234$$ 0 0
$$235$$ 150093. 0.177293
$$236$$ 655008.i 0.765538i
$$237$$ 0 0
$$238$$ −462420. −0.529169
$$239$$ 1.19805e6i 1.35669i 0.734743 + 0.678346i $$0.237303\pi$$
−0.734743 + 0.678346i $$0.762697\pi$$
$$240$$ 0 0
$$241$$ 1.16629e6i 1.29349i 0.762707 + 0.646744i $$0.223870\pi$$
−0.762707 + 0.646744i $$0.776130\pi$$
$$242$$ 586604.i 0.643882i
$$243$$ 0 0
$$244$$ 926720. 0.996492
$$245$$ 294882.i 0.313858i
$$246$$ 0 0
$$247$$ 136890. + 699660.i 0.142767 + 0.729701i
$$248$$ 615936. 0.635926
$$249$$ 0 0
$$250$$ 744396. 0.753276
$$251$$ −648996. −0.650216 −0.325108 0.945677i $$-0.605401\pi$$
−0.325108 + 0.945677i $$0.605401\pi$$
$$252$$ 0 0
$$253$$ 126000.i 0.123757i
$$254$$ 811016.i 0.788760i
$$255$$ 0 0
$$256$$ 65536.0 0.0625000
$$257$$ 945885. 0.893317 0.446658 0.894705i $$-0.352614\pi$$
0.446658 + 0.894705i $$0.352614\pi$$
$$258$$ 0 0
$$259$$ −914445. −0.847048
$$260$$ −95472.0 487968.i −0.0875876 0.447670i
$$261$$ 0 0
$$262$$ 1.21542e6i 1.09389i
$$263$$ −1.01222e6 −0.902375 −0.451188 0.892429i $$-0.649000\pi$$
−0.451188 + 0.892429i $$0.649000\pi$$
$$264$$ 0 0
$$265$$ 38250.0i 0.0334593i
$$266$$ 491400.i 0.425825i
$$267$$ 0 0
$$268$$ 364992.i 0.310418i
$$269$$ 1.01772e6 0.857527 0.428763 0.903417i $$-0.358949\pi$$
0.428763 + 0.903417i $$0.358949\pi$$
$$270$$ 0 0
$$271$$ 463461.i 0.383345i 0.981459 + 0.191673i $$0.0613912\pi$$
−0.981459 + 0.191673i $$0.938609\pi$$
$$272$$ 281856. 0.230996
$$273$$ 0 0
$$274$$ −254952. −0.205155
$$275$$ 62880.0i 0.0501396i
$$276$$ 0 0
$$277$$ 332528. 0.260393 0.130196 0.991488i $$-0.458439\pi$$
0.130196 + 0.991488i $$0.458439\pi$$
$$278$$ 55364.0i 0.0429651i
$$279$$ 0 0
$$280$$ 342720.i 0.261243i
$$281$$ 49122.0i 0.0371116i 0.999828 + 0.0185558i $$0.00590684\pi$$
−0.999828 + 0.0185558i $$0.994093\pi$$
$$282$$ 0 0
$$283$$ −1.55848e6 −1.15674 −0.578371 0.815774i $$-0.696311\pi$$
−0.578371 + 0.815774i $$0.696311\pi$$
$$284$$ 1.01986e6i 0.750314i
$$285$$ 0 0
$$286$$ −287040. + 56160.0i −0.207504 + 0.0405987i
$$287$$ −995400. −0.713334
$$288$$ 0 0
$$289$$ −207656. −0.146251
$$290$$ 837216. 0.584578
$$291$$ 0 0
$$292$$ 941856.i 0.646439i
$$293$$ 218463.i 0.148665i 0.997234 + 0.0743325i $$0.0236826\pi$$
−0.997234 + 0.0743325i $$0.976317\pi$$
$$294$$ 0 0
$$295$$ 2.08784e6 1.39682
$$296$$ 557376. 0.369759
$$297$$ 0 0
$$298$$ −1.10570e6 −0.721271
$$299$$ 627900. 122850.i 0.406174 0.0794689i
$$300$$ 0 0
$$301$$ 1.04948e6i 0.667661i
$$302$$ 1.28533e6 0.810957
$$303$$ 0 0
$$304$$ 299520.i 0.185884i
$$305$$ 2.95392e6i 1.81823i
$$306$$ 0 0
$$307$$ 321102.i 0.194445i 0.995263 + 0.0972226i $$0.0309959\pi$$
−0.995263 + 0.0972226i $$0.969004\pi$$
$$308$$ −201600. −0.121092
$$309$$ 0 0
$$310$$ 1.96330e6i 1.16033i
$$311$$ −3.33725e6 −1.95654 −0.978269 0.207340i $$-0.933519\pi$$
−0.978269 + 0.207340i $$0.933519\pi$$
$$312$$ 0 0
$$313$$ 1.16568e6 0.672538 0.336269 0.941766i $$-0.390835\pi$$
0.336269 + 0.941766i $$0.390835\pi$$
$$314$$ 1.35802e6i 0.777290i
$$315$$ 0 0
$$316$$ −1.01123e6 −0.569683
$$317$$ 73518.0i 0.0410909i −0.999789 0.0205454i $$-0.993460\pi$$
0.999789 0.0205454i $$-0.00654028\pi$$
$$318$$ 0 0
$$319$$ 492480.i 0.270964i
$$320$$ 208896.i 0.114039i
$$321$$ 0 0
$$322$$ 441000. 0.237028
$$323$$ 1.28817e6i 0.687016i
$$324$$ 0 0
$$325$$ −313352. + 61308.0i −0.164560 + 0.0321965i
$$326$$ 1.58287e6 0.824901
$$327$$ 0 0
$$328$$ 606720. 0.311389
$$329$$ −309015. −0.157395
$$330$$ 0 0
$$331$$ 632682.i 0.317406i 0.987326 + 0.158703i $$0.0507313\pi$$
−0.987326 + 0.158703i $$0.949269\pi$$
$$332$$ 887328.i 0.441813i
$$333$$ 0 0
$$334$$ 1.70683e6 0.837191
$$335$$ 1.16341e6 0.566398
$$336$$ 0 0
$$337$$ −326843. −0.156771 −0.0783853 0.996923i $$-0.524976\pi$$
−0.0783853 + 0.996923i $$0.524976\pi$$
$$338$$ 559728. + 1.37566e6i 0.266493 + 0.654967i
$$339$$ 0 0
$$340$$ 898416.i 0.421483i
$$341$$ 1.15488e6 0.537837
$$342$$ 0 0
$$343$$ 2.37184e6i 1.08856i
$$344$$ 639680.i 0.291452i
$$345$$ 0 0
$$346$$ 64104.0i 0.0287869i
$$347$$ −2.96275e6 −1.32090 −0.660452 0.750868i $$-0.729635\pi$$
−0.660452 + 0.750868i $$0.729635\pi$$
$$348$$ 0 0
$$349$$ 866325.i 0.380730i 0.981713 + 0.190365i $$0.0609672\pi$$
−0.981713 + 0.190365i $$0.939033\pi$$
$$350$$ −220080. −0.0960308
$$351$$ 0 0
$$352$$ 122880. 0.0528597
$$353$$ 1.66291e6i 0.710282i −0.934813 0.355141i $$-0.884433\pi$$
0.934813 0.355141i $$-0.115567\pi$$
$$354$$ 0 0
$$355$$ −3.25079e6 −1.36905
$$356$$ 1.67645e6i 0.701076i
$$357$$ 0 0
$$358$$ 2.76018e6i 1.13823i
$$359$$ 625536.i 0.256163i −0.991764 0.128081i $$-0.959118\pi$$
0.991764 0.128081i $$-0.0408819\pi$$
$$360$$ 0 0
$$361$$ 1.10720e6 0.447155
$$362$$ 385912.i 0.154781i
$$363$$ 0 0
$$364$$ 196560. + 1.00464e6i 0.0777574 + 0.397427i
$$365$$ 3.00217e6 1.17951
$$366$$ 0 0
$$367$$ 1.08327e6 0.419829 0.209914 0.977720i $$-0.432681\pi$$
0.209914 + 0.977720i $$0.432681\pi$$
$$368$$ −268800. −0.103469
$$369$$ 0 0
$$370$$ 1.77664e6i 0.674674i
$$371$$ 78750.0i 0.0297041i
$$372$$ 0 0
$$373$$ −1.78896e6 −0.665775 −0.332888 0.942967i $$-0.608023\pi$$
−0.332888 + 0.942967i $$0.608023\pi$$
$$374$$ 528480. 0.195366
$$375$$ 0 0
$$376$$ 188352. 0.0687069
$$377$$ −2.45419e6 + 480168.i −0.889314 + 0.173996i
$$378$$ 0 0
$$379$$ 868614.i 0.310620i 0.987866 + 0.155310i $$0.0496376\pi$$
−0.987866 + 0.155310i $$0.950362\pi$$
$$380$$ 954720. 0.339170
$$381$$ 0 0
$$382$$ 2.83272e6i 0.993220i
$$383$$ 1.07972e6i 0.376108i 0.982159 + 0.188054i $$0.0602179\pi$$
−0.982159 + 0.188054i $$0.939782\pi$$
$$384$$ 0 0
$$385$$ 642600.i 0.220947i
$$386$$ 1.39145e6 0.475334
$$387$$ 0 0
$$388$$ 2.56723e6i 0.865737i
$$389$$ −1.28822e6 −0.431634 −0.215817 0.976434i $$-0.569241\pi$$
−0.215817 + 0.976434i $$0.569241\pi$$
$$390$$ 0 0
$$391$$ −1.15605e6 −0.382415
$$392$$ 370048.i 0.121631i
$$393$$ 0 0
$$394$$ 3.59836e6 1.16779
$$395$$ 3.22330e6i 1.03946i
$$396$$ 0 0
$$397$$ 5.46909e6i 1.74156i −0.491672 0.870781i $$-0.663614\pi$$
0.491672 0.870781i $$-0.336386\pi$$
$$398$$ 572464.i 0.181151i
$$399$$ 0 0
$$400$$ 134144. 0.0419200
$$401$$ 1.58612e6i 0.492577i 0.969196 + 0.246289i $$0.0792112\pi$$
−0.969196 + 0.246289i $$0.920789\pi$$
$$402$$ 0 0
$$403$$ −1.12601e6 5.75515e6i −0.345365 1.76520i
$$404$$ −1.80998e6 −0.551723
$$405$$ 0 0
$$406$$ −1.72368e6 −0.518969
$$407$$ 1.04508e6 0.312726
$$408$$ 0 0
$$409$$ 6.44192e6i 1.90418i 0.305825 + 0.952088i $$0.401068\pi$$
−0.305825 + 0.952088i $$0.598932\pi$$
$$410$$ 1.93392e6i 0.568171i
$$411$$ 0 0
$$412$$ −400736. −0.116310
$$413$$ −4.29849e6 −1.24005
$$414$$ 0 0
$$415$$ −2.82836e6 −0.806147
$$416$$ −119808. 612352.i −0.0339432 0.173487i
$$417$$ 0 0
$$418$$ 561600.i 0.157212i
$$419$$ 4.30545e6 1.19807 0.599037 0.800721i $$-0.295550\pi$$
0.599037 + 0.800721i $$0.295550\pi$$
$$420$$ 0 0
$$421$$ 1.51346e6i 0.416164i 0.978111 + 0.208082i $$0.0667221\pi$$
−0.978111 + 0.208082i $$0.933278\pi$$
$$422$$ 1.35892e6i 0.371462i
$$423$$ 0 0
$$424$$ 48000.0i 0.0129666i
$$425$$ 576924. 0.154934
$$426$$ 0 0
$$427$$ 6.08160e6i 1.61417i
$$428$$ 398784. 0.105227
$$429$$ 0 0
$$430$$ 2.03898e6 0.531792
$$431$$ 1.43116e6i 0.371105i 0.982634 + 0.185552i $$0.0594074\pi$$
−0.982634 + 0.185552i $$0.940593\pi$$
$$432$$ 0 0
$$433$$ 429613. 0.110118 0.0550589 0.998483i $$-0.482465\pi$$
0.0550589 + 0.998483i $$0.482465\pi$$
$$434$$ 4.04208e6i 1.03010i
$$435$$ 0 0
$$436$$ 2.31730e6i 0.583802i
$$437$$ 1.22850e6i 0.307731i
$$438$$ 0 0
$$439$$ 552038. 0.136712 0.0683562 0.997661i $$-0.478225\pi$$
0.0683562 + 0.997661i $$0.478225\pi$$
$$440$$ 391680.i 0.0964494i
$$441$$ 0 0
$$442$$ −515268. 2.63359e6i −0.125452 0.641199i
$$443$$ −2.15255e6 −0.521128 −0.260564 0.965457i $$-0.583908\pi$$
−0.260564 + 0.965457i $$0.583908\pi$$
$$444$$ 0 0
$$445$$ 5.34368e6 1.27921
$$446$$ −2.49503e6 −0.593934
$$447$$ 0 0
$$448$$ 430080.i 0.101240i
$$449$$ 1.40429e6i 0.328731i −0.986400 0.164365i $$-0.947442\pi$$
0.986400 0.164365i $$-0.0525576\pi$$
$$450$$ 0 0
$$451$$ 1.13760e6 0.263359
$$452$$ 1.60426e6 0.369341
$$453$$ 0 0
$$454$$ −710448. −0.161768
$$455$$ −3.20229e6 + 626535.i −0.725157 + 0.141879i
$$456$$ 0 0
$$457$$ 1.32818e6i 0.297485i −0.988876 0.148743i $$-0.952477\pi$$
0.988876 0.148743i $$-0.0475226\pi$$
$$458$$ 4.74820e6 1.05771
$$459$$ 0 0
$$460$$ 856800.i 0.188793i
$$461$$ 5.89070e6i 1.29096i −0.763775 0.645482i $$-0.776656\pi$$
0.763775 0.645482i $$-0.223344\pi$$
$$462$$ 0 0
$$463$$ 2.37139e6i 0.514104i 0.966398 + 0.257052i $$0.0827511\pi$$
−0.966398 + 0.257052i $$0.917249\pi$$
$$464$$ 1.05062e6 0.226544
$$465$$ 0 0
$$466$$ 449268.i 0.0958387i
$$467$$ −7.17827e6 −1.52310 −0.761548 0.648108i $$-0.775560\pi$$
−0.761548 + 0.648108i $$0.775560\pi$$
$$468$$ 0 0
$$469$$ −2.39526e6 −0.502829
$$470$$ 600372.i 0.125365i
$$471$$ 0 0
$$472$$ 2.62003e6 0.541317
$$473$$ 1.19940e6i 0.246497i
$$474$$ 0 0
$$475$$ 613080.i 0.124676i
$$476$$ 1.84968e6i 0.374179i
$$477$$ 0 0
$$478$$ −4.79221e6 −0.959326
$$479$$ 7.25193e6i 1.44416i −0.691810 0.722079i $$-0.743186\pi$$
0.691810 0.722079i $$-0.256814\pi$$
$$480$$ 0 0
$$481$$ −1.01895e6 5.20798e6i −0.200813 1.02638i
$$482$$ −4.66514e6 −0.914634
$$483$$ 0 0
$$484$$ −2.34642e6 −0.455294
$$485$$ 8.18305e6 1.57965
$$486$$ 0 0
$$487$$ 2.53364e6i 0.484087i −0.970265 0.242043i $$-0.922182\pi$$
0.970265 0.242043i $$-0.0778176\pi$$
$$488$$ 3.70688e6i 0.704626i
$$489$$ 0 0
$$490$$ 1.17953e6 0.221931
$$491$$ −8.46186e6 −1.58403 −0.792013 0.610504i $$-0.790967\pi$$
−0.792013 + 0.610504i $$0.790967\pi$$
$$492$$ 0 0
$$493$$ 4.51850e6 0.837293
$$494$$ −2.79864e6 + 547560.i −0.515976 + 0.100952i
$$495$$ 0 0
$$496$$ 2.46374e6i 0.449667i
$$497$$ 6.69280e6 1.21539
$$498$$ 0 0
$$499$$ 1.95383e6i 0.351265i −0.984456 0.175633i $$-0.943803\pi$$
0.984456 0.175633i $$-0.0561971\pi$$
$$500$$ 2.97758e6i 0.532646i
$$501$$ 0 0
$$502$$ 2.59598e6i 0.459772i
$$503$$ −119778. −0.0211085 −0.0105542 0.999944i $$-0.503360\pi$$
−0.0105542 + 0.999944i $$0.503360\pi$$
$$504$$ 0 0
$$505$$ 5.76932e6i 1.00669i
$$506$$ −504000. −0.0875093
$$507$$ 0 0
$$508$$ 3.24406e6 0.557738
$$509$$ 1.03653e7i 1.77332i 0.462420 + 0.886661i $$0.346981\pi$$
−0.462420 + 0.886661i $$0.653019\pi$$
$$510$$ 0 0
$$511$$ −6.18093e6 −1.04713
$$512$$ 262144.i 0.0441942i
$$513$$ 0 0
$$514$$ 3.78354e6i 0.631670i
$$515$$ 1.27735e6i 0.212222i
$$516$$ 0 0
$$517$$ 353160. 0.0581092
$$518$$ 3.65778e6i 0.598954i
$$519$$ 0 0
$$520$$ 1.95187e6 381888.i 0.316550 0.0619338i
$$521$$ 1.04899e7 1.69307 0.846537 0.532330i $$-0.178684\pi$$
0.846537 + 0.532330i $$0.178684\pi$$
$$522$$ 0 0
$$523$$ 4.42662e6 0.707649 0.353824 0.935312i $$-0.384881\pi$$
0.353824 + 0.935312i $$0.384881\pi$$
$$524$$ −4.86168e6 −0.773496
$$525$$ 0 0
$$526$$ 4.04890e6i 0.638076i
$$527$$ 1.05960e7i 1.66194i
$$528$$ 0 0
$$529$$ −5.33384e6 −0.828707
$$530$$ 153000. 0.0236593
$$531$$ 0 0
$$532$$ −1.96560e6 −0.301104
$$533$$ −1.10916e6 5.66904e6i −0.169113 0.864354i
$$534$$ 0 0
$$535$$ 1.27112e6i 0.192001i
$$536$$ 1.45997e6 0.219498
$$537$$ 0 0
$$538$$ 4.07088e6i 0.606363i
$$539$$ 693840.i 0.102870i
$$540$$ 0 0
$$541$$ 2.26377e6i 0.332536i 0.986081 + 0.166268i $$0.0531717\pi$$
−0.986081 + 0.166268i $$0.946828\pi$$
$$542$$ −1.85384e6 −0.271066
$$543$$ 0 0
$$544$$ 1.12742e6i 0.163339i
$$545$$ 7.38638e6 1.06522
$$546$$ 0 0
$$547$$ 7.21090e6 1.03044 0.515218 0.857059i $$-0.327711\pi$$
0.515218 + 0.857059i $$0.327711\pi$$
$$548$$ 1.01981e6i 0.145066i
$$549$$ 0 0
$$550$$ 251520. 0.0354540
$$551$$ 4.80168e6i 0.673774i
$$552$$ 0 0
$$553$$ 6.63621e6i 0.922799i
$$554$$ 1.33011e6i 0.184125i
$$555$$ 0 0
$$556$$ −221456. −0.0303809
$$557$$ 273507.i 0.0373534i −0.999826 0.0186767i $$-0.994055\pi$$
0.999826 0.0186767i $$-0.00594533\pi$$
$$558$$ 0 0
$$559$$ −5.97701e6 + 1.16942e6i −0.809011 + 0.158285i
$$560$$ 1.37088e6 0.184727
$$561$$ 0 0
$$562$$ −196488. −0.0262419
$$563$$ 959349. 0.127557 0.0637787 0.997964i $$-0.479685\pi$$
0.0637787 + 0.997964i $$0.479685\pi$$
$$564$$ 0 0
$$565$$ 5.11357e6i 0.673911i
$$566$$ 6.23394e6i 0.817940i
$$567$$ 0 0
$$568$$ −4.07942e6 −0.530552
$$569$$ 1.19403e7 1.54609 0.773044 0.634352i $$-0.218733\pi$$
0.773044 + 0.634352i $$0.218733\pi$$
$$570$$ 0 0
$$571$$ 7.20205e6 0.924413 0.462206 0.886772i $$-0.347058\pi$$
0.462206 + 0.886772i $$0.347058\pi$$
$$572$$ −224640. 1.14816e6i −0.0287076 0.146728i
$$573$$ 0 0
$$574$$ 3.98160e6i 0.504403i
$$575$$ −550200. −0.0693986
$$576$$ 0 0
$$577$$ 1.66990e6i 0.208810i −0.994535 0.104405i $$-0.966706\pi$$
0.994535 0.104405i $$-0.0332938\pi$$
$$578$$ 830624.i 0.103415i
$$579$$ 0 0
$$580$$ 3.34886e6i 0.413359i
$$581$$ 5.82309e6 0.715671
$$582$$ 0 0
$$583$$ 90000.0i 0.0109666i
$$584$$ 3.76742e6 0.457101
$$585$$ 0 0
$$586$$ −873852. −0.105122
$$587$$ 8.29913e6i 0.994117i −0.867717 0.497059i $$-0.834413\pi$$
0.867717 0.497059i $$-0.165587\pi$$
$$588$$ 0 0
$$589$$ 1.12601e7 1.33738
$$590$$ 8.35135e6i 0.987704i
$$591$$ 0 0
$$592$$ 2.22950e6i 0.261459i
$$593$$ 4.48969e6i 0.524300i 0.965027 + 0.262150i $$0.0844315\pi$$
−0.965027 + 0.262150i $$0.915568\pi$$
$$594$$ 0 0
$$595$$ 5.89586e6 0.682738
$$596$$ 4.42282e6i 0.510015i
$$597$$ 0 0
$$598$$ 491400. + 2.51160e6i 0.0561930 + 0.287209i
$$599$$ −1.38261e6 −0.157446 −0.0787232 0.996897i $$-0.525084\pi$$
−0.0787232 + 0.996897i $$0.525084\pi$$
$$600$$ 0 0
$$601$$ 1.04021e7 1.17472 0.587359 0.809327i $$-0.300168\pi$$
0.587359 + 0.809327i $$0.300168\pi$$
$$602$$ −4.19790e6 −0.472107
$$603$$ 0 0
$$604$$ 5.14133e6i 0.573433i
$$605$$ 7.47920e6i 0.830743i
$$606$$ 0 0
$$607$$ −4.78668e6 −0.527306 −0.263653 0.964618i $$-0.584927\pi$$
−0.263653 + 0.964618i $$0.584927\pi$$
$$608$$ 1.19808e6 0.131440
$$609$$ 0 0
$$610$$ −1.18157e7 −1.28568
$$611$$ −344331. 1.75991e6i −0.0373141 0.190717i
$$612$$ 0 0
$$613$$ 1.04783e7i 1.12627i 0.826366 + 0.563134i $$0.190404\pi$$
−0.826366 + 0.563134i $$0.809596\pi$$
$$614$$ −1.28441e6 −0.137493
$$615$$ 0 0
$$616$$ 806400.i 0.0856246i
$$617$$ 1.79106e7i 1.89407i 0.321128 + 0.947036i $$0.395938\pi$$
−0.321128 + 0.947036i $$0.604062\pi$$
$$618$$ 0 0
$$619$$ 4.43222e6i 0.464938i −0.972604 0.232469i $$-0.925320\pi$$
0.972604 0.232469i $$-0.0746804\pi$$
$$620$$ −7.85318e6 −0.820477
$$621$$ 0 0
$$622$$ 1.33490e7i 1.38348i
$$623$$ −1.10017e7 −1.13564
$$624$$ 0 0
$$625$$ −7.85355e6 −0.804203
$$626$$ 4.66270e6i 0.475556i
$$627$$ 0 0
$$628$$ −5.43210e6 −0.549627
$$629$$ 9.58861e6i 0.966338i
$$630$$ 0 0
$$631$$ 1.43291e7i 1.43267i 0.697756 + 0.716335i $$0.254182\pi$$
−0.697756 + 0.716335i $$0.745818\pi$$
$$632$$ 4.04493e6i 0.402827i
$$633$$ 0 0
$$634$$ 294072. 0.0290556
$$635$$ 1.03405e7i 1.01767i
$$636$$ 0 0
$$637$$ −3.45764e6 + 676494.i −0.337622 + 0.0660565i
$$638$$ 1.96992e6 0.191601
$$639$$ 0 0
$$640$$ −835584. −0.0806381
$$641$$ −6.65869e6 −0.640094 −0.320047 0.947402i $$-0.603699\pi$$
−0.320047 + 0.947402i $$0.603699\pi$$
$$642$$ 0 0
$$643$$ 1.55224e7i 1.48058i 0.672286 + 0.740291i $$0.265312\pi$$
−0.672286 + 0.740291i $$0.734688\pi$$
$$644$$ 1.76400e6i 0.167604i
$$645$$ 0 0
$$646$$ 5.15268e6 0.485794
$$647$$ 2.44454e6 0.229581 0.114791 0.993390i $$-0.463380\pi$$
0.114791 + 0.993390i $$0.463380\pi$$
$$648$$ 0 0
$$649$$ 4.91256e6 0.457821
$$650$$ −245232. 1.25341e6i −0.0227664 0.116361i
$$651$$ 0 0
$$652$$ 6.33149e6i 0.583293i
$$653$$ −1.16500e7 −1.06916 −0.534580 0.845118i $$-0.679530\pi$$
−0.534580 + 0.845118i $$0.679530\pi$$
$$654$$ 0 0
$$655$$ 1.54966e7i 1.41135i
$$656$$ 2.42688e6i 0.220185i
$$657$$ 0 0
$$658$$ 1.23606e6i 0.111295i
$$659$$ −1.33185e7 −1.19465 −0.597326 0.801999i $$-0.703770\pi$$
−0.597326 + 0.801999i $$0.703770\pi$$
$$660$$ 0 0
$$661$$ 1.35722e7i 1.20822i −0.796900 0.604112i $$-0.793528\pi$$
0.796900 0.604112i $$-0.206472\pi$$
$$662$$ −2.53073e6 −0.224440
$$663$$ 0 0
$$664$$ −3.54931e6 −0.312409
$$665$$ 6.26535e6i 0.549403i
$$666$$ 0 0
$$667$$ −4.30920e6 −0.375044
$$668$$ 6.82733e6i 0.591984i
$$669$$ 0 0
$$670$$ 4.65365e6i 0.400504i
$$671$$ 6.95040e6i 0.595941i
$$672$$ 0 0
$$673$$ −1.58674e7 −1.35042 −0.675209 0.737626i $$-0.735947\pi$$
−0.675209 + 0.737626i $$0.735947\pi$$
$$674$$ 1.30737e6i 0.110854i
$$675$$ 0 0
$$676$$ −5.50264e6 + 2.23891e6i −0.463132 + 0.188439i
$$677$$ 2.24264e7 1.88056 0.940281 0.340398i $$-0.110562\pi$$
0.940281 + 0.340398i $$0.110562\pi$$
$$678$$ 0 0
$$679$$ −1.68475e7 −1.40236
$$680$$ −3.59366e6 −0.298034
$$681$$ 0 0
$$682$$ 4.61952e6i 0.380308i
$$683$$ 8.11034e6i 0.665254i −0.943059 0.332627i $$-0.892065\pi$$
0.943059 0.332627i $$-0.107935\pi$$
$$684$$ 0 0
$$685$$ 3.25064e6 0.264693
$$686$$ −9.48738e6 −0.769726
$$687$$ 0 0
$$688$$ 2.55872e6 0.206088
$$689$$ −448500. + 87750.0i −0.0359927 + 0.00704205i
$$690$$ 0 0
$$691$$ 2.00020e7i 1.59359i 0.604246 + 0.796797i $$0.293474\pi$$
−0.604246 + 0.796797i $$0.706526\pi$$
$$692$$ 256416. 0.0203554
$$693$$ 0 0
$$694$$ 1.18510e7i 0.934020i
$$695$$ 705891.i 0.0554339i
$$696$$ 0 0
$$697$$ 1.04375e7i 0.813793i
$$698$$ −3.46530e6 −0.269217
$$699$$ 0 0
$$700$$ 880320.i 0.0679040i
$$701$$ 2.22272e6 0.170840 0.0854200 0.996345i $$-0.472777\pi$$
0.0854200 + 0.996345i $$0.472777\pi$$
$$702$$ 0 0
$$703$$ 1.01895e7 0.777617
$$704$$ 491520.i 0.0373774i
$$705$$ 0 0
$$706$$ 6.65162e6 0.502245
$$707$$ 1.18780e7i 0.893708i
$$708$$ 0 0
$$709$$ 2.03634e7i 1.52137i 0.649122 + 0.760684i $$0.275136\pi$$
−0.649122 + 0.760684i $$0.724864\pi$$
$$710$$ 1.30032e7i 0.968062i
$$711$$ 0 0
$$712$$ 6.70579e6 0.495736
$$713$$ 1.01052e7i 0.744425i
$$714$$ 0 0
$$715$$ 3.65976e6 716040.i 0.267724 0.0523808i
$$716$$ −1.10407e7 −0.804850
$$717$$ 0 0
$$718$$ 2.50214e6 0.181135
$$719$$ 1.98255e7 1.43022 0.715108 0.699014i $$-0.246377\pi$$
0.715108 + 0.699014i $$0.246377\pi$$
$$720$$ 0 0
$$721$$ 2.62983e6i 0.188404i
$$722$$ 4.42880e6i 0.316186i
$$723$$ 0 0
$$724$$ 1.54365e6 0.109446
$$725$$ 2.15050e6 0.151948
$$726$$ 0 0
$$727$$ −9.24667e6 −0.648857 −0.324429 0.945910i $$-0.605172\pi$$
−0.324429 + 0.945910i $$0.605172\pi$$
$$728$$ −4.01856e6 + 786240.i −0.281023 + 0.0549828i
$$729$$ 0 0
$$730$$ 1.20087e7i 0.834041i
$$731$$ 1.10045e7 0.761687
$$732$$ 0 0
$$733$$ 1.48114e7i 1.01821i −0.860704 0.509105i $$-0.829976\pi$$
0.860704 0.509105i $$-0.170024\pi$$
$$734$$ 4.33309e6i 0.296864i
$$735$$ 0 0
$$736$$ 1.07520e6i 0.0731635i
$$737$$ 2.73744e6 0.185642
$$738$$ 0 0
$$739$$ 5.67210e6i 0.382061i −0.981584 0.191031i $$-0.938817\pi$$
0.981584 0.191031i $$-0.0611830\pi$$
$$740$$ −7.10654e6 −0.477067
$$741$$ 0 0
$$742$$ −315000. −0.0210039
$$743$$ 2.75704e7i 1.83219i 0.400960 + 0.916095i $$0.368677\pi$$
−0.400960 + 0.916095i $$0.631323\pi$$
$$744$$ 0 0
$$745$$ 1.40977e7 0.930590
$$746$$ 7.15582e6i 0.470774i
$$747$$ 0 0
$$748$$ 2.11392e6i 0.138145i
$$749$$ 2.61702e6i 0.170452i
$$750$$ 0 0
$$751$$ −4.09636e6 −0.265032 −0.132516 0.991181i $$-0.542306\pi$$
−0.132516 + 0.991181i $$0.542306\pi$$
$$752$$ 753408.i 0.0485831i
$$753$$ 0 0
$$754$$ −1.92067e6 9.81677e6i −0.123034 0.628840i
$$755$$ −1.63880e7 −1.04630
$$756$$ 0 0
$$757$$ 1.09396e7 0.693844 0.346922 0.937894i $$-0.387227\pi$$
0.346922 + 0.937894i $$0.387227\pi$$
$$758$$ −3.47446e6 −0.219641
$$759$$ 0 0
$$760$$ 3.81888e6i 0.239829i
$$761$$ 1.36940e6i 0.0857172i −0.999081 0.0428586i $$-0.986354\pi$$
0.999081 0.0428586i $$-0.0136465\pi$$
$$762$$ 0 0
$$763$$ −1.52073e7 −0.945670
$$764$$ 1.13309e7 0.702312
$$765$$ 0 0
$$766$$ −4.31886e6 −0.265948
$$767$$ −4.78975e6 2.44809e7i −0.293984 1.50259i
$$768$$ 0 0
$$769$$ 1.08375e7i 0.660867i −0.943829 0.330433i $$-0.892805\pi$$
0.943829 0.330433i $$-0.107195\pi$$
$$770$$ 2.57040e6 0.156233
$$771$$ 0 0
$$772$$ 5.56579e6i 0.336112i
$$773$$ 2.05445e7i 1.23665i 0.785922 + 0.618325i $$0.212188\pi$$
−0.785922 + 0.618325i $$0.787812\pi$$
$$774$$ 0 0
$$775$$ 5.04298e6i 0.301601i
$$776$$ 1.02689e7 0.612168
$$777$$ 0 0
$$778$$ 5.15287e6i 0.305211i
$$779$$ 1.10916e7 0.654863
$$780$$ 0 0
$$781$$ −7.64892e6 −0.448717
$$782$$ 4.62420e6i 0.270408i
$$783$$ 0 0
$$784$$ 1.48019e6 0.0860058
$$785$$ 1.73148e7i 1.00287i